A function-valued trait approach to estimating the genetic basis of size at age and its potential role in fisheries-induced evolution.

Natural selection is inherently a multivariate phenomenon. The selection pressure on size (natural and artificial) and the age at which selection occurs is likely to induce evolutionary changes in growth rates across the entire life history. However, the covariance structure that will determine the path of evolution for size at age has been studied in only a few fish species. We therefore estimated the genetic covariance function for size throughout ontogeny using Atlantic silversides () as the model system. Over a 3-year period, a total of 542 families were used to estimate the genetic covariance in length at age from hatch through maturity. The function-valued trait approach was employed to estimate the genetic covariance functions. A Bayesian hierarchical model was used to account for the unbalanced design, unequal measurement intervals, unequal sample sizes, and family-aggregated data. To improve mixing, we developed a two-stage sampler using a Gibbs sampler to generate the posterior of a well-mixing approximate model followed by an importance sampler to draw samples from posterior of the completely specified model. We found that heritability of length is age-specific and there are strong genetic correlations in length across ages that last 30 days or more. We used these estimates in a hypothetical model predicting the evolutionary response to harvesting following a single generation of selection under both sigmoidal and unimodal patterns of gear selectivity to illustrate the potential outcomes of ignoring the genetic correlations. In these scenarios, genetic correlations were found to have a strong effect on both the direction and magnitude of the response to harvest selection.