Using rare mutations to estimate population divergence times: a maximum likelihood approach

Ethnogenomic diversity of Caucasus, Daghestan

Autosomal short-tandem repeats (STRs) were typed in ethnic populations of Kubachians, Dargins, Avars, Lezgins, Kumiks, and Nogais of the Caucasus (Daghestan, Russia) at the University of Utah. Daghestan ethnic populations demonstrated differences in STR allele frequency distributions, but these differences were much lower among these ethnic groups compared to worldwide ethnic groups. The observed genetic diversity was low while F(ST) values were high, both of which provided supporting evidence for small population sizes and high levels of isolation among the ethnic groups. An analysis of genetic distance from the three major continents, encompassing Daghestan populations and groups, reveals three distinct clusters: all populations of African affiliation, European and Daghestan populations except the Nogais, and Asian populations with ethnic Nogais.

Statistical phylogeography

While studies of phylogeography and speciation in the past have largely focused on the documentation or detection of significant patterns of population genetic structure, the emerging field of statistical phylogeography aims to infer the history and processes underlying that structure, and to provide objective, rather than ad hoc explanations. Methods for parameter estimation are now commonly used to make inferences about demographic past. Although these approaches are well developed statistically, they typically pay little attention to geographical history. In contrast, methods that seek to reconstruct phylogeographic history are able to consider many alternative geographical scenarios, but are primarily nonstatistical, making inferences about particular biological processes without explicit reference to stochastically derived expectations. We advocate the merging of these two traditions so that statistical phylogeographic methods can provide an accurate representation of the past, consider a diverse array of processes, and yet yield a statistical estimate of that history. We discuss various conceptual issues associated with statistical phylogeographic inferences, considering especially the stochasticity of population genetic processes and assessing the confidence of phylogeographic conclusions. To this end, we present some empirical examples that utilize a statistical phylogeographic approach, and then by contrasting results from a coalescent-based approach to those from Templeton's nested cladistic analysis (NCA), we illustrate the importance of assessing error. Because NCA does not assess error in its inferences about historical processes or contemporary gene flow, we performed a small-scale study using simulated data to examine how our conclusions might be affected by such unconsidered errors. NCA did not identify the processes used to simulate the data, confusing among deterministic processes and the stochastic sorting of gene lineages. There is as yet insufficient justification of NCA's ability to accurately infer or distinguish among alternative processes. We close with a discussion of some unresolved problems of current statistical phylogeographic methods to propose areas in need of future development.

Estimating allele age

The age of an allele can be estimated both from genetic variation among different copies (intra-allelic variation) and from its frequency. Estimates based on intra-allelic variation follow from the exponential decay of linkage disequilibrium because of recombination and mutation. The confidence interval depends both on the uncertainty in recombination and mutation rates and on randomness of the genealogy of chromosomes that carry the allele (the intra-allelic genealogy). Several approximate methods to account for variation in the intra-allelic genealogy have been derived. Allele frequency alone also provides an estimate of age. Estimates based on frequency and on intra-allelic variability can be combined to provide a more accurate estimate or can be contrasted to show that an allele has been subject to natural selection. These methods have been applied to numerous cases, including alleles associated with cystic fibrosis, idiopathic torsion dystonia, and resistance to infection by HIV. We emphasize that estimates of allele age depend on assumptions about demographic history and natural selection.

Using linked markers to infer the age of a mutation

Advances in sequencing and genotyping technologies over the last decade have enabled geneticists to easily characterize genetic variation at the nucleotide level. Hundreds of genes harboring mutations associated with genetic disease have now been identified by positional cloning. Using variation at closely linked genetic markers, it is possible to predict the times in the past at which particular mutations arose. Such studies suggest that many of the rare mutations underlying human genetic disorders are relatively young. Studies of variation at genetic markers linked to particular mutations can provide insights into human geographic history, and historical patterns of natural selection and disease, that are not available from other sources. We review two approaches for estimating allele age using variation at linked genetic markers. A phylogenetic approach aims to reconstruct the gene tree underlying a sample of chromosomes carrying a particular mutation, obtaining a "direct" estimate of allele age from the age of the root of this tree. A population genetic approach relies on models of demography, mutation, and/or recombination to estimate allele age without explicitly reconstructing the gene tree. Phylogenetic methods are best suited for studies of ancient mutations, while population genetic methods are better suited for studies of recent mutations. Methods that rely on recombination to infer the ages of alleles can be fine-tuned by choosing linked markers at optimal map distances to maximize the information available about allele age. A limitation of methods that rely on recombination is the frequent lack of a fine-scale linkage map. Maximum likelihood and Bayesian methods for estimating allele age that rely on intensive numerical computation are described, as well as "composite" likelihood and moment-based methods that lead to simple estimators. The former provide more accurate estimates (particularly for large samples of chromosomes) and should be employed if computationally practical.