Note on the Effect of Non-regular Spatial Patterns of Plants on Yield per Area Based on a Logarithmic Relationship between Single Plant Yield and Individual Area

Based on several simplifying assumptions, a previously developed stochastic approach allows an estimation of the effects of non-regular spatial patterns of the distribution of individual plants on yield per area (F). In this approach, two random variables were attached to each plant: single plant yield (E) and individual space per plant (A). The latter was estimated by the area of Thiessen-polygons. Yield per area was calculated theoretically by the expectation of the ratio E/A. Based on a logarithmic relationship between E and A the expectation of E/A can be expressed by an approximation which depends on the mean and on the variance of the individual plant spaces. An improvement of this approximation can be easily obtained by including skewness and kurtosis of the distribution of individual plant areas. Finally, all theoretical concepts and results were applied to an experimental data set of winter oilseed rape ( Brassica napus L.).     

Effects of Nonregular Spatial Distribution of Plants on Yield per Area: A Theoretical Approach with Applications to Winter Oilseed Rape (Brassica napus L.)

In this study a stochastic approach, based on several simplifying assumptions, is developed that allows an estimation of the effects of nonregular spatial patterns of the distribution of individual plants on yield per area. In this approach, two random variables were attached to each individual plant: single plant yield and individual space per plant. The latter can be estimated, for example, by the area of Thiessen polygons. Yield per area is calculated theoretically by the expectation (=mean) of the ratio between individual yield and area. Based on the logarithmic relationship between single plant yield and individual space per plant, yield per area can be broken down into three additive terms: the first term depends only on the mean of individual plant areas, while the second depends on their mean and variance simultaneously. This second term is the product of the variance and a factor which depends only on the mean. The third term is a function of the mean and of higher order (≥ 3) central moments of a fractional linear transformation of individual plant area. Finally, these theoretical concepts were applied to 17 experimental data sets of three cultivars of winter oilseed rape (Brassica napus L.) with measurements for single plant yields and individual areas for the Thiessen polygon tesselations. Since yield per area is theoretically defined by the expectation of the ratio between individual yield and area, it is estimated by the arithmetic mean of the individual yield/area‐ratios. The agreement between this estimate and the sum of the estimated terms from the aforementioned additive decomposition of yield per area is particularly good. For the 17 data sets, percentages for these additive terms of approximately 71.4 % up to 98.4 % (mean: 89.0 %) for the first term, 1.6 % up to 20.0 % (mean: 9.8 %) for the second term and 0 % up to 8.7 % (mean: 1.2 %) for the third term are obtained. As a consequence it may be concluded, that yield per area can be explained mainly by dependencies on the means of individual plant areas while the variance of individual plant spaces is of only minor importance. The effect of the third term is insignificant. These results clearly indicate an answer to the main issue raised in the paper, namely the importance of seeding density as opposed to seeding accuracy/uniformity: nonuniformity is of limited influence and seeding density is the main correlate of yield/area. Seed placement accuracy of seeding technology therefore plays an only minor role.     

Irrigation Water Management for Efficient Water Use in Mulched Onion

Caused by the necessarily imperfect seed placement accuracy of sowing machines and, additionally, caused by many other biotic and abiotic factors, the resulting plant stands exhibit nonregular spatial distributions of its plants. Based on several simplifying assumptions, a stochastic approach is developed which allows an estimation of the effects of nonregular spatial patterns on yield per area. In this approach, two random variables are attached to each plant: single plant yield E and individual space A . The latter is estimated by the area of Thiessen polygons. Yield per area, calculated by the expectation of the ratio E/A , can be approximately expressed dependent on the means ( Ē and Ā ) and coefficients of variation ( v _E and v _A ) of E and A and their correlation ( r _EA ). In relation to the commonly used estimate Ē/Ā for yield per area, one obtains yield decreases if v _A / v _E  <  r _EA . This inequality, however, will be usually valid in the field of applications. The theoretical approaches and results were applied to three experimental data sets for drilled seeds of winter oilseed rape ( Brassica napus L.) (plant density: 60 plants m⁻², row distance: 10 cm). These data sets are characterized by different accuracies of longitudinal distributions within rows (58 %, 101 %, 150 %): yield depression increases with an increasing variability of plant distances within rows.     

Ein allgemeiner Ansatz zur Quantifizierung des Einflusses der Güte der Sätechnik auf den Flächenertrag

A general approach to determine the effect of accuracy of sowing technique on yield per area
Caused by nonperfect seed placement accuracy of sowing machines as well as by many other abiotic and biotic factors the resulting plant stands exhibit nonregular plant distributions. Based on several simplifying assumptions a stochastic approach provides a quantitative determination of the effects of accuracy of sowing technique on yield per area. In this approach, two random variables are assigned to each individual plant: single plant yield E and single plant area A, which is calculated in this paper by the construction and quadrature of the so-called Thiessen-polygons. The yield per area F is calculated as the expectation of the ratio E/A. By assuming a deterministic mathematical relationship between E and A, the calculation of F reduces to the calculation of the expectation of a function of only one random variable A. A simple approximation with sufficient accuracy for many applications only depends on the mean and on the variance of the areas of the individual plants. For demonstration purposes, the theoretical approaches and results have been finally applied to three data sets for drilled seeds of winter oilseed rape (plant density: 60 plants/m² and distance between rows: 10 cm). These data sets exhibit different accuracies of the longitudinal distributions within rows which have been quantitatively measured by the coefficient of variation for the distances between plants within rows: Yield depression increases with an increasing variability of plant distances within rows.     

Stability Analysis of Winter-rape (Brassica napus L.) by Using Plant Density and Mean Yield per Plant

The yield F per area can be expressed multiplicatively by using yield components. For the most simple case of including only two yield components one obtains: F = X₁− X₂ with X₁= number of plants per area (= plant density) and X₂= mean yield per plant.
For normal variables X₁ and X₂ the phenotypic yield stability of F, which has been measured quantitatively by the variance V(F) of F, can be explicitly expressed dependent on 1) the component means, 2) the component variances and 3) the correlation between the two components. V(F), therefore, depends on 5 parameters.
For many applications the use of the coefficient of variation v of F instead of the variance itself may be advantageous, v can be explicitly expressed dependent on 1) the coefficients of variation of the yield components and 2) the correlation between the components, v, therefore, depends on 3 parameters.
The different conditions leading to the same phenotypic yield stability can be investigated by using these explicit expressions for V(F) and v.
The main purpose of the present paper is the application of these theoretical models and results to the data of an extensive field trial with winter-rape, which has been performed for 5 years with 4 plant densities and 3 row distances.
For the lowest plant density (40 plants/m²) there results a very good agreement between the theoretically expected and the experimentally obtained values for the phenotypic stability of yield per area. But, for the higher plant densities this result don't hold true. Possible causes and explanations are discussed in detail.     

Yield stability studies of soybean (Glycine max (L.) Merrill) under rhizobia inoculation in the savanna region of Nigeria

Soybean (Glycine max (L.) Merrill) production is expanding into temperate and tropical environments. Yield stability studies under rhizobia inoculation were investigated in 24 soybean genotypes over two successive growing seasons at three agro‐ecological zone of Nigeria, during the 2015–2016 rainy seasons. Treatments were arranged in a split‐plot design and replicated three times. Treatments were 24 soybean genotypes and three levels of rhizobia inoculation. Results indicated that the variation of genotypes and inoculation on percentage emergence, height, number of leaves, number of branches per plant, total biomass yield, above‐ground biomass and seed yield was significant (p = .05). The effects of genotypes (G), environment (E) and G × E interactions on seed yield were also significant. Two soybean genotypes (TGx 1989‐45F and TGx 1990‐110FN) were identified as the most promising in relation to yield stability. Of the three locations, Abuja produced the least interaction effects followed by Igabi and may be most appropriate environments for large‐scale soybean production. Appropriate inoculation of soybean with inoculants (LegumeFix and or NoduMax) should be encouraged in farmer's field.     

向日葵单株幼苗活力对产量形成的影响

1990～1991年以出苗期为指标.着重研究了单株幼苗活力对向日葵植株籽粒产量的影响.旨在改进Wade等(1988)提出的向日葵苗期估产数学模型.结果表明.向日葵单株葵盘重量与单株籽粒产量之间呈极显著的回归关系(R~2=0.97～0.99),由前者预测后者非常可靠.可作为成熟期测产的参考.在苗期根据向日葵苗情预测收获时的籽粒产量.尽管Wade等模型有效.但加入单株幼苗活力这个因素后.整个多元回归模型的可信度大为提高.原模型中的预测因子仅包括单株面积印株距变异系数时.多元回归方程的决定系数R~2为0.25;当模型中再加入单株幼苗活力指标后,R~2增加到0.44.而且,单株面积与株距变异系数之间和单株面积与单株幼苗活力之间的互作也达到显著水平.改良模型中影响单株籽粒产量的各因素间,以单株面积和单株幼苗活力最为重要.     

串叶松香草种子产量构成因子分析

采用方差分析、相关分析、通径分析和逐步回归分析对串叶松香草种子产量构成因子进行了研究,结果表明:在串叶松香草株高、每株生殖枝数、每株花序数、每花序种子数、千粒重和单株种子产量这6个产量因子中,除株高和千粒重在不同生长年限之间不存在显著差异外,其它因子均存在显著差异;每株花序数和每花序种子数与单株种子产量间存在极显著相关,是串叶松香草种子产量的主要影响因子;串叶松香草单株种子产量的回归模型为:Y=-87.50047+0.14578X3+4.19497X4(F=23.51,Pr0.0001)。     

Early Generation Selection for Grain Yield in Narrow-Leaf Lupin (Lupinus angustifolius L.)

Experiments were conducted with early segregating generations of a selected narrow-leaf lupin cross to determine the effectiveness of selection for yield based on alternative criteria. F2 plants were selected on the basis of seed yield and several other yield-related characters to generate separate F3 populations. Randomly selected plants from each population were grown over the summer (off-season) in a glasshouse to generate F4 populations. Analyses of relationships between F2 plant measurements and F3 progeny mean yields revealed significant correlations only for those characters with the highest heritabilities - flowering time, 100 seed weight and harvest index. However, selection for the earliest flowering F2 plants followed by selection within this group of plants with the highest number of pod bearing branches would result in the greatest increase in F3 mean yield. The F2-derived F4 populations with the highest seed yields were those obtained by selection for total plant dry weight, number of pod bearing branches and number of pods per plant. Improvement in commercial crop yield should therefore be obtained through selection in early generations for those characters contributing to the greatest number of pods per unit area. A scheme involving selection for early flowering and high number of pod bearing branches in the F2 combined with replicated yield tests in the F4 is proposed.     

Injuries induced in different strawberry genotypes by winter freeze and their effect on subsequent yield

Severe frosts without snow cover are disastrous for the garden strawberry, Fragaria × ananassa Duch. The objectives of this study were to determine injuries, caused by freeze to crowns and roots of 13 and five different cultivars/lines in 2002 and 2003, respectively; to observe subsequent plant behaviour; to measure yield and to find out its dependence upon the injuries. Based on percentages of injured branch crowns and roots, estimates of plant growth and yields, the relationships between the indices have been established. Root injury has had a stronger effect on plant growth compared with crown injury. Yield has been found to be correlated only with plant growth, root damage and root‐to‐crown ratio of per cent survival when root damage was heavy. Two different strategies of the cultivars/lines, associated with their morphological characteristics and physiological peculiarities influencing plant survival, growth and yield, have been revealed. To discern the characters and cultivar types that can be valuable in such extreme conditions, differences in the genotypes responses to freeze are examined and thoroughly analysed in the paper.     

微生物菌肥拌种及减少化肥用量对燕麦生长的影响

为明确微生物菌肥拌种及减少一定量的化肥用量对燕麦生长和产量的影响,给微生物菌肥在燕麦上的推广应用提供依据,研究了微生物菌肥配合不同用量的化肥对燕麦出苗、各生育期株高、干物质含量和产量的影响。结果表明,各处理间燕麦产量差异显著(F=601.346,P=0.00<0.05),处理C（菌肥+ 75%化肥）下产量最高为达4189.5 kg/hm²;处理A（全化肥）和B（菌肥+50%化肥）次之,产量分别为3546 kg/hm²和3468 kg/hm²;处理D（对照）产量最低,为3064.5 kg/hm²。因此,使用微生物菌肥对燕麦拌种,可以减少一定量的化肥用量,减轻土壤板结程度,提高燕麦产量。     

玉米产量-密度关系年代演化趋势的Meta分析

为明确中国玉米产量-密度试验结果的年代演化趋势,进一步探索提高玉米产量的突破方向和理论依据,汇集从1950s到2000s中国玉米产量-密度的文献结果,拟合产量-密度抛物线模型,剔除异常后进行直方图、相关、通径等Meta分析。结果表明,1950s和1960s玉米产量明显低于1970s和1980s,1990s以来产量持续增加,2000s最大,为10.5 t hm^-2,1960s以来年均增益150 kg hm^-2。最佳密度年代均值在4.5~6.8株 m^-2之间,呈现1950s 和1960s<1970s 和1980s<1990s,但是, 2000s却小于1990s。单株产量年代均值在0.08~0.17 kg之间,呈现1950s>1960s和1970s<1980s,且1990s以来持续上升,2000s上升幅度更为明显。1990s以来密度偏离最佳值引起的减产幅度呈现上升趋势。在持续增加密度的同时,通过育种和栽培途径提高单株产量,是玉米更高产的努力方向。     

山东省区试小麦产量与产量构成因素的相关和通径分析

采用相关和通径分析法,对山东省2008～2009年度小麦高肥组区试165个小麦品种（系）的产量及其构成因素进行统计分析。结果表明：产量构成因素的变异系数大小为：666.7m2穗数＞穗粒数＞千粒重;产量构成因素与产量的相关程度为：666.7m2穗数＞穗粒数＞千粒重;偏相关分析,666.7m2穗数和千粒重均与产量呈极显著正相关,穗粒数与产量呈显著正相关,产量构成因素之间的偏相关均极显著负相关;三个产量构成因素对产量的直接通径系数都为正值,这与偏相关分析的结果是一致的。根据分析结果和山东省生态条件及目前种植条件特点,小麦高产育种和高产栽培应以选育和选用多穗型大群体品种为主,同时要稳定穗粒数,提高千粒重。     

Non-regular spatial patterns of plants and their effect on several agronomic traits per area

Based on several simplifying assumptions, a stochastic approach is developed that allows an estimation of the effects of non-regular spatial patterns of the distribution of individual plants on the mean value (K) of trait per area. In this approach, two random variables are attached to each plant: single plant trait measurement (E) and individual space per plant (A). The latter is estimated by the area of Thiessen polygons. K is calculated theoretically by the expectation of the ratio E/A. Appropriate approximations of this expectation depend on the means (Ē and Ā), coefficients of variation (v_E and v_A) of E and A and their correlation (r_EA). K can be decomposed into two additive terms: the first term gives the commonly used estimate Ē/Ā. If a functional relationship, E=h(A), between E and A is assumed, this first term is h(Ā)/Ā. In this study, the two relationships E=k₁+k₂ ln A and E=A/(k₃+k₄A) were used (with appropriately chosen constants k₁, k₂, k₃ and k₄). The second term in the decomposition of K can be interpreted as the effect of variable individual plant spaces on K.In this paper, these theoretical concepts were applied to 17 experimental data sets of three cultivars of winter oilseed rape (Brassica napus L.) with single plant measurements for the traits grain yield, number of pods, grain yield per pod, total dry matter, harvest index, 1000-grain weight, number of seeds and number of seeds per pod. The means, standard deviations and coefficients of variation of the individual plant areas exhibit a large variability. The differences within cultivars are larger than the differences between cultivars. The correlation coefficients between E and A can be positive and large (for grain yield, number of seeds and number of pods), small (for 1000-grain weight and number of seeds per pod) or intermediate (for total dry matter, harvest index and grain yield per pod). There were no significant differences in the goodness-of-fit for either of the tested relationships between E and A, although the logarithmic relationship seems to be slightly superior. There were only a few data sets where negative values were found for the percentage (K=100%) of the second term in the decomposition of K. This indicates an overestimation of K by the commonly used estimates Ē/Ā and h(Ā)/Ā, respectively. These overestimations, however, are less than 5.2%. In all other cases with positive values for the second term, K is underestimated by the common estimates with values from 0 up to 40%. With regard to the numerical amount of the second terms, the eight traits can be clearly partitioned into two distinct groups: group 1={grain yield, total dry matter, number of pods, number of seeds} with small percentages for the second term and group 2={1000-grain weight, harvest index, grain yield per pod, number of seeds per pod} with large percentages for the second term. The Spearman rank correlation coefficients of second term percentages (based on replications=data sets) for pairs of traits belonging to the same group are positive and large with larger values for group 2 than for group 1. The correlations between traits belonging to different groups, however, are intermediate or small.     

A Proposed Index for Assessment of Row-replacement Intercropping System

A new index has been proposed for assessing an intercropping system where the component crops are in row replacement senes. It determines the Actual Yield Loss or gain (AYL) in respect to a component crop in an intercropping situation Here the sown proportion of the component crops with regard to its sole one is to be considered. This index appears to be more appropriate than other established indices like land equivalent ratio, relative yield loss, etc., particularly when per plant yield is considered. Partial AYLs (which are the two components of this index) can be considered as indicators regarding the competition existing between the component intercrops.     

植物生长调节剂对寒地水稻产量和品质的影响

为了研究不同植物生长调节剂对寒地水稻产量和品质的影响,在大田条件下,以寒地水稻‘空育131’为材料,叶面喷施4种植物生长调节剂,调查叶龄及茎蘖动态变化,研究水稻抽穗后物质生产、转运和输出变化,比较农艺性状、产量构成、产量及品质变化的差异。结果表明：与CK相比,叶面喷施ND调节剂明显加速了水稻叶龄进程,增加了水稻分蘖茎数、穗长以及抽穗至乳熟阶段水稻茎鞘物质的输出率和转运率,显著提高了水稻抽穗期的光合势和净同化率,提高了水稻籽粒千粒重、穗粒数以及单株产量,进而提高了水稻产量,实现产量增幅7.04%,BaDao调节剂次之;另一方面,叶面喷施ND和BaDao提高了稻谷糙米率和精米率,以ND表现最佳。而喷施PY显著降低植株高度和节间长度,抑制了水稻株高和节间长度的正常生长,明显降低了稻米的垩白率、垩白大小和垩白度,其次是BaDao调节剂。以上试验研究表明,叶面喷施ND和BaDao调节剂,可提高寒地水稻籽粒产量,改善稻米品质。     

密度对超高产春大豆农艺性状的影响

研究了超高产条件下,不同种植密度对春大豆植株性状、产量性状和产量的影响以及单株叶面积和叶面积指数变化特点。结果表明,随密度的增加,株高和底荚高度增高,茎粗、节数、分枝数、分枝总长度降低,倒伏加重,单株有效结荚数、单株粒数、单株籽粒重降低,百粒重与种植密度关系不显著。叶面积指数随密度增加呈上升趋势,以45.0万株/hm2处理最佳,产量达5547.81kg/hm2。     

吉林省大豆品种遗传改良过程中主要农艺性状的变化

以吉林省1923—2005年间育成的30个大豆品种为材料, 两年的研究结果表明, 大豆种子产量随育成年代呈线性增加, 根据回归方程计算, 产量从1923年的1 197.80 kg hm^-2到2005年的2 305.54 kg hm^-2, 82年来增加了 1 107.73 kg hm^-2, 平均每年增加14.60 kg hm^-2。随着产量的提高, 株高降低, 主茎直径增加, 节数增多, 节间缩短, 分枝减少。相关和通径分析表明, 产量与单株荚数、单株粒数、单株叶面积、叶面积指数和单株复叶数目呈显著正相关(P<0.05), 单株荚数和单株粒数对于产量的提高贡献最大; 产量与株高、单株分枝数和倒伏指数呈显著负相关(P<0.05), 表明大豆产量的遗传改良过程中, 植株抗倒伏能力提高, 库容量增加, 源器官叶片的同化能力增强。     

内蒙古平原灌区高产春玉米(15 t hm-2以上)产量性能及增产途径

针对内蒙古平原灌区春玉米高产(15 t hm^-2以上)群体产量进一步提高难度大,产量挖潜途径不明确的问题,采用产量构成因素分析与产量性能参数分析相互验证的方法,在4年52点次高产(15 t hm^-2以上)群体产量构成因素分析的基础上,设计不同品种密度试验,研究增密对不同品种群体产量性能的影响,明确不同类型玉米品种的增产途径和栽培调控的主攻方向。结果表明,穗数和穗粒数是决定高产(15 t hm^-2以上)群体产量的主要因素。实现15 t hm^-2以上群体的产量结构为：穗数(7.08~9.60)×10⁴穗,穗粒数477~654粒,千粒重324.7~388.7 g,穗粒重168.9~234.0 g。其合理群体结构衡量指标是LAI_max在6.5以上,平均LAI在5左右,收获期LAI在3.5以上。高秆大穗型品种理想的产量结构是：67 500~75 000穗 hm^-2,每穗610~640粒,千粒重380 g左右,单穗粒重220~240 g,产量大于15 t hm^-2;株高适中的中小穗型品种,理想产量结构是： 75 000~97 500穗 hm^-2,每穗520~600粒,千粒重340~355 g,单穗粒重180~220 g,产量在16.5 t hm^-2以上。密度增加促进平均作物生长率(MCGR)和单位面积总籽粒数(TGN)的增加进而提高产量,但增密后平均净同化率(MNAR)降低导致穗粒数显著降低并限制了TGN的提高潜力。通过增密为主的结构性挖潜,使得群体功能的增益大于个体生产性能的降低,实现高产(15 t hm^-2以上),属于“得失性补偿增产”;在优化群体结构的基础上,提高个体生产能力,突破个体库容降低的限制,进行功能性挖潜,实现群体结构和个体功能协同增益的“差异性补偿增产”,是产量进一步提高的重要途径。     

New strategies for increasing heterozygosity in crops: Vicia faba mating system as a study case

Our research assesses the feasibility of using artificial selection on pre-mating floral traits to modify the mating system of faba bean (Vicia faba). This analysis considered two synthetic populations, which were derived from different genetic pools and had undergone five years of multiplication. For these populations, we identified floral and inflorescence traits that influence outcrossing per plant and examined the relative importance of these traits in governing yield. Codominant isozyme loci and the mixed-mating model were used to estimate the multilocus female outcrossing rate. A maternal half-sib design was used to evaluate the additive genetic component of floral and inflorescence traits, yield and yield components. Multiple regression was used to assess the effects of floral and inflorescence traits on outcrossing and yield and components of yield. The two populations exhibited mixing mating. Self-fertilization appears to result from the action of pollinating bees, so that its incidence could be modified by selection on floral and inflorescence traits that affect pollination. Floral and inflorescence traits affected individual differences in outcrossing unequally, with most variation being associated with the numbers of displayed flowers and inflorescences. Variation among plants in reward traits and in shape, although statistically significant, had limited and inconsistent influences on individual differences in outcrossing. Yield and its components varied strongly with aspects of floral display and, to a lesser extent, floral design, except for seed weight. Overall, our results imply that both outcrossing and yield could be enhanced by selection for plants that produce more inflorescences, each with relatively few flowers.