Multiplicative Genotype-Environment Interaction as a Cause of Reversed Response to Directional Selection

In experiments with directional selection on a quantitative character a "reversed response" to selection is occasionally observed, when selection of individuals for a higher (lower) value of the character results in a lower (higher) value of the character among their offspring. A sudden change in environments or random drift is often assumed to be responsible for this. It is demonstrated in this paper that these two causes cannot account for the reversed response at least in some of the experiments. Multiplicative genotype-environment interaction is discussed as a possible cause of a reversed response to directional selection. Such interaction entails either disruptive or stabilizing genotypic selection, even when the phenotypic selection is directional.     

Hybrid rye performance under natural drought stress in Europe

Several rye growing regions of Central Europe suffered from severe drought stress in the last decade. Rye is typically grown on sandy soils with low water-holding capacity in areas with low rainfall, thus drought-tolerant varieties are urgently needed. The main objective of our study was to evaluate the drought stress tolerance of rye hybrids using large-scaled field experiments. Two biparental populations (Pop-A, Pop-B) each consisting of 220 F_2:4 lines from the Petkus gene pool and their parents were evaluated for grain yield testcross performance under irrigated (I) and rainfed (R) regime in six environments. We observed for most environments severe drought stress leading to an average grain yield reduction of 23.8 % for rainfed compared to irrigated regime in drought stress environments. A decomposition of the variance revealed significant (P < 0.01) genotypic and genotype × environment interaction variances but only a minor effect of drought stress on the ranking of the genotypes with regard to grain yield. In conclusion, separate breeding programs for drought-tolerant genotypes are not superior to the currently practiced selection under rainfed conditions without irrigation in hybrid rye breeding in Central Europe.     

The origin of subfunctions and modular gene regulation

Evolutionary explanations for the origin of modularity in genetic and developmental pathways generally assume that modularity confers a selective advantage. However, our results suggest that even in the absence of any direct selective advantage, genotypic modularity may increase through the formation of new subfunctions under near-neutral processes. Two subfunctions may be formed from a single ancestral subfunction by the process of fission. Subfunction fission occurs when multiple functions under unified genetic control become subdivided into more restricted functions under independent genetic control. Provided that population size is sufficiently small, random genetic drift and mutation can conspire to produce changes in the number of subfunctions in the genome of a species without necessarily altering the phenotype. Extensive genotypic modularity may then accrue in a near-neutral fashion in permissive population-genetic environments, potentially opening novel pathways to morphological evolution. Many aspects of gene complexity in multicellular eukaryotes may have arisen passively as population size reductions accompanied increases in organism size, with the adaptive exploitation of such complexity occurring secondarily.     

A Ranking Approach to Genomic Selection

Background

Genomic selection (GS) is a recent selective breeding method which uses predictive models based on whole-genome molecular markers. Until now, existing studies formulated GS as the problem of modeling an individual’s breeding value for a particular trait of interest, i.e., as a regression problem. To assess predictive accuracy of the model, the Pearson correlation between observed and predicted trait values was used.

Contributions

In this paper, we propose to formulate GS as the problem of ranking individuals according to their breeding value. Our proposed framework allows us to employ machine learning methods for ranking which had previously not been considered in the GS literature. To assess ranking accuracy of a model, we introduce a new measure originating from the information retrieval literature called normalized discounted cumulative gain (NDCG). NDCG rewards more strongly models which assign a high rank to individuals with high breeding value. Therefore, NDCG reflects a prerequisite objective in selective breeding: accurate selection of individuals with high breeding value.

Results

We conducted a comparison of 10 existing regression methods and 3 new ranking methods on 6 datasets, consisting of 4 plant species and 25 traits. Our experimental results suggest that tree-based ensemble methods including McRank, Random Forests and Gradient Boosting Regression Trees achieve excellent ranking accuracy. RKHS regression and RankSVM also achieve good accuracy when used with an RBF kernel. Traditional regression methods such as Bayesian lasso, wBSR and BayesC were found less suitable for ranking. Pearson correlation was found to correlate poorly with NDCG. Our study suggests two important messages. First, ranking methods are a promising research direction in GS. Second, NDCG can be a useful evaluation measure for GS.     

Relationships among analytical methods used to study genotypic variation and genotype-by-environment interaction in plant breeding multi-environment experiments

Following the recognition of the importance of dealing with the effects of genotype-by-environment (G ×E) interaction in multi-environment testing of genotypes in plant breeding programs, there has been substantial development in the area of analytical methodology to quantify and describe these interactions. Three major areas where there have been developments are the analysis of variance, indirect selection, and pattern analysis methodologies. This has resulted in a wide range of analytical methods each with their own advocates. There is little doubt that the development of these methodologies has greatly contributed to an enhanced understanding of the magnitude and form ofG ×E interactions and our ability to quantify their presence in a multi-environment experiment. However, our understanding of the environmental and physiological bases of the nature ofG ×E interactions in plant breeding has not improved commensurably with the availability of these methodologies. This may in part be due to concentration on the statistical aspects of the analytical methodologies rather than on the complementary resolution of the biological basis of the differences in genotypic adaptation observed in plant breeding experiments. There are clear relationships between many of the analytical methodologies used for studying genotypic variation andG ×E interaction in plant breeding experiments. However, from the numerous discussions on the relative merits of alternative ways of analysingG ×E interactions which can be found in the literature, these relationships do not appear to be widely appreciated. This paper outlines the relevant theoretical relationships between the analysis of variance, indirect selection and pattern analysis methodologies, and their practical implications for the plant breeder interested in assessing the effects ofG ×E interaction on the response to selection. The variance components estimated from the combined analysis of variance can be used to judge the relative magnitude of genotypic andG ×E interaction variance. Where concern is on the effect of lack of correlation among environments, theG ×E interaction component can be partitioned into a component due to heterogeneity of genotypic variance among environments and another due to the lack of correlation among environments. In addition, the pooled genetic correlation among all environments can be estimated as the intraclass correlation from the variance components of the combined analysis of variance. WhereG ×E interaction accounts for a large proportion of the variation among genotypes, the individual genetic correlations between environments could be investigated rather than the pooled genetic correlation. Indirect selection theory can be applied to the case where the same character is measured on the same genotypes in different environments. Where there are no correlations of error effects among environments, the phenotypic correlation between environments may be used to investigate indirect response to selection. Pattern analysis (classification and ordination) methods based on standardised data can be used to summarise the relationships among environments in terms of the scope to exploit indirect selection. With the availability of this range of analytical methodology, it is now possible to investigate the results of more comprehensive experiments which attempt to understand the nature of differences in genotypic adaptation. Hence a greater focus of interest on understanding the causes of the interaction can be achieved.     

The Genetic Structure of Natural Populations of Drosophila melanogaster. Xx. Comparison of Genotype-Environment Interaction in Viability between a Northern and a Southern Population

In order to examine the operation of diversifying selection as the maintenance mechanism of excessive additive genetic variance for viability in southern populations in comparison with northern populations of Drosophila melanogaster, two sets of experiments were conducted using second chromosomes extracted from the Ogasawara population (a southern population in Japan) and from the Aomori population (a northern population in Japan). Chromosomal homozygote and heterozygote viabilities were estimated in eight kinds of artificially produced breeding environments. The main findings in the present investigation are as follows: (1) Significant genotype-environment interaction was observed using chromosomes extracted from the Ogasawara population. Indeed, the estimate of the genotype-environment interaction variance for heterozygotes was significantly larger than that of the genotypic variance. On the other hand, when chromosomes sampled from the Aomori population were examined, that interaction variance was significant only for homozygotes and its value was no more than one quarter of that for the chromosomes from the Ogasawara population. (2) The average genetic correlation between any two viabilities of the same lines estimated in the eight kinds of breeding environments for the chromosomes sampled from the Ogasawara population was smaller than that for the chromosomes from the Aomori population both in homozygotes and in heterozygotes, especially in the latter. (3) The stability of heterozygotes over homozygotes against fluctuations of environmental conditions was seen in the chromosomes from the Ogasawara population, but not from the Aomori population. (4) From the excessive genotype-environment interaction variance compared with the genotypic variance in heterozygotes, it was suggested for the chromosomes from the Ogasawara population that the reversal of viability order between homozygotes took place in some environments at the locus level. On the basis of these findings, it is strongly suggested that diversifying selection is operating in a southern population of D. melanogaster on some of the viability polygenes which are probably located outside the structural loci, and the excessive additive genetic variance of viability in southern populations is maintained by this type of selection.     

among-Environment Heteroscedasticity and Genetic Autocorrelation: Implications for the Study of Phenotypic Plasticity

The impact of among-environment heteroscedasticity and genetic autocorrelation on the analysis of phenotypic plasticity is examined. Among-environment heteroscedasticity occurs when genotypic variances differ among environments. Genetic autocorrelation arises whenever the responses of a genotype to different environments are more or less similar than expected for observations randomly associated. In a multivariate analysis-of-variance model, three transformations of genotypic profiles (reaction norms), which apply to the residuals of the model while preserving the mean responses within environments, are derived. The transformations remove either among-environment heteroscedasticity, genetic autocorrelation or both. When both nuisances are not removed, statistical tests are corrected in a modified univariate approach using the sample covariance matrix of the genotypic profiles. Methods are illustrated on a Chlamydomonas reinhardtii data set. When heteroscedasticity was removed, the variance component associated with the genotype-by-environment interaction increased proportionally to the genotype variance component. As a result, the genetic correlation r(g) was altered. Genetic autocorrelation was responsible for statistical significance of the genotype-by-environment interaction and genotype main effects on raw data. When autocorrelation was removed, the ranking of genotypes according to their stability index dramatically changed. Evolutionary implications of our methods and results are discussed.     

Experimental evidence for the adaptive value of sexual reproduction

It is generally believed that recombination by sexual reproduction is unfavourable in constant environments but is of adaptive value under changing environmental conditions. To test this theory, experimental populations of yeast (Saccharomyces cerevisiae) were set up and maintained at different levels of environmental heterogeneity. Recombination was estimated by determining sporulation rates. Sporulation rates first increased in populations living in highly variable environments, but after some time began to decrease. The decrease started last and was slowest in populations which were maintained under the same conditions for a sufficiently long time, to allow some adaptation of the gene pool to the respective environment. Patterns of genotypic variability could not be interpreted in such simple terms, but there was a statistically significant correlation between sporulation rate and genotypic variability. This correlation is to be expected because recombination generates genotypic variability. Summing up, recombination by sexual reproduction is advantageous in changing environments if the population can track the changes in the environment by changing its genotypic structure.     

Factor regression for interpreting genotype-environment interaction in bread-wheat trials

Summary The French INRA wheat (Triticum aestivum L. em Thell.) breeding program is based on multilocation trials to produce high-yielding, adapted lines for a wide range of environments. Differential genotypic responses to variable environment conditions limit the accuracy of yield estimations. Factor regression was used to partition the genotype-environment (GE) interaction into four biologically interpretable terms. Yield data were analyzed from 34 wheat genotypes grown in four environments using 12 auxiliary agronomic traits as genotypic and environmental covariates. Most of the GE interaction (91%) was explained by the combination of only three traits: 1,000-kernel weight, lodging susceptibility and spike length. These traits are easily measured in breeding programs, therefore factor regression model can provide a convenient and useful prediction method of yield.     

蔊菜杂草性的研究

本文通过对十字花科常见杂草芹菜[Rorippa in lica(L.)Hiern]在南京地区的自然群体的周期性观察,以了解其在不同生态环境下的生活周期。本文还通过一系列实验来观察其繁育系统、种子传播的动因、结实力、种子发芽率和植物抗人为干扰的耐受性。花蕾套袋试验证明蔊菜主要是自交可亲和的,即使存在异型杂交也是微不足道的。种子传播效应试验揭示水和风都是种子传播的自然力。该种具有范围很广的耐受性,踏践和刈割试验证明在严重的人为于扰下仍能完成其生活周期。蔊菜尽管本质上属于多年生草本,能产生大量的种子,在很大程度上靠种子繁殖。种子萌芽试验证明它的种子萌发参差不齐。总之,蔊菜具有典型杂草的许多特性,而这些特性给它以适合在多种自然的和人为干扰的环境中正常地生长的能力。     

Reinventing quantitative genetics for plant breeding: something old,something new,something borrowed,something BLUE

The goals of quantitative genetics differ according to its field of application. In plant breeding, the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments. Keeping quantitative genetics current requires keeping old concepts that remain useful, letting go of what has become archaic, and introducing new concepts and methods that support contemporary breeding. The core concept of continuous variation being due to multiple Mendelian loci remains unchanged. Because the entirety of germplasm available in a breeding program is not in Hardy–Weinberg equilibrium, classical concepts that assume random mating, such as the average effect of an allele and additive variance, need to be retired in plant breeding. Doing so is feasible because with molecular markers, mixed-model approaches that require minimal genetic assumptions can be used for best linear unbiased estimation (BLUE) and prediction. Plant breeding would benefit from borrowing approaches found useful in other disciplines. Examples include reliability as a new measure of the influence of genetic versus nongenetic effects, and operations research and simulation approaches for designing breeding programs. The genetic entities in such simulations should not be generic but should be represented by the pedigrees, marker data, and phenotypic data for the actual germplasm in a breeding program. Over the years, quantitative genetics in plant breeding has become increasingly empirical and computational and less grounded in theory. This trend will continue as the amount and types of data available in a breeding program increase.Subject terms: Plant sciences, Genetics     

Environment-dependent performance and fitness of Iris brevicaulis, I. fulva (Iridaceae), and hybrids

We tested the relative fitness of two Louisiana Iris species (Iris brevicaulis and I. fulva) and their first-generation backcross hybrids in three experimental watering treatments: dry, field capacity, and flooded. Leaf area expansion rate, gas exchange (A(max), g(s), c(i)), and biomass at final harvest were measured for each species and hybrid class in all three environmental treatments. Fitness (based on total biomass) of the four genotypic classes differed significantly with environment. All genotypic classes performed most poorly in the dry treatment. The fitness ranking of genotypic class also changed across environments (significant genotypic class by treatment interaction) with hybrid genotype fitness shifting relative to parental genotypes. Integrating over all treatments, backcrosses to I. fulva showed the lowest fitness, whereas backcrosses to I. brevicaulis outperformed I. fulva. The differences in fitness were apparently achieved by a combination of differences in photosynthesis and allocation. In this system, hybrids are not necessarily less fit than their parents, and the relationship between hybrid and parental fitness is influenced by environmental conditions, lending support to the Hybrid Novelty model of hybrid zone evolution.     

Selection on laying date is connected to breeding density in the pied flycatcher

Timing of reproduction and clutch size are important determinants of breeding success, especially in seasonal environments. Several recent bird population studies have shown changes in breeding time and in natural selection on it. These changes have often been linked with climate change, but few studies have investigated how the traits or natural selection are actually connected with climatic factors. Furthermore, the effect of population density on selection has been rarely considered, despite the potential importance of density in demographic processes. We studied variation in natural selection on laying date and on clutch size in relation to measures of spring phenology and population density in a long-term study of pied flycatchers in SW Finland. The phenological stage of the environment at mean egg-laying did not affect the direction of selection on either laying date or on clutch size. There was, however, stronger selection for earlier laying date when the breeding density of the population was high, suggesting that early breeding is not necessarily beneficial as such, but that its importance is emphasized when high population density increases competition. In addition, early breeding was favoured when the pre-breeding period was cool, which may indicate an increased advantage for the fittest individuals in harsher conditions. In the middle of the twentieth century, there was selection for large clutch size, which subsequently ceased, along with an overall decrease in recruit production. Our results indicate that attention should be paid to demographic factors such as breeding density when studying natural selection and temporal changes in it.     

A review of phosphorus efficiency in wheat

More efficient utilization of phosphorus by wheat plants is needed to extend the useful life of the phosphate reserves in the world, to reduce the cost of producing crops, and to improve the value of the grain and the straw produced. In this paper definitions of efficient use of phosphorus by wheat are reviewed, genotypic variation in phosphorus efficiency is reported, some consequences of breeding for greater efficiency are discussed, and ways to select more efficient genotypes are suggested.     

Performance comparison of dwarf laying hens segregating for the naked neck gene in temperate and subtropical environments

This study compares laying performances between two environments of dwarf laying hen lines segregating for the naked neck mutation (NA locus), a selected dwarf line of brown-egg layers and its control line. Layers with one of the three genotypes at the NA locus were produced from 11 sires from the control line and 12 sires from the selected line. Two hatches produced 216 adult hens in Taiwan and 297 hens in France. Genetic parameters for laying traits were estimated in each environment and the ranking of sire breeding values was compared between environments. Laying performance was lower, and mortality was higher in Taiwan than in France. The line by environment interaction was highly significant for body weight at 16 weeks, clutch length and egg number, with or without Box-Cox transformation. The selected line was more sensitive to environmental change but in Taiwan it could maintain a higher egg number than the control line. Estimated heritability values in the selected line were higher in France than in Taiwan, but not for all the traits in the control line. The rank correlations between sire breeding values were low within the selected line and slightly higher in the control line. A few sire families showed a good ranking in both environments, suggesting that some families may adapt better to environmental change.     

Genotype x environment interaction of crossover type: detecting its presence and estimating the crossover point

Genotype-environment interaction (GEI) introduces inconsistency in the relative rating of genotypes across environments and plays a key role in formulating strategies for crop improvement. GEI can be either qualitative (i.e., crossover type) or only quantitative (i.e., non-crossover type). Since the presence of crossover-type interaction has a strong implication for breeding for specific adaptation, it is important to assess the frequency of crossover interactions. This paper presents a test for detecting the presence of crossover-type interaction using the response-environment relationship and enumerates the frequency of crossovers and estimation of the crossover point (CP) on the environment axis, which serves as a cut-off point for the two environments groups where different/specific selections can be made. Sixty-four barley lines with various selection histories were grown in northern Syria and Lebanon giving a total of 21 environments (location-year combinations). Linear regression of the genotypic response on the environmental index represented a satisfactory model, and heterogeneity among regressions was significant. At a 5% level of significance, 38% and 19% of the pairs showed crossover interactions when the error variances were considered heterogeneous and homogeneous, respectively, implying that an appreciable number of crossovers took place in the case of barley lines responding to their environments. The CP of 1.64 t/ha, obtained as the CP of regression lines between the genotype numbers 19 and 31, provided maximum genotype x environment-group interaction. Across all environments, genotype nos. 59 and 12 stood first and second for high yield, respectively. The changes in the ranks of genotypes under the groups of environments can be used for selecting specifically adapted genotypes. Received: 25 January 1999 / Accepted: 16 March 1999     

Timing of avian reproduction in unpredictable environments

Organisms living in periodically varying environments adjust their life history events to the changes in food availability. When these changes are not entirely predictable animals face a trade-off between maintaining physiological preparedness (which can be costly) and being unprepared (which decreases the chances of successful reproduction). To investigate this problem, we developed an optimal annual routine model of gonad regulation in birds. Most birds regress their reproductive organs during non-breeding periods, but to start breeding again they need to have functional gonads. Maintaining the gonads in this state is costly, but because it takes time to achieve this state, if gonads are not functional the bird may miss a possible breeding opportunity. We explore the resolution of this trade-off in environments where favorable periods can occur at any time of the year and variability in the length of good and bad periods can be altered. Consistent with empirical studies of reproductive behavior in unpredictable environments, we find that birds maintain the gonads partially activated during unfavorable conditions in many cases. However, gonad regulation may differ strikingly depending on the consistency of the good and bad periods. Furthermore, seasonal changes in food availability lead to the entrainment of reproduction and the segregation of the breeding and non-breeding season, even if the magnitude of seasonality is small compared to the degree of environmental fluctuations. These results indicate that several aspects of the environment need to be taken into account to understand reproductive behavior in unpredictable environments. Given that the trade-off between the costs and benefits of maintaining physiological preparedness is not limited to birds, our results have implications for understanding behavioral flexibility in other organisms as well.     

Be flexible and adapt easily—The great role of plasticity relative to genetic variation for aggressiveness of Fusarium culmorum isolates

The phenotypic variation in an array of pathogen isolates in natural environments can be partitioned into genotypic variation and environmental plasticity. The present study uses a mixed-model approach to partition the relative contribution of both factors among isolates of Fusarium culmorum from natural field populations in various environments. Twenty-eight and 38 isolates from an international collection were phenotyped for aggressiveness and deoxynivalenol (DON) accumulation across two locations during the years 2015 and 2016, respectively, on four winter type cereals as hosts: bread wheat, durum wheat, triticale and rye, thus providing 16 environments. Aggressiveness, measured as Fusarium head blight (FHB) severity, was assessed by visually rating the symptoms of all isolates on infected hosts, and for 10 isolates, additionally the mycotoxin deoxynivalenol (DON) was measured in the grain after harvest. Despite significant genotypic variation among the isolates, the interactions with years and locations explained the largest proportion of variance which disentangled the overwhelming role of plasticity. Host-by-isolate interaction was not significant and no significant (p < .001) change in the ranking of isolates from one host to another was detected. As the main factor of plasticity was isolate-by-year interaction, this implies that seasonal changes might be an important evolutionary driver in F. culmorum populations.     

Gene action of canopy temperature in bread wheat under diverse environments

While canopy temperature (CT) shows a strong and reliable association with yield under drought and heat stress and is used in wheat breeding to select for yield, little is known of its genetic control. The objective of this study was to determine the gene action controlling CT in five wheat populations grown in diverse environments (heat, drought, and well-irrigated conditions). CT showed negative phenotypic correlations with grain yield under drought and well-irrigated environments. Additive × additive effects were most prevalent and significant for all crosses and environments. Dominance and dominance × dominance gene actions were also found, though the significance and direction was specific for each environment and genotypic cross. The use of CT as a selection criterion to improve tolerance to drought was supported by its significant association with grain yield and the genotype differences observed between cultivars. Our results indicated that genetic gains for CT in wheat could be achieved through conventional breeding. However, given some dominance and epistatic effects, it would be necessary to delay the selection process until the frequency of heterozygous loci within families is reduced.     

Response to Selection Under Non-Random Mating I. Partitioning Genetic Variance

In analogy to the concept of breeding value defined for random mating equilibrium populations, the “transmittable genetic value” of an individual is defined as the average value of its expected progeny for any system of mating. The genotypic value is then characterised in terms of transmittable and residual genetic values and components of genetic variance redefined which can be estimated by the conventional procedure based on resemblance between relatives.