Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere without the permission of the Author. GROWTH STUDIES WITH LETTUCE A thesis presGnted in partial fulfilment of the requir&ments for the de�ee of Doctor of Philosophy at Massey University . Michael Ad.air Nichols 1970 ABSTRACT Grov•th studies were made in the field using two cul tivars of head lettuce , Webbs Vlonderful (a crisphead type ) and Cobham Green (a butterhead type ) . In a fertilizer and density experiment using a systematic spacing design superimposed on a rotatable fertilizer design evidence is presented to suggest that the 'normal' reciprocal yield-densi ty model -1 W Ap + B (when W is the mean plant weight at density p, and A and B are constants ) is only applicable when there is competition at all densities . A 1modified1 model is proposed which includes an additional parameter C, the density at which competition begins . The modified model i s : w -1 = Ap + B if p > c W -l AC + B if p � C The plant weights in a non-competitive situation were fitted to a logi stic model using a ' heat unit ' environmental time s cale, and an analysis of the logistic parameters showed a response only to serpentine superphosphate . This quadratic response was due to an increased relative growth rate (due mainly to an increased net ass imilation rate) from the use of serpentine superphosphate up to 40 crwt ./acre . At low plant densities Webbs Wonderful has a higher relative growth rate compared with Cobham Green due to a slower rate of leaf production, and a higher net assimilation rate. This- net assimilation rato difference is attributed to the heaviGr leaves of Webbs Wonderful being light saturated at a hi2,her radiation level than the leaves of Cobham Green. This theory is supported by the similarity in the yields f1·om the two varieties at high de:nsi ties . 'rhe o:ptimwn Qarketable yi8ld spacing for Cobhem Green was found to be 1 .4 plants/sq.ft. and for Webbs Vfonderful l .l plants/s•l·ft . In spite of a lov·er plant density the marketable yield from V!ebbs Wonderful was arproximut&ly double that from Gobham Green (at their respective optimum densities ) due mai!-.ly to the later maturity of Webbs Fonde:r:ful, but also due to its higher grm:.rth ratG • . In an CX}•eriment carried out in EP..gland, and later in New Zealand , succcssive sowi::1gs (over a total period of 22 months) .... .-ere sampled at rr::.gular intervals from errwrgE:nce until :past ma tu:ci ty. The rJry weight per plant data were then fitted to a logistic model, with a single set of :parameters f0r , ::-�eh vc.riety over all the sowinGB, using chronological time, end a nwnber of environmental time scales . All the environmental time scalts tested provided a better fit than chronological time, with solar radiation being superior to 1hePt units'. A further improvement with the solar radiation time scale we_s obtained by valueing all radiation above a certain daily integral at only so%. In spite of the marked improvement when using environmental time scales , the results have l ittle commercial application at present as a predictive tool beceuse substantial differences were found in the logistic parameter estimates for the t�o sites, and also in the estimates of the asymptotes for tho different smrings . It is es sontiel that the asymptotes be the same over all sowintS;s , or that the reason for any variation be known, because being based on a loe·. s cale even a snall variation would result in a la.rge differe11ce in absolute weight . ACI\l'TOW1EDGEt.1E.RTS I wish to express my trwnks <1nd appreciation to:- Professor J.A. Veale Professor J.P. Hudson Dr. W. Heydecker for his supervision, oncouragenwnt , and guidt>...nce; who initially stimulatad my interest in the plant and the environment ; for his enthusiasm and help while at Nottingham; Mr . L . Jenkins and the library staff for their invaluable assistance in obtaining and checking references ; I'1Irs. Rose Couling for her assistance in typing the thesis; The New Zealand Univ0rsity Research Grants Comrrlittee for financial assistancr:: to collect the plant and we2.ther CL'1ta; :My wife, Lyn, and our children, Jam:, Timothy, and Catherine for the patience they hnve shown over the past years . TABLE OF CONTENTS Introduction Literature Review The plant environment Crop yield in the n:1turol environment Fa.ctors affecting J'hotosynthesis in Crops The He�t Unit Concept Pl:mt spncing Plunt Density a.nd Competi ti(;n ModE:ls Experiment I The �ffect of spacing and fcrtilizurs on the growth of lettuce . Ma terinls and I1kthods Hesults o.nd Discussion Da.tu Reduction Analysis of Plant Dry Weight Data An interpretation of the results in terms of Growth Analysis Analysis of A and B parnmeters Plant losses Marketable yield Page 1 3 ll 16 18 24 3 1 35 38 38 44 50 57 61 62 cont'd • • • . • • cont 1 d • • • • • • Discussion Conclusions ;ExperimEmt II Growth and Develor.mcnt of Two Lettuce vrJrieties in the YJ£' turo.l er!vironment Tls terials and Methods Nottinghar.1 experiment 1fusscy experiment Results and Discussion Discussion Conclusions Future V1ork 67 70 71 71 75 79 99 103 105 I II LIST OF TABLES 'l'he effect of calcula tint; heat un�. ts by five methods. Levels of H-P-K used in the experiment Ill Residual sums of squares, A parameters calculated for Web bs 1iJonderful using 1 normal' and 1 modified 1 reciprocal yield density model . IV V VI VII VIII IX X XI Mean error sums squares for Cobham and Webbs 1furnber of leaves exceP.ding t' length Logistic parameters for Cobham and Webbs Leaf area/gm. dry weight leaf Percentage of lc�af dry weight/total plant dry weight Dry matter distrj_bution, phosphate treatments Calculated polynomial parameters , with derived maximum marketable yield and related density Logi stic gTovrth curve parameters and Error Mean Square s •. Method l XII Logisti c growth curve parameters and Error Mean XIII Squares . Method 2 Logistic parameters and Error Mean Squares for complex time scales XIV Logistic parameters fitted to better fitting XV environmental time scale s for the two sites Example showing the derivation of hourly radiation integrals XVI Logisti c parameters for solar radiation time scales, for Webbs at two sites Page 22 35 42 46 48 48 54 54 55 64 81 82 85 86 89 90 XVII XVIII XIX XX XXI Logistic parameters for solar radiation time scales, �or Cobham at two sites Total error sums of squares for all smvings for a single set of parameters, or with only K constant for all sowings a p&.rameter variances Effect of variety and_ soning date on the rate of production of le.o.ves in excess of i" long IvTeEm leaf areas/ gm. leaf dry >veight for different sov:ings and varieties 91 93 94 96 98 LIST OF FIGURES Between Pages 1. Competition-density effect in soybean (after Kira et al., 1953). 2. ·Hypothetical relationship showing the effect of plant density on the reciprocal of total yield per plant at 3 levels of fetility (High, Medium and Low), on 3 harvest dates, with A and B parameters independent1 B constant (old model), and B constant (modified model). C is the density at which competition commences. 3. 4· 5. 6. 1· 8 . 9. Webbs Wonderful Harvest 5. Sho·wing a comparison of the old and modified reciprocal yield density models. a ' k and e parameters for the combined Cobham/Webbs dry weight per plant data fitted to serpentine superphosphate applice.tion rates. Combined Cobham/Webbs dry weights per plant fitted to the 4 parameter logistic model for 3 levels of serpentine superphosphate application. Dry weights/plant for Cobham and Webbs fitted to the 4 parameter logistic model. Based on 0-0-0 plots. Relative growth rate time trends for Cobham and Webbs. Relative growth rate time trends for joint Cobham/ Webbs data at 3 levels of serpentine superphosphate Net assimilation rate time trends for Cobham and Webbs. 10. Net assimilation rate time trends for joint Cobham/ Webbs data at 3 levels of serpentine superphosphate. ll. Leaf area ratio time trends for Cobham and Webbs. 31-2 39-40 41-2 49-50 50-51 51-52 56-7 56-7 56-7 56-7 56-7 12. Leaf area ratio time trends for joint Cobham/VIebbs data e.t 3 levels of serpentine superphosphate. 13 . Log8 B (from reciprocal yield density model) for Webbs and Cobham fitted to an exponential model. 14 . Log A (from the reciprocal yield density model) for e 3 levels of serpentine superphosphate, fitted to an exponential model. 15. Plant losses due to Sclorotinic., showing the number of dead plants (out of 13 ) with reference to harvest date and v2.riety. lG. :Marketable yield of lettuce/sq. ft. Cobham, harvest 8, with quadratic function fitted. 17 . !1iarketable yield of lettuce/sq.ft. Webbs, harvest 9 with quadratic function fitted. 18. Total dry weight per plant Webbs fitted to the 4 parameter logistic with a solar radiation time scale (Ra 50 + Xjd2y) with K constant for all sowings. 19 . Total dry weight per plant Cobhe� fitted to the 4 parameter logistic with a solar radiation time scale (Ra lOO + X/day) with K constant for all sov;ings. 56-7 58-9 59-60 61-2 63-4 63-4 94-5 96-7 - 1 - INTRODUCTION A detailed knmvledge of the relationship between crop yield and the physical and cheDical factors affecting plant development is essential if we arc to exploit the resourcus of the biosphere efficiently. To understand these complex relationships, and the equally important genotype-environment interaction, will demand the harnessing of scientific skills from all disciplines. The rewards, however, provided that dynamic long-term �e�ther forecasting lives up to its early promise, will be increased crop yields, and for pe-rishable horticultural crops, more predictable production and less wastage. The probleu of relating crop yield to the environment is being attacked in a number of ways , namely: l ) The seeking of correlation between growth (or yield) and the environ- ment in the natural environment, using statistical techniques. ' 2) Studies in a controlled (or partially-controlled ) environment in which the level of one or more of the environmental factors is changed, and the plants response noted. 3) Micro-meteoroiogical studies within and above the crop canopy, leading to the development of plant growth models (e.g. Duncan et al . (1967) , Idso (1968) ) . 4 ) Biochemical studies in the laboratory, leading to a further under- standing of the mechanism of specific reactions. � 2 - Montei th (l966a) considers that statistics is the wrong tool for exploring crop-weather relationships because it tries to bypass the search for funda.11 ental mechanisms and causes! Novortheless, tho field corre- lation technique, combined with th� judicial use of controlled climate facilities ap�ears to offur the possibility of results of practical value far more rapidly than the potentially more useful (but more long term ) crop modelling, micro-meteorologicHl approach. It could be argued that controlled climo.te exper�nonts will provide all the necessary answers, but it must be ror.tenberc=:d that no phytotron has yet been able to simulate the na tu:ral environment, and in the f�nal ana.lysis, it is in the natural environment that the J:rmjori ty of crops are to be grown, at least in the fc;resoeable future. For this reason the work described in this thesis was carried out in the field. It had been intended to test some of the results in a controlled environment, but this was not possible due to delay in the developnen t of sui table f;:;.cili ties! It must be realised that the testing of field results in controlled climate facilities must be considered an essential part of any crop-wo2ther study, for only in this way is it possible to isolate the independent effects of the different factors which comprise climate. - 3 - The Plant Environment The principal physical and chemical factors affecting plant development can be grouped as follows (de Vries, 1963): Climatic factors l ) Radiation, including light 2) Cloudiness 3) Precipitation 4 ) Wind 5 ) Air temperature 6) Humidity of the air 7 ) Carbon dioxide content of the a.ir 8) Air pollution Edaphic factors 1) Composition of soil solid material, including organic matter 2) Soil texture and struct�e 3) Soil temperature 4 ) Soil moisture 5) Composition of soil solution 6) Composition of soil air, expecially its carbon dioxide and oxygen contents A more comprehensive list, which includes three additional groupings (Geographic, Pyric, and Biotic ) has been proposed by Billings (1952), but apart from the Biotic effects, which de Vries did not consider, the Geographic and Pyric effects appear to work through the Climatic and - 4 - Edaphic factors. The principa.l biotic factors affGcting plant development are : Biotic factors (after Billings) 1 ) Competition 2 ) Pathogens 3) Man Climatic factors 1 ) Radiation, including livpt In a recent account on radiation and crops , Monteith ( 1965 ) cites three features of radiation which are of biological importe�ce . These are : - a) Intensity i . e . the amount of o:;nergy received by a unit surface in b ) c ) l.a) a unit time . The distribution of this ener�J within the elcctro magnetic spectrum . The distribution of the energy in time . Radiation intensity The intensity of radiation at the earths surface will depend upon the intensity of radiation just above the earths atmosphere perpendicular to the solar beam , the solar angle , and the losses due to absorption and s cattering in the atmosphere . Because the earth moves round the sun in an �ipse , the intensity of the solar beam varies slightly, with a mean value of 2.0 cal . /cm2 /min - called the solar constant. Solar radiation at the earths surface is normally measured by nteans of an Eppley , or a - 5 - Kipp pyrheliometer but a reasonable estimate cn.n be obtained by measuring the number of bright sunshine hours by means of a Campbell-Stokes recorder, and then using e.n empirical formula (e.g. Penman, 195 3 ) to estimate the solar radiation c..t the earths surface. whE'n R radiR.tion at the earths surface c R radiation above the atmosphere a n bright suns hi no hours N possible bright sunshine hours The radiation above the atmosphere (parallel to tho earths surface ) can be obtained fron1 the Smithsonian Tables, or calculated from the following formula: R a H ( sin � sin o + cos � cos o cos2 � when R a radiation above the atmosphere H solar constant 9 latitude t time ( 24 hour clock ) t 12.00 0 0 declination l.b ) p�e2tral composition ) Over 99% of the solar radiation reaching the earths surface is between the wavelengths 0. 3 1-L and 4 .0 1-L. The visible spectrum (from 0.4 fJ. to 0. 7 fJ.) is of particular importance, mainly because of photo- synthesis, but wavelengths outside the visible spectrum can also play a major role in plant growth and development. Short waves such as cosmic, gamma, and X-rays can modify (sometimes drastically) the genetic - 6- constitution of a plant, VThile beyond the visible spectrum is the heating eff£ct of the infrared. Of particular importance in plant development are the red ( 660 !l) and far red ( • 730 1-L). Van der Veen and Meijer ( 1 959) proposed that from a plant point of view the spectrum be divided into 8 wave bands, based on their physiological effect on plants. l.c ) Distribution of energy with time The phenomena knmvn as photoperiodism controls the development of a large number of crop plants , e.g. Chrysanthemum. Photoperiodism appears to VTork through the protein phytochrome, which comprises two interconvert- ible forms P660, with absorption maximum at . 660 !l and P730 with absorp - tion maximum at . 7 30 !l • The conversion in the dark of P730 to P660 appears to be the basis of photoperiodism (Hendricks and Borthwick, 1963). 2) Cloudiness Cloudiness affect the physical environment in a number of ways : a) The intensity of solar radiation is decreased, due to the reflection of a fraction of the solar beam away from the earth. b) The proportion of indirect/direct radiation is increased. c) Long-wave radiation losses from the earth are reduced. 3) Precipitation Precipitation is important mainly in relation to its effect on soil moisture . Under certain circumstances, however, precipitation in the form of snow, hail, or even large drop s of rain may physically damage plants. Rain can also play an important part by leaching essential minerals from leaves (Tukey and Morgan, 1962). 4 ) Wind - 7 - There appears to bo considerable doubt ae to the value of low wind speeds over the crop as a means of improving photosynthesis ( e.g. Tanner ( 1963 ) , Gaastra ( 196 3 ) ) , but th8re is no doubt that wind can have a serious effect on plant growth well bofore physical damage occurs. This effect a.ppea.rs to be due to the increased transpiration which occurs as wind speeds increase, and this leads to increased water stress in the leaves, resulting in reduced leaf expe.nsion (Montci th, l966a) . At higher v;ind speeds, the stomata may close, leading to a virtual cessation of photosynthesis (�inter, 1965 ) . 5 ) Air temperature The growth of higher plants is ma.inly restricted to temperatures b8tween 0°C and 60°C , and for crop production the range is further reduced 0 0 to 10 C - 40 C. Temperature plays a. major role in plant growth, because the rate at which the majority of reactions occur is temperature dependent. Species differ in their temperature requirements, for example Maize and Sorghum requires warmer temperatures than oats and peas in order to produce heavy yields. This may be due to the differences in photosyn- thetic pathways ( i.e. the Hatch cycle) , b�t Van Dobben ( 1962 ) has postulated that peas and oats will yield less at temperatures above optimum conditions, due to the rate of development exceeding the rate of carbohydrate production. Overall the concept of cardinal temperature ( maximum, optimum, and minimum) appears to be outdated because the optimum temperature may alter according to the condition of the plant. - 8 - Thermoperiodicity has been extensively investigated (Went, 1953) and affords an explanation of the failure of certain temperate crop plants in the tropics. Agronomically 'temperature' can be transformed into 'heat units', and this concept is considered in more detail later in this thesis. 6 ) Humidity of tho air Humidity of the air can affect plants in a number of direct and indirect ways. The main effect is on transpirn.tion where the greater the vapour pressure deficit in the air the higher the transpiration rate -- all other things being equal. If the internal water status of the plant is such that it cannot support a higher rate of water loss -- due perhaps to soil moisture limitations, then the stomata will close and photosyn­ thesis will be reduced. The humidity of the air can also affect plant development (Heydecker and Pareek, 1969 ), e�d can be an important factor in relation to pathogens, especially certain fungous diseases. 7 ) Carbon dioxide content of the air This is considered in tho section on photosynthesis. 8) Air pollution The major air pollution chemicals are sulphur dioxide, fluorides, and photochemical smog (ozone and Pan) (Middleton, 1969) . These materials, even at low concentrations can cause severe damage to plants and provide a major threat to agriculture in industrial nations (e.g. U . S . A . ) . In New Zealand this is unlikely to prove important, except in special localised areas, because of the relative isolation, strong winds, and - 9 - lack of heEJ.vy industry. Close to busy highways it is possible for plants to contain excessive amounts of lead, and this is a potential health hazard, Edaphic factors Edaphic factors can plry a major part in influencing plant develop- ment. Compared with climatic factors, the edaphic factors tend to fluctuate less rapidly, mainly because the soil acts as a substantial buffer. Choice of site will play a major role in determining the compo­ sition, texture, and structure of the soil, although man can ameliorate or degrade these chare_cteristics by different husbandry techniques. Soil temperature ce� be explained in terms of heat transfer, which can be looked upon as a periodic phenomena, with important agronomic implications, especially in terms of seed germination. Too much, or too little soil moisture can reduce plant growth. Soil type will determine the soil moisture characteristics, while climatic factors determine water loss or gaih. The composition of the soil solution, i. e. the nutrient status, will depend on soil type, and the rate at which nutrients are added to the soil. Nutrients will also be removed by leaching, fixing, and by plant uptake. - 10 - Plant development will depend not only upon the presence of essential minerals, but their relP.tive proportions, and their overall total. If the composition of the soil solution is too concentrated, then osmotic effbcts can reduce the soil water f.l.Vc.ilable to plants. Actively growing plant roots require oxygE-n for respiration. The oxygen content of the soil a tmosphcrG is less with increEwing depth, while the carbon dioxide content increasec. Soil type and structure play an important role in determining the rate at which oxygen moves down the soil profile. This determines to a large extent the effective rooting depth of 8. crop, and therefore the volume of soil that the crop can exploit for water and nutrients. At germination Hoydecker (1962) has found thnt seeds \'rere more susceptible to low oxygen rather than high carbon dioxide concentrsti8n. Later growth, however was reduced. by high carbon dioxide concentration in the soil atmosphere. Biotic Factors The effect of competition is considered later in this thesis, while Man and Pathogens con be major influences on plant duvelopment. - ll - Crop yield and the nc.turcl environecnt Tho factors nhich cor:1prise tho natural environment are in m2ny cases interrelated, nany of them being highly correlated. For cx2.mple the level of solar rndiation can greatly influence air ter.1perature, while precipitation and soil r.1oisture can be highly correlated. At this point it is pertinent to draw a distinction bet .. een climate and weELther. Climate conprises the interaction of the clir.1atic factors listed previously, with normally a seasonal pattern cf change which is si:::1ilar each year. imy dcvie.tion from this seasonal pattern is called weather. In modern terminology climate is the wave, and weather is the noise. Climate is a function of latitude, modified by position (altitude etc. ) , and weather is any short term deviation fron normal. The relative importance of climate and weather vary, for example in some countries (e.g. Egypt ) climate is the dominant factor, and variations from the mean are small, whilo in New Zealand or the British Isles climatic averages are a very poor guide, and variations from the mean have greater importance. As a generalisation it can be stated that 1cli��te determines the crops which can be grown, and weather determines the yield.' The relationship between crop yield and the weather is one which has intrigued agronomists for at least lOO ye8rs. A number of major efforts have been made to relate yield to the weather·with what can only be described as a marked lack of success. For example Watson (1963 ) has described the work by La.wes .md Gilbert (1880 ) , Fisher ( 1924), and Buck ( 1 96 1 ) on the winter wheat at Rothamsted in which "after 80 years of intermittent but intensive study of a set of data that appears uniquely - 12 - suited for the purpose, all that has been established with statistical certai:r1ty about the dependence of the wheat yielc', of Broadba.�k is that it decre&ses �ri th increase in armual r.£J.infall above average . 11 Watson continues "Past experience , therefors does not encourage us to expect that knovl edge of how yield clepends on weather can coEJG fro!!'. ncasurements of yi(:;lds in naturally varying E:nviror�.ncnts." Though perhaps sowewhat overstating the case, there is little doubt that there has been a marked lack of success in obtaining satisfactory correlations between yield and the weather. This is not to SEtY that some sui table correln tic.ns have not been found - for examplE:: Cornish (1950) has obtained n satisfactory relationship between rainfall and v:hoa t yield in South Australia. In fact it would be surprising to find that in an arid clim!lte such a relationship did not exist, as the availability of water is ono of tho major factors liciting production, and would tend to override any of the other envirorunent&l fEtctors. The complexity of the problem becomes apparent when with a crop of irrigate2d cotton in the Sudan Gezira, Jackson ( 1969) found that a major cause of variation in yield from year to year was due to variations in insect pest damage, and it has been suggested by plant pathologists that a possible cause of the r.educed yield of wheat with increased rainfall at Rothamsted is partially due to a more severe infection of disease in the ��etter conditions, No doubt, however, a major difficulty in relating crop yield and the weather has been the complex nature of the relationship between plants and the environment, e�d the difficulty of knowing what parameters to measure, and how accurately. The difficulty also liGs in the fact that the physics of the environment, and the physiological basis of plant - 13 - growth are still far from cloarly understood (Smith, 1967) . This is not to say thet it is impossible to determine useful yield/ environment relationships in the field, but is to eP.!phasise thst for an empirical relationship to be of real v�.lue we need to know a lot more about the crop and the environnent. In fact Brougham (1959) has shown that by developing a suitable model (Glenday, 1959 ) i.-!; is possible to detomine the effects of seasonal climate and of weekly weathE:r variations on crop growth rate in the field. A study involving replication in tine (29) A.nd space, with each 1tim&1 replicute supplying 14 weekly harvGst saBples. This afproach (of repli­ cations in time) permits a consideration of the interaction between ontogeny and climate. A most important effect as far as crop production is concerned, and one which most physiologists have avoided in their studies of growth and climate (e. g. Blackman et al., 1955; V/arren Vlilson, 1967 ) by using young widely spaced plants at a standard development stage. Penman (1962) has proposed that crop-wenther relationships involve at least 5 divisions, nanely: 1) Tho zero order relationship The problem of photosynthesis, respiration, and photosynthetic efficiency. 2) The lst order relationships The seasonal and secular changes in yield caused by weather changes. 3) The 2nd order relatjsnships - 14 - Those arising from pests and diseases , the intensity of their devt1lopment anct sprE:sd being frequently associated with the weather . 4 ) The 3rd order relationships ThosE: rE: la tionships associated l'li th nans stewardship of the ee.rth - i . e . mainly cdaphic factors . 5 ) The 4th order relationships The:: effo::;cts 0f me:teorological abnormality (e . g . hail, gale. etc.) , and the e ffect of cortnin biological threshhold values being surpassed. ship , Penman emphP.sises the need to understand the zero order relation­ He considers thFJ.t until we find out why the green plant is so inefficient as an energy converter , crop weather relationships must be empirical , and the criterion of a successful analysis may be no more than the ability to express growth as a linear function of some weather parameter . Nevertheless he concludes that valuable lst order relation- ships can be determined, provided that the effects of 2nd , 3rd , and 4th order relationships are absent , avoided , or neutralised. Using this approach , Penman has obtained a satisfactory correlation between the growth (as measured by dry matter accumulation) of grass and accumulated potential transpiration. Gloyne ( 1965 ) considers that the correlation between dry matter increases and water usage would seem capable of application to a wide range of food crops, but Milthorpe ( 1961 ) has emphasised that transpiration and growth are not causally - 15 - related , while Monteith (l966b ) has sho\vn that potential photosynthesis i s governed by the income o f solar radiation and potential transpiration by net radiation , and tha� the constancy of the transpiration/photosynthesis ratio depends on solar and net radiation relationship . This means thCJ.t, with increased solar radiation , photosynthesis may be limited due to light saturation , but transpiration will not be limited in this way. This effect i s likely to be of most importance for young plants (with a low leaf area index ) . Even if a satisfactory ratio between photosynthesis and water usage can be determined , the value of such a correlation will depend upon a near constant ratio between photosynthesis and respiration over the growth of the crop . Wang ( 1967 ) has proposed a system of crop prediction without weather forecasting. He suggests that the current weather is revealed in later crop performance , and that this is more important than future weather condi tions . Such a system may be of value where climate is the dominant factor , but aprJears to offer little of value for countries V!here climatic variations are of great importance . Finally reference must be made to the work of Runge (l969 ) who, using statistical techniques, has shown that in Illinois it is possible to predict corn yields from a knowledge of the temperature and rainfall during the growing season . - 16 - Factors affecting Photosynthesis in Crops The rate of photosynthesis of a leaf is determined by three main extern..al factors : l ) Light intensity ( Df the right wavelength) 2 ) Carbon dioxide concentration of the air 3 ) Temperature In simplified form , photosynthesis can be divided into a ) A photochemical process b) A C02 transport process c ) A biochemical process All these processes are interrelated, and the speed of the whole is the speed of the slowest part . Gaastra (1963 ) has shown that at low l ight intensities photosyn• thesis i s limited by the photochemical reaction , while at higher light intensities the diffusion process of co2 from the atmosphere to the chloro­ plasts will be limiting. With normal atmospheric concentrations of co2 ( 300 ppm) temperature mas virtually no effec t (at least over the range 10-30°C ) but with higher concentration of co2 , the temperature controlled biochemical processes are limiting. This effect is exploited by growers who combine 1 C02 fertilisation ' with higher tempera tures in their glass­ houses . In a crop , efficient light utilisation occurs when the l eaf area below the compensation point or above light saturu tion is minimum . This will occur '\Vi th a crop with erect rather than horizontal leave s , and - 17 - in this respect the rosette shape of lettuce is particularly inefficient . In most field crops the co2 diffusion process i s in fact limiting, because many of the leaves are exposed to saturating light intensities . The rate at Vlhich plants produce dry matter i s not sclely dependent upon photosynthesis , but also depends upon the rate of respiration . - 18 - The F�T UNIT Concept A historical account of the development of heat units has been written by Wang (1960 ) . The heat unit concept was introduced over 200 years ago , and was worked out in some detail by Boussingault and De Cqndolle over lOO years ago . In i ts simplest form the theory pro- poses that for each plant a threshold temperature exists below which it does not develop . The amount of "effective heat" accumulating during -FroM. the day is obtained by subtracting" the daily mean tem1)erature - _ the base ( threshold) temperature . The "effective heat" called heat units , degree days , day degrees , or growing degree days , is considered to be a measure of plant development . Initially this concept was used by geo- graphers and ecologists to help characterise climate (Livingston and Livingston , 1913 ) , ru1d it was not until the mid-1930 ' s that degree days were used commercially to schedule plantings and to predict maturity of process vegetable cro�s (Seaton, 1955 ) . This development followed work by a number of workers (e . g. Boswell , 1924 , 1929 ) in the 1920 ' s who found that the ' heat sum ' ( the sum of heat units ) above a specified base temper- ature was closely correlated with development of peas and (above a dif- ferent base temperature ) sweet corn . It was found that for any one variety, the figure resulting from summing the number of degree days from sowing date to maturity was nearly the same for each season for a parti- cular location. This figure is knoTin as the 1 slliurnation constant ' or the remai�der index . The heat unit theory assumes that : l ) The plant rcspnnse to temperature is linear over the whole temperature range . - 19 - 2) Day and night temr,eratures are of equal importance . 3) There i s only a single 1Jase tem1-erature over the life of the plant . 4) Temperature i s the major environnental factor influencing plant development . Both Went ( 1950 , 1953) and Wang ( 1960) have strongly criticised. the heat unit system on (apf2rently) sound physiological grou11ds , but , nevertheless heat units have been of considerable practical value to agri- culture , as a predictive tool , and for s cheduling plantings . Ample evidence exists in the literat�1re of the application of heat units for ensuring a steady flow of ran products of optimal maturi ty to the factory (e . g. Seaton) , but in addition , heat units have been used for example to determine the maturity of table gra:pes (Winkler , 1948 ) , and for forecasting the incidence of pest (Lienk , 1963) and disease (Boewe , 1953) occurrence . There is nevertheless , no doubt that the heat unit system i s far from perfect as i t tends (Arnold, 1959) to overestimate the rate of plant development in : 1 ) warm compared with cold parts of the season . 2) warm compared with cool years . 3) low compared with high latitudes . 4) low compared with high altitudes . These errors may be due to the failure of the l inear system to adequately describe a curvilinear temperature response and/or because of the increasing importance of other environmental factors . - 20 - Katz ( 1952 ) attempted to use an exponential index and found for peas that the difference obtained by direct summation and by the exponen- tial system was small . Large errors can occur with the exponential index method when a high value i s given to a high temperature which may in fact be deleterious to plant development . Gilmore and Rogers ( 1958) modified the heat unit calculation by correcting for the partial effect of tempera- tures above and below an optimum range . This consisted of : l ) If the daily minimum was less than the base temperature it was given a value equal to the base temr:erature . 2 ) If the daily maximum exceeded a selected upper limit a) the daily maximum was equated to the upper limit b) the excess temperature above the selected upper limit �as subtracted from the daily mean temperature . Arnold (1960 ) has shown that from a graphic s tandpoint the ' heat sum ' is the area beneath the temperature curve and above the base tempera- ture . This is the same as the mean temperature minus base temperature (as s tated previously , except that some modification is necessary when the base temperature lies between the minimum and maximum temperature ) . A number of modifications have been propo sed to take account of this possible error . � ) Gilmore and Rogers see earlier. 2 ) Lindsey and Newman ( 1956 ) determined the area under the curve by using the formula : - 21 - (max . temp . base temp . ) 2 Heat units 1 2 max . temp . min. temp . 3 ) Anon . ( 1954 ) determined the area under the curve by using one of two formulae , depending on the position of the ba se temperature in relation to the mean temperature . 1 ) Base tem�erature greater than mean temperature max . temp . base temp . Iieat units = 4 2 ) Base temperature less than mean tempera ture max . temp . - base temr . · base temp . - min . temp . Heat units = 2 4 4 ) Arnold ( 1960 ) showed that a normal temperature curve (although skewed) is very similar to a sine curve , and the areas under the curves show close agreement . Arnold proposed that the area under the tern}cerature curve be based on sine curve calculations . The choice of method used to calculate the heat sum when the base temperature is between the minimum and maximum could be of some importance . In Table I is shown the effect of using these different methods of cal- culation on the heat sum. B3.Se Temp. Method - 22 - ma.x + min - base (1) 10. 00 8.00 6.00 4.00 2.00 0. 00 0. 00 0. 00 0.00 0.00 0.00 2 Gilmore and ( 2 ) 10 . 00 9.00 8.00 7.00 6. 00 s.co 4-00 3.CD 2.00 1.00 o.oo Rogers Lindsay and ( 3 ) 10. 0() 8.10 6. 40 4-90 3-Eb 2. 50 1. 60 0. 9) 0.40 0. 10 0.00 Newman Anon. (4) 10. 00 8.50 7.00 s. so 4-00 2. 50 2 .CD 1. 50 1.00 o. so o.oo Arnold (sine ) ( 5 ) JD.OO 8.27 6. 77 5 -44 4- 24 3. 18 2. 24 1. 44 0. 77 0. 27 0.00 Table I . The effect of calculating heat units by five methods from a temperature curve with maximum 50° , minimum 30° , and a range of base temperatures . Clearly there are differences in the heat sum calculated by the different methods , and these differences would increase with increasing amplitude of the temperature curve . If we consider the sine curve to provide the best fit , then methods 1 ) and 3 ) consistently under-estimate the heat sum, method 2 ) consistently over-estimates the heat sum - though not excessively , and method 4) gives an under-estimate when the base temperature i s near the mean temperature , and an over-estimate when the base temperature is near maximum or minimum temperatures . Errors in 4 ) eould thus tend to cancel out . In any case , as we are normally using heat units to calculate remainder index ' s for •raps between 1 , 000 and 2 , 000 units , small errors are unlikely to be important . - 2 3 - The choice OI a satisia ctory base te mpe rature is cri�al for the succe ssful application of heat units to plant de velopment. A rnold ( 1959 ) has e mphasised the empiric al nature of heat sums, and has strongly criti­ cised the re je ction of satisfacto ry ( statisticall y) b ase temperature s o n the basis of phys iological feasibility. Heat units are usually ba sed o n air tenpe rature s measure d in a S teve nson screen by me ans of maximum and minimum thermomete rs. Arnold ( 1960) h as sho wn that the re may be lo cational and se aso nal erro rs in cal- culating the daily mean from d aily maximum and minimum tem1: e ra tu re s, compared with a mean tem� e rature , de rived f rom a the rmograph. The se e rrors may account for some of the difference s in the ' summation constant' fo r particular crops in diffe re nt locations, and/or diffe rent time s of the year. huttonso n ( 1955 ) has sugge sted that photo- the rmal units ( obtained by multiplying the day- length by the de gree days) could be a mo re va luable develo pme ntal unit, and has used this method extensively in se ve ral climate studies carried out a t a numbe r of latitudes. Measuring the te mpe rature of the air ( some 4-6ft above the ground ) and attempting to re la te this to plant tempe rature at ground le vel is o pe n to serious criticism, and this is fair comment o n the heat unit concept in ge neral, with the proviso that it see ms to work reasonably well - in spite of all its obvious faults. - 24 - Plant SFacing A knowledge of plant spacing is essential if �e are to exploit our resources efficiently . Plant spacing relationships have potential not only as yield predictive models , but also offer scope as a means of analysing and interpreting experimental results more preci sely (e . g . Dov;ker and Mead , 1969 ) . In vegetable production plant spacing is impor- tant not only because of the influence it exerts on yield , but also for the effect it can exert on quality. Spacing comprises a consideration of tvro distinct factors . l . Plant Density: the number of plants per unit area, and 2 . Plant Arrangement : the spatial distribution of these plants . PLANT DENSITY As plant density increases so the yield per plant ( total , or marketable ) decreases , although the yield per unit area may in fact increase . The reduction in yield per plant with increased plant density i s due t o competition. Donald (1963 ) has stated that " competition begins when the immediate supply of a s ingle necessary factor falls below the combined demands of the plants" . The main competition factors are : light , soil moisture , soil nutrients , and on occasions carbon dioxide in the aerial environment , and oxygen in the soil atmosphere . Holliday (1960a) in an attem:r,t to characterise yield-density relationships , proposed that there were in fact two relationships - 25 - a) An asymptotic one in which with increasing density, yield rises to a maximum and then remains constant at higher densities . b ) A parabolic one in which v1i th increasing density , yidd rises to a maximum , and then declines at higher densities . The suggestion by Eolliday (l960b ) that total crop dry matter always follows an asymptotic relationship has been shown to be incorrect by (among others ) Bleasdale ( l966a ) and Farazdaghi ( 1 968 ) who found that in certain situations a falling off in total crop dry matter may occur at high densities . nevertheless the asymptotic relationship ap}Jears to provide a reasonable relationship , not only for total crop dry matter, but also in certain cases for the yield of a vegetative part of the crop e . g. Potato tubers . Holliday ' s ( l960b ) suggestion that reproductive forms of yield conform to a parabolic relationship ap�ears to be supported by experi- mental results over the past decade . Certain forms of vegetative yield also appear to show this relationship , for example , the root yield of Red­ Beet , and the sprout yield from Brussel Sprouts . Harper (l96l ) has sug­ ges ted that although the total plant dry matter - density relationship i s asymptotic the partitioning of assimilates to the various organs o f the plant may change with change in density . Bleasdale and Thompson (1966 ) have demonstrated that a parabolic relationship also exists when some form of size grading is practised . This provides a good example of the need to consider ' biological ' yield initially rather than ' agronomic ' yield which may depend entirely on arbitrary grading standards . - 26 - PLANT AR.liANGEl\IJENT For row crop s , plant arrangement comprises : - a ) the relationship betv;een the in- the-row , and the between-the-row spacing. This is termed rectangularity , and is obtained numerically by dividing the largest distance by the smallest . b ) The orientation of the rows . c ) The regularity of spacing in the ro�s . In broadcast crops , plant arrangement can be defined by the unevenness of distribution. Mead ( 1966 ) has proposed that each plant i s in its own polygon of area , and eccircularity the deviation of the polygon from circular is a measure of rectangularity. An uneven plant distribution , although it may effect crop yield is primarily of impor­ tance in vegetable production because it results in uneven competition which leads to a �ider variation in the size of the individual plants . The effect of spatial arrangement on crop yield appears to vary with the plasticity of the species , for example Bleasdale ( 1963 ) has demonstrated marked increases in yield per unit area for Carrots by keeping the plant density constant , and reducing the between- the-row spacing, while Frappell ( 1968 ) suggests that for Red-Beet there may be little advantage in reducing the betv1een- the-row spacing to less than 14" . In general honever , one might expect that increased rectangularity will lead to decreased yield per acre , and may also result in a decrease in the optimum density . - 27 - On theoretical grounds Loomis and \'.'illiams ( 1969 ) have demon- strated the advantages ( irrespective of latitude and season) of orientating plant rows N - S rather than F: - W, in order to get increased photosyn- thesis . Unfortunately this increase may be more than nullified by locelised condi t ions, for example if the 11revailing wind is in the wrong direction for the rows . The regularity of spacing in the rows i s of far more importance at high rather than low rectangularitics . Nevertheless the accurate spacing of seed (and hence we hope , plants ) in the rows even at low rectangula­ rities is highly desirable as a means of obtaining even-sized plants . The development of precision drills has done much to make this possible . a) Light Competition Competition for light may be caused whenever a plant shades i t- self or another plant . It i s present therefore , in most crors except in the case of newly emerged seedlings . The effect of early shading i s not clear , but Bleasdale ( l966a) has postulated that no yield advantage will occur provided that the initial plant densi ty is in excess of that where a constant final yield condition exists . This appears to 9hallenge Watson ' s (1956 ) concept of an optimal leaf area index. b ) Soil Nutrients Lang et al . ( l956 ) have demonstrated for grain yield of Maize , - 28 - which shows a parabolic yield-density relationship , that by increased Ni trogcm application, not only Y{as the yield at all densities increased, but the higher the density the greater the increase , and the greater the lhtrogen applica tion , the greater the density at v.rhich the maximum yield nas achieved. c ) Soil I' �oisture Salter ' s ( 1961 ) work dth CauliflowGr provides a classical example of the interaction between plant density and soil moisture . In this work , Cauliflowers v1ere grovm at four den si ties , and no irrigation was compared with regular irrigation. The results demonstrate : - l ) Increase in total yield with increased density , irrespective of irrigation treatment . 2) Heavier total yield at higher densities with irrication compared with no irrigation. 3 ) A substantially higher marketable yield from the irrigated higher densities , compared with the marketable yield with no irrigation at these densities . This is due primarily to the effect of quality grading on the already low non-irrigated yield. The Effect of Density On The Plant So far I have considered only the effect of plant density on the population. . In vegetable production we are frequently interested in crops which produce only one marketable unit per plant , e . g. Lettuce , Cabbage , Onion. Under these circumstances we are interested not only in the mean weight per plant , but also in the distribution about that mean. - 29 - Information on this subject is very limited. Koyama and Kira ( 1956 ) suggest that in a population of initially near uniform plants, the distribution will tend to + ve skewness with time , i . e . the population will comprise an increasing proportion of small plants, and a decreasing proportion of large plants . They suggest that such a tendency occurs independent of competition , but that increased competition vmuld tend to accelerate the move tov�ards riha t may Viell bE: a log. normal distribution . Mead ( 1966) , however, doubts whether the distribution apr•roxima tes to a log. normal one . Changes in density can affect maturity in two ways . l ) It may alter the time of maturity . 2 ) It may change the spread of maturity The effects will vary with the crop, for example, widely spaced Cabbages heart earlier than closely spaced ones , whereas widely spaced Onions mature later than closely spaced ones . It is however, the effect of density on spread of maturity which is one of the more valuable attri- butes of high density production . Snap Beans (Jones, 1967 ) provide a good example of this effect as at high densities virtually all the lateral growth fails to develop and a concentrated maturity crop suitable for a single destructive harvest is produced . Other examples of high density concentrating maturity are found with Sweet Corn, Brussel Sprouts and Tomatoes . This poses the question of whether the efforts expended by plant breeders to obtain concentrated maturity is really justified? - 30 - Density/Arrangement Interactions Fr8quently in plant spacing experiments the independent effects of density and arrangement are irrevocably los t , for example in experi- ments ·Fi th a constant between- the-row spacing, with variod in the row spacings to give different densities (e . g . Webster , 1969 ) . In order to exD.mine spacing effects efficiontly , l'Jelder ( 1962£-) has developed a series of systematic spacing designs in "'hich the effect of densi ty or rectan- gularity can be independ8ntly determined. These designs offer a means of exa.Dining the effect of a wide re.nge of sracings in a small area of land. - 31 - Plant Density and Corn}.�eti tion Models The analysis and interpretation of plant density experiments has been facilitated by the development of equations (models ) aimed at charac­ terising plant density relationships . Kira et al ( 1953 ) proposed an empirical law , the Competition­ Density Effect , which attemvted to describe the effect of plant densi ty on the average yield of a plant population , by the equation : w � = K When W is the average weight per plant at pla.nt density P , and a and K are constants (with plant density the only variable ) . Similar models have been proposed by Warne (1951 ) and by Duncan ( 1958) , who also proposed a semi-log. model . The effect of harvest date on Kira ' s model has been described by Shinozaki and Kira (1956 ) , who show that the model is only applicable when there i s competition . This means ( see figure 1 ) that the log w � log p relationship approximates to two straight lines , one horizontal covering the lower densities (with no competition) , and the other inclined, and covering the higher densities . With increasing time the slope of the inclined line gets s teeper , and the range of densities it covers becomes greater , and the horizontal line becomes more restricted. Kira 1 s model only describes the inclined line . With increasing time , the slope of the inclined line tends to 45° -- thus substantiating at any one time the law of constant final yield per unit area , regardless of plant population . Once the slope reaches 45° only the intercept (K) changes (increases ) with ··�------------�--�----------------� 10 SO lOO Soo I 000 Numb� t of pla.nt\ p�(' mc:tre.1 Fig. 1 . Competition-density effect i n soybean (after Kira et al . , 1 953) - 31 - successive harvests . This model also appears to w0rk fer weight per plant part ( e . g . root , seed) , although the final slope may not , under these circumstances be 45 ° . Thi s power m·Jdel can present a number of anomalies , for example extrapolation of Kira ' s soybec:;n ret;ression lines suggest that a higher yield could be obtained. from a high densHy sowing harvested at day 45 , compared with one harvested at day 84 . This type of anomaly , and the difficulty of deciding at what density competition begins led tJ the development by Shinoze.ld and Kira (1956) of the reci�rocal equation (based on the logistic model of plant grov.rth ) in which to quote the authors ' both the horizontal and inclined part of the log -;; rv log p line are represented by a smooth curve , covering the whole range of density ' . l w The model proposed was : A p + B when 'iv i s the mean �'leight per plant at density p , and A and B are con- stants , and plant density is the only VE!riable . Inherent in this model is an asymptotic relationship between yield per unit area , and plant density , i . e , The yield per unit area = v..r p , vthich v:hen p -� c-c thE:n W -:- Thus A can be considered to be a measure of the yield potential of the environment . By the same process when p O , B � 1. and thus W' l A . B can b e considered to be a measure o f the genetic pctential of a single plant growing without comvetition . Although this model adequately describes the yield-density - 3J - relationship , for the whole plant , the yield of a plant part frequently results in a parabolic rather than as.YIDlJtotic relationship . Bleasdale and Nelder ( 1960 ) therefore proposed a modification to Shinozaki and Kira ' s equa tion by adding two further constants : -- e 0 Vi = A p + B However further experience suggested that the ratio of e and 0 were more important than the absolute values , so setting � as unj_ ty results in an equation : - tl W = AP + B Bleasdale ( 1967 ) has pro_JJosed a simr,le method (based on allometry) of ca lculating P for any plant part if the total ':·eight per plant , and the weight of the biologically significant plant :r:-art are known at two plant densities , when W is the total �eight per plant , and �l is the weight of the plant part . K is a constant , as is e . The law of constant total plant final yield per unit area , on which the reciprocal model is based, has been queried by Farazdaghi and Harris ( 1968 ) 7 who propose a model a l A p + :S w for the whole of plant relationship , and Vl' I - e A p + B for examining the yield density relationship for the weight of a plant part . This equation is similar to that proposed by Blea.sdale and Nelder ( 1960) . - 34 - In additio11 to �lant density effects on yield, plant arrangement i s also important . This ha s led to the extension of the simplified Bleasdale and Nelder model by Berry ( 1 967) to include the effect of varying the between rov. , and the in the row spacing. The model n; - Q .. A p + B + incorporates an additional constant C , when a in the in the row s�acing, a nd b i s the between the ro·-.- spacing. - 3 5 - THE EFFECT OF SJ:-ACING AND FEBTILIZERS ON THE GROWTH OF LETTUCE Materials and Methods The experimental area ( of approximately i acre ) was ::,. i_ ted on Manawatu silt loam soil . The area was fumiga ted with a mixtu:ce of Methyl Bromide ( 2 parts ) and Chloropicrin ( 1 part ) applied by a contractor at the rate of 400 lb/acre in early C·ctober 1966 . The purpose of this fumigation was to kill weeds , and weed seeds , wi th any control of soil- borne pathogens regarded as a bonus . Prior to fumigation the area was rotary hoed to a dei-·th of 10 - 12" in order to produce a fine deep til th , and after fumigation, the polythene film was removed , and the area rotary hoed to a deiJth of 4 - 6" to ensure the rapid dispersal of the fumigants into the atmosphere . The experimental design used was the 2nd order rotatable design of �ox and Hunter ( 1957) and for this , the area was divided into 20 plots , each being 2 5 1 x 40 ' . This ex�erimental design enables linear and quad- ratic responses of 3 factors at 5 levels to be determined. The levels used for each factor are shown in Table II . Level Factor -a - 1 0 l + a Nitrolime (21% N) 0 4 10 16 20 cwt/ Serpentine superphosphate ( 7% P) 0 16 40 64 80 acre Sulphate of Potash (4o% K) 0 2 5 8 10 Table II . Levels of N-P-K used in the experiment . - 36 - Superimposed on each plot was a systematic spacing design (Type Ia ) of Nelder ( 19628), with a rectangularity of 1 . 0 ( a square spacing) , comprising plant densities ranging from 0 . 4 - 4 . 0 plants per square foot . This spacing design is frequently called the fan design . The two varieties used in the experiment were : - Cobham Green - a butterhead lettuce - hereafter called 1 Cobham 1 • Webbs Wonderful - a crisphead lettuce - hereafter called 1Webbs 1 • The position of the close spaced portion of the fan was randomized to either the North or South end of each plot . The position in each plot of the two varieties was randomized to be either on the East or West side of each plot . The fertilizer for each plot v•as spread by hand on 16-17 November 1966 and cultivated in ap:f:roximately 6" deep with a rotary hoe . The whole area was then rolled with a Cambridge Ring Roller . On 18 November 17 rows ( the spokes of the fan design ) were sown with each variety per plot using pelleted s eeds , and a hand operated Stanhay precision drill calibrated to sow 1 pellet every lt' . The pellets were manufactured by Nelson Lime and Marble Ltd . , Port 1fupua , Nel son , and con- sisted of a single lettuce seed surrounded by an inert clay pellet . Immediately after emergence , poisoned wheat was distributed in the experimental area to reduce bird damage , the lettuces were sprayed with Metasystox to control aphis and the plants thinned to their correct spacings . A total of ten harvests were taken at weekly intervals , commencing on 29th November 1966 . The first two harvests were taken from the ends of each plo t , and harvests 3 - 10 inclusive were taken from a single random spoke from each variety and plot . Each sample spoke has a single guard spoke on each side . The following data were recorded for - 37 - each plot and variety. a ) for the first two harvests : - 1 ) fresh weight o f top . 2 ) dry weight of leaves , stem and roots . 3 ) leaf area (measured by the ' blueprint ' method) . 4 ) number of leaves over i" i n length . b ) for the last eight harvests : - 1) fresh weight of top of each plant in the spoke . 2 ) s tage of maturity o f plant . 3 ) dry weight o f leaves , stem and roots of a close , medium and wide spaced sample plant for each plot and variety . 4) dry leaf weight/unit leaf area of a medium spaced plant by the ' punch ' method. 5) missing plants . Rainfall was fairly evenly distributed over the period of the experiment , and only one irrigation was required when the estimated soil moisture deficit was l inch . - 38 - RESULTS A}ID DISCUSSION Data Reduction It was considered essential to reduce the data to a more manageable amount . Initially the 'fresh weight of top' data was converted to ' total plant dry weight 1 using the ' fresh weight of top 1 / ' total plant dry weight ' relationship for each harvest , variety , plot and spacing. The total plant dry weight data were fitted to the reciprocal yield-density model : W -l = A p + B (Shinozaki and Kira , 1956 ) when W is the mean weight per plant at density p , and A and B are con- s tants for each plot, variety and harvest . This model was preferred to the more complex models of Bleasdale and Nelder ( 1960 ) because : 1 ) the comparatively low plant densities used in the experiment could make the accurate estimate of 9 or 0 difficult , if in fact they do differ from 1 . 0 2 ) the apparent tendency (Donald , 1963 ) for total plant weight per unit area to be asymy;totically related to plant density . In fact the yield-density model - 9 W = Ap + B was fitted for each variety and harvest , resulting in the best estimate s of C being � . 6 for Cobham Green and � .8 for Webbs Wonderful . • �tcll\aTc S These �QB�l�s however appeared to be due to the constancy of the yield per plant at low plant densities , where competition is absent , i . e . - 39 - the reciprocal model is only valid when there is competition. Farazdaghi and Harris (1968) have previously questioned the validity of the reciproca+ model at low densities , although they offer no experimental evidence to sup::ort their concern , Inherent in the Shinozaki and Kira (1956 ) reciprocal model is an asymptotic relationship between yield per unit area and plant densi ty, i . e � Yield per unit area w p . When p � oc Similarly Y:rhen p � 0 , then W -+ l B . then W -+ l A . Nichols (1967 ) has presented data \7hich supports Bleasdale�( l966 ) contention that B i s independent of soil fertility , and is a measure of genetic potential . These concepts become incompatible for the early harvests of any yield-density experiment which includes different soil fertilities , unless the reciprocal model is valid only where there is competition . Three possible relationships are shown in figure 2 which includes 3 harvest dates and 3 soil fertilities , with a) A and B independent b ) A independent , B constant at all densities c ) A independent , B constant only where there i s competition. At the first harvest date , there is no competition over the range of densities being studied, at the second harvest competition begins at half the maximum density studied, and at the third harvest there i s cam- petition at all densitie s . L _, w 2· • M L.O'-" �: R o.c\c& \ 1"\IOt\lf'l' i" cl�.-f\clo.t\t M ICU( I• 0 I I ' · I I I ' •01 . 0 1 0 f 1 0 0 t 1 0 -.o f • ·o -· -· ..,.\.. w \J �0 I L lVI \.. 6 t•f\-'0.""" M M (o\cl MOd�\) M H H •o • I •01 0 0 a.o 0 ro c l L _, ·L -· w w �-o-, / •I M / ·M - ---"' "" 8 con�.d' mod\ �ittl modet � --...,. -- . 1\ - - , , , ..,. ,.. - _,_ , , , " I �= H � -- 1-o I Figure 2. -"- ' " .,. , � c I :a . i • I I " I I •0 20 .-0 H o.t""c.st 1. f H o..-vt st 3 Hypothetical relationship showing the effect of plant density on the reciprocal of total yield per plant at 3 levels of ferti l ity (H igh, Medium, and Low), on 3 harvest dates, with A and B parameters independent, B constant (old model ) and B constant (modified model ) . C is the density at which competition commences. �0 t.-0 ,-0 - 40 - When yield-density data are fitted to the reciprocal model over a number of harvest dates , it is possible for the estimates of A in the early harvests to be smaller than the estimates of A for later harvests , in fact if we can assume that B is constant for any one harvest ( and genotype ) it i s possible in soil fertility experiT!lents for A to be nega­ tive . These anomalies were noted when analysing the lettuce data , and similar anomalies can be noted in Shinozaki and Kiras ( 1956 ) soybean analysis . This suggests tha t the reciprocal yield-density model is only valid where there is competition , and this theory was tested by fit­ ting the total plant dry weight data from the lettuce experiment to the model : assuming that : W -l A p + B l ) the model fits at all densities 2 ) the model fits only where there i s competition ( the modi­ fied model ) . A weighted least squares criterion (Nelder, l963 ) was used, and in order to determine the density at which competition began ( c ) , the R . S . S . (Residual sum of squares ) was minimised over a range of C ' s for any one harvest , 611 plants at a smaller density than C being considered to have a density of C . The results ( for the variety Webbs ) shown in Table TIT demon­ strates that : - 41 - 1 ) there was a marked reduction in the densi ty at which compe- tition begins ( C ) vri th successive harvests . 2 ) Using the modified model , the R . S . S . i s reduced , the anomaly in the estimate of A at �est 4 was eliminated, and the es timates of A in the earlier harvests were increased . Similar results were obtained from analysing the data from the variety Cobham in the same manner . A comparison between the two models is shown in Figure 3. There does not appear to be any reason when the �arameters A and B calculated by the ' modified method ' should not have the same biological meaning e s those derived from the normal model ( i . e . yield and genetic­ potential respectively) . In fact it could be argued that the parameters obtained using the ' modified model ' are better estimates than those obtained by the ' normal model ' . It could also be argued that the more sophisticated reciprocal yield-density models are also only valid when there is competition . An account of these findings has already been published (Nichols , 1970) . Having demonstrated the validity of the reciprocal yield-density model only where there i s com1-·eti tion, the total dry weight per plant data for the whole of the experiment were fitted to the modified model , with ' B ' constant for each harvest and varie ty , ' A ' independent and ' C ' constant for each variety and harvest . The yield per plant when there i s no competition was calculated for each variety , harvest date , and fertilizer plot using the formula : -· w (q"'s d.w./plQ.ct) •4.· ·3 - - '1:. KEY Mocli�ie cl lftocl� I 01 cl mode. I X ---- - X - •2*-----------�------------------------�------------ 0 . � N Ut"\Ot.c- ()� p\ �1\-tS /.ft.:t 3 Figure 3. Webbs Wonderful Harvest 5. Showing a comparison of the old and modified reciprocal yield density models. 4 - 42 - Weight per plant 1 B + A X c The results of this calculation, and the total plant dry weight9 from the first two harvests were now fitted to the four parameter logistic model (Nelder et al. , 1960; Nelder , l96la ; Nelder , 1962 b ) w = I 1 harvest 1 ' normal model ' ' modified model ' No . n . s . s . A R . s . s . A c 3 39 . 02 . 226 34 - 70 3 - 751 3 . 6 4 40 . 48 . 018 38 . 91 . 063 3 . 0 5 28 . 99 . 029 27 . 90 . 047 1 . 7 6 30 . 77 . 020 29 . 94 . 02 3 l .O 7 21 . 79 . 014 2 1 . 70 . 15 . 7 8 21 . 08 . 012 20 . 99 , 01 3 . 6 9 20 . 47 . 009 20 . 2 3 . 009 . 6 10 17 . 68 . 010 17 . 68 . 010 < - 4 Table ill. Residual sums of squares , A parameters calculated for Webbs Wonderful , using normal , and modified reciprocal yield density models . � hen W i s the weight per plant at time t , A i s the asymptote , K r�a-ii\1� is the ini tialA.growth rate , 0 defines the point of inflection, and f... is the constant of integration . t can be chronological time , or some environmental time scale , and the first essential was to determine a - 43 - suitable time scale , by fitting the model to chronological , and a number of environmental time scales . The weather records were obtained from D . S . I .R . Plant Physiology Division Meteorological site - some 200 yards from the lettuce experimental area . The time scales considered were g 1 ) chronological time . 2 ) solar radiation (measured by an Eppley solarimeter ) . 3 ) Heat Units above a range of base temperatures . Calculated from daily maximum and minimum screen air temperature using the 1 Air :1\Iinistry Method ' (Anon , 1954) . The results (Table IV) show a clear improvement in the goodnes s of fit (as measured by the reduction in the error sums of squares of log ·F) with any e of the environmental time scales , compared with chronological time . Heat Units above a 42°F base temperature provided the most satisfactory fit o This result is in agreement with Salters ( 1 960 ) findings for cauliflowers , but Nichols ( 1968 ) has shovm tha t over a 9 month period , solar radiation i s a better time scale for lettuce , than either Heat Units or chronological time . This aspect will be considered elsewhere in this thesis . The choice of a suitable time scale in this �articular experiment i s probably not critical , }Jrovided that the error term is reduced to a reasonable level . For this reason the time scale used for the remaining analyses 0 was the 1 heat sum 1 above a 42 F terr:.rJera ture . - 44 - Analysis of Plant Dry Weight Data The logis tic model was fitted to the yield per plant when there is no competition ( calculated previously) for each plot and variety . The parameters a (= log A ) , K and 0 for each variety were then fitted to the e response surface , and the coefficients (l inear , quadratic , and linear interaction ) were tested for statistical significance . The results are shown in the appendix . In all cases the response model showed that the quadratic phosphate coefficient was of major importance , even though significance (P < . 05 ) only occurs in one analysis - the Webbs 0 analysis in which in addition to the qua�atic phosphate coefficient , the linear nitrogen, and linear phosphate coefficients are also significant . The lack of significance in the other analyses is somewhat surprising particularly with respect to Cobham 0 which has a quadratic phosphate coefficient approximately double the equivalent Webbs coefficient (which is significant ) . Examination of the Cobham data shows that the absence of s ignificance for 0 is due to plot 1 3 , one of the central (0-0-0) plot s from which the error variance is calculated . It was deci- ded to reject this value , and substitute a value estimated as follows : - �0 . Cobham () est. Plot 13 Cobham = 40 Webbs x 0 Webbs plot 13 . 475 This was done because of the size of the dis:tJarity between the different 0-0-0 plot i ' s for Cobham . - 4S - Fitting the response curve to these data with a new estimate of D plot 13 sho,�s that the quadratic phosphate coefficient is now significant (P < . os ) . It is pertinent at this stage to consider why the linear nitrogen coefficient is significant for Webbs , and not for Cobham. The para- meters 0 , K, a and "- are all correlated to some extent , and a high value of B is usually associated with a low K . This means tha t the increased value of 0 with increased nitrogen i s associated with a ' ow&r initial relative growth rate with increased nitrogen . two possible explanations of the phenomena : There appear to be 1 ) The increased nitrogen application has resulted i n larger plants at the first harves t , and hence a reduced R . G .R . when fitted to the logistic model . ( see appendix) 2 ) Because 0 i s the least precisely determined o f the para­ meters ; and small changes in K can greatly modify O. In fact fitting the logis tic model with 0 constant ( for \iiebb 0 = . 22 6 , for Cobharn 0 = .362 ) only emphasised the importance of the quadratic phosphate term , although only K for 'debbs was significant ( P < . os ) . Similarly an analysis of the j oint 0 1 s for the two varieties ( e . g . for plot 1 , 0 j oint = ( . 62 3 + . 423 ) / 2 = . S2 3 ) results in only the quadratic phosphate coefficient being significant . For these reasons no further attention was given to the linear nitrogen coefficient for 0 Webbs , and it was concluded that phosphate exerts the major effect on o. - 46 - Time scale Cobham Webbs Total Time ( chronological ) . 1630 . 1828 . 3458 Solar radiation . 0889 . 1305 . 2194 H . U . 30 . 0966 . ll69 . 2135 H .U . 40 . 0676 . 0910 . 1 587 H . U . 50 . 0728 . ll25 . 1853 H .U . 39 . 0702 . 0928 . 1630 H . U . 41 . 0661 . 0897 . 1 558 H .U . 42 . 0641 . 0882 . 1 523 H .U . 4 3 . 0661 . 0935 . 1597 Table IV . Hean error sums squares for Cobham and Webbs . - 47 - With e now fixed for each variety and phosphate level , new a� and K 1 s were estimated for each plot and variety using the logistic model . These 0 1 s were not estimated from the response surface model , but were obtained from the mean of the logisti.c model estimates . e . g . G for P = l ( . 514 + . 304 + . 27s + . 63s ) I 4 = . 344 V�ben the response model was fitted to the a 1 s and K ' s calculated with e fixed according to variety and phosphate level the analysis ( see appendix ) again demonstrated the significance of the phosphate coefficients , P < . 0 5 for Cobham quadratic and Webbs linear , and P < . 001 for Webb quadratic . K ' s were now fixed for each variety (as for 6 previously ) according to the phosphate level , and new a 1 s were calculated for each variety and plot . None of the coefficients of the surface response model for a were significant (P < . 05 ) , although both the quadratic phosphate and linear N x P coefficients were close to significance for both varie ties . In view of the similarity in the results for the two varieties , the weight per plant data were now combined ( by adding the logarithms ) , in the hope of reducing some of the exrerimental error . The logistic model was used to determine a , K and 0 for each plot , and these para- meters were fitted to the response surface . This analysis in no case produced any significant coefficients ( see appendix) , but once again emphasised tl1e importance of the quadratic phosphate term . In fact the quadratic phosphate coefficient was significant at P < . 1 , and the lack of a higher l evel of significance appears to be due once again to Plot 1 3 . The data were then fitted t o the logistic model , with 0 fixed according to the phosphate level , and the response model was fitted to - 48 - the a 1 s and K 1 s . Only the quadratic phosphate coefficient for K was significant (P < • 001 ) 0 and K were now fix.;;d according to the plots phospha te level , and the logistic model a.gain fitted to each plot , and the a ' s then fitted to the surface response model . Only the quadratic phosphate coefficient is significant (P < . 05 ) , but the magnitude of the N x P term should be noted . The results are in the ap:fJendix and are shovm graphically in Figure 4 . The logistic growth curves for 3 levels of superphosphate are sh: Jim in Figure 5 . Of the fertili zers under consideration clearly phosphate exerted the major effect on plant dry weight , irrespective of variety . There does however appear to be a difference between the two varieties in their response to fertili zer . The peak of the phosphate response curve is much sharper for Cobham than for Webbs . In fact Cobham tends to�:.-ards a quadratic response , vrhile Webb tends towards a quadratic plus linear response . ( see Appendix ) . Apart from this , the h o varieties differ fundamentally: in their growth curves ( see Figure 6 ) . Webbs having a larger a and K , and a smaller :...1., ( see Table VI ) than Cobham , V!ith the result that , in the later harvests Webbs is the larger let tuce , although , at the early harvests Cobham., at least in this experi- ment , i s larger because of more initial capital . It i s postulated that this cross-over i s partially due to the differences between the two varieties in the rate of leaf production . Cobham , having a greater rate of leaf productio� results in shading between leaves on the same plant at an earlier stage than Webbs , and hence a less efficient ( see Table V ) photos�1thetic apparatus . Harvest Table · V • l 2 3 4 5 Parameter Table VI a K 0 - 46 - Cobham Webbs S . E . ( 5 . D . F . ) 0 . 8 0 . 6 :!: 0 . 11 4 . 0 2 . 9 + 0 . 12 9 . 3 6 . 7 j: O . l7 16 . 6 12 . 1 .± o . 39 26 . 3 20 . 1 :!: 1. 17 Number of . leaves exceeding t' length. Analysi s of 6 , 0-0-0 plots . Cobham Webbs S .E . ( 5. D . F . ) 3 . 79 4 . 64 + . 05 . 0189 , 0201 + . 0011 . 286 . 227 + . 056 Analysis based on the 6 , 0-0-0 plots . Finally the near significance of the N x P coefficient for the joint �lys� of a s�sts tl'>...at given a more se:nai tive experimental design , some response to nitrogen application might be anticipated. e \ •011.0 -+- -----.------.-----�-------, d.. 4·2 4 0 6, 0 1·1�------�-----------------r--------0 Figure 4. o( , k, and 9 parameters for the combined Cobham/Webbs dry weight per plant data .fitted to serpentine superphosphate appl ication rates. · - 50 - An interpretation of the results in terms of Growth Analysis The clas sical methods of growth analysis as exemplified by Watson ( 1952 ) involves the calculation of the Relative Grov1th Hate (R . G .R) , and its components , the N"et Assimilation Rate (N .A .R . ) and Leaf Area Ratio (LA .R . ) . Radford ( 1 967 ) has defined these growth analysis formulae at an instant of time ( t ) when 1 ) W i s a measure of plant material present , and 2 ) A i s a measure o f the magnitude of the assimilatory system as follows � The relative growth rate i s the increase of plant material per unit area of material per unit of time . i . e . R . G .R . = 1 dVl w· dt The net assimilation rate is the increase of plant material per unit of assimilatory material per unit of time i . e . N .A .R . l dW A. · dt The leaf area ratio is the ratio of assimilatory material per .unit o.f. plant material present . i . e . L . A .R . A w The traditional use of these formulae involves the calculation of mean R . G .R 1 s . , N .A .R 1 s . , and L .A .R 1 s . over the t ime periods using the · formulae : R .G .R . N .A .R . ( Log 8 w2 - Loge W 1 ) ( T2 - Tl ) (w2 - ·'�\) . (Loge A2 - Log8 A1 ) (T2 - Tl ) " X . (A2 - Al) Lo�e d.w.jp\ ant +4. 0 -2 . I . I . I I I 9 . I I I . I I I I I -4 I I I • I .'p 1 1 I I I I I I I I I O l I I I I " . " .rp .'/ / I . I I I • I I d • I I I . I � I • I I I I / 6 I I I I I I KEY er - - -o 0 c.wt/ o c.�-. ><-·- ·X l b c wt/oc. rQ. A 6 40 c.wt/ oc.re. -��------�-------r-------r-------r------�------� 0 200 400 600 800 1000 1'100 Cumu\o.:t.i"e. \-tc.o.t. u" it� , base. 4�0F. Figure 5. Combined Cobham/Webbs dry weights per plant fitted to the 4 parameter logistic model for 3 levels of serpentine superphosphate application. L . A . R . - 51 - (A2 - Al ) (w - w ) 2 l X (Loge w2 - Log e wl ) ( Loge A2 - Log e Al ) wl ' w2 is usually the p lant dry weight , and A1 , A2 the leaf area at times Tl , T2 . Radford (1967) has emphasised that it i s the relationships between time and A , and time and W, which should be our primary conside- ration , v:i th a view to dis covering the form of these grm,rth curves . Both Vernon and Allison ( 1963 ) , and Hughes and Freeman ( 1967 ) have used a polynomial function to examine these &,Tot:th curves . Vernon and Allison fitted their data to : W a + bt + ct2 so tha t at any instant of time : R . G . R . l d1i·! w · dt N .A .R . l dW 'A · dt L .A .R . A w b + 2 et ct2 a + bt + b + 2 et l + b1 t l t2 a + c l b1t + c1 t2 a + a + bt + et 2 This was for Zea majs post-tas selling data , and the variances for the I different harvest s were not excessively different . Hughes and Freeman fitted their data to log functions . e so that : log W e log A e R . G .R. L . A . R . l dW v; · dt d ( log w) e A W == antilog. e dt ( log A - Log W) e e 0 I I -� -4 I I I KEY er- -o We.hbs >f � Cobhcun -��------�------�--------r-------�------�------- a.oo 4-00 6 o soo to o 1 too Cum u \o:t. ive. "e.o..'\:. un i t.. s , b4St. 4�· F. Figure 6. Dry weights/plant for Cobham and Webbs fitted to the 4 parameter logistic model. Based on 0-0-0 plots. - 52 - H . A . R . L . A .ll . Radford ( 1967 ) has used an exponential function t o des cribe the growth of tal l fescue � w {I . . weighting each point according to the inverse of its variance � so tha t : * R . G . R . L . A . H . v'· �:__� y·­a-:-i:'e .., 'Y'L (f-,'t) V -C� l.. . I I ,f y -:_; a +P o , . . I /, ,...' y t �': .+PG_� �- There is an error in Radfor d ' s formula for N.ii. .R . a.s tho prime for in the denominator has been omi tted in his paper . Having used the logi stic mo del to examine ary wdght • ·..J t i:ne trends , i t i s logical to use the same model to exaTiine the leaf area rv time relationships . For the fir·st t'.70 harvests , l eaf areas mJre measured directly , using an air flov; planime ter , but i t Fas necessary to determine the leaf areas for tht.: other 8 harves t s indire ctly . Thi s was done by calculating the a l lometri c relationship between leaf dry weight (vVL) and tot a l plant dry weight (WT ) for each vari ety , harvest , and plot � using a s data the sampl e plant parts yields o f the wide , medium and close spaced plant s . The formula used was : Log WL x 0 + Log K e e The leaf dry weight of the hypotheti cal plant in a non- competi t ive situa tion was determined us ing the allometric relationship for that - 53 - particular variety , plot and harvest date . As the leaf dry weight/leaf area relationship had previously been determined for each variety , plot , and harvest by the ' punch ' method (albeit for a medium spaced plant ) , the determination of the l eaf area of the hypothetical plant was then straight- forward . The leaf areas for each variety (and the mean leaf areas for the tv:o varieties , obteined by combining the logs . ) , for all 20 plots , v1ere now fitted to the logi stic model , using the heat units above a base of 42°F . time scale . From the logistic growth curves for total plant dry weight (obtained earlier) and for leaf area , it i s now possible to cal- culate plant leaf areas , or dry weights at the various harvest date s . Having deternined W for any particular time , it i s a simple oatter t o cal­ culate �� from the differential equation on which the logistic model i s based: J. dW dt kW � 1 - (�) 8 _7 Then R . G . R . N .A .R . L .A .R . l dW w . dt l dW A • dt ! w These results clearly demonstrate a higher overall relative growth rate for Webbs compared with Cobham . This appears to be due to a higher net assimilation rate for Webbs , in spite of Cobham having a larger leaf area ratio . The higher net assimilation rate of Webbs may be due to its smaller leaf . area/gm. dry weight of leaf . ( s ee Table VII ) - 54 - Var ./HarvE::st l 2 3 4 5 6 7 8 9 10 Mean Cobham 351 Webbs 218 Table VII . 484 430 351 354 352 2 99 leaf area/ 351 552 586 470 534 485 317 413 423 386 408 362 dry weight leaf . (t�M�/'l• ·) The mechanis� for the increased nGt assimilation rate could be either a 452 360 greater rate of photosynthesi s , or a slo�er rate of respiration or both . One possibility could be that the thicker leaf is able to absorb more radiation . This would be important while plants are small , and not corn- peting for light , but at high densities all the radie.tion would be absorbed by the crop canopy. This appeal'S to be borne out by the similarity of the yield potential for the two varieties . The differences in leaf area ratio betv;een the tvm varieties apllear to be due solely to differences in leaf area/gm. leaf dry weight , and not due to differences in the parti- tioning of photosynthate ( see Table VIIT ). The differences at the last two harvests is due to the increasing proportion of stem in the variety Cobham . Var./ Harvest l 2 3 4 5 6 7 8 9 10 Cobham 69 81 88 91 89 92 89 87 84 81 Webbs 70 82 89 91 89 90 89 86 87 84 Table VIII . Percentage of leaf dry weight/total plant dry weigh� An examination of the relative gTowth rate for the different phosphate levels shows �n increasing rate with increased phosphate � 55 - application up to 40 cwt . Thi s i s due predominantly to differences in net ass imilation rate . See Figure 9 . There YlaS no apparent di fference between the l eaf area/gm . leaf dry weight for the different phosphate treatments , and the leaf area ratios were similar . There was , hov:ever , a difference in the dis tribution of photosynthate when the Ocnt/acre phosphate level -vms compared with the other l evels . Harvest l 2 3 4 5 - % Lvs , 60 . 0 76 . 1 86 . 0 90 . 8 88 . 3 Table IX • a phosphate Mean -l and 0 phosphate 1�Stm . %Rts . % Lvs . % stm . 'foRts . 8 . 1 33 - 9 69 . 0 6 . 1 24 . 9 7 . 1 16 . 8 80 . 7 6 . 2 1 3 . 1 3 - 4 10 . 6 88 . 3 3 - 5 8', 2 3 . 5 5 . 7 90 . 2 4 . 2 5 . 6 4 - 4 7 · 3 88 . 8 5 - 7 5 - 5 Tiry matter distribution , phosphate treatments . This effect could not be checked as in the experimental design there i s only a single n o phosphate plot . The prolonged period of exponential growth which occurs in spite of a falling net assimilation rate for the first 5 or 6 weeks appears to be due to changes in the dist­ ribution of dry matter , i . e . an increase in the shont/root ratio with time . Some of this effect i s probably due to the failure to obtain more than a nominal amount of roots from the soil in the later harvests , but nevertheless the trend appears to be real . - 56 - The near linear manner in which the net assimilation rate falls ( see Fit,>Ure 10 ) for the - a , -1 , E\ phospba t e treatment may be due to the use of the logi stic model to fit the data , and smooth the curve , but could be a real effec t . The reason for the effect of phosphate fertilizer on net assimilation rate appears to have no simple explanation . Relative grov:th rate , and leaf area ratio t ime trends for the tv..ro varieties , and for 3 phosphate levels are shown in Figures 7 and 8 (Relative Growth Rates ) and in Figures ll and 12 (Leaf Area Ratios ) . • 02 -r--------------------------------------- - - - - - - - - - - .... ....._ ...... K EY - 'We b\,s Cob'-'am - - ' \ " ' ' '\ ' 0�--------r-------�--------,-------�r--------y--------, 0 bOO SOO \ 000 He..- · - · -o 1 6 ct.Jt/ac re *- - --x 0 cwi/ �c.ote. ....... ......._ X ...... .......... .......... .......... ... - ·- ·- - - ·­·- - - - - - 5;-------�------�------�------�------�------�------� -, q 10 Figure 14. Lo9e A (from the reciprocal yield-density model) for 3 levels of serpentine superphosphate, fitted to an exponential model . - 60 - phosphate levels are sho¥m of log 1 a ' against time . e merely to show the re sults more clearly graphically . Log ' a ' i s used e - 61 - Plant Losses An unreasonable nwnber of plants were lost towards the end of the experiment due to Sclerotinia , particularly in the variety Cobham . In New Zealand , lettuce i s particularly susceptible to Sclerotinia during the summer , but the nwnber lost ?as far more than one might expect , and the severity of the attack could have been caused by changes in the soil ecological balance folloning sterilization. In <:.ny fu tu:re experiment wi tp lettuce the systemic fungicide 1 Benlate ' could reduce the severity of such an attack . An examination of the pattern of plant losses due to Sclerotinia showed that fertilizer treatment had li ttle effect , and the main differences af1 eared to be between th8 varieties , and the effect of time . There was no apparent effect of plant density on the pattern of plant loss with the exce;:.tion of the final harvest of Cobha.rn - when losses Here significantly greater at densities in excess of 2 plants per sq . f t . As Cobham was ' going to seed ' at this harvest in terms of marketable yield this is of no commercial importance . An analysis of variance of the plants missing due to Sclerotinia for the last 4 harvests shows a significant (P < . 001 ) variety effect , and a significant (P < . 001 ) effect of harvest , but the variety x harvest interaction was not significant . The linear component for harvests was highly significant , and the results are shown in Figure 15 . Wu���f' o� t\an't\ dt.ad. 8 4 kEY x Cobhom o We.bb6 0�--------�--------�------�--------� 7 , Nu mb�(" 1 0 ' Figure 15. Plant losses due to Sclerotinia, showing the number of dead plants (out of 13) with reference to harvest date and variety. - 62 - Marketable Yield Although dry �eight per plant (or per unit area ) can be a useful measure for the physiologist , it is of little value to the horticulturist unless it can b8 related to marketable yield . Marketable yield for lettuce is itself a very nebulous attribute , as it depends entirely upon the market requirements 9 and the harvesters subjective asses sment of maturity. What constitutes a marketable lettuce '.vill vary with the market , the time of the year , and the demand . In this experiment , a marketable l ettuce uas one which vras con- sidered to be acceptable on a British market in the surr@er . The reason for basing this on Britain is because Butterhead lettuce is not grown commercially in New Zealand , while both t;ypes are grown in Britain in the summer months . Because of small samfles , a reliable assessment of marketable yield proved difficult . The method used was as follows : The percentage of marketable lettuce for each spacing, variety and harvest was obtained . The ratio of fresh weight of top/total plant dry weight was determined for each variety and harvest . This fresh weight of top constitutes the potential marketable yield , which becomes the market­ able yield when multiplied by the percentage marketable . Total plant dry weight for the different treatments , spacings , harvests , and varieties >lere derived from the reciprocal yield-density model results . cetain anomalies had to be ' smoothed out ' . Even so , - 63 - As marketable lettuce were only harvested from harvest 7 - 10 , linear regressions were calculated on the reciprocal yield-density para- meters A , and B , i . e . The was plotted against time . 1 genetic potential ' (�) for Cobham, and Webbs The ' yield potential ' (�) for the - a , - l , and 0 , phosphate levels was plotted against time . This ' yield poten- tial 1 i s a joint one between Cobham and Webbs because .of the lack of significance between the varieties in this respect . These 5 regression lines were used to calculate A � and B parameters for the final four harvests , and from these parameters \Jere C8lcu.lated the total plant dry weight ·per square _..foot · · · ->- to-tal ·f-resh weight of top per .square f.oot, -� marketable yield/square - foot . . Plotting these estimated marketable yields/sq . ft . against plant density can be shown as R simple quadratic curve , of the form 2 Y "" ax + bx which can be fitted by plotting i . e . 2 y = a x + b x y:_ against x X y = x (a + bx ) :1. = a + bx X The plant population which has :maximum marketable yield is obtained by differentiating i . e . a + 2 bx but 0 for maximum marketable yield, X = - a 2b The results are sho\m in Table X , and graphically for each variety in Figures 16 , and 17 . ozj.f+'l. 30 to 0 0 2. 3 N vmhe.r of p l�"-ts /H.� Figure 16. Marketable yield of lettuce/sq.ft. Cobham, harvest 8, with quadratic function fitted. oz/ftll. X 30 X 2.0 1 0 X 0 �-------.--------r-----��------� 0 � 3 NuMbe.t" af pl a nTs / ft.2. Figure 17. Marketable yield of lettuce/sq.ft. Webbs, harvest 9, with quadratic function fitted. - 64 - Varie ty Harvest Phosphate a b X max Yield at Level X max Cobham 7 0 10 . 44 - -2 . 61 2 . 00 10 . 4 Cobham 8 c: 1 3 . 75 -3 . 53 L 95 13 . 4 Cobham 8 ·- l 15 . 58 - 3 . 88 2 . 00 15 . 6 Cobham 8 0 16 . 07 -· 3 , 97 2 . 02 16 . 2 Cobham 9 0 20 . 75 -5 . 57 1 . 87 1 9 . 4 v,'ebbs 9 - C: 37 . 71 -13 . 90 1 . 36 25 . 6 Webbs 9 - l 44 . 63 -- 16 . 30 1 . 37 30 . 6 Webbs 9 0 46 . 70 -16 . 99 1 . 37 32 . 0 vrebbs 10 0 62 . 05 -22 . 51 1 . 38 42 . 8 Table Ca lculated polynomie.l parameters , with derived maximum mE,rkett=lble yield and related density . A lthough the results for Cobham (harvest 9 ) and Webbs , (harvest 10 ) are included as I:larketable lettuce , it must be stated that although they had not 1 gone to seed 1 they were tending tovmrds overma turi ty with the exception of the - c: phosphate plot , nnd the optimum harvest da te- for quality and yield v,8s harves t 8 for Cobham and harvest 9 for Webbs , As there was only a single . . e:: phosphate plot in the eXIJeriment it is impossible to draw any conclusions in this resfect . For the same reason although i t is probably that the percentage of marketable lettuce from the - a phospha te plot was l8ss than the other plots , the absence of replicates prevented this from being examined , - 6 5 - From these result s , for maximum marketable yield , Cobham should be grown at 2 . 0 �lants }-er syuare foot , and Vfebbs at 1 . 4 plants/square foot , but this takes no account of mis s ing ple.nts something that it i s hoped would not norma lly occur . A8 about 25% of the Cobham plants were missing at harve st 8 , somE) modifi cation in the density for maximum marketable yield i s nece sse.ry . The simflest approach appears to be to incren so the area per plant by 25% i . e . 2 . 0 plants/sq . ft . \i'hich + 2 5% 72 sq . ins . per plant 90 sq . ins . �:er plant i . e . about %" x 9i' ' 1 . 4 plants/sq . ft . For Webbs at harvest 9 , about 2a(. of the plants v1ere missing, and carrying out a similar calcula tion as tha.t for Cobham , resul ts in a decrease in the optimum plant densi ty from 1 . 38 to 1 . 15 plants per s q . ft . (approx . 1 1 11 X l l " ) Nelder ( l96lb ) has sugge2ted that optimum dens ity for maximum marketable yield of lettuce i s greater for high yielding compared with l ow yielding crops . This a.l:-'1-ears to disregard the fact tha t a mRrketable l ettuce must not only be of ' acceptable ' size , and hearted , but should have a fairly fla t bas e , for ease of packing . At high plant densities l ettuce tend to develop pointed bases (peaky lettuce ) , and this has been noted by Sale ( 1966 ) who found that maximum marketable yields were achieved for the butterhead variety Borough Wonder at 9" - 10" square under wet or irrigated conditions , and at 1 2 " square under dry conditions . Sales marketable yields - ranging from 10 - 14 oz/sq . ft . at the optimum spacing for a butterhead lettuce , are similar to those obtained in this experiment . - 66 - The reason why we c2n expect a heavier mark0table yield from Webbs compared with CobhaQ. - assuming optimum harvest date and plant densi ty , i s due mainly to the delay in maturity of Vlebbs , resulting in additiona l yield . Nichols (1965 ) has noted this previously with two butterhead varieties of different maturity times . In the case of Webbs and Cobham , this effect would be supr lemented by the difference in carbohydrate assirnilation efficiency. - 67 - Discussion It is easy, in retrospect to say that the decision to use a rotatable design in this experiment vas \";Tong, and that some form of randomised block design v:ould have been a more efficient use of resouces . There ce.n be little doubt that the inherent lack of robustness in the rotatable design reduc0d the value of the results , and substantiDlly increased the number of computing man hours required to obtain meaningful results . Probably the relative lack of success stems from the extremely small sample taken a.t each harvest , but sample size had to be limited because no technical assistance \7a s avf1 ilable . Webster ( 1969) has had some success \Jith this design with vegetable fetilizer studies , and Dillon ( 1968 ) ha s Rdvocated this ty� ·e of design in agronor1ic fertili zer exp<::riments . Faced uith the same problem today , my first strategy vould be to increase the range of plant densi ties under examination , particularly at the high density end , v;here a population of ( say) 144 plants/square foot should enable a more accurate determination of the yield-density relation- ship to be obtained, es!)ecially at the very early harvests . With plant populations of this density , the systematic designs are no longer feasible , and an alternative could be to sow beds (by means of a Stanhay tandem precision drill ) , of the different plant populations . Then , providing that adequate resources in terms of labour and facilities were available , randomised block design would be substituted for the rotatable design. The need for the ' optimum response ' to occur near the central points , and the lack of replication at the - a and + a levels would be important reasons for such a decision . Nevertheless it - 68 - is conceded that starting ,.,i th very li ttle idea of the type of response one might expect on this soil type: , the rotatable design has proved an efficient method to enable a single person to grow and record the effGct of variety , spacing, and five levels of N , P , and K . Analysis and interpretation of the results l'iould not necessarily be different although initially i t would be necessary with the more precise data to test my assumption that the genetic potential in the reciprocal yield-density model is constant for any one harvest nnd variety. fiore precise data could also allow my modified yield-dtnsity model to be more stringently tested , particularly at the ee.rly harvests . More precise de ta uould perhaps permit e. different type of analysi s o f the A and B parameters from the yield-densi ty J)lodel . It would be especially valuable to deterDine how the yield potential is affected by time and nutrition, and this should be possible by using higher plant densities , particularly at the early harvests . Larger samples might perr!lit the analysis of growth at the different densiti0s to be examined solely in terms of a logistic function , although efforts to do this with my data were not successful . The plants response to soil fertilizer appli cation i s very much a function of soil type , e>.nd in this particular case the soil type was known to have a big response to phosphate for vegetable s , as previous work (Nichols , 1967 ) with vegetables had shown . The use of the logistic model to help in interpreting fertilizer - 69 - responses is not new , having been used with mixed success by Austin e t al ( 1964 ) at Wellesbourne . Although one reason for their lack of success was the overriding effect of soil moisture stres s , it ap�ears likely that another reason could be the difficulty of separating the effect of nutrition and plant density, •:;hich becor.w confounded in a very complex manner . - 70 - Conclusions The growth of two varieties of lettuce ( Cobham Green , and Webbs Wonderful ) was examined in relation to plant density and Nitrogen , Phos­ phate and Potash fertilizer application , using a systematic spacing design � and a rotatable fertilizer design . The results were analysed by modify- ing the reciprocal yield-density model to include the case :: ·here there i s no competition , and then fitting total plant dry weights , and leaf areas estima ted for plants in a non-com1,eti tive situation , to a logistic model with a suitable environmental time scale . The logistic model parameters of total plant dry weight showed a significant response to serpentine superphosphate , when fitted to the rotatable design model , but no other fertilizer was significant . The effect ·of serpentine superphos�hate (up to 40 cwt/acre ) was to increase the relative growth rate by increasing the net assimilation rate . Evidence is presented to suggest that the yield-potential at very high density is the same for both varieties , but the genetic potential i s lower for Cobham Green due to a lower net assimilation rate , and a more rapid rate of leaf production . Marketable yields of Webbs Wonderful were found to be higher than for Cobham Green at the optimum plant density for marketable yield ( Cobham Green 1 . 4 plants/sq . ft . , Webbs Wonderful 1 . 1 plants/sq . ft . ) mainly due to the additional week required for Webbs Wonderful to reach optimum maturity , but also due to the greater genetic potential . - 71 - GROWTH AND DEVELOP}J1ENT OF TWO LETTUCE VARIETIES IN THE NATURAL E:t-IVIRONMENT Materials and Methods The varieties used were : l . Cobham Green a butterhead type (hereafter called 1 Cobham 1 ) 2 . Webbs Wonderful -- a crisphead type (hereafter called 1Webbs ' ) Virus tested seed of the two varieties was obtained from Harrisons Seeds , Leicester , England. The experiments were sited at two places : a ) At the University of Nottingham , School of Agriculture , Sutton Bonington , Loughborough , England . (Latitude 52° 49 ' N. ) on a sandy loam, overlying Keuper marl . b ) At Massey University, Palmerston North , New Zealand. (Latitude 40° 20 1 S . ) on a lVIanawatu silt-loam. The University of Nottingham Experiment (March - December 1963) The site had been used to grow a Sweet Corn crop in 1962 , using simazine for weed control . Because of the danger of simazine residues affecting the growth of the lettuce precautions were taken to dilute the simazine residues with a large volume of soil . After the Sweet Corn crop residues had been removed from the area the soil was rotary hoed to a depth of 6 inches . Following the rotary hoeing, the site vras then ploughed ( early in November 1962 ) and sub-soiled, and 12 concrete posts (8ft . tall ) were erected in a 4 x 3 pattern at 25ft intervals for bird - 72 - control ( see later ) . A soil tes t , analysed by the National Agriculture Advisory Service , provided the following information. pH 6 . 3 Phosphate 100 (High ) Potash 29 (Medium ) Nitrogen . 181 % In order to improve the moisture holding capacity of the soil , as well as the nutritional status , spent mushroom compost at the rate of approximately 2 5 tons per acre was evenly spread over the experimental area early in January 196 3 . This wo.s followed on 21 .March ( just prior to the first sowing) with a base dressing over all the area of Hydrated Lime ( 10 cwt/acre ) , and Triple Superphosphate (2 owt/acre ) . It had been intended to make the first sowing early in January, but a particularly cold winter resulted in the ground being frozen to a depth of 12 inches until late February , with the result that the ground was unworkable until Hid-March . The mushroom compost , lime and superphosphate was cultivated into the soil by means of a rotary hoe on 22 March , and the first sowing was made on 26 March 1963 . Birds are a major problem at Sutton Bonington , particularly early in the spring , and so to prevent the small lettuce seedlings being damaged , wires were stretched between the concrete posts , which had been erected the previous autumn , and black nylon thread was s tretched between the wires at approximately 12 inch intervals , over and around the whole experimental area . - 73 - Seed of the two varieties of lettuce was sown at 3 weekly intervals , commencing on 2 6 1Jiarch 1963 , and ending on 10 October 1963 , a total of 10 sowings . The seed was sown by means of a planet junior drill , set to deposit the seed at a depth of i inch as recommended by Heydecker ( 1956 ) . The seed was dus ted with Thiram fungicide prior to drilling . Weed control was by push hoeing between the rows , and hand hoeing in the rows . Each sowing was made into a soil close to Field capacity and no other supplementary irrigation was ap1�lied. The experimental design was a fully randomized split plot one , with three blocks , 8 main treatments ( the sovJing dates ) , and two sub-treat­ ments ( the two varieties ) . Sowings numbers 9 and 10 were sown where sowings 1 and 2 had been grown . Each main plot consisted of 6 rows of lettuce , 12 inches apart , with the outside row of each main treatment plot being separated from the outside row of the adjoining main treatment plot by 18 inches . There were 3 rows of each variety , and the outside rows of the main plots were treated as guard rows . Harvesting was carried out at 7 day intervals from emergence until the sowing had ' gone to seed ' with the exception of the last sowings , when harvesting ceased early in December 1963 follo1ling a damaging frost . The posi tions of the plants taken as samples at each harvest were randomized , and to further reduce positional effects , each replicate was divided into half , and a sample taken from each half at each harvest , and then bulked. Soon after emergence the two outside rows of each main plot (the guard rows ) were thinned to 12 inches apart , while the four centre rows were thinned to 3 inches . Each main plot was sub-divided into 20 plots 3 ft . long, and the first 3 harvest samples were obtained from - 74 - plants growing at the 3 inch and 9 inch positions in the plot s selected. Following these harvests the plants were then all thinned to 6 inches apart , and the 4th harvest was obtained. from plants growing at the 6 inch position in the plots selected. The plants rrere then thinned to a 12 inch spacing . Twenty plants per ser1rle ( 10 from each half of the replicate ) were usually taken for each variety and replicate at each of these early harvests . For the later harvests only 8 plants were usually taken per variety and replicate , 4 plants from each half of the replicate . These plants Fere guarded on all sides by at least one row of lettuce , but there were no guard rows betv1een the two varieties , and so the randomization for harvest date was the same for the two varieties . This sampling technique. was suggested by Mr . R . Mead , \"hO was at that time a Biometrician at the National Vegetable Research Station , Wellesbourne , England . It was necessary because of the restrictions placed upon the design because of space . The following data were obtained from each sample : l ) Fresh weight o f top . 2 ) Number of leaves ( in excess of i" long) . 3 ) Length of stem . 4 ) Stage of maturity of plants (i . e . immature , marketable , overma ture ) • 5 ) Dry weight of leaves . 6) Dry weight of s tem . 7 ) Dry weight of roots . * * No effort was made to obtain all the roots exce:pt in the early harvests the main aim being to obtain the swollen part of the tap root , and the nearby fibrous roots . - 75 - Leaf areas were measured by the ' blue print ' method for the early harvests only . The data for the two sample rows of each variety (i . e . ( l ) the row guarded on both sides by the same variety , and ( 2 ) the row guarded by different varieties ) were kept separate . Weather data were obtained for the duration of the experiment from the standard meteorological station ( 50 yards anay ) . Solar radiation data were obta ined by means of a ' Kipp ' solarimeter , some 200 yards from the ex�erimcntal area . Wea.ther da ta were also obtained by a number of resistance thermometers placed within the experimental area , and recording on to paper charts by means of a multi-channe l recorder . These data were later discarded because of the physi cal imposs ibility of handling such masses of data without some form of automatic recording which would faci litate immediate computer analysi s . The Massey University Experiment (April 1967 - March 1968) The site of the experiment ( of approximate t acre ) adjoined the the site of the lettuce spacing, fertilizer , and variety experiment reported earlier . The area was fumigated with a mixture of Methyl Bromide ( 2 parts ) and Chloropicrin (l part ) applied by a contractor at the rate of 400 lb/acre in early March 1 967 . As in the earlier experiment , the purpose of the fumigation was predominantly for weed control . Prior to fumigation , the area was rotary hoed to a depth of 10-12 inches , in order to produce a fine til th . Following fumigation the polythene film �as removed , and the area was cultivated to a depth of 4-6 inches to facilitate - 76 - the rapid dispersal of the fumigants from the soil into the atmosphere . The experimental design was the s ame as in the Nottingham experi­ ment , i . e . 3 blocks , 8 main treatments ( the s o1ving dates ) , and 2 sub- treatments (the 2 varieties ) . There were 10 soviings , soYiings numbers 9 and 10 were sited where sowings numbers 1 and 2 had been grown . Because a larger experimental area was available , each sowing comprised 8 rov.rs of lettuce , 4 rows of each variety , with only the tvvo centre rows of each variety being used as sample plants . The sampling technique was similar to that used at Nottingham except Hat because the samr le plants were now guarded on all s ides by the same variety , it was no longer necessary to take samples for the two varieties from the same position . Sowings of the two varieties were made at approximately monthly intervals in rows 12 inches apart using a Stanhay precision drill and pelleted seed . The drill was calibrated to sow one pellet every li" � Sowings were made at approximately monthly intervals , on : 2 April 1 967 , 4 1fuy 1967 , 7 June 1967 , 2 July 1967 , 28 July 1967 , 6 September 1967 , 2 9 September 1967 , l November 1967 , 2 December 1967 , and 5 January 1968 . Plant samples were obtained at 14 day intervals between April and September inclusive , and at 7 day intervals for the rest of the experiment . In spite of the soil fumigation s ome weed control was required . This via s by push hoeing between the rows , and hand hoeing in the rows . Prior to drilling the seed , a base dressing of fertilizer v.ras spread on the soil and cul tivated in . The fertilizer comprised : - 77 - Serpentine superphosphate 40 cwt/acre Nitro-lime 10 cwt/acre Sulphate of Potash 5 cwt/acre The rate applied was based on the results obtained from the l ettuce spacing/fertilizer experiment reported earlier in this thesis . The applica tion of Nitrogen and Potash was not justified by the results , but was applied as an insurance . In sowings nlli�bcrs 9 and 10 the application of serlJentine superphosphate was reduced to 20 cwt/ acre . The following data were obtained from each plant sample : 1 ) Fresh weight of top . 2 ) Number o f leaves in excess of i" in length . 3 ) Dry weight of leaves . 4 ) Dry weight of stem . 5 ) Dry weight of roots . 6 ) Stage of maturity of plant , i . e . immature , mature , overma ture . 7 ) Leaf area , either by air-flow planimeter (when small ) or by the punch method . Once again no real effort was made to obtain all the roots except in the early harvests . Weather data were obtained from the nearby D . S . I .R . Plant Physio- logy Division Meteorological Station . Regular sprays were applied of Metasystox ( 16 fl . o z ./acre ) in order to control Aphis , and of Difolotan ( 2 lb/acre ) in order to control the various fungus diseases which can . afflict lettuce in the Manawatu . - 78 - Irrigation (l" ) was applied whenever the soil moisture deficit exceeded 1" . The soil moisture deficit was estimated from a soil moisture budget , with the potential evapo-transpiration being derived from mean monthly weather records using Thornthwaites formula. - 79 - Results and Discussion In an effort to smooth out the effect of year to year variation in crop yield , Nelder et al. ( 1960 ) proposed the use of the four parameter logistic equation : dW K W ( l _ (� ) 1/ e ) dt A TLis differential equation comprises a family of curves , of "·hich the Gompertz (when e = 0) is a special case . When e is positive , a solution i s : when w is K is A is a is and "- i s w the weight of a A (l + e - ( f.. + Kt)/ C ) e plant or plant part at time t . the relative growth rate at t = () the asymptote related to the point of inflexion the constant of integration. t may be chronological time , or some environmental time scale , such as solar radiation, or degree days above a specified base temperature . Nelder ( l96la ) has described a. method of determining the least squares fit of data to this model , using an iterative technique because no explicit solution exists , and this technique was used in an attempt to determine a suitable time scale to describe the growth of lettuce in two different climates , and varying weather conditions . The data used in this analysis were the total plant dry weight per plant obtained from the Nottingham and Massey University experiment s described earlier , plus thGt from the spacing/fertilizer experiment - 80 - carried out at Massey in 1966-67 . The latter data were only for the 40 cwt/acre serpentine su:per:phoslJhate :plots , vlith the total :plant dry weights converted via the modified yield density model (Nichols , 1970 ) to a :p lant density of 1 . 0 :per sq . ft . A number of :rra .j or :problems had to be solved before a satisfactory solution could be obtained. The r.•Iassey University I . B .M . 1620 computer in addition to being a slov1 ma chine (at least by modern stand&.rds ) has only 40 K rapid access storage . 'I'h:;se :problems v:ere ovc;rcome by using a series of linked :programnes , and by storing these :programmes , and the data on disk . Nelders 1 method of fitting the model i s only applicDble for a single set of data , and a modification was necessary in order to fit 2 1 sets of data simultaneously to produce a single set of :parameters . This involves some ffiani:pulation of the time scales in order to 1 su:perimpose 1 the growth curves . In a :previous report on thi s work , Nichols ( 1 968 ) did this by as suoing that t for each curve occurred at a constant � 0 calculated :plant weight (actually ex:p - 10 ) . Using this method e (15ethod l ) the model w�s fitted to a number of environmental time scales , and -the result s are shov!n in table XI There i s little value in reducing the Error mean square of the fit to the logistic model belmJ that of the E . IVI . S . of the experiment . The experiments E .J,·� . S . was determined by doing an analysis of variance (Blocks , Varie tie s , Harvests ) on the whole :plant dry weight data ( log e trcmsformed) for each sovling separately! The Degrees of Freedom for Error , and the Sums of Squares for Error were summed ( E D . F . error , and Z S . S . error ) , and Z S . S . error wa s then divided by l: D . F . error , to obtain the error mean square for the whole experiment . The Error - 81 - Degrees of Freedom , and Error Sums of Squares and Error Means squares for each sowing , for oach site , and for tho exr)eriment as a whole are shovm in the Appendix . The E .M . S . for the vrhole exp�Jriment was . 03514 . Time scale a = Log A K e Error Mean c Square COBH.AM H .U . 30 2 . 9752 -12 . 94 1 5 . 00659535 . 6903 • 3773596 E .U . 40 3 . 0396 -1 3 . 2052 . 0117417 · 5736 . 2479726 H .U . 50 2 . 9575 -11 . 81 38 . 0303209 . 6428 . 43 31032 H . U . 45 3 . 0394 - 1 3 . 0292 . 0179354 . 5418 . 2408410 H .U . 41 3 . 0437 -13 . 2 107 . 0126777 . 5628 . 2 393253 H . U . 42 3 . 0463 -1 3 . 2019 . 01 37418 . 5536 . 2 33513 V/EBBS H .U . 30 3 . 6114 -1 3 . 8631 , 00709491 · 4436 . 4042178 H .U . 40 3 . 7705 -14 . 3901 . 0131974 . 3 342 . 242 3707 H .U . 50 3 . 5767 -12 . 5 367 . 0322674 . 4271 . 4213000 H . U . 4 5 3 - 7415 -14 . 1 1 36 . 0200430 . 3285 . 2218607 H .U . 41 3 . 7765 -14 . 4017 . 0142885 . 3276 . 2 302097 H .U . 42 317772 -14 . 3874 . 01 55056 • 3 2 32 . 2 211421 H .U . 43 3 . 7717 -14 . 3 380 . 0168647 . 3216 , 2 160509 Table XI • Logistic growth curve parameters and Error Mean Square * Method 1 . * H.U . 40 etc . = Heat Units (Degree F x days ) above a base 0 temperature of 40 F . - 82 - These results demonstrate that as far as a Heat Units time scale i s concerned , that t o improve the fit of the model (as measured by reducing the error sums of squares ) requ ires a ' heat sum ' with a base temperature In an effort to furth,;r improve the fit , a weighted linear regression of : log e A e against time ( chronological or envlromnental ) was calculated for each sowing, Then using the mean slope for all the sowings used in the calculation , the time scales were adjusted until all the regression lines had the same intercept . Thi s method (Method 2 ) was found to give a better fit of the data to the model t��n the previous method (Method 1 ) . �Phe results are shovm in Table XII • Because of this improvement , Method 2 was used in all future calculations . In Table .Y.I I , Time is chronological time in days , H . U . 40 is Heat units in degree F . x days calculated from daily maximum and minimum so..:-een air temperatures above a designated base temperature ( e . � . 40 , 41 , 42 etc . ) by the method advocated by the Air :Ministry (Anon . 1954 ) . . Solar radiation is the number of calories/cm2/day measured by a Kipp solari- meter at Nottingham, and by an Eppley solarimeter at Massey . These results clearly demonstrate the improved fit to the model which results from usint any of the environmental time scales compared with chronological time . With regard to the heat units analysi s the 0 best fit occurs for Cobham with a base temperature at 42 F , and for Webbs - 83 - 0 at a base temperature of 43 F . I t could b e argued from thi s , that Cobham will grow at a slightly lower temperature than Webbs , but the substantial improvement in the fit by using a solar-radiation time s cale suggests that radiation rather than temperature offers a better time scale . Tim'" Scale a = Log A -. K 0 Errr,r Mean e " Square COBHAN Time 2 .·, 7993 - -116280 . 141583 1 . 4462 . 6859785 H . U . 40 3 . 0329 -12 . 6490 . 0111420 - 6726 . 2038196 H . U . 41 3 . 0371 -12 . 6593 , 0120370 . 6579 . 1985831 H .U . 42 3 . 0397 - -12 . 6529 , 01 30501 . 6463 . 1959627 H . U . 43 3 . 0�01 ·12 . 6231 . 0142055 , 638!: o l967073 n .u . 44 3 , 0380 -12 . 5635 . 01 55132 . 63 54 . 2014350 H . U . 45 3 . 0328 --12 . 4688 . 0170005 . 6391 • 2115363 Sol2T radiation 3 . 1146 -12 . 7479 . C00529362 . 5371 . 1403739 VVEBBS rp · .. lme 3 , 3077 -11 . 7630 - 138655 L l857 . 7610687 H .U . 40 3 . 7398 ·-1 3 . 6552 . 0120200 . 4123 . 1929416 H .U . 41 3 . 7459 - 13 . 6814 . 01 30374 . 4015 . 18 35874 H .U . 42 3 . 7478 --13 , 6840 . 0141808 . 3933 . 1769881 H .U . 43 3 . 7445 -13 , 6532 . 0154670 . 3884 . 17 39216 H .U . 44 3 . 7357 -13 . 5816 , 0168961 . 3875 . 17 52 500 H .U . 45 3 . 7209 -1 3 . 4630 . 0184888 . 3915 . 1822985 Solar radiation 3 . 7723 -1 3 . 6137 . 0005663 31 . 3636 . 1005017 Table XII . Logistic Growth curve parameters and Error Mean square . * Method 2 . * H . U . 40 etc . = Heat Units (Degree Fx days ) above a base temperature 0 of 40 F . - 84 - In an effort to improve the fit to a hea t unit time scale , a new time scale , heat units above a base temperature of 42°F minus heat units above a base temperature of 70°F was used , on the assumption that time above a certain temperature , if not deleterious , did not result in more rapid dry matter accumulation . The choice of a temperature of 70°F was purely arbitrary , but the fa ct that this gave a worse fit to the model than H .U . 42 alone suggests t��t there was little to be gained by further adjustments using a heat unit scale . H .U . 42 x solaz radiation time scale proved to be only slightly superior to chronological time . Finally the mean solar radiation figure per day for the experimen t was determined ( 337 cal ./cm2/day) and a substantial improvement in the fit to the model was obtained if i t wa.s assumed that any calories in excess of 3 37cal/cm2/ day were only 5o% as efficient as radiation below 337 cal ./cm 2 /day. This is shown in Table XIII as Ra (imp . ) . Clearly from these results , some form of solar radiation time scale is the most satisfactory. I t i s axiomatic that the parameters calculated for the logistic model should be the same for the Nottingham data , as for the r&lssey data, provided that a suitable time scale has been chosen . That thi s is not so , is clearly an indictment of the failure of the time scales chosen to adequately describe the environment . See Table XIV • Because a solar radiation time scale reduced the error mean square for the logistic model lower than any other time scale considered , i t was decided to consider if some further improvement could be obtained by making certain assu�ptions regarding the effectiveness of radiation at different intensities . Time Scale COBHAM H .U . 42-H .U . 70 H . U . 42 x Ra Ra ( ir.1p ) Vi/EBBS H .U - 42-H .U . 70 H .U . 42 x Ra Ra ( imp ) Table XIII . - 85 ... a = Log A A. K Error Mean e Square 3 . 0407 -12 . 6712 . 01 31676 . 645 3 . 1967615 2 . 9003 -10 . 0166 3 . 679 5xl5 · 9493 . 6000883 3 . 1 2 56 -13 . 0001 . 0587286 - 5325 . 1121773 3 - 7 514 -13 . 7055 . 0143103 . 3923 . 1788897 3 . 4678 -10 . 5003 3 . 785 3 5 . 6070 - 5447312 3 . 7939 -1 3 . 8801 . 0626602 . 3629 .0847703 3 Parameters and E .Iv1 . S . for various complex time scales . H .U . 42 = Heat units ( degree F x days ) above a base temperature of 42°F (H .U . 70 = same above a base temperature of 70 °F ) . Ra = solar radiation , and Ra ( imp ) = solar radiation with any radiation in excess of 337 cal ./cm2/day being valued at so%. - 86 - Time Scale a = Log A "A. K 8 E .M . S . e COBHAM Nottingham Ha 3 - 0965 -12 . 9959 . 0618466 . 4608 . 1101767 Ra ( imp ) 3 . 1009 -13 . 0726 . 0662232 . 4725 . 08704389 H . U . 42 2 . 972 3 -12 . 7702 . 0130885 . 5670 . 22 37472 COBHAM Massey Ra 3 - 1393 -1 3 . 0143 . 0461118 . 6237 . 1166282 Ra (imp ) 3 . 1481 -13 . 2 364 . 0524242 . 6099 . 1065092 H .U . 42 3 . 0903 -12 . 9999 . 01 30955 . 7354 . 155 5072 VillEBS Nottingham Ra 3 - 9496 - 14 . 2284 . 0684903 . 2786 . 07770041 Ra (imp ) 3 . 9786 -14 . 2768 . 072 5278 . 2876 . 05952406 H .U . 42 3 . 8484 -1 3 . 6 315 . 0134996 . 3667 . 2 347610 WEBBS Massey Ra 3 - 7523 -13 . 9661 . 052 9092 - 3 596 . 07690591 Ra (imp ) 3 . 7396 -14 . 1105 . 0592911 - 3710 .08644751 H . U . 42 3 . 6746 -13 . 9480 . 0148247 . 4217 . 09404228 Table XIV • Logistic parameters fitted to better fitting environmental time scales for the two sites . - 87 - Four assumptions were considered 1 ) That any solar radiation exceeding a certain daily integral was ineffec tive . 2 ) That any solar radiation exceeding a certain daily integral was only se% as efficient as radiation below that figure . 3 ) That any solar radiation exceeding a certain hourly integral was ineffective . 4 ) That any solar radiation exceeding a certain daily integral was was ineffective provided that the plant was below a certain dTy weight . The plant dry weight between two harvests ·was considered to be the mean plant dry vwight , calculated by obtaining the mean of the log dry weights at the two harvests . e Some difficulty was obtained in d6termining hourly integrals of solar radiation for use in assumption 3 ) , as only daily integrals were available . The method used to deternine hourly integrals was as follows : The solar angle was calculated for the two sites , for the 21st of each month , and for every hour of daylight , using the formula : ,.,.. cN-12 6 ) . Solar angle = sin 6 sin cp - cos 8 cos '+' cos � x 3 0 when ({J is the latitude , o the declination , and N is the time in hours (conti- nental clock ) . From these solar angles an estimate can then be made of the radiation occurring per hour as a proportion of the total daily radiation. The method used was to calculate the solar angle at midday, - 88 - and then at hourly intervals until night (a negative solar angle ) , From these solar angles an estimate was made of the amount of solar radiation per hour ( i . e . i an hour on either side of the hour) , as a proportion of the daily solar radiation integral . This was done by dividing the solar angle at a specific hour , by the total of the days hourly solar angles , ' e . g. for 1 . 30 p . m . - 2 . 30 p . m . . 622 . 106 5 . 903 This method slightly overestimates the 11 . 30 a . m . - 12 . 30 p .m. figure by about 1%. If the daily measured solar ra.dia tion integral is multiplied by the proportion of radiation occurring per hour ( derived from the solar angle calculation ) , an estimate of the hourly solar radiation integral can be obtained. This derivation has a number of possible errors , e . g. ( l ) it assumes that solar radiation at any time is proportional to the dai ly solar radiation integral , and does not consider the fact that radiation from a clear sky would be about 4x the radiation from a cloudy sky at any one time and place . nevertheless in the absence of more detailed solar radiation data it does offer a means -- if somewhat crudely, of considering not only the daily solar radiation integral , but also the duration , which as Brouwer and Huyskes ( 1968 ) has shown is of importance in determining dry matter accumulation in lettuce . In the four conditions considered, a number of solar radiation integrals at which radiation becomes ineffective ( or 5o% ineffective ) were considered, in order to find the one at which the logistic model fitting minimised the error mean square . Because of the limitations placed upon the use of the computer , and the slow speed of the machine ( each fitting of a single time scale to the 21 sowings of a single variety took about 30 minutes ) , it was decided to test to the nearest 50calories/cm 2/day in - 89 - the daily estimates , or to 5 calories/cm2/ hour in the hourly estimates . 12 l pm 2 pm 3 pm 4 pm 5 pm 6 pm 7 pm noon l . . 703 . 683 . 62 3 • 528 . 403 . 2 59 . 104 - . 05 2 . . 1 19 . ll6 . 106 . 089 .068 . 044 . 018 0 3 . 47 . 6 46 . 4 42 . 4 3 5 . 6 27 . 2 12 . 6 7 . 2 0 4 . 30 30 30 30 27 . 2 1 2 . 6 7 . 2 0 Table XV Example showing the derivation of hourly radiation integrals . l . Solar angles calculated for Nottingham in April for afternoon . 2 . Proportion of solar radiation occurring over 60 minute period ( solar angle ) � solar angles · 3 . Hourly solar radiation integral , assuming daily solar radiation integral is 400 ca1 ./cm2/day . 4 . As for 3 , except asouming plants light saturated at 30 cal ./cm2/ hour . The most satisfactory fit ( the least square fit ) for each variety, and method was then tested independently for the Massey and Nottingham data . The results of the various interactions are shown in the appendix , and only the best fi ttir.g results for each varie ty and method , and site are sho• in Tables XVI ani XVII . There is , in all cases an improvement in the - 90 - Time Scale a = Log A K e E .M . S . e Webbs (both S itES ) Ro. 600/day 3 . 7700 - 1 3 . 8788 . 0581502 . 3634 . 08993986 Ra 45/hr . 3 . 8144 -1 4 . 0459 . 0614856 . 3538 . 0792 9785 Ra 50 + X/day 3 . 8200 -14 . 0597 . 0962069 . 3628 . 06943987 Ra 400 ( -4 ) 3 . 8086 -1 3 . 9427 . 061054 9 . 3121 . 09211650 Webbs (NottinghiJ.I!l) Ra 600/day 3 . 9541 -14 . 2235 . 0689744 . 2856 . 06968397 Ra 45/hr . 3 · 9405 -14 . 1 347 . 0683456 . 3005 . 0742 3527 Ra 50 + X/day 4 . 0350 -14 . 6723 . 113371 . 2 751 . 04585009 Ra 400 (-4 ) 3 . 9739 -14 . 3949 . 0717848 . 2 556 . 07486623 Webbs (Iviassey ) Ra 600/day 3 · 7569 -14 . 3035 . 0545757 . 3 583 . 07067694 Ra 45/hr . 3 . 7492 -14 . 2704 . 0580791 . 3790 . 07562589 Ra 50 + X/day 3 . 7780 -14 . 3788 . 0911359 . 3635 . 06109875 Ra 400 (-4 ) 3 . 8025 -14 . 3929 . 0589122 . 2899 . 07001027 Table XVI . Logistic parameters calculated for solar radiation time scales for variety and site . Key : See Appendices IX and X. - 91 - Time Scale a = Log e A K fJ E .M . S . Cobham (both site s ) Ra 500/day 3 . 142 -1 3 . 0785 . 0568925 - 5344 . 1180087 Ra 40/hr . 3 . 1 380 -13 . 1495 . 0594338 . 5297 . 1052 571 Ra lOO + X/day 3 . 1 320 -13 . 0784 . 0793031 - 5487 . 1013797 Rn 400 (-2 ) 3 . 1476 -1 3 . 2757 . 0618478 . 4029 . 1158129 Cobl1am (Nottingham) Ra 500/day 3 . 0920 -12 . 9792 . 0637885 . 4887 . 09779068 Ra 40/hr . 3 . 0970 -13 . 0175 . 06485 38 . 4820 . 09706146 Ra lOO + X/day 3 . 1204 -1 3 . 3101 . 0886214 . 4769 . 06962685 Ra 400 ( -2 ) 3 . 1216 -13 . 3118 . 0684119 . 3872 . 09953221 Cobha.m (Massey ) Ra 500/day 3 . 1 509 -13 . 3917 . 0506763 . 6040 . 1068187 Ra 40/hr . 3 . 1 561 -1 3 . 4106 . 0541464 . 6188 . 1022 377 Ra lOO + X/day 3 - 1 542 -13 . 4307 . 0710502 . 6279 . 1027460 Ra 400 (-2 ) 3 . 1849 -13 . 7761 . 0551950 . 4291 . 09718628 Table XVII . Logistic parameters calculated for solar radiation time scales for varie ty and site . Key : See Appendices IX and X. - 92 - fit to the model , compared with a straight solar radiation time scale . • In fact in most cases the improvement is in the region of about 25%. In all cases � however , there is still a wide divergence between the K pa.rruneters (initial relative growth rates ) for the two sites , and from this one can only conclude that none of the environmental time scales chosen is entirely satisfactory. In fact the only time scale in which the K parameters for the two sites are similar is Heat Units 42°F , but the error mean square i s approximately double that o f the better solar radiation time scales . In a previous analysis of the data from Nottingham , Nichols ( 1968 ) showed that a substantial amount of error could be removed by not making the asymptote ( a ) constant over all sowings, however because all these paramGters are correlated it was decided to fit the logistic model to each sowing and variety with only K ( the initial relative growth rate ) constant for each variety, This was done using the best environmental time scale for each variety, nrunely: For Webbs Ra 50 + X/day , i . e . solar radiation up to 50 cal ./cm 2 /day plus 5o% of any additional radiation. For Cobham Ra 100 + X/day, i . e . 2 solar radiation up to 100 cal ./cm /day plus 5o% of any additional radiation. - 93 - Because of the similarities in the estimates of the K parameters for the two sites when using a heat unit time scal e , the data was also fitted to the logistic model using a heat units above a base temperature of 42°F . (H .U . 42 ) time scale , with only K constant for each varie ty over all sowings . The full results are shown in the appendix, but the consolidated results for the error sums of squares clearly demonstrated that fitting the model with only K constant for each sowing approxiraately halves the error sums of squares (Table XVIII ) . Time scale Ra lOO + X H .U . 42 Ra 50 + X H . U . 42 Table XVIII . Error sums of squares Variety single set parameters only K constant Cobham 24 . 432 1 1 . 163 Cobham 47 . 227 2 1 . 379 Webbs 16 . 666 5 . 868 Webbs 42 . 654 20 . 342 Total error sums of squares for all sowings determined for for a single set of parameters over all sowings , or with only K constant for all sowings , for 2 varieties , and different environmental time scales . These results further confirm the earlier findings that solar radiation provides a better environmental time scale than heat units at least in the experiment . - 94 - In this respect Emecz ( 1962 ) proposed that light would provide a more meaningful time scale than chronological time using the classical technique of growth analysis . It is pertinent to note that these results are still within the limits set by the experimental error which is . 03514 , as the error mean square obtained for fitting the model to the best solar radiation tiae scales , for both varieties , with K constant , is . 0483 . The results of fitting the nodel to the data, with only K constant are shown in figures 18 , and 19 , and clearly demonstrate a marked falling off in the asymptote ( a ) in the Nottingham data with successive sowings . No such trend is apparent in the N�ssey data. This time trend appears to be more marked for Webbs than for Cobham and a linear regression of asymptote against sowing number for Nottingham results in : We.bbs Cobham slope slope - . 304 - . 2 3 3 In addition the variances of the a parameters for the different sowings of the two varieties shows a larger variance for Webbs ( see table XIX ) . Webbs Cobham Table XIX • Nottingham + �fussey 6 .079 4 . 05 Nottingham 4 . 184 2 . 343 a parameter variances Massey 1 . 330 0 . 647 As the major purpose of this experiment was to determine whether a satisfactory time scale exists in order to develop a predictive model 0 -:l. -6 -s • 0 • 7UN A .... 1 9 63 Figure 18. Total dry weight per plant Webbs fitted to the 4 parameter logistic with a solar radiation time scale (Ra 50 + X/day} with K constant for all sowings. • oC.TC& 1%7 0-�---"0 0 • • • X " .1 9 (:,8 • • kEY x sow-1Mr.s. 1 1 S',q , t3 ,n,'l l. Q 6owu..aco.s 2, b , I O , l .lt., IS. * s ..... ... 3,7, 1 1 , 1 5, 1 '1 . e S�;��wu•IG.OS, 4-19 , \�, \ b ,'J.O c:aowu.ar. No. � l . ·:u�.wo�tl-'1 \ '\ b J lo�e d.w.jplo.'