Estimators for QST and coalescence times

Heritability within groups is uninformative about differences among groups: Cases from behavioral, evolutionary, and statistical genetics

Without the ability to control or randomize environments (or genotypes), it is difficult to determine the degree to which observed phenotypic differences between two groups of individuals are due to genetic vs. environmental differences. However, some have suggested that these concerns may be limited to pathological cases, and methods have appeared that seem to give-directly or indirectly-some support to claims that aggregate heritable variation within groups can be related to heritable variation among groups. We consider three families of approaches: the "between-group heritability" sometimes invoked in behavior genetics, the statistic [Formula: see text] used in empirical work in evolutionary quantitative genetics, and methods based on variation in ancestry in an admixed population, used in anthropological and statistical genetics. We take up these examples to show mathematically that information on within-group genetic and phenotypic information in the aggregate cannot separate among-group differences into genetic and environmental components, and we provide simulation results that support our claims. We discuss these results in terms of the long-running debate on this topic.

Multivariate morphometrics, quantitative genetics, and neutral theory: Developing a "modern synthesis" for primate evolutionary morphology

Anthropologists are increasingly turning to explicit model-bound evolutionary approaches for understanding the morphological diversification of humans and other primate lineages. Such evolutionary morphological analyses rely on three interconnected conceptual frameworks; multivariate morphometrics for quantifying similarity and differences among taxa, quantitative genetics for modeling the inheritance and evolution of morphology, and neutral theory for assessing the likelihood that taxon diversification is due to stochastic processes such as genetic drift. Importantly, neutral theory provides a framework for testing more parsimonious explanations for observed morphological differences before considering more complex adaptive scenarios. However, the consistency with which these concepts are applied varies considerably, which mirrors some of the theoretical obstacles faced during the "modern synthesis" of classical population genetics in the early 20th century. Here, each framework is reviewed and some potential stumbling blocks to the full conceptual integration of multivariate morphometrics, quantitative genetics, and neutral theory are considered.

Estimators for QST and coalescence times

Comparisons of QST to FST can provide insights into the evolutionary processes that lead to differentiation, or lack thereof, among the phenotypes of different groups (e.g., populations, species), and these comparisons have been performed on a variety of taxa, including humans. Here, I show that for neutrally evolving (i.e., by genetic drift, mutation, and gene flow alone) quantitative characters, the two commonly used QST estimators have somewhat different interpretations in terms of coalescence times, particularly when the number of groups that have been sampled is small. A similar situation occurs for FST estimators. Consequently, when observations come from only a small number of groups, which is not an unusual situation, it is important to match estimators appropriately when comparing QST to FST.