Predicting Response to Selection on a Quantitative Trait: A Comparison between Models for Mixed-mating Populations

Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS, 66045, USA.
Journal of Theoretical Biology (Impact Factor: 2.12). 12/2000; 207(1):37-56. DOI: 10.1006/jtbi.2000.2154
Source: PubMed


Two different theoretical frameworks have been developed to predict response to selection in a mixed mating population (in which reproduction occurs by a mixture of outcrossing and self-fertilization). The genotypic covariance model (GCM) and the structured linear model (SLM) rely on the same assumptions regarding quantitative trait inheritance, but use different genetic summary statistics. Here, we demonstrate the algebraic relationships between the various genetic metrics used in each theory. This is accomplished by reformulating the GCM in terms of the Wright-Kempthorne equation. We use stochastic simulations to investigate the relative accuracy of each theory for a range of selfing rates. The SLM is generally more accurate than the GCM, the most pronounced differences emerging in simulations with inbreeding depression for fitness. In fact, with strong inbreeding depression and high selfing rates, evolution can occur opposite the direction predicted by the GCM. The simulations also indicate that direct application of random mating models to partially selfing populations can produce very inaccurate predictions if quantitative trait loci exhibit dominance.

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Available from: John K Kelly, Feb 04, 2015
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    • "In partially selfing populations, responses to selection can depart from those predicted by additive genetic variances and covariances, depending on the strength of directional dominance. Models suggest that such effects are expected to be similar between the two species of Schiedea, assuming dominance variation is similar (Kelly and Williamson 2000), because they have similar levels of inbreeding depression (0.6–0.8 in S. adamantis and S. salicaria, respectively ) as well as outcrossing rates. Effects of inbreeding may be low in any case because a fixation index near zero in flowering adults suggests that inbred individuals do not survive to flower in S. adamantis (Sakai et al. 1997) or S. salicaria (A. "
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    Evolution 11/2010; 65(3):757-70. DOI:10.1111/j.1558-5646.2010.01172.x · 4.61 Impact Factor
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    • "The partitioning of the mean phenotype (eq. 1) can also be used to predict response to multivariate selection with inbreeding. Each trait is associated with a specific value for ␮ O and ␮ I and the population is described by the two vectors of means (Kelly and Williamson 2000). A distinct matrix of genetic quantities is used to predict changes in the values of ␮ O and ␮ I for each trait (Kelly 1999b). "
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    ABSTRACT: The mating system of a population profoundly influences its evolution. Inbreeding alters the balance of evolutionary forces that determine the amount of genetic variation within a population. It redistributes that variation among individuals, altering heritabilities and genetic correlations. Inbreeding even changes the basic relationships between these genetic statistics and response to selection. If populations differing only in mating system are exposed to the same selection pressures, will they respond in qualitatively different ways? Here, we address this question by imposing selection on an index of two negatively correlated traits (flower size and development rate) within experimental populations that reproduce entirely by outcrossing, entirely by self-fertilizing, or by a mixture of outcrossing and selfing. Entirely selfing populations responded mainly by evolving larger flowers whereas outcrossing populations also evolved more rapid development. Divergence occurred despite an equivalent selection regime and no direct effect of mating system on fitness. The study provides an experimental demonstration of how the interaction of selection, genetic drift, and mating system can produce dramatic short-term changes in trait means, variances, and covariances.
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    • "If alleles are nearly additive in their effects, the inbreeding components will be small relative to V A . Under these conditions, a model based on V A alone can yield accurate predictions of evolutionary change even with high levels of inbreeding (Kelly and Williamson, 2000). If dominance is substantial, however, the model based on V A can be very inaccurate. "
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    ABSTRACT: The additive genetic variance, V(A), is frequently used as a measure of evolutionary potential in natural plant populations. Many plants inbreed to some extent; a notable observation given that random mating is essential to the model that predicts evolutionary change from V(A). With inbreeding, V(A) is not the only relevant component of genetic variation. Several nonadditive components emerge from the combined effects of inbreeding and genetic dominance. An important empirical question is whether these components are quantitatively significant. We use maximum likelihood estimation to extract estimates for V(A) and the nonadditive 'inbreeding components' from an experimental study of the wildflower Mimulus guttatus. The inbreeding components contribute significantly to four of five floral traits, including several measures of flower size and stigma-anther separation. These results indicate that inbreeding will substantially alter the evolutionary response to natural selection on floral characters.
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