A Dynamic Equation for Plant Interaction and Application to Yield-density-time Relations

A model for plant interaction is developed based on a definitionof space in terms of actual and potential amount of growth factorsabsorbed per unit of time. The resulting equation is a second-orderdifferential equation which is solved by dynamic simulation.Five data sets on yield-density relations are used to demonstratethe model's excellent predictive power. Competition model, plant interaction, yield-density relations, Richards function, subterranean clover (Trifolium subterraneum L.), Wimmera ryegrass (Lolium loliaceum Hand-Mazz.), lettuce (Lactuca sativa L.), maize (Zea mays L.), lucerne (Medicago sativa L     

A New Model Relating Crop Yield and Plant Arrangement

A new model is proposed which relates the weight of plants totheir spatial arrangement. The weight of each plant is calculatedas the integral of the function f(r) = L(cr² + 1)^–2 overan area allocated to it, r being distance from the plant, withL and c parameters to be specified. The model is thus concise,general, in that it can be used to describe the effects of anyspatial arrangement on plant weight, and the parameters L andc have a biological interpretation. It is also consistent withthe commonly-used relationship between plant weight (w) anddensity (p), w^–1 = a+bp. We show for carrots (Daucus carota L.) and red beet (Beta vulgarisL.), that the mean weights fitted by the model agree as wellwith the experimentally observed mean plot weight as those fittedby more complex models with more parameters, some of which arenot as general. We show also that the parameter c can be predictedfrom the time from sowing to harvest, with good results whentested on sets of data independent of those to which the modelhad been fitted. The assumptions on which the model is based,its application, and extensions to it are discussed. Crop yield, plant density, plant arrangement, carrot, Daucus carota L., red beet, Beta vulgaris L., soya bean, Glycine max L., mathematical model     

A Model for Plant and Crop Growth, Allowing for Competition for Light by the use of Potential and Restricted Projected Crown Zone Areas

Relations for competition for light are developed and used ina plant growth model applicable to the isolated plant, to plantsin even-aged monoculture and to plants in mixed-aged monoculture.In an isolated plant, it is assumed that a leaf area, proportionalto the plant mass, is contained within a crown whose projectedzone area is proportional to plant mass to the 2/3 power. Self-shadingprogressively reduces the specific growth rate. If light werethe sole limiting resource and were constant, one can derivea growth equation, dw/dt = rw[1 - exp (-KW^1/3)]KW^1/3, which,integrated, gives w^1/3 = K^-1 ln {1 + [exp (KW^1/3₀)-1] exp (rt/3)}.It approximates, initially, to a particular case of the Richards(1959) empirical growth equation. In even-aged evenly-spaced monocrops competing only for light,it is assumed that the zone areas merge at canopy closure, andgrowth then follows the expolinear equation of Goudriaan andMonteith (1990), giving a continuous function based on groundcover. For mixed-aged monocrops, we assume a phase of canopyclosure that affects the younger plants earlier than the olderones. Under varying environmental conditions in the field, plant growthmay be affected by other factors in addition, e.g. temperature.In the growth conductance model of Aikman and Scaife (1993),the shading expressions are applied to the light-dependence. Data from two sowings of cabbage and carrot in even-aged andmixed-aged monocrops were used to test the model. The parametervalues derived from the even-aged monocultures predict the growthrates in the mixed-aged monocultures better than models whichassume uniform canopies.Copyright 1994, 1999 Academic Press Growth, model, monocrop, even-aged, mixed-aged, PAR, density, competition, light, shading, zone area, ground cover, temperature, carbon dioxide, expolinear, carrot, Daucus carota L., cabbage, Brassica oleracea L     

Predicting the Growth Interactions between Plants in Mixed Species Stands using a Simple Mechanistic Model

The Conductance model is a simple mechanistic model used topredict the growth of species in monoculture or mixtures fromparameter values derived from plants grown in isolation. Incontrast to many mechanistic models that require extensive parameterization,the Conductance model is able to capture the growth of a broadrange of species using a few simplified assumptions regardingplant growth and easily derived species-specific parameter values.We examine the assumptions within the Conductance model thattotal leaf area per plant is proportional to total plant weight,and that an isolated plant has a projected crown zone area thatis proportional to the 2/3 power of its weight. Power ratherthan linear relations were found between weight and leaf areafor Brassica oleracea, Daucus carota, Matricaria inodora, Solanumnigrum,Stellaria media , Trifolium repens and Veronica persica.For all seven species, the value of the power was less thanunity. All species also exhibited a power relation between crownzone area and weight, with the slope of this relation beingless than 2/3 for B. oleracea, D. carota and S. media. Althoughmorphology type accounted for some of the variation in the parametervalues relating to light interception, there were considerabledifferences between species within upright or prostrate foliagespecies groups. The Conductance model was used to predict yieldsof B. oleracea, S. nigrum and V. persica grown in both monocultureand binary weed-crop mixtures over a range of temporal and spatialscales. After calibrating the model to non-competing plants,the model was used to predict growth of the weed and crop speciesin contrasting densities and stand types. In some crop-weedcombinations, predicted crop and weed weights were within 17%of observed values, with no systematic deviations. In others,systematic and large deviations occurred.Copyright 2001 Annalsof Botany Company Brassica oleracea L., Daucus carota L., Matricaria inodora L., Solanum nigrum L.,Stellaria media L., Trifolium repens L., Veronica persica L., competition, growth, leaf area, crown zone area, light, shoot morphology, canopy architecture     

Plant Growth Analysis: Allometry, Growth and Interference in Orchardgrass and Timothy

A multiple regression procedure was used to evaluate allometricresponses to stand age and species population densities in monoculturesand mixtures of orchardgrass (Dactylis glomerata L., also knownas cocksfoot) and timothy (Phleum pratense L.). In each speciesthe allometry between shoot dry weight and either leaf areaor tiller number per plant was studied. Population density treatmentsaffected allometry by changing allometric exponents expressingthe ratio of relative growth rates of different plant characteristics.Allometric relationships changed as growth proceeded, and thetwo species differed in their allometric responses to treatments. Plant growth analysis, allometry, competition, Dactylis glomerata L., Phleum pratense L.     

The Effects of Temperature on Leaf Growth in Cyperus longus, a Temperate C4 Species

Plants of the C₄ sedge Cyperus longus L. were grown at 10, 20and 30 °C. An asymptotic growth curve, the Richards function,was fitted to growth data for successive leaves. The mean rateof leaf appearance was a linear function of temperature with0.014 leaves appearing per day for every 1 °C increase intemperature. The instantaneous relative rate of leaf extensionshowed a marked ontogenetic drift which was most rapid at 30°C and slowest at 10 °C. The mean absolute extensionrate for foliage had a temperature coefficient of 0.16 cm d^–1° C^–1 in the range from 10 to 30 °C. The durationof leaf growth was independent of leaf number at 10 and 20 °Cbut increased linearly with leaf number at 30 °C. The smalldifferences in relative growth rate at the three temperaturesresulted in large differences in foliage area produced at theend of a 30 d growth period. The final foliage areas at 20 and10 °C were 51 and 9% respectively of that at 30 °C. Cyperus longus, temperature, leaf growth, Richards function, growth analysis     

Leaf Growth in Cotton (Gossypium hirsutum L.) 1. Growth in Area of Main-stem and Sympodial Leaves

A model is presented for growth of individual and successivemain-stem leaves of cotton, based on a series of indoor experimentsand data sets from the literature. Three variable parametersare used to describe individual leaf growth: relative growthrate of meristematic tissue (R¹), relative rate of approachof final area (R₂) and a ‘position parameter’ (t_0.5)which governs the transition from meristematic to extensiongrowth. Final area of a leaf does not occur in the model asa deterministic quantity but it is a result of the processesduring growth. The model generates successive mainstem leavesand sympodial leaves as an integrated system. Assimilate shortagesoccurring in the plant operate on R₁ leading to the characteristicchange of final leaf area along the mainstem. Gossypium hirsutumL., cotton, leaf growth, relative growth rate, meristematic tissue, extension growth, mathematical model     

Plant Growth Analysis: Additive and Multiplicative Components of Growth

Three techniques used to investigate whole-plant growth areplant growth analysis, yield component analysis and demographicanalysis. Each subdivides growth into morphological or physiologicalcomponents. This paper derives several relationships which definethe contributions made by components to the performance of thewhole plant. For example, the additive contributions by differentplant parts to overall unit leaf rate may be determined. Also,for multiplicative components, the relative growth rate of yieldis the sum of the relative growth rates of yield components.The relationships developed here serve to link different approachesto growth analysis, and they are illustrated using data fromgrowth studies of bean and sunflower. Plant growth analysis, yield component analysis, demographic analysis, Phaseolus vulgaris L., Helianthus annus L.     

A Single Equation to Quantify the Hierarchy in Plant Size Induced by Competition Within Monocultures

The following empirical model: Ra(i) = r(1+ln(w(i)/wm)Kn)(1–(w(i)/W))(1–(y/Y)) which is based on the logistic growth equation, is developedto describe the growth of differently sized individuals withinplant communities. The model is tested against extensive setsof carrot (Daucus carota L.) and red beet (Beta vulgaris L.)data and is shown to fit well. The model was used to predictindividual plant weights in independent data. The agreementsbetween observed and predicted weights were often close butsome systematic deviations did occur. Thus, a single equationdescribed most of the complex interactions that occurred withinmonocultures of annual crop plants. Carrot, Daucus carota L., red beet, Beta vulgaris L., model, growth, variation     

Biomass Accumulation and Main Stem Elongation of Durum Wheat Grown under Mediterranean Conditions

Detecting and exploiting genetic variation in biomass accumulationis of great importance for increasing wheat yield when the harvestindex is close to its upper limit. This study was undertakento analyse the pattern of biomass accumulation and main stemelongation in 25 durum wheat (Triticum turgidum L. ‘Durum’)genotypes. Field experiments were conducted over 2 years intwo environments contrasting in the amount of available water,in northeastern Spain. Plants were sampled at the main stagesof Zadoks' scale, and dry weight per plant, crop dry weight(CDW) and main stem length were measured at each stage. Measurementsfor growth traits and thermal time from sowing fitted betterto an asymmetric logistic peak curve than to the Richards logisticmodel. Four biological variables were computed from the curve.Differences among curves describing changes in biomass werefound to be greater between irrigated and rainfed sites thanbetween years. Drought stress had less effect on main stem elongationthan on biomass accumulation. Average dry weight per plant andCDW were reduced by drought by 42 and 38%, respectively, duemainly to similar reductions in the mean rate of growth of thetwo variables. In contrast, cycle length from sowing to themaximum values of dry weight per plant and CDW was only slightlymodified by drought. Copyright 2001 Annals of Botany Company Triticum turgidum L. ‘Durum’, durum wheat, biomass, crop dry weight, stem length, rate of growth, modelling, growth analysis, logistic peak curve     

A Comparison of the Growth of the C4 Grass Spartina anglica with the C3 Grass Lolium perenne at Different Temperatures

Dunn, R., Thomas, S. M., Keys, A. J. and Long, S. P. 1987. Acomparison of the growth of the C₄ grass Spartina anglica withthe C₃ grass Lolium perenne at different temperatures.—J.exp. Bot. 38: 433–441. S. anglica is one of the few C₄ species which occurs naturallyin cool temperate zones. It is known to attain photosyntheticrates which equal or exceed those of C₃ grasses over the temperaturerange typical of the spring and summer in cool temperate climates.This study examines whether S. anglica can also attain comparablegrowth rates at these temperatures. Seedlings of S. anglicaand L. perenne cv. S23 were grown in controlled environmentsat 10,15,20 and 25 °C. Quantitative growth analysis wasconducted by taking frequent harvests to determine the progressionsof leaf area and plant weight of individual plants with time.Quadratic regressions were found to describe these progressionswell. Instantaneous derived growth parameters were calculatedfrom the fitted regressions. Both absolute and relative growthrates of S. anglica were significantly lower than for L. perenne,this being largely attributable to a lower ratio of leaf areaproduction per unit of plant dry weight. Although the amountof dry matter invested into leaves was similar, the leaf areaper unit of leaf dry weight was lower in S. anglica. In comparisonto L. perenne, the rate of dry matter accumulation per unitof leaf area (ULR) was higher in S. anglica at 25 °C andinitially equal at 10 °C. Prolonged exposure to 10 °Csteadily reduced ULR in S. anglica which approached zero at80 d. Although growth in S. anglica is reduced more by low temperaturethan it is in L. perenne, by comparison to other C₄ speciesthe assimilatory capacity of S. anglica is more tolerant oflow temperature exposure. Key words: C4 photosynthesis, temperature, quantitative growth analysis     

Growth of Individuals in Plant Populations

Relationships between individual plant weight and net photosynthesisper day (G(t, x) function of plant weight) in plant populationsof various stand structures were simulated based on a canopyphotosynthesis model. The G(t, x) functions of plant weightare determined mainly by LAI (leaf area index), the relationshipbetween individual plant weight and leaf area, canopy structureand extinction coefficient. The concave relationship betweenindividual plant weight and leaf area at small LAI (<2),at small extinction coefficient (< 0.5), or at the canopystructure having the maximum leaf area density at the bottomproduces a concave G(t, x) function, which generates negativeskewness of plant weight. The linear relationship between individualplant weight and leaf area at large LAI (> 2) produces aconvex G(t, x) function, which generates positive skewness ofplant weight. These simulation results coincide with G(t, x)functions obtained experimentally and with the well-known phenomenonof stand dynamics in which skewness of plant weight becomesnegative in the early growth stage and then increases to a positivevalue as a stand grows and becomes crowded. Helianthus annuus L., individual plant size, mean growth rate, canopy photosynthesis model, skewness, stand structure     

Examination of a Model and Data Describing the Effect of Temperature on the Respiration Rate of Crop Plants

Some of the published evidence used in the synthesis and maintenancemodel of plant respiration is discussed in relation to the effectof temperature. Recalculations from the data of de Vries (1975b) give different results from those claimed by him. The modelis considered in terms of the use of substrate in the dark andits production in the light. It is suggested that starvationestimates of maintenance are not valid. The most reliable methodof observing synthesis respiration in whole plants appears tobe by following a discrete pool of substrate, as is possiblewith labelled carbon. Triticum aestivum L., Zea mays L., Helianthus annuus L., Vicia faba L., carbon dioxide, respiration, temperature, substrate content     

Growth Analysis of Atrazine-Resistant and Atrazine-Sensitive Biotypes of Chenopodium album

Seed from atrazine-sensitive and atrazine-resistant biotypesof lambsquarters (Chenopodium album L.) was sown in pots containingquartz sand. Plants were grown under a controlled environmentin a growth room. On the 15th day after planting, four randomly-selectedplants of each biotype were harvested, and both fresh and dryweights of leaves, stems, roots and whole plants, together withleaf area, were determined for each plant. This was repeatedat 5-day intervals until the 60th day after sowing. Data from the resulting replicated 2 x 10 factorial configurationwere analysed using BMDP multiple regression programmes andorthogonal polynomials to produce best fit polynomial expressionsof time-to-harvest and biotype for the natural logarithm ofeach response. From these empirical models of plant growth,predictor functions for relative growth rates, leaf area andweight ratios, specific leaf area and unit leaf rate were generated. Examination of computer-generated plots of the various growthindices suggested that time-of-harvest was the most importantfactor in determining the magnitude of the responses. However,the two biotypes exhibited different growth patterns as indicatedby the presence of a significant biotype effect or biotype xtime interaction in all cases. The faster-maturing atrazine-sensitiveplants tended to have fairly dense leaves with relatively smallarea whereas the atrazine-resistant plants initially producedsmall root systems and relatively low density leaves. Moreover,the resistant biotype, despite being lighter at 2 weeks, weighedthe same as the sensitive plants by the 60th day due to a consistentlyhigher relative growth rate. The advantages of using balancedor orthogonal configurations together with multiple regressionprocedures to derive data-based empirical models of plant growthare discussed. Limitations to the routine use of empirical modelsare also considered. Chenopodium album L., lambsquarters, atrazine resistance, growth analysis, orthogonal polynomials, multiple regression analysis     

The Application of Growth Analysis to Structured Experimental Designs and a New Procedure for Estimating Unit Leaf Rate and its Variance

A method is presented for estimating relative growth rates andother growth parameters using data from randomized block designs,prior to conventional or functional growth analysis. This methodcan be extended to other experimental designs where an additivemodel is applicable. The effects of this approach are illustratedusing the most commonly derived growth quantities, relativegrowth rate, leaf area ratio and unit leaf rate (net assimilationrate), from an extensive data set available for the growth ofthe biennial Arctium tomentosum. Comparisons are made betweendifferent growth analytical techniques and a new procedure fordetermining unit leaf rate, with a rigorous statistical treatment,is presented for the particular case when the logarithms ofthe variates for leaf area and total dry weight are linearlyrelated. Arctium tomentosum, burdock, growth analysis, randomized block design, unit leaf rate, relation of leaf area and total dry weight     

Canopy Photosynthesis of Tomato, Cucumber and Sweet Pepper in Greenhouses: Measurements Compared to Models

Two models for canopy photosynthesis (modified versions of thoseof Acock et al. , 1978 and of Thornley, 1976) were examinedby comparison with experimental photosynthesis data of cucumber(Cucumis sativus L.), sweet pepper (Capsicum annuum L.) andtomato (Lycopersicon esculentum Mill.). The data were obtainedin six large-scale, long-term, semi-commercial cultivationsin greenhouses (Nederhoff and Vegter, 1994). Measured environmentalconditions and measured LAI were input to the model. The emphasiswas on the models' sensitivity to the prevailing CO₂ concentration. The (modified) Acock model with 'standard' (originally published)parameters underestimated the photosynthesis rate. This modeltuned to one of our experimental data sets did not fit verywell to the other data sets. As expected, if the model was tunedto each particular data set, it was fairly in agreement withthe measurements, but the fitted parameter values were sometimesquestionable. With the (modified) Thornley model it was obligatoryto estimate or tune the light extinction. The model performedreasonably if all parameters were tuned and also if only thelight extinction was tuned. The modified models were considered usable for practical applications,after parameter tuning. As the sensitivity to CO₂ was not alwaysequal among the models and the measurements, care should betaken when applying the models for CO₂ supply control.Copyright1994, 1999 Academic Press Canopy photosynthesis, Capsicum annuum L., carbon dioxide, cucumber, CO₂, Cucumis sativus L., glasshouse, greenhouse, Lycopersicon esculentum Mill., measurements, model, sweet pepper, tomato     

Use of the Expolinear Growth Model to Analyse the Growth of Faba bean, Peas and Lentils at Three Densities: Fitting the Model

The expolinear equation for crop growth (Goudriaan and MonteithAnnalsof Botany66: 695–701, 1990) was fitted to measurementsof above ground dry weight made on two cultivars of each ofthree species, faba bean (Vicia fabaL.), peas (Pisum sativumL.)and lentils (Lens culinarsMedic.), each grown at three densitiesat the University of Reading, UK in 1992 and 1993. The expolinearequation fitted the data well but required frequent samplingto obtain good estimates of the parameters. The equation hasthree parameters,R_mthe maximum relative growth rate,C_ma maximumcrop growth rate, andt_bthe time at which the crop effectivelyreaches a linear phase of growth.R_mdid not differ between densities,cultivars or species but differed between years.C_mincreasedwith increased density and was lower for lentils than for fababeans or peas.t_bdecreased with increased density for faba beanbut not for the other species. Incorporating an extinction coefficientfor solar radiation and the maximum fraction of radiation interceptedenabled reasonably accurate time courses of leaf area indexto be derived, as suggested by Goudriaan (1994. In: MontiethJL, Scott RK, Unsworth MH, eds.Resource capture by crops. Nottingham:Nottingham University Press, 99–110).Copyright 1998 Annalsof Botany Company Expolinear equation, grain legumes, crop growth rate, crop density, relative growth rate, growth modelling, faba bean,Vicia fabaL., peas,Pisum sativumL., lentils,Lens culinarsMedic.     

Yield-Respiration Relationships at Different Bean (Phaseolus vulgaris) Plant Densities

Bean (Phaseolus vulgaris L.) plants were grown, one to fiveplants per pot, with a non-limiting supply of mineral nutrients.As plant density increased, seed and N yield per plant decreased,but those per pot remained fairly constant. The shoot: rootratio and the contribution of roots to total plant respirationwere also almost constant with changing density; the Q₁₀ forshoot respiration was higher at maximal densities. However,growth respiratory C losses per plant over the growth periodon a seed dry matter of N yield basis were not dependent onplant densities tested. Phaseolus vulgaris L., yield, respiration, plant density