Simulation models are heuristic tools for integrating diverse processes and help to increase our understanding of complex processes and systems. Models that predict crop development can serve as decision-support tools in crop management. This paper describes a phenology simulation model for the winter wheat shoot apex and reports validation and sensitivity analysis results.

The complete developmental sequence of the winter wheat shoot apex is quantitatively outlined and correlated with commonly recognised phenological growth stages. The phyllochron is used to measure the thermal time between most phenological growth stages, thereby increasing the flexibility over the growing degree-day (GDD) and photothermal approaches. Nineteen site-years covering a range of climatic conditions, cultural practices and cultivars across the Central Great Plains, USA, are used to validate the model.

Validation results show that the predicted phyllochron (108 GDD) agrees well with the observed phyllochron (107 GDD) for ten cultivars. Mean seedling emergence is predicted to within 2 days in almost all of the 19 site-years. The ability of the model to predict growth stages accurately increased successively from jointing to heading to maturity. Maturity is generally predicted to within 5 days of the observed day.

After validation, recalibration of the phyllochron estimates between growth stages are provided, and corrections for mesic and xeric conditions are suggested. Further validation of the entire developmental sequence of the shoot apex is recommended.

The effects of a preceding (1986/87) season's crop of vetch (Vicia saliva) or oats (Avena sativa), either singly or as two different mixtures, on the nitrogen uptake and growth of a succeeding barley crop (Hordeum vulgare) were examined in Cyprus in 1987/88, on field plots previously labelled (1984/85) with 15N enriched organic matter. Grain as well as the vegetative material were harvested before planting the barley. Barley after vetch accumulated 61 % more nitrogen than barley after oats, while, for the mixtures, the nitrogen yields in the succeeding barley crop did not differ significantly from those of barley grown after oats. The 15N enrichment in barley indicated that fixed N2 from vetch contributed little nitrogen to the available soil nitrogen pool and to the nitrogen in barley. Most of the increased assimilation of nitrogen in barley following vetch (compared to barley after oats) was attributable to a greater availability of soil nitrogen arising from the lower soil nitrogen uptake by the preceding vetch than oats. The dry matter yield of barley following vetch was 84% higher than for barley after oats, while barley after the vetch-oats mixtures yielded 38–54% higher than barley following oats. It was concluded that greater nitrogen availability to the cereal following the legume was not the sole cause of the dry matter yield responses observed.

Experiments on winter barley at Rothamsted, testing different sowing dates, were sampled in 1987–89 to measure effects on take-all caused by the fungus Gaeumannomyces graminis var. tritici. The experiments used the same plots in each year, and in 1988 and 1989 the randomization was restricted so that sowing dates were balanced for sowing dates in the previous year.

The site had been used to grow barley since at least 1979 (spring barley from 1979 until 1985), and take-all was much more severe than expected. It was usually most severe in the earliest-sown plots and decreased almost linearly as sowing was delayed. There was also evidence that the sowing dates of the preceding crop had a continuing, residual effect. In the two years that the effects of previous sowing dates were tested, there was usually least take-all in plots where the crop followed one sown very early or very late in the previous year, and most where it followed one sown at the end of September or in early October. These effects probably reflect differences in amounts of inoculum and in the rate of development of take-all decline.

Four varieties of rice straw, MRl, MR71, MR84 and MR27, were separated into the following botanical fractions; inflorescence, stem, leaf blade and leaf sheath. The relative proportion of each fraction in whole straw was estimated and analysed for its chemical composition and in vitro digestibility (IVD). The composition and IVD of whole straw was then calculated. Cluster analysis showed that MRl was distinct from the other varieties. This could be attributed to a high proportion of stem (32·3%), high IVD (36·9%), low insoluble ash (4·0%) and a low silica content (2·7%) in the whole straw. The genetic distance between any two varieties ranged from 5·4 × 10-3 to 47·8 × 10-3 and was largest between MRl and the other varieties. Cluster analysis also showed that within a variety, the chemical composition and IVD of the stem, leaf blade and leaf sheath were similar, suggesting that sampling errors may be reduced if the inflorescence, which comprises 7–13% of the whole straw, is excluded when the material is analysed. Stepwise and canonical discriminant analyses indicated that the important variables to be measured when comparing straw varieties were IVD, crude protein and insoluble ash.

Thirty-two experiments examining the effects of the weight and within-row spacing of potato seed tubers on graded tuber yields of five varieties were conducted on eight sites from 1980 to 1985. A complex analysis technique was used to combine these data and estimate the optimum tuber planting densities for different ratios of seed cost to small (40–60 mm) and large (60–80 mm) ware value. The same technique could be applied to any other combination of seed cost, ware size and ware value.

The optimum tuber planting density decreased with increasing seed-tuber weight. Differences in optimum planting density between varieties were much greater with small (35 g) than with large (105 g) seed tubers and decreased as the cost of seed increased relative to the value of ware. As large ware became worth more than small ware the influence of increasing seed cost on the optimum density was reduced. As the value of large ware increased, net returns increased and the effect of seed cost on net returns was reduced. Mean tuber size decreased with increasing stem density at harvest and at the same stem density was lower in varieties producing more daughter tubers/stem. Changes of mean tuber size (μ) and the spread of yield across size grades (σ) with time were well described by parallel curves in different varieties. It is suggested that in future it may not be necessary to determine optimum tuber planting densities by complex experiments involving several seed-tuber weights and spacings. Instead μ and σ could be estimated from simple experiments and tuber spacings determined by comparison with control varieties.

A series of experiments to quantify the response of diverse potato genotypes to production and storage conditions in hot climates was carried out in 1984–87 at three sites in Peru, two of which were characterized by at least one hot season per year. Yield stability and field performance of seed tubers of six clones produced in situ, and stored in diffused light (DLS) or cold stored (CS), were compared with those of good quality seed tubers produced and stored in cool conditions. The yield potential of tubers produced in hot climates and grown as (i) a double crop per year with short DLS (1–4 months) (ii) a single crop per year with long DLS (c. 8 months) and (iii) a single crop per year with long CS (c. 8 months) was compared with that of seed tubers produced in cool conditions and introduced in successive crops.

The first replanting of tubers produced in hot climates resulted in lower yield than that of coolproduced tubers. Yield reductions in clones ranged from 30 to 93% when replanted within 4 months, from 10 to 100% when replanted after 7–10·5 months of DLS and from 0 to 82% after similar periods of CS. Reduced yield was often due to poor plant vigour and crop growth leading to inefficient interception of solar radiation. There was, however, no evidence that the efficiency of utilization of intercepted radiation for tuber dry matter production was influenced by storage treatment. Poor sprout growth at planting reduced yield considerably for late clones in double cropping. Low dry matter content of tubers produced in hot climates did not influence emergence rate, but was related to poor plant vigour in the first replant under warmer conditions. Replanting and storage in hot climates did not enhance the initial reduction of tuber dry matter, which was evident after the first hot season. Tuber yields continued to decline, particularly under single cropping with long DLS.

For the clones studied, CS would be a feasible storage method for potato production in hot climates if replanted tubers were used on an annual basis. For double cropping, short dormancy is essential; however, poor plant vigour results in additional yield reductions. Our data indicate that clonal selection for maximum production in hot climates should take into account the proposed or existing production and storage schemes.

Results are reported from four carrot experiments (1987/88) to measure edge effects in crops of different ages grown in beds. A wide range of cultivars, densities and contrasting row-spacing systems was used to determine how effectively these edge effects could be eliminated by increasing the seeding rate in the outer rows relative to that in the inner ones.

Edge effects were first significant between 50 and 100 days after sowing. Where each row was sown with the same quantity of seed, carrots in the outer rows were 1·5 to 2·0 times heavier than those in the inner rows.

Increasing the seeding rate in the outer rows to between 1·5 to 3·0 times that in the inner rows, whilst holding the overall density constant, resulted in equal mean root weight in all rows. There was no evidence of alternate large and small plants in successive rows across the bed, as has been suggested in the literature.

A previously published spacing model gave large systematic deviations when fitted to these data, but this was rectified by a simple modification to the model, which did not entail the incorporation of more parameters.

Growth regulators were applied to faba bean (field bean) plants in order to study hormonal control of premature reproductive abscission. Combined data from pairs of racemes sited in a consistently yielding region of the main stem indicated effects of growth regulator treatments. Decapitation increased pod numbers, but the inhibitory influence of the upper shoot could not be replaced completely by indol-3yl-acetic acid (IAA) applied to the cut stem stump. Blockage of auxin transport through the stem with the auxin-transport inhibitors 2, 3, 5-triiodobenzoic acid (TIBA) or methyl-2-chloro-9-hydroxyfluorene-9-carboxylate (CF, chlorflurenol) reduced pod numbers above the application point. The latter effects might have been indirect and due to elevated ethylene levels, since pod retention in this shoot region was decreased when sprayed with the ethylene-releasing compound 1-aminocyclopropane carboxylic acid (ACC) and increased when sprayed with ethylene-biosynthesis inhibitors 2-aminoethoxyvinyl glycine (AVG) or l-amino-2-cyclopropylcyclopropane carboxylic acid (cyclopropyl-ACC). Pod numbers were increased when the reproductive structures themselves were sprayed with IAA, gibberellic acid (GA3) or 6-benzylaminopurine (BAP), although a corresponding increase in total seed weight occurred only with the latter growth regulator. Application of BAP or abscisic acid (ABA) as root drenches showed that levels of reproductive abscission were raised or lowered with BAP treatment, depending on its concentration, and lowered with ABA treatment. It is suggested that growth regulator treatments leading to decreased ethylene production in the shoot and/or increased cytokinin and abscisic levels in the xylem sap are those most likely to reduce abscission.

The relationship between values of 85Sr concentration ratios (CRs) and exchangeable bases, expressed in absolute (mmol/kg) or relative (percentage of cation exchange capacity (CEC)) terms, was considered using the results of a glasshouse pot experiment conducted in 1989, for soils and crops of Greece. Exchangeable calcium, expressed in mmol/kg, presented, in most instances, a significant (P = 0·05–0·01) or highly significant (P < 0·01) negative correlation with the CRs of various crops or plant parts, while exchangeable calcium plus magnesium or total exchangeable bases (expressed also in mmol/kg) showed an even better correlation (higher values of r, lower variability). Expression of the amounts of exchangeable bases in relative terms further improved the correlation coefficient in each comparison. The correlations between the percentage of exchangeable (Ca + Mg) or exchangeable bases and CRs, which were always negative, were significant or highly significant for all tested crops or plant parts. The correlation between CRs and soil properties was greatest for exchangeable (Ca + Mg) expressed as a percentage of CEC (r = -0·92) and followed the order: Exchangeable (Ca + Mg) as % of CEC ≈ exchangeable bases as % of CEC ≈ exchangeable (Ca + Mg) in mmol/kg ≈ exchangeable bases in mmol/kg > exchangeable Ca as % of CEC > exchangeable Ca in mmol/kg.

Quantitative relationships between CRs of the tested crops or plant parts and exchangeable calcium plus magnesium (% of CEC) of soils are also presented.

In a glasshouse pot experiment in Athens, Greece in 1989, 85Sr to calcium observed ratios (OR) based on the values of exchangeable Ca instead of soil Ca (ORexCa), were determined for crops or plant parts grown in eight soils widely differing in their physical and chemical properties. Compared to the values of concentration ratio (CRs) the values of ORexCa did not show as wide variation with the soil type. They were relatively constant and usually not related to soil properties. The ORexCa values were essentially the same as OR values for the non-calcareous soils and much smaller than the OR values for calcareous soils, considering as soil Ca in the calculation of OR, the sum exchangeable, watersoluble and CaCO3 Ca.

The values of 85Sr/Ca + Mg observed ratios (ORexCaMg) were just as good as the ORexCa values, while those of 85Sr/Ca + Mg + K + Na (ORex bases) showed more variation.

Highly significant (P <0·01) correlations were observed between the fractions of the observed ratios ORexCa, ORexCaMg and ORex bases, for each crop or plant part tested.

Phosphorus (P) cycling and losses in irrigated, sheep-grazed pastures receiving superphosphate (SP) applications for 35 years at annual rates of 0, 188 and 376 kg/ha were studied using a massbalance approach which accounted both for P inputs to and outputs from the soil-plant-animal system. Total recoveries of applied P in the soil-plant-animal systems in the 188 and 376 kg SP/ha treatments were 94 and 83% respectively. Approximately 52–53% of the applied P was recovered in the soil within the major plant rooting zone (0–300 mm soil depth). These data suggest that P leaching losses from SP fertilizer, plant litter, root residue and sheep faeces were unlikely to occur beyond the major plant rooting zone. However, the transfer of excretal P to stock camps and the transport of P from SP fertilizer, plant litter and sheep faeces via the irrigation water along the border from the top to the bottom of the irrigated border strip accounted for less than 6% of the applied P. Superphosphate applications resulted in the accumulation of both soil inorganic and organic P fractions to a depth of 225 mm. The accumulation of soil inorganic P was most pronounced when SP was applied annually at the rate of 376 kg/ha, which was in excess of pasture P requirements.

Sulphur (S) cycling and losses in irrigated, sheep-grazed pastures receiving annual superphosphate (SP) applications for 35 years at rates of 0, 188 and 376 kg/ha were studied using a mass-balance approach which accounted both for S inputs to and outputs from the soil-plant-animal system. Total recoveries of applied S in the 188 and 376 kg SP/ha treatments were estimated to be 35·2 and 21·2% respectively. Over 65·0% of the applied S was not recovered, and this was attributed to leaching losses beyond the major rooting zone (0–300 mm), lateral S transfer by irrigation water and cxcretal S transfer to stock camps. The lower S recovery in the 376 compared with the 188 kg/ha per year treatment was probably due to a higher accumulation of soil phosphorus (P), which might have competed with sulphate (SO42-) for adsorption sites on soil colloids. Superphosphate applications resulted in the accumulation of soil organic S (S0) fractions (hydriodic acid-reducible and carbonbonded S) to a soil depth of 300 mm in both camp and non-camp areas. However, an increase in SP applications from 188 to 376 kg/ha per year did not lead to a further accumulation of soil S0 fractions. Approximately 50% of this additional S input was estimated to be leached beyond the 300 mm depth. The presence of soil So fractions at 300 mm soil depth, especially in camp areas, suggests that leaching occurred, involving not only SO42- but also So fractions from soil, plant litter, root residues and animal excreta, as the soil had a low SO42- retention capacity. These leaching losses may limit the ability of soil S reserves to sustain adequate S for pasture production when S fertilizer application is withheld.

Varied quantities of concentrate supplement were fed to three groups of pregnant West African Dwarf (WAD) goats at different gestational periods, while forage was provided ad libitum throughout pregnancy. One group (A) was fed on concentrate at the rate of 50 g/kg metabolic weight (W0·75) per day throughout pregnancy, a second group (B) was offered concentrate from Days 61 to 120, and 121 to term at the rate of 50 g and 25 g/kg metabolic weight per day, respectively, and a third group (C) was provided with concentrate from Days 61 to 120 and 121 to term at the rate of 25 g and 50 g/kg metabolic weight per day, respectively.

Results showed that there were no abortions, although two animals from group A had dystocia (difficult birth). There was no significant difference between the mean birthweight and neonatal growth rates of kids from groups A and B. The mean birthweight and neonatal growth rates of the kids from group C were significantly (P < 0·01) lower than those of groups A and B. There was no significant (P >0·05) difference between the mean udder circumference of animals in group C and those in groups A and B. All the neonatal deaths were recorded among the kids in group C. It is concluded that for economic animal production although it may not be necessary to feed pregnant WAD goats on high concentrate rations throughout the gestational period, they should not be underfed between Days 61 and 120 of pregnancy.

Exposure of sheep to a long-day photoperiod during late pregnancy results in greatly increased plasma prolactin concentrations in both the ewe and her fetuses compared to values in animals experiencing short days. To investigate whether the endocrine changes resulting from provision of additional lighting might also influence the pre- and postnatal growth of lambs or udder development in winter-housed ewes, two experiments were carried out. In the first, a group of housed Mule ewes, lambing in early January 1989, were given additional lighting to provide a long-day photoperiod [16 h light: 8 h dark] from 6 weeks before delivery until 6 weeks after lambing. In the second experiment, 50 housed Mule ewes were given additional light for 7 weeks before delivery at the end of March 1990. In both experiments, comparable groups of housed Mule ewes experiencing only the natural shortday winter photoperiod served as controls.

In both experiments, provision of the long-day photoperiod resulted, within 3 weeks, in highly significant increases in plasma prolactin concentrations in the ewes. Plasma prolactin concentrations in the lambs from ewes experiencing the long-day photoperiod were also increased at birth (8-fold) and throughout the suckling period (3–5-fold) compared to values in short-day control lambs.

Despite these large differences in plasma prolactin concentrations, there was no significant effect of photoperiod on the birth weight of the lambs in either experiment. There was also no effect of photoperiod on the postnatal growth of lambs in Experiment 1.

Provision of a long-day photoperiod resulted in some increase in the rate of growth of linear measurements of udder size in ewes during both experiments, but only resulted in a significant increase in estimated udder size at delivery in ewes with twins or larger numbers of fetuses in the first experiment. In both experiments the effect of a long-day photoperiod on udder size was similar to or less than the effect of one additional fetus.

The results do not suggest that prenatal photoperiodic experience results in any major alteration in somatic development in lambs at birth or during early postnatal life. They do, however, give some support to other observations that ambient photoperiod may influence pre-partum udder development in the ewe.

This group, which is concerned with the applications of mathematics to agricultural science, is sponsored by the Agricultural and Food Research Council. It was formed in 1970, and has since met at approximately yearly intervals in London for one-day meetings. The twenty-second meeting of the group, chaired by Professor J. M. Forbes of the Department of Animal Physiology and Nutrition at the University of Leeds, was held in the Wellcome Meeting Room at the Royal Society, 6 Carlton House Terrace, London on Friday, 10 April 1992, when the following papers were read.