Quantitative Genetic Theory Research Articles

Response to commentary on "Examples of overlooking common sense solutions: the domestication gene and selection against mortality".

In a commentary in Frontiers, Van Rooijen (2014) states: “Today the developments in genetics are exciting. Perhaps this explains why geneticists sometimes seem to overlook common sense solutions. One example of this is the selection experiment done by Bijma et al. (2007a,b). ……As a result their selection seemed not very efficient.” In those two papers, however, we do not report a selection experiment. The first paper presents general quantitative genetic theory, showing how interactions among individuals alter heritable variation in traits, and how this can affect response to selection. The second paper presents general methodology to estimate the quantitative genetic parameters for such traits, and illustrates this methodology using a population of laying hens showing high mortality due to pecking behavior. Neither of those papers report results of a selection experiment.

Macroevolutionary patterns of sexual size dimorphism in copepods.

Major theories compete to explain the macroevolutionary trends observed in sexual size dimorphism (SSD) in animals. Quantitative genetic theory suggests that the sex under historically stronger directional selection will exhibit greater interspecific variance in size, with covariation between allometric slopes (male to female size) and the strength of SSD across clades. Rensch's rule (RR) also suggests a correlation, but one in which males are always the more size variant sex. Examining free-living pelagic and parasitic Copepoda, we test these competing predictions. Females are commonly the larger sex in copepod species. Comparing clades that vary by four orders of magnitude in their degree of dimorphism, we show that isometry is widespread. As such we find no support for either RR or for covariation between allometry and SSD. Our results suggest that selection on both sexes has been equally important. We next test the prediction that variation in the degree of SSD is related to the adult sex ratio. As males become relatively less abundant, it has been hypothesized that this will lead to a reduction in both inter-male competition and male size. However, the lack of such a correlation across diverse free-living pelagic families of copepods provides no support for this hypothesis. By comparison, in sea lice of the family Caligidae, there is some qualitative support of the hypothesis, males may suffer elevated mortality when they leave the host and rove for sedentary females, and their female-biased SSD is greater than in many free-living families. However, other parasitic copepods which do not appear to have obvious differences in sex-based mate searching risks also show similar or even more extreme SSD, therefore suggesting other factors can drive the observed extremes.

Long-term perspective of hybrid versus line breeding in wheat based on quantitative genetic theory.

The predicted future yield potential of hybrids was competitive with lines in the near future, but on a long term the competitiveness of hybrids depends on a number of factors. The change from line to hybrid breeding in autogamous crops is a recent controversial discussion among scientists and breeders. Our objectives were to employ wheat as a model to: (1) deliver a theoretical framework for the comparison of the selection gain of hybrid versus line breeding; (2) elaborate key parameters affecting selection gain in this comparison; (3) and evaluate the potential to modify these parameters in applied breeding programs. We developed a prediction model for future yield potential in both breeding methods as the sum of the population mean and the expected selection gain. The expected selection gain was smaller in hybrid than in line breeding and depended strongly on the hybrid seed production costs and the genetic variance available in hybrid versus line breeding. Owing to heterosis, the predicted future yield potential of hybrids was competitive with lines in the near future. On a long term, however, the competitiveness of hybrid compared to line breeding is questionable and depends on a number of factors. However, market specifications and political reasons might justify the current high interest in hybrid wheat breeding.

Quantitative genetic versions of Hamilton's rule with empirical applications

Hamilton's theory of inclusive fitness revolutionized our understanding of the evolution of social interactions. Surprisingly, an incorporation of Hamilton's perspective into the quantitative genetic theory of phenotypic evolution has been slow, despite the popularity of quantitative genetics in evolutionary studies. Here, we discuss several versions of Hamilton's rule for social evolution from a quantitative genetic perspective, emphasizing its utility in empirical applications. Although evolutionary quantitative genetics offers methods to measure each of the critical parameters of Hamilton's rule, empirical work has lagged behind theory. In particular, we lack studies of selection on altruistic traits in the wild. Fitness costs and benefits of altruism can be estimated using a simple extension of phenotypic selection analysis that incorporates the traits of social interactants. We also discuss the importance of considering the genetic influence of the social environment, or indirect genetic effects (IGEs), in the context of Hamilton's rule. Research in social evolution has generated an extensive body of empirical work focusing—with good reason—almost solely on relatedness. We argue that quantifying the roles of social and non-social components of selection and IGEs, in addition to relatedness, is now timely and should provide unique additional insights into social evolution.

SELECTION AND EVOLUTION OF CAUSALLY COVARYING TRAITS

When traits cause variation in fitness, the distribution of phenotype, weighted by fitness, necessarily changes. The degree to which traits cause fitness variation is therefore of central importance to evolutionary biology. Multivariate selection gradients are the main quantity used to describe components of trait-fitness covariation, but they quantify the direct effects of traits on (relative) fitness, which are not necessarily the total effects of traits on fitness. Despite considerable use in evolutionary ecology, path analytic characterizations of the total effects of traits on fitness have not been formally incorporated into quantitative genetic theory. By formally defining "extended" selection gradients, which are the total effects of traits on fitness, as opposed to the existing definition of selection gradients, a more intuitive scheme for characterizing selection is obtained. Extended selection gradients are distinct quantities, differing from the standard definition of selection gradients not only in the statistical means by which they may be assessed and the assumptions required for their estimation from observational data, but also in their fundamental biological meaning. Like direct selection gradients, extended selection gradients can be combined with genetic inference of multivariate phenotypic variation to provide quantitative prediction of microevolutionary trajectories.

The relation between the genetic architecture of quantitative traits and long-term genetic response

The genetic architecture of a quantitative trait refers to the number of genetic variants, allele frequencies, and effect sizes of variants that affect a trait and their mode of gene action. This study was conducted to investigate the effect of four shapes of allelic frequency distributions (constant, uniform, L-shaped and U-shaped) and different number of trait-affecting loci (50, 100, 200, 500) on allelic frequency changes, long term genetic response, and maintaining genetic variance. To this end, a population of 440 individuals composed of 40 males and 400 females as well as a genome of 200cM consisting of two chromosomes and with a mutation rate of 2.5 × 10(-5) per locus was simulated. Selection of superior animals was done using best linear unbiased prediction (BLUP) with assumption of infinitesimal model. Selection intensity was constant over 30 generations of selection. The highest genetic progress obtained when the allelic frequency had L-shaped distribution and number of trait-affecting loci was high (500). Although quantitative genetic theories predict the extinction of genetic variance due to artificial selection in long time, our results showed that under L- and U-shapped allelic frequency distributions, the additive genetic variance is persistent after 30 generations of selection. Further, presence or absence of selection limit can be an indication of low (<50) or high (>100) number of trait-affecting loci, respectively. It was concluded that the genetic architecture of complex traits is an important subject which should be considered in studies concerning long-term response to selection.

Evaluation of using half-sibling beef cows to increase growth and carcass uniformity of calf crops

<h2>ABSTRACT</h2> Uniformity of growth and carcass traits of calves resulting from commercial beef cows that were either half-siblings (HS) or similar phenotype but unknown genetic relationship (PS) were determined over 5 calf crops. Residuals (n = 853) of 205-d adjusted weaning weight from a repeated-measures ANOVA model were evaluated for homogeneity of variance between cow groups with Levene's test in PROC GLM of SAS. Adjusted weaning-weight SD was not different between cow groups (22.4 and 21.6kg for HS and PS cows, respectively; P=0.56). Lifetime weaning-weight production SD was 320kg for HS cows and 322kg for PS cows (P = 0.95). Healthy calves from each year were finished in a commercial feedlot. Standard deviation of HCW, LM area, and LM area per unit of HCW of calves from HS cows tended to be less (P ≤ 0.15) than SD of calves from PS cows, whereas finishing-period ADG tended to be greater. Observed differences in calf-trait SD were small (approximately 1.5%) and overall were similar to expectations calculated from quantitative genetics theory. However, observed differences in SD fluctuated widely from expectations for any given trait, indicating that very large samples may be needed to reliably observe the small differences that are expected. Therefore, preferentially selecting commercial beef cows so that they have half-sibling genetic relationships, over and above phenotypic selection criteria, appears to have limited ability to reduce phenotypic variability of calf crops, especially for traits with low heritabilities.

Erratum to: The Big Five Personality Traits: Psychological Entities or Statistical Constructs

On the third page of the article, first paragraph, the A and D factors in DZ twins are incorrectly stated to correlate 5 and 25, respectively, instead of .5 and .25. The correct sentence is thus: ‘‘Based on quantitative genetic theory (Falconer and Mackay 1996; Mather and Jinks 1971), the A factors are known to correlate 1 across MZ twins and .5 across DZ twins, and D factors are known to correlate 1 across MZ twins and .25 across DZ twins.’’

Toward a “Quantitative Genetic” Approach to Lithic Variation

Lithic artifacts are increasingly being used to address questions in evolutionary, i.e., historical, terms. The explicit assumption in such analyses is that lithic attributes reflect patterns of inheritance via social learning. However, both raw material and reduction factors are known to be potential sources of lithic variation. The cultural–evolutionary analysis of lithic variability must, therefore, reconcile heritable and nonheritable sources of variation under a single coherent framework. Moreover, there is a frequent assumption that conveniently measureable features, such as the relative shape of a biface at a specific point of its length, can be used as indicators of heritable variation. The use of such traits, however, is potentially questionable, especially in the light of controlled experiments that indicate that traits such as platform depths and angles influence the form of individual flakes. As such, it may be reasonable to consider whether such features represent more appropriate analytical units. Here, we contend that the solution to these problems lies in application of a “quantitative genetics” approach, which was designed to solve directly analogous problems in biology. This approach explicitly models multiple sources of variation simultaneously. Moreover, it provides a logical rationale for how evolutionary forces (e.g., drift and selection) can operate when only part of this variation is potentially heritable. We outline specifically how quantitative genetic theory can be rewritten for use with lithic artifacts. Thereafter, we provide example analyses of data, which support our case. We conclude by summarizing the merits of this framework and outline future extensions.

On the Additive and Dominant Variance and Covariance of Individuals Within the Genomic Selection Scope

Genomic evaluation models can fit additive and dominant SNP effects. Under quantitative genetics theory, additive or "breeding" values of individuals are generated by substitution effects, which involve both "biological" additive and dominant effects of the markers. Dominance deviations include only a portion of the biological dominant effects of the markers. Additive variance includes variation due to the additive and dominant effects of the markers. We describe a matrix of dominant genomic relationships across individuals, D, which is similar to the G matrix used in genomic best linear unbiased prediction. This matrix can be used in a mixed-model context for genomic evaluations or to estimate dominant and additive variances in the population. From the "genotypic" value of individuals, an alternative parameterization defines additive and dominance as the parts attributable to the additive and dominant effect of the markers. This approach underestimates the additive genetic variance and overestimates the dominance variance. Transforming the variances from one model into the other is trivial if the distribution of allelic frequencies is known. We illustrate these results with mouse data (four traits, 1884 mice, and 10,946 markers) and simulated data (2100 individuals and 10,000 markers). Variance components were estimated correctly in the model, considering breeding values and dominance deviations. For the model considering genotypic values, the inclusion of dominant effects biased the estimate of additive variance. Genomic models were more accurate for the estimation of variance components than their pedigree-based counterparts.

Correlated Evolution of Allometry and Sexual Dimorphism across Higher Taxa

Empirical evidence suggests that Rensch's rule of allometric scaling of male and female body size, which states that body size divergence is greater across males than across females of a clade, is not universal. In fact, quantitative genetic theory indicates that the sex under historically stronger directional selection will exhibit greater interspecific variance in size. Thus, the pattern of covariance between allometry of male and female body size and sexual size dimorphism (SSD) across related clades allows a test of this causal hypothesis for macroevolutionary trends in SSD. We compiled a data set of published body size estimates from the amphibians, a class with predominantly female-biased SSD, to examine variation in allometry and SSD among clades. Our results indicate that females become the more size-variant sex across species in a family as the magnitude of SSD in that family increases. This rejects Rensch's rule and implicates selection on females as a driver of both amphibian allometry and SSD. Further, when we combine our data into a single analysis of allometry for the class, we find a significant nonlinear allometric relationship between female body size and male body size. These data suggest that allometry changes significantly as a function of size. Our results illustrate that the relationship between female size and male size varies with both the degree of sexual dimorphism and the body size of a clade.

Optimizing the allocation of resources for genomic selection in one breeding cycle

We developeda universally applicable planning tool for optimizing the allocation of resources for one cycle of genomic selection in a biparental population. The framework combines selection theory with constraint numerical optimization and considers genotype × environment interactions. Genomic selection (GS) is increasingly implemented in plant breeding programs to increase selection gain but little is known how to optimally allocate the resources under a given budget. We investigated this problem with model calculations by combining quantitative genetic selection theory with constraint numerical optimization. We assumed one selection cycle where both the training and prediction sets comprised double haploid (DH) lines from the same biparental population. Grain yield for testcrosses of maize DH lines was used as a model trait but all parameters can be adjusted in a freely available software implementation. An extension of the expected selection accuracy given by Daetwyler et al. (2008) was developed to correctly balance between the number of environments for phenotyping the training set and its population sizein the presence of genotype × environment interactions. Under small budget, genotyping costs mainly determine whether GS is superior over phenotypic selection. With increasing budget, flexibility in resource allocation increases greatly but selection gain leveled off quickly requiring balancing the number of populations with the budget spent for each population. The use of an index combining phenotypic and GS predicted values in the training set was especially beneficial under limited resources and large genotype×environment interactions. Once a sufficiently high selection accuracy is achieved in the prediction set, further selection gain can be achieved most efficiently by massively expanding its size. Thus, with increasing budget, reducing the costs for producing a DH line becomes increasingly crucial for successfully exploiting the benefits of GS.

DEVELOPMENTAL INSTABILITY IS GENETICALLY CORRELATED WITH PHENOTYPIC PLASTICITY, CONSTRAINING HERITABILITY, AND FITNESS

Although adaptive plasticity would seem always to be favored by selection, it occurs less often than expected. This lack of ubiquity suggests that there must be trade-offs, costs, or limitations associated with plasticity. Yet, few costs have been found. We explore one type of limitation, a correlation between plasticity and developmental instability, and use quantitative genetic theory to show why one should expect a genetic correlation. We test that hypothesis using the Landsberg erecta × Cape Verde Islands recombinant inbred lines (RILs) of Arabidopsis thaliana. RILs were grown at four different nitrogen (N) supply levels that span the range of N availabilities previously documented in North American field populations. We found a significant multivariate relationship between the cross-environment trait plasticity and the within-environment, within-RIL developmental instability across 13 traits. This genetic covariation between plasticity and developmental instability has two costs. First, theory predicts diminished fitness for highly plastic lines under stabilizing selection, because their developmental instability and variance around the optimum phenotype will be greater compared to nonplastic genotypes. Second, empirically the most plastic traits exhibited heritabilities reduced by 57% on average compared to nonplastic traits. This demonstration of potential costs in inclusive fitness and heritability provoke a rethinking of the evolutionary role of plasticity.

Propagation of genetic variation in gene regulatory networks

A future quantitative genetics theory should link genetic variation to phenotypic variation in a causally cohesive way based on how genes actually work and interact. We provide a theoretical framework for predicting and understanding the manifestation of genetic variation in haploid and diploid regulatory networks with arbitrary feedback structures and intra-locus and inter-locus functional dependencies. Using results from network and graph theory, we define propagation functions describing how genetic variation in a locus is propagated through the network, and show how their derivatives are related to the network’s feedback structure. Similarly, feedback functions describe the effect of genotypic variation of a locus on itself, either directly or mediated by the network. A simple sign rule relates the sign of the derivative of the feedback function of any locus to the feedback loops involving that particular locus. We show that the sign of the phenotypically manifested interaction between alleles at a diploid locus is equal to the sign of the dominant feedback loop involving that particular locus, in accordance with recent results for a single locus system. Our results provide tools by which one can use observable equilibrium concentrations of gene products to disclose structural properties of the network architecture. Our work is a step towards a theory capable of explaining the pleiotropy and epistasis features of genetic variation in complex regulatory networks as functions of regulatory anatomy and functional location of the genetic variation.

О проблемах эволюционной оптимизации онтогенеза. II. К обоснованию критерия оптимизации для нелинейной модели лесли

The paper considers the problems in the adaptive evolution of life-history traits for individuals in the nonlinear Leslie model of age-structured population. The possibility to predict adaptation results as the values of organism's traits (properties) that provide for the maximum of a certain function of traits (optimization criterion) is studied. An ideal criterion of this type is Darwinian fitness as a characteristic of success of an individual's life history. Criticism of the optimization approach is associated with the fact that it does not take into account the changes in the environmental conditions (in a broad sense) caused by evolution, thereby leading to losses in the adequacy of the criterion. In addition, the justification for this criterion under stationary conditions is not usually rigorous. It has been suggested to overcome these objections in terms of the adaptive dynamics theory using the concept of invasive fitness. The reasons are given that favor the application of the average number of offspring for an individual, R(L), as an optimization criterion in the nonlinear Leslie model. According to the theory of quantitative genetics, the selection for fertility (that is, for a set of correlated quantitative traits determined by both multiple loci and the environment) leads to an increase in R(L). In terms of adaptive dynamics, the maximum R(L) corresponds to the evolutionary stability and, in certain cases, convergent stability of the values for traits. The search for evolutionarily stable values on the background of limited resources for reproduction is a problem of linear programming.

A quantitative genetic and epigenetic model of complex traits.

BackgroundDespite our increasing recognition of the mechanisms that specify and propagate epigenetic states of gene expression, the pattern of how epigenetic modifications contribute to the overall genetic variation of a phenotypic trait remains largely elusive.ResultsWe construct a quantitative model to explore the effect of epigenetic modifications that occur at specific rates on the genome. This model, derived from, but beyond, the traditional quantitative genetic theory that is founded on Mendel’s laws, allows questions concerning the prevalence and importance of epigenetic variation to be incorporated and addressed.ConclusionsIt provides a new avenue for bringing chromatin inheritance into the realm of complex traits, facilitating our understanding of the means by which phenotypic variation is generated.

Comparison of Family History and SNPs for Predicting Risk of Complex Disease

The clinical utility of family history and genetic tests is generally well understood for simple Mendelian disorders and rare subforms of complex diseases that are directly attributable to highly penetrant genetic variants. However, little is presently known regarding the performance of these methods in situations where disease susceptibility depends on the cumulative contribution of multiple genetic factors of moderate or low penetrance. Using quantitative genetic theory, we develop a model for studying the predictive ability of family history and single nucleotide polymorphism (SNP)–based methods for assessing risk of polygenic disorders. We show that family history is most useful for highly common, heritable conditions (e.g., coronary artery disease), where it explains roughly 20%–30% of disease heritability, on par with the most successful SNP models based on associations discovered to date. In contrast, we find that for diseases of moderate or low frequency (e.g., Crohn disease) family history accounts for less than 4% of disease heritability, substantially lagging behind SNPs in almost all cases. These results indicate that, for a broad range of diseases, already identified SNP associations may be better predictors of risk than their family history–based counterparts, despite the large fraction of missing heritability that remains to be explained. Our model illustrates the difficulty of using either family history or SNPs for standalone disease prediction. On the other hand, we show that, unlike family history, SNP–based tests can reveal extreme likelihood ratios for a relatively large percentage of individuals, thus providing potentially valuable adjunctive evidence in a differential diagnosis.

Phenotypic Constraints and Phenotypic Hitchhiking in a Promiscuous Enzyme

Covarying phenotypic traits can limit natural selection's ability to modify these traits. Most evolutionary stud- ies on trait covariation use the comparative method to study complex traits of multicellular organisms. Simpler traits have the advantage of being amenable to experimental evolution. Here we study such a simple molecular system, the TEM-1 beta-lactamase protein, a promiscuous enzyme that hydrolyses antibiotics, and thus confers antibiotic resistance to bacte- ria. We mutagenized large populations of TEM-1, and selected in these populations for activity on the four different anti- biotics ampicillin, carbenicillin, oxacillin, and penicillin G. While mutagenesis alone lead to highly correlated changes in enzyme activity on the four antibiotics, subsequent selection was able to modify this activity covariation substantially, and even lead to uncorrelated activities. We found that selection on one antibiotic A may be more effective in increasing activ- ity on another antibiotic B then selection on antibiotic B itself. We call this phenomenon phenotypic hitchhiking. It can be readily explained through quantitative genetic theory as a consequence of differing variances in covarying traits. It may help engineer macromolecules with desirable properties through directed evolution. Our analysis is a first step towards systematic analysis of trait covariation in experimental molecular systems. It shows that selection may readily modify the phenotypic constraints that limit its efficacy.

Fuzzy-Based Self-Interactive Multiobjective Evolution Optimization for Reverse Engineering of Biological Networks

S-system modeling from time series datasets can provide us with an interactive network. However, system identification is difficult since an S-system is described as highly nonlinear differential equations. Much research adopts various evolution computation technologies to identify system parameters, and some further achieve skeletal-network structure identification. However, the truncated redundant kinetic orders are not small enough as compared with the preserved terms. In this paper, we integrate quantitative genetics, bacterium movement, and fuzzy set theory into evolution computation to develop a new genetic algorithm to achieve convergence enhancement and diversity preservation. The proposed exploration and exploitation genetic algorithm (EEGA) can improve the best-so-far individual and ensure global optimal search at the same time. The EEGA enhances evolution convergence by golden section seed selection, normal-distribution reproduction, mixed inbreeding and backcrossing, competition elitism, and acceleration operations. Search-then-conquer evolution direction operations, eugenics-based screen-sifting mutation, eugenic self-mutation, and fuzzy-based tumble migration preserve population diversity to avoid premature convergence. Furthermore, to ensure that a reasonable gene regulation network is inferred, fuzzy composition is introduced to derive a reconstruction index. This performance index let EEGA possess self-interactive multiobjective learning. The proposed fuzzy-reconstruction-based multiobjective genetic algorithm is examined by three dry-lab biological systems. Simulation results show that a safety pruning action is guaranteed (the truncation threshold is set to be 10-15), and only one- or two-step pruning action is taken.

The effects of migration and drift on local adaptation to a heterogeneous environment

Local adaptation experiments are widely used to quantify the levels of adaptation within a heterogeneous environment. However, theoretical studies generally focus on the probability of fixation of alleles or the mean fitness of populations, rather than local adaptation as it is commonly measured experimentally or in field studies. Here, we develop mathematical models and use them to generate analytical predictions for the level of local adaptation as a function of selection, migration and genetic drift. First, we contrast mean fitness and local adaptation measures and show that the latter can be expressed in a simple and general way as a function of the spatial covariance between population mean phenotype and local environmental conditions. Second, we develop several approximations of a population genetics model to show that the system exhibits different behaviours depending on the rate of migration. The main insights are the following: with intermediate migration, both genetic drift and migration decrease local adaptation; with low migration, drift decreases local adaptation but migration speeds up adaptation; with high migration, genetic drift has no effect on local adaptation. Third, we extend this analysis to cases where the trait under selection is continuous using classical quantitative genetics theory. Finally, we discuss these results in the light of recent experimental work on local adaptation.