Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.     

The Beanbag Genetics Controversy: Towards a synthesis of opposing views of natural selection

The beanbag genetics controversy can be traced from the dispute between Fisher and Wright, through Mayr's influential promotion of the issue, to the contemporary units of selection debate. It centers on the claim that genic models of natural selection break down in the face of epistatic interactions among genes during phenotypic development. This claim is explored from both a conceptual and a quantitative point of view, and is shown to be defective on both counts.Firstly, an analysis of the controversy's theoretical origins demonstrates that this claim derives from a misinterpretation of the conceptual foundations of Fisher's genetical theory of natural selection, and confounds his fundamentally different concepts of the average excess and average effect of a gene. Secondly, an extension of the genic approach is proposed which models the dynamics of selection among epistatically interacting complexes of many genes. Paradoxically, this preliminary, but fundamentally genic model provides quantitative support for some controversial qualitative claims regarding the evolutionary consequences of strong gene interactions made by opponents of genic selectionism, including Mayr's theory of peripartric speciation. These findings foster hope that the proposed approach may eventually nudge the beanbag controversy out of its conceptual trenches into a more empirically oriented dialogue.     

Quantitative genetic study of the adaptive process

The additive genetic variance with respect to absolute fitness, V_A(W), divided by mean absolute fitness, , sets the rate of ongoing adaptation. Fisher''s key insight yielding this quantitative prediction of adaptive evolution, known as the Fundamental Theorem of Natural Selection, is well appreciated by evolutionists. Nevertheless, extremely scant information about V_A(W) is available for natural populations. Consequently, the capacity for fitness increase via natural selection is unknown. Particularly in the current context of rapid environmental change, which is likely to reduce fitness directly and, consequently, the size and persistence of populations, the urgency of advancing understanding of immediate adaptive capacity is extreme. We here explore reasons for the dearth of empirical information about V_A(W), despite its theoretical renown and critical evolutionary role. Of these reasons, we suggest that expectations that V_A(W) is negligible, in general, together with severe statistical challenges of estimating it, may largely account for the limited empirical emphasis on it. To develop insight into the dynamics of V_A(W) in a changing environment, we have conducted individual-based genetically explicit simulations. We show that, as optimizing selection on a trait changes steadily over generations, V_A(W) can grow considerably, supporting more rapid adaptation than would the V_A(W) of the base population. We call for direct evaluation of V_A(W) and in support of prediction of rates adaptive evolution, and we advocate for the use of aster modeling as a rigorous basis for achieving this goal.     

QUANTITATIVE GENETICS OF BRYOZOAN PHENOTYPIC EVOLUTION. II. ANALYSIS OF SELECTION AND RANDOM CHANGE IN FOSSIL SPECIES USING RECONSTRUCTED GENETIC PARAMETERS

The roles of natural selection and random genetic change in the punctuated phenotypic evolution of eight Miocene-Pliocene tropical American species of the cheilostome bryozoan Metrarabdotos are analyzed by quantitative genetic methods. Trait heritabilities and genetic covariances reconstructed by partitioning within- and among-colony phenotypic variance are similar to those previously obtained for living species of the cheilostome Stylopoma using breeding data. The hypothesis that differences in skeletal morphology between species of Metrarabdotos are entirely due to mutation and genetic drift cannot be rejected for reasonable rates of mutation maintained for periods brief enough to account for the geologically abrupt appearances of these species in the fossil record. Except for one pair of species, separated by the largest morphologic distance, directional selection acting alone would require unrealistically high rates of selective mortality to be maintained for these periods. Thus, directional selection is not strongly implicated in the divergence of Metrarabdotos species. Within species, rates of net phenotypic change are slow enough to require stabilizing selection, but mask large, relatively rapid fluctuations, all of which, however, can be attributed to chance departures from the mean phenotype by mutation and genetic drift, rather than to tracking environmental fluctuation by directional selection. The results are consistent with genetic models involving shifts between multiple adaptive peaks on which phenotypes remain more or less static through long-term stabilizing selection. Regardless of the degree to which directional selection may be involved in peak shifts, phenotypic differentiation is thus related to processes different than the pervasive stabilizing selection acting within species.     

The effect of a population bottleneck on the evolution of genetic variance/covariance structure

It is well known that standard population genetic theory predicts decreased additive genetic variance (V(a) ) following a population bottleneck and that theoretical models including interallelic and intergenic interactions indicate such loss may be avoided. However, few empirical data from multicellular model systems are available, especially regarding variance/covariance (V/CV) relationships. Here, we compare the V/CV structure of seventeen traits related to body size and composition between control (60 mating pairs/generation) and bottlenecked (2 mating pairs/generation; average F = 0.39) strains of mice. Although results for individual traits vary considerably, multivariate analysis indicates that V(a) in the bottlenecked populations is greater than expected. Traits with patterns and amounts of epistasis predictive of enhanced V(a) also show the largest deviations from additive expectations. Finally, the correlation structure of weekly weights is not significantly different between control and experimental lines but correlations between necropsy traits do differ, especially those involving the heart, kidney and tail length.     

ESTIMATING NONLINEAR SELECTION GRADIENTS USING QUADRATIC REGRESSION COEFFICIENTS: DOUBLE OR NOTHING?

The use of regression analysis has been instrumental in allowing evolutionary biologists to estimate the strength and mode of natural selection. Although directional and correlational selection gradients are equal to their corresponding regression coefficients, quadratic regression coefficients must be doubled to estimate stabilizing/disruptive selection gradients. Based on a sample of 33 papers published in Evolution between 2002 and 2007, at least 78% of papers have not doubled quadratic regression coefficients, leading to an appreciable underestimate of the strength of stabilizing and disruptive selection. Proper treatment of quadratic regression coefficients is necessary for estimation of fitness surfaces and contour plots, canonical analysis of the gamma matrix, and modeling the evolution of populations on an adaptive landscape.     

Maintaining evolvability

Although molecular methods, such as QTL mapping, have revealed a number of loci with large effects, it is still likely that the bulk of quantitative variability is due to multiple factors, each with small effect. Typically, these have a large additive component. Conventional wisdom argues that selection, natural or artificial, uses up additive variance and thus depletes its supply. Over time, the variance should be reduced, and at equilibrium be near zero. This is especially expected for fitness and traits highly correlated with it. Yet, populations typically have a great deal of additive variance, and do not seem to run out of genetic variability even after many generations of directional selection. Long-term selection experiments show that populations continue to retain seemingly undiminished additive variance despite large changes in the mean value. I propose that there are several reasons for this. (i) The environment is continually changing so that what was formerly most fit no longer is. (ii) There is an input of genetic variance from mutation, and sometimes from migration. (iii) As intermediate-frequency alleles increase in frequency towards one, producing less variance (as p → 1, p(1 − p) → 0), others that were originally near zero become more common and increase the variance. Thus, a roughly constant variance is maintained. (iv) There is always selection for fitness and for characters closely related to it. To the extent that the trait is heritable, later generations inherit a disproportionate number of genes acting additively on the trait, thus increasing genetic variance. For these reasons a selected population retains its ability to evolve. Of course, genes with large effect are also important. Conspicuous examples are the small number of loci that changed teosinte to maize, and major phylogenetic changes in the animal kingdom. The relative importance of these along with duplications, chromosome rearrangements, horizontal transmission and polyploidy is yet to be determined. It is likely that only a case-by-case analysis will provide the answers. Despite the difficulties that complex interactions cause for evolution in Mendelian populations, such populations nevertheless evolve very well. Longlasting species must have evolved mechanisms for coping with such problems. Since such difficulties do not arise in asexual populations, a comparison of epistatic patterns in closely related sexual and asexual species might provide some important insights.     

Dynamic sensitivity and nonlinear interactions influence the system-level evolutionary patterns of phototransduction proteins

Determining the influence of complex, molecular-system dynamics on the evolution of proteins is hindered by the significant challenge of quantifying the control exerted by the proteins on system output. We have employed a combination of systems biology and molecular evolution analyses in a first attempt to unravel this relationship. We employed a comprehensive mathematical model of mammalian phototransduction to predict the degree of influence that each protein in the system exerts on the high-level dynamic behaviour. We found that the genes encoding the most dynamically sensitive proteins exhibit relatively relaxed evolutionary constraint. We also investigated the evolutionary and epistatic influences of the many nonlinear interactions between proteins in the system and found several pairs to have coevolved, including those whose interactions are purely dynamical with respect to system output. This evidence points to a key role played by nonlinear system dynamics in influencing patterns of molecular evolution.