A non-zero variance of Tajima's estimator for two sequences even for infinitely many unlinked loci.

The population-scaled mutation rate, θ, is informative on the effective population size and is thus widely used in population genetics. We show that for two sequences and n unlinked loci, the variance of Tajima's estimator (θˆ), which is the average number of pairwise differences, does not vanish even as n→∞. The non-zero variance of θˆ results from a (weak) correlation between coalescence times even at unlinked loci, which, in turn, is due to the underlying fixed pedigree shared by gene genealogies at all loci. We derive the correlation coefficient under a diploid, discrete-time, Wright-Fisher model, and we also derive a simple, closed-form lower bound. We also obtain empirical estimates of the correlation of coalescence times under demographic models inspired by large-scale human genealogies. While the effect we describe is small (Varθˆ∕θ2≈ONe-1), it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci.

Empirical Bayes Estimation of Coalescence Times from Nucleotide Sequence Data.

We demonstrate the advantages of using information at many unlinked loci to better calibrate estimates of the time to the most recent common ancestor (TMRCA) at a given locus. To this end, we apply a simple empirical Bayes method to estimate the TMRCA. This method is both asymptotically optimal, in the sense that the estimator converges to the true value when the number of unlinked loci for which we have information is large, and has the advantage of not making any assumptions about demographic history. The algorithm works as follows: we first split the sample at each locus into inferred left and right clades to obtain many estimates of the TMRCA, which we can average to obtain an initial estimate of the TMRCA. We then use nucleotide sequence data from other unlinked loci to form an empirical distribution that we can use to improve this initial estimate.

Effects of the population pedigree on genetic signatures of historical demographic events.

Genetic variation among loci in the genomes of diploid biparental organisms is the result of mutation and genetic transmission through the genealogy, or population pedigree, of the species. We explore the consequences of this for patterns of variation at unlinked loci for two kinds of demographic events: the occurrence of a very large family or a strong selective sweep that occurred in the recent past. The results indicate that only rather extreme versions of such events can be expected to structure population pedigrees in such a way that unlinked loci will show deviations from the standard predictions of population genetics, which average over population pedigrees. The results also suggest that large samples of individuals and loci increase the chance of picking up signatures of these events, and that very large families may have a unique signature in terms of sample distributions of mutant alleles.

Gene genealogies within a fixed pedigree, and the robustness of Kingman's coalescent.

We address a conceptual flaw in the backward-time approach to population genetics called coalescent theory as it is applied to diploid biparental organisms. Specifically, the way random models of reproduction are used in coalescent theory is not justified. Instead, the population pedigree for diploid organisms--that is, the set of all family relationships among members of the population--although unknown, should be treated as a fixed parameter, not as a random quantity. Gene genealogical models should describe the outcome of the percolation of genetic lineages through the population pedigree according to Mendelian inheritance. Using simulated pedigrees, some of which are based on family data from 19th century Sweden, we show that in many cases the (conceptually wrong) standard coalescent model is difficult to reject statistically and in this sense may provide a surprisingly accurate description of gene genealogies on a fixed pedigree. We study the differences between the fixed-pedigree coalescent and the standard coalescent by analysis and simulations. Differences are apparent in recent past, within ≈

Contrasting theory with the empirical data of species recognition.

We tested hypotheses on how animals should respond to heterospecifics encountered in the environment. Hypotheses were formulated from models parameterized to emphasize four factors that are expected to influence species discrimination: mating and territorial interactions; sex differences in resource value; environments in which heterospecifics were common or rare; and the type of identity cues available for species recognition. We also considered the role of phylogeny on contemporary responses to heterospecifics. We tested the extent these factors explained variation among taxa in species discrimination using a meta-analysis of three decades of species recognition research. A surprising outcome was the absence of a general predictor of when species discrimination would most likely occur. Instead, species discrimination is dictated by the benefits and costs of responding to a conspecific or heterospecific that are governed by the specific circumstances of a given species. The phylogeny of species recognition provided another unexpected finding: the evolutionary relationships among species predicted whether courting males within species-but not females-would discriminate against heterospecifcs. This implies that species recognition has evolved quite differently in the sexes. Finally, we identify common pitfalls in experimental design that seem to have affected some studies (e.g., poor statistical power) and provide recommendations for future research.