Temperature and Seed Storage Longevity

Seed survival data for eight diverse species, namely the cerealbarley (Hordeum vulgare L.), the grain legumes chickpea (Cicerarietinum L.), cowpea [Vigna unguiculata (L.) Walp.] and soyabean [Glycine max (L.) Merr.], the timber trees elm (Ulmus carpinifoliaGleditsch.), mahogany (Swietenia humilis Zucc.), and terb (Terminaliabrassii Exell.), and the leaf vegetable lettuce (Lactuca sativaL.) were compared over a wide range of storage environments(temperatures from –13 °C to 90 °C, seed moisturecontents from 1.8 to 25% f. wt) using a viability equation developedpreviously. In accordance with that equation, the effect oftemperature on seed longevity was dependent upon the temperaturerange. The temperature coefficients of the viability equationdid not differ significantly (P > 0.05) among the eight speciesdespite their contrasting taxonomy. Thus the quantitative relationbetween seed longevity and temperature does not vary among diversespecies. The same conclusion was obtained for the coefficientsof a proposed alternative model of the relation between seedlongevity and temperature. The implications of the two temperaturemodels in the viability equation for extrapolations to low andvery low temperatures are discussed. Seed storage, seed longevity, seed moisture, temperature, viability equation, genetic resources conservation, Cicer arietinum L., Glycine max (L.) Merr., Hordeum vulgare L., Lactuca sativa L., Swietenia humilis Zucc., Terminalia brassii Exell., Ulmus carpinifolia Gleditsch., Vigna unguiculata (L.) Walp     

Plasma Membrane Permeability of Root-Tip Cells Following Temporary Exposure to Al Ions Is a Rapid Measure of Al Tolerance among Plant Species

No correlations were recognized between Al tolerance among fourplant species, rice (Oryza sativa L.), maize (Zea mays L.),pea (Pisum sativum L.), and barley (Hordeum vulgare L.), inrank order of Al tolerance, and cation exchange capacities ofroot-tip (0-1 cm) cells or of their cell walls. The plasma membraneof root-tip of Al sensitive plant species (pea and barley) wasconsiderably permeabilized with elongation of root in Al-freesolution following 0.5 h pretreatment with Al. K⁺ release fromand Al permeation into the protoplasts isolated from the root-tipof Al-sensitive plant species were more significant than thosefor Al-tolerant plant species (rice and maize) on 10 or 30 mintreatment with Al. The permeability of the plasma membrane forprotoplasts isolated from Al sensitive plant species was considerablyincreased by treatment with hy-potonic Al-free control solutionfollowing 10 min pretreatment with Al. To our knowlege, theseare the most rapid responses to Al ions reported to date, i.e.,within 0.5 h in whole plant and within 10 min in protoplast.These results suggest that a temporary contact with Al ionsirreversibly alters the plasma membrane of root-tip cells ofAl-sensitive plant species: the cells become more leaky andrigid due to binding of Al ions to the plasma membrane. (Received January 5, 1998; Accepted February 26, 1998)     

Time of Flowering of Pea (Pisum sativum L.) as a Function of Leaf Appearance Rate and Node of First Flower

In order to assess the influence of environmental conditionson time of flowering of pea (Pisum sativum L.), a serial sowingtrial was conducted over 2 years at Dijon, France, on two wintercultivars Frisson and Frilene. Time of flowering was analysedaccording to two variables: the leaf appearance rate R_L andthe node of first flower N_I. R_L was linearly related to temperature (r² = 0·94). Thebase temperature was 2°C for both varieties. Growth rateaccounted for the residual variability of R_L . Photoperiod andtemperature acted on N_I in an additive way. Frilene, the latergenotype, was more responsive than Frisson. A model for predicting time of flowering based upon these resultsis proposed. Deviations from this model were related to N nutritionin interaction with the plant water relations. Steps for improvingthe model are then discussed.Copyright 1993, 1999 Academic Press Pisum sativum L., pea, flowering, temperature, photoperiod, phyllochron, model     

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 Low-Moisture-Content Limit to Logarithmic Relations Between Seed Moisture Content and Longevity

Seeds of quinoa (Chenopodium quinoa Willd.), sunflower (Helianthusannuus L.) and linseed (Linum usitatissimum L.) showed negativelogarithmic relations between longevity and moisture contentsbetween 4.4 and 15.4, 3.2 and 13.0, and 3.2 and 15.5%, respectively,in hermetic storage at 65 °C. However, between 1.8 and 3.1,1.1 and 1.9, and 1.1 and 2.1%, respectively, longevity did notvary. The critical moisture content, below which further reductionin moisture content no longer increased longevity in hermeticstorage at 65 °C, for each species was 4.1, 2.04 and 2.7%,respectively. Quinoa, Chenopodium quinoa Willd., sunflower, Helianthus annuus L., linseed, Linum usitatissimum L., seed storage, improved viability equation, seed longevity, seed moisture content     

Inhibition of germination and α-amylase induction by 6-methoxy-2-benzoxazolinone in twelve plant species

6-Methoxy-2-benzoxazolinone (MBOA) inhibited germination of rice (Oryza sativa L.), wheat (Triticum aethiopicum Jakubz), rye (Secale cereale L.), onion (Allium cepa L.), wild oat (Avena fatua L.), barnyard grass [Echinochloa crus-galli (L.) Beauv.], ryegrass (Lolium rigidum Gaudin), cress (Lepidium sativum L.), lettuce (Lactuca sativa L.), tomato (Lycopersicum esculentum Mill.), carrot (Daucus carota L.) and amaranth (Amaranthus retroflexus L) and the inhibition increased with increasing MBOA concentrations. MBOA also inhibited the induction of α-amylase in these plant seeds and the inhibition increased with increasing MBOA concentrations. There were variations in sensitivity of these plant species to MBOA, and species of family Poaceae (barnyard grass, wild oat, rice, rye, ryegrass, and wheat) were less sensitive to MBOA than the other plant species.     

The Effects of a Hydrogel Polymer on the Growth of Certain Horticultural Crops under Saline Conditions

The effects of incorporating a hydrogel polymer into sand onthe development of selected horticultural plants grown undersaline conditions has been demonstrated. In separate experiments,the seeds of tomato (Lycopersicon esculentum Mill.), lettuce(Lactuca sativa L.) and cucumber (Cucumis sativus L.) were germinatedin sand/swollen hydrogel polymer mixture (25: 75, v: v) withadded Hoagland nutrient solution. At cotyledon + first trueleaf stage, the plantlets were transplanted into polythene growbagscontaining a range of sand/swollen hydrogel polymer combinations(0: 100, 25: 75, 50: 50, 75: 25 and 100: 0, v: v). Saline solutionscontaining NaCl, CaCl² and MgCl² were prepared as molar solutionsand applied at combined concentrations as follows; Control (Hoagland),2000, 4000, 8000, and 32 000 ppm. Application of the appropriatesolution to the growbags was made twice per week, alternatingwith a comparable watering regime. Harvesting was carried outafter 14 and 28 d. Polymer incorporation encouraged growth ofall species under all saline conditions, the order of effectivenessof the polymer contents being as follows; 75%>50% 25% 100%>0%.At high salinity (32 000 ppm) plants of the test species werereduced in growth but appeared to be tolerant at all levelsof polymer incorporation; in pure sand the level of tolerancein tomato and cucumber was <8000 ppm and in lettuce <4000 ppm. Generally, dry weight, leaf area, succulence, chloroplastpigments (chlorophyll a, chlorophyll b, and carotenoids), photosyntheticactivity, total amino acids, proline, and protein contents wereincreased with polymer incorporation compared with pure sand.This hydrogel polymer appears to be highly effective for useas a soil conditioner in horticulture, to improve crop toleranceand growth in a sand or light gravel substrate under salineconditions. It is intended to confirm the results of these studiesby field trials. Key words: Tomato (Lycopersicon esculentum Mill.), lettuce (Lactuca sativa L.), cucumber (Cucumis sativus L.), salinity, hydrogel, polymer, salt tolerance, growth, free amino acid, free proline, and protein     

The Role of Different Daily Irradiations on Shoot Growth and Root/Shoot Ratio in Lucerne (Medicago sativa L.)

The effect of two levels of daily irradiation on shoot growthand root/shoot partitioning was investigated on two lucernevarieties (Medicago sativa L.). Individual plants were studiedunder constant temperature and optimal water and mineral nutritionconditions. For both lucerne varieties, daily irradiation did not changebiomass partitioning between shoots and roots. It can be shownthat leaf area expansion occurs independently of daily irradiationand that the process of shoot dry matter production is strictlyproportional to daily irradiation, since the ratio leaf area/shootdry matter is inversely proportional to it. From a model of shoot production of the isolated plant, we showthat the relative shoot specific activity is not affected bydaily irradiation. A simple model of partitioning leads us todetermine why partitioning remains the same for the two at thelevels of daily irradiation. Finally, the allocation between shoot and root turns out tobe independent of the main stem extension rate, which is fasterat the higher daily irradiation. Medicago sativa L., lucerne, daily irradiation, shoot production, root/shoot ratio, leaf area expansion, partitioning model     

Abscisic Acid and Water Relations of Rice (Oryza sativa L.): Effects of Drought Conditioning on Abscisic Acid Accumulation in the Leaf and Stomatal Response

The effects of a period of water stress (drought conditioning)on responses to a second (challenge) stress were examined inyoung vegetative rice (Oryza sativa L.) plants. Drought conditioningdid not affect the rate of subsequent stress development, nor,in a first experiment, did it influence relations between turgor(_p) and total () leaf water potential. However, conditioningdid extend the range of _p over which stomata remained open andsignificantly reduced the amount of ABA which accumulated inthe leaf at a given _p. The change in stomatal behaviour (stomataladjustment) was quantitatively accounted for by the change inleaf ABA accumulation. The reduction in ABA accumulation due to conditioning did notinvolve a change in the potential capacity to produce ABA, asABA accumulation in partially dehydrated detached leaves wasnot reduced by conditioning. It is suggested that effects ofconditioning on leaf ABA content in the intact plant involvechanges in the rate of ABA export from the leaf. Oryza sativa L, rice, drought conditioning, stomata, water stress, abscisic acid     

A Comparison of the Quantitative Effects of Seed Moisture Content and Temperature on the Accumulation of Chromosome Damage and Loss of Seed Viability in Lettuce

The rate of accumulation of cells containing chromosome aberrationsin lettuce (Lactuca sativa L.) seeds is a positive functionof temperature and moisture content. It may be described byan equation similar to that for loss of seed viability. Therelative effect of temperature on the rates of loss of viabilityand accumulation of chromosome aberrations is the same. In contrast,the relative effect of moisture on the rate of loss of viabilityis greater than that for the rate of accumulation of aberrations.Hence considerably more chromosome damage accumulates beforedeath in drier lettuce seeds. Lactuca sativa, lettuce, seed storage, seed viability, seed longevity, chromosomal aberrations temperature, moisture content     

Regulation of Growth at Steady-state Nitrogen Nutrition in Lettuce (Lactuca sativa L.): Interactive Effects of Nitrogen and Irradiance

The morphological and physiological adaptation of Lactuca sativaL. (‘Vegas’) to different irradiance levels andrates of nitrogen supply was analysed in such a way that effectsof irradiance were clearly distinguished from the effects ofnitrogen. Lettuce was grown in a glasshouse in aerated nutrientsolutions containing all necessary nutrients except nitrogen.Nitrogen was supplied in excess and at limiting rates in relationto plant growth to provide steady state nutrition. Shading theplants created the low irradiance level. The effects of nitrogensupply and irradiance on growth showed a marked interaction.Dry matter production decreased strongly with decreasing nitrogensupply at high irradiance, but decreased only slightly at lowirradiance. Nitrogen had no effect on radiation use efficiencyexcept for the lowest nitrogen treatment at high irradiance.The effect of nitrogen on growth was mainly mediated by itseffect on leaf area development and hence on light interception.Decreases in leaf area were due to decreases in specific leafarea and dry matter partitioning towards the leaves, while thedecrease in specific leaf area was the result of an increasein leaf dry matter percentage at low nitrogen supply. Dry matterand nitrogen partitioning, and nitrate concentration were closelyrelated to plant nitrogen concentration. Irradiance did notaffect these relationships. Irradiance influenced partitioningonly indirectly by affecting plant nitrogen concentration. Thedemand for organic nitrogen per unit leaf area was lower atlower irradiance. Organic nitrogen per unit leaf area appearedto be adjusted to the irradiance level, independently of thenitrogen supply, suggesting priority of nitrogen usage in photosynthesis.Copyright 2000 Annals of Botany Company Lactuca sativa L., lettuce, growth, irradiance, leaf area, nitrogen, radiation use efficiency, partitioning     

Rates of Hydrogen Ion Efflux by Nodulated Legumes Grown in Flowing Solution Culture with Continuous pH Monitoring and Adjustment

The net efflux of H⁺ from lucerne (Medicago saliva L.), redclover (Trifolium pratense L.) and white clover (Trifolium repensL.) growing in flowing solution culture and dependent upon symbioticfixation of atmospheric N, was measured over a 75 d experimentalperiod. Considerable and rapid increases in acidity of the nutrientsolution of up to 1.45 pH units were recorded when the pH wasriot held constant over a 30 h period. There was little differencein H⁺ efflux when solution pH was held constant at 4.75, 5.75or 6.75, but there was an immediate cessation when it was adjustedto 3.75. Differences in the daily net efflux of H⁺ closely followedthe pattern of daily differences in incoming radiation, andthere was also evidence of a diurnal pattern of H⁺ efflux. Althoughthere were initially distinct differences between the speciesin the calculated rate of net H⁺ efflux (µg H⁺ g^–1dry shoot d^–), by day 75 these had diminished. In allspecies, however, the maximum rate of efflux per unit of shootsoccurred during the earlier rapid phases of growth. The measuredefflux of H⁺ was well equated with the plant content of excesscations (as measured by ash alkalinity) and, on average, theratio of acidity produced to N assimilated (expressed as anequivalent) was 0-24. Medicago sativa L., Trifolium pratense L., Trifolium repens L., lucerne, red clover, white clover, acidification, cation/anion balance, flowing solution culture, H⁺ efflux, nitrogen fixation     

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     

Photothermal Responses of Flowering in Rice (Oryza sativa)

Durations from sowing to panicle emergence in 16 diverse genotypesof rice (Oryza sativa L.) were recorded in 13 different photothermalregimes, comprising constant and diurnally alternating temperaturesbetween 16 and 32 °C and photoperiods between 10.5 and 15.0h d^–1—all provided by controlled-environment growthcabinets. In 11.5 h days and at sub-optimal temperatures, relationsbetween the rate of progress towards panicle emergence and meantemperature were linear in all genotypes, and amongst thesethe base temperature at that photoperiod varied between 6.6and 11.9 °C. In most cases progress was most rapid at 24–26°C, i.e. the optimum temperature was much cooler than expectedfrom previously published values of times to panicle emergencein a less extensive range of photothermal regimes. Only in threecultivars was it warmer than 28 °C, and in these there weresufficient data to establish that relations between rates ofprogress to panicle emergence and photoperiod in the diurnallyalternating temperature regime of 28–20 °C are alsolinear. Also, the responses of these three cultivars provideno evidence of any interaction between the effects of photoperiodand temperature. We conclude, then, that the model in whichrate of development is a linear function of both temperatureand photoperiod with no interaction, which has been shown tobe common to many other species, also applies to rice. Differencesamong genotypes in relative sensitivity of rate of progresstowards panicle emergence to both temperature and to photoperiodwere considerable; japonica cultivars tended to be more sensitiveto temperature and less sensitive to photoperiod than indicacultivars. Four indica cultivars bred and selected at The InternationalRice Research Institute (IRRI) in the Philippines did not differ(P > 0.10) in their relations between rate of progress towardspanicle emergence and sub-optimal temperatures in a daylengthof 11.5 h, but the optimum temperature for cv. IR 36 was appreciablywarmer than that for the cvs IR 5, IR 8 and IR 42. Oryza sativa, rice, flowering, temperature, photoperiod, photothermal responses     

Silica and Ash in Seeds of Cultivated Grains and Native Plants

Silica and ash contents and the depositional patterns of opalinesilica have been determined in the seeds of 31 plant species.Included were 13 monocotyledons, eight dicotyledons and theseeds of eight common cereal grains. The cereal grains, exceptfor Oryza sativa L. (3.2%) and Avena sativa L. (1.4%), werequite low in silica. The silica in these cereals was in thelemma. In seeds with high silica content it often makes up morethan 50% of the ash. Silica in seeds occurs largely in the outercoating of the seed. Dicotyledon seeds tend to have less silicathan those of monocotyledons. Energy-dispersive X-ray analysisshows that the distribution of the element silicon is clearlyrelated to certain epidermal structures such as ridges, raisedareas, trichomes and hairs. It also occurs in cell walls. Membersof a specific plant family tend to have very similar silicadepositional patterns in their seeds. Small amounts of K, S,Cl and Ca are also found in seeds. Light-microscopy studiesshow that the silica in the lemma of seeds such as Oryza sativaL. is deposited in cellular sheet-like structures with crenateedges. Silica in seeds also occurs in fibres and in other cellularstructures (silica cells) that become phytoliths. Seeds, epidermis, seed coat, silica and ash content, scanning electron microscopy, energy-dispersive X-ray analysis, silica depositional patterns, trichomes     

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     

A Modified Self-thinning Equation to Describe Size/Density Relationships for Defoliated Swards

Use of the self-thinning rule to describe size/density compensation(SDC) in defoliated swards is examined. It is shown that defoliationrelated variation in leaf area and associated morphogeneticchanges in plant structure necessitate slope corrections, designatedC_a and C_r , respectively. The theory predicts that reduced leafarea in more heavily defoliated swards will result in SDC atslopes more negative than -3/2 (variable leaf area SDC), andthat there will be a transition to -3/2 (constant leaf area)SDC at higher herbage mass. Empirical data from previous experiments with Lolium perenneL. and Medicago sativa L. are examined, and appear to confirmthe theoretical predictions, including the slope change at thepoint of transition from variable to constant leaf area SDC.This transition point, designated d_i , is subject to interspecificvariation and is related to the mature shoot size of a particularspecies. Some applications of this theory are discussed, andin particular a sward productivity index is proposed.Copyright1995, 1999 Academic Press Variable leaf area self-thinning, size/density compensation, Lolium perenne, Medicago sativa, sward productivity index     

Germination and Early Growth of Plants Studied Using Neutron Radiography

Seed swelling, germination, root extension, lateral root initiationand shoot growth were studied in soils of different water contents,using non-destructive, serial neutron radiography. Seeds fromthree varieties of soya beans (Glycine max L.) and one varietyeach of maize (Zea mays L.) and vetch (Vicia sativa L.) wereused. The seeds germinated when they had increased in size bya certain amount, if germination is taken as the time when theradicle first appears. The rate at which roots and shoots extendalso depend on soil water content. Glycine max L., Vicia sativa L., Zea mays L., Soya bean vetch, maize, seed germination, root extension, lateral root initiation, neutron radiography     

Low Moisture Content Limits to Relations Between Seed Longevity and Moisture

Discontinuities at low moisture contents in the otherwise logarithmicrelations between seed longevity and seed moisture content (%,f. wt basis) in hermetic storage at 65 °C were detectedat 2–0% in groundnut (Arachis hypogaea L.), 3·5%in onion (Allium cepa L.), 4·5% in sugar beet (Beta vulgarisL.), 4·6% in barley (Hordeum vulgare L.), 5·3%in chickpea (Cicer arietinum L.) and wheat (Triticum aestinumL.), and 5·6% in cowpea [Vigna unguiculata (L.) Walp.].In contrast, the equilibrium relative humidity of seeds at thesevalues was similar, varying between 9·9% (onion and sugarbeet) and 11·5% (wheat). The mean value was 10·5%r.h. (s.e. 0.2). There was no significant (P > 0·05)effect of further reduction in seed moisture content below thesecritical values on longevity, except in wheat (P < 0·005),in which there was a further increase in longevity. In soyabean [Glycine max (L) Merrill], the logarithmic relation continueddown to the lowest moisture content investigated, 3·3%(11·4% equilibrium relative humidity). Above the criticalvalue, seed longevity in groundnut showed the least sensitivityto increase in percentage moisture content, while barley showedthe greatest, the values of the viability constant C_w (slopeof the negative logarithmic relation between longevity and moisture)being 4·089 (s.e. 0·278) and 5·966 (s.e.0·325), respectively. These differences in the valueof C_w among the eight crops were significant P < 0·005),whereas the relative sensitivity of seed longevity to changein equilibrium relative humidity above the critical moisturecontent did not differ significantly among the eight (P >0·10) and was equivalent to a doubling of longevity foreach 8·7% reduction in equilibrium relative humidity.Accordingly it is concluded that the relative effect of waterpotential on seed longevity can be considered to be the samefor these and probably also for many other orthodox species. Barley, chickpea, cowpea, groundnut, onion, soya bean, sugar beet, wheat, seed storage, seed longevity, seed moisture content, viability equation, water relations     

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.