The impact of simplifications on the performance of a finite element model of a Macaca fascicularis cranium.

In recent years finite element analysis (FEA) has emerged as a useful tool for the analysis of skeletal form-function relationships. While this approach has obvious appeal for the study of fossil specimens, such material is often fragmentary with disrupted internal architecture and can contain matrix that leads to errors in accurate segmentation. Here we examine the effects of varying the detail of segmentation and material properties of teeth on the performance of a finite element model of a Macaca fascicularis cranium within a comparative functional framework. Cranial deformations were compared using strain maps to assess differences in strain contours and Procrustes size and shape analyses, from geometric morphometrics, were employed to compare large scale deformations. We show that a macaque model subjected to biting can be made solid, and teeth altered in material properties, with minimal impact on large scale modes of deformation. The models clustered tightly by bite point rather than by modeling simplification approach, and fell out as being distinct from another species. However localized fluctuations in predicted strain magnitudes were recorded with different modeling approaches, particularly over the alveolar region. This study indicates that, while any model simplification should be undertaken with care and attention to its effects, future applications of FEA to fossils with unknown internal architecture may produce reliable results with regard to general modes of deformation, even when detail of internal bone architecture cannot be reliably modeled.

Type I error rates for testing genetic drift with phenotypic covariance matrices: a simulation study.

Studies of evolutionary divergence using quantitative genetic methods are centered on the additive genetic variance-covariance matrix (G) of correlated traits. However, estimating G properly requires large samples and complicated experimental designs. Multivariate tests for neutral evolution commonly replace average G by the pooled phenotypic within-group variance-covariance matrix (W) for evolutionary inferences, but this approach has been criticized due to the lack of exact proportionality between genetic and phenotypic matrices. In this study, we examined the consequence, in terms of type I error rates, of replacing average G by W in a test of neutral evolution that measures the regression slope between among-population variances and within-population eigenvalues (the Ackermann and Cheverud [AC] test) using a simulation approach to generate random observations under genetic drift. Our results indicate that the type I error rates for the genetic drift test are acceptable when using W instead of average G when the matrix correlation between the ancestral G and P is higher than 0.6, the average character heritability is above 0.7, and the matrices share principal components. For less-similar G and P matrices, the type I error rates would still be acceptable if the ratio between the number of generations since divergence and the effective population size (t/N(e)) is smaller than 0.01 (large populations that diverged recently). When G is not known in real data, a simulation approach to estimate expected slopes for the AC test under genetic drift is discussed.