A multivariate analysis of genetic constraints to life history evolution in a wild population of red deer.
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We use factor analytic modeling of the genetic variancecovariance matrix ( G: ) to reduce the dimensionality of the problem and take a multivariate approach to estimating genetic constraints.We found limited support for genetic constraint through genetic covariances between traits, both within sex and between sexes.We discuss these results with respect to other recent findings and to the problems of estimating these parameters for natural populations.
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Affiliation: Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh, EH9 3JT, United Kingdom craig.walling@ed.ac.uk.
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Mentions: Estimates of β and G have associated error and thus so do values calculated from them [e.g., , θ, and e(β)]. Errors in these estimates were approximated using an MC simulation algorithm (see also Morrissey et al. 2012a). Briefly, we drew 100,000 multivariate random normal (MVN) values of S, P, and G, using the maximumlikelihood estimates of these parameters (from ASReml) as the mean and the variance covariance matrices of these parameter estimates as the variance (again these are given in ASReml). These 100,000 values were then combined as appropriate in Equations 5, 4, 6, 7, and 9 to produce 100,000 estimates of β, , θ, e(β), and Re. The 95% credible interval (CI) around these values was then calculated using the quantile function in R and used as an estimate of the 95% credible interval around each parameter estimate. It should be noted that this method assumes the sampling errors in the estimates of variances and covariances are multivariate normal. For angles θ1, θ2, θ3, θ5_bs, and θ6_bs (which are all defined as angles between two vectors) and for all values of evolvability, estimates cannot be negative and thus interpreting a lack of overlap of the 95% CI with zero as indicative of the value differing from zero is not valid. As such, statistical hypothesis tests have limited meaning and we therefore assessed statistical support for substantially nonzero values by examining the distribution of MC samples (see Figure 2, Figure 3, and Figure 4). In practice, this involves visual inspection of the distributions of estimates and, when the distribution is concentrated close to zero (i.e., is associated with left truncation and strong right skew), drawing conclusions equivalent to those associated with failure to reject a hypothesis. 
View Article: PubMed Central  PubMed
Affiliation: Institute of Evolutionary Biology, School of Biological Sciences, University of Edinburgh, Edinburgh, EH9 3JT, United Kingdom craig.walling@ed.ac.uk.