Field heritabilities and lack of correlation of snail shell form and anti-predator function estimated using Bayesian and maximum likelihood methods

Problem: It is often assumed that the heritability of performance traits (function) can be estimated by the heritability of primary traits (e.g. form). It is also frequently assumed that performance traits should be less heritable than primary traits. These assumptions should be carefully evaluated rather than assumed. One common area of study in which these assumptions have been made is anti-predator traits and performance. Organisms: A freshwater aquatic snail species, the Mexican banded spring snail Mexipyrgus churinceanus, endemic to the isolated Cuatro Ciénegas valley in Mexico. The crushing predator of this snail species, the fish Herichthys minckleyi, is also endemic to the valley. We studied the free-ranging snail population. Methods: We estimated narrow-sense heritability of shell thickness and shape (form), and crushing resistance (function) under field conditions. We used multi-locus genotyping to reconstruct a pedigree in a small wild population, and used animal models to estimate genetic and environmental variance components needed to estimate heritabilities. We estimated variance components using Bayesian inferences and also, for comparison, the traditional restricted maximum likelihood approach. We also estimated pairwise phenotypic correlations between traits. Results: The two methods produced similar results, although the maximum likelihood approach was more conservative. The trait closest to fitness (crushing resistance) exhibited the greatest heritability: the heritability of crushing resistance was at least twice as high as the heritability of thickness and shape. No phenotypic correlations were evident between