Academic journal article Genetics

Selection for Environmental Variation: A Statistical Analysis and Power Calculations to Detect Response

Academic journal article Genetics

Selection for Environmental Variation: A Statistical Analysis and Power Calculations to Detect Response

Article excerpt


Data from uterine capacity in rabbits (litter size) were analyzed to determine whether the environmental variance was partly genetically determined. The fit of a classical homogeneous variance mixed linear (HOM) model and that of a genetically structured heterogeneous variance mixed linear (HET) model were compared. Various methods to assess the quality of fit favor the HET model. The posterior mean (95% posterior interval) of the additive genetic variance affecting the environmental variance was 0:16 (0:10; 0:25) and the corresponding number for the coefficient of correlation between genes affecting mean and variance was -0:74 (-0:90;-0:52). It is argued that stronger support for the HET model than that derived from statistical analysis of data would be provided by a successful selection experiment designed to modify the environmental variance. A simple selection criterion is suggested (average squared deviation from the mean of repeated records within individuals) and its predicted response and variance under the HET model are derived. This is used to determine the appropriate size and length of a selection experiment designed to change the environmental variance. Results from the analytical expressions are compared with those obtained using simulation. There is good agreement provided selection intensity is not intense.

(ProQuest: ... denotes formulae omitted.)

THE classical model of quantitative genetics assumes that genotypes affect themeanof a trait but that the environmental variance (variance of phenotype, given genotype) is the same for all genotypes. An extension postulates that both mean and variability differ between genotypes (San Cristobal-Gaudy et al. 1998). The extended model has interesting implications in animal and plant improvement (e.g., Hill and Zhang 2004; Mulder et al. 2007) since it offers the possibility to decrease variation by selection leading to more homogeneous products. In evolutionary biology, a central problem is to understand the forces that maintain phenotypic variation. With the exception of recent work (Zhang andHill 2005),most of the models assume that environmental variance is constant and explain the level of phenotypic variation by invoking a balance between the gain of genetic variance by mutation and its loss by different forms of selection and drift.

Early evidence for a genetic component affecting environmental variation stems from comparison of levels of variation between inbred lines and the F1 cross between them, with inbreds showing in general larger variance (reviewed in Falconer and Mackay 1996). More recent evidence has come fromfitting the model to data on litter size in pigs (SorensenandWaagepetersen 2003), adult weight in snails (Ros et al. 2004), body weight in poultry (Rowe et al. 2006), slaughter weight in pigs (Ibáñez et al. 2007), and litter size and weight at birth in mice (Gutierrez et al. 2006). Stronger, more direct support, not derived from fitting the genetically structured heterogeneous variance model, but from analyses of experiments with isogenic chromosome substitution lines of Drosophila, was provided byMackay and Lyman (2005). Here, homozygote inbred lines that differed in chromosome 2 or 3 were created, and variation between individuals in abdominal and sternopleural bristle number was computed. Difference in within-line variance, between lines, was confirmed. Since individuals within a line are effectively replicates of the same genotype, difference in within-line variance, between lines, provides evidence for the presence of genes located in chromosomes 2 and 3 affecting environmental variance.

With the exception of experimental organisms such as Drosophila and some plant or fish species where replicated individuals of the same genotype (clones) can be produced and variation between individuals composing the clone measured directly, support for the presence of genes controlling environmental variation can be found, fitting themodel to data and studying the quality of the fit using modern computational tools. …

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