Latent mutations in the ancestries of alleles under selection.

We consider a single genetic locus with two alleles A and A in a large haploid population. The locus is subject to selection and two-way, or recurrent, mutation. Assuming the allele frequencies follow a Wright-Fisher diffusion and have reached stationarity, we describe the asymptotic behaviors of the conditional gene genealogy and the latent mutations of a sample with known allele counts, when the count n of allele A is fixed, and when either or both the sample size n and the selection strength |α| tend to infinity.

Bursts of coalescence within population pedigrees whenever big families occur.

We consider a simple diploid population-genetic model with potentially high variability of offspring numbers among individuals. Specifically, against a backdrop of Wright-Fisher reproduction and no selection, there is an additional probability that a big family occurs, meaning that a pair of individuals has a number of offspring on the order of the population size. We study how the pedigree of the population generated under this model affects the ancestral genetic process of a sample of size two at a single autosomal locus without recombination.

TRAILS: Tree reconstruction of ancestry using incomplete lineage sorting.

Genome-wide genealogies of multiple species carry detailed information about demographic and selection processes on individual branches of the phylogeny. Here, we introduce TRAILS, a hidden Markov model that accurately infers time-resolved population genetics parameters, such as ancestral effective population sizes and speciation times, for ancestral branches using a multi-species alignment of three species and an outgroup. TRAILS leverages the information contained in incomplete lineage sorting fragments by modelling genealogies along the genome as rooted three-leaved trees, each with a topology and two coalescent events happening in discretized time intervals within the phylogeny.

Recurrent mutation in the ancestry of a rare variant.

Recurrent mutation produces multiple copies of the same allele which may be co-segregating in a population. Yet, most analyses of allele-frequency or site-frequency spectra assume that all observed copies of an allele trace back to a single mutation. We develop a sampling theory for the number of latent mutations in the ancestry of a rare variant, specifically a variant observed in relatively small count in a large sample.

Evaluating the structure-coefficient theorem of evolutionary game theory.

In order to accommodate the empirical fact that population structures are rarely simple, modern studies of evolutionary dynamics allow for complicated and highly heterogeneous spatial structures. As a result, one of the most difficult obstacles lies in making analytical deductions, either qualitative or quantitative, about the long-term outcomes of evolution. The "structure-coefficient" theorem is a well-known approach to this problem for mutation-selection processes under weak selection, but a general method of evaluating the terms it comprises is lacking.

Assessing the performance of qpAdm: a statistical tool for studying population admixture.

qpAdm is a statistical tool for studying the ancestry of populations with histories that involve admixture between two or more source populations. Using qpAdm, it is possible to identify plausible models of admixture that fit the population history of a group of interest and to calculate the relative proportion of ancestry that can be ascribed to each source population in the model. Although qpAdm is widely used in studies of population history of human (and nonhuman) groups, relatively little has been done to assess its performance.

The consequences of switching strategies in a two-player iterated survival game.

We consider two-player iterated survival games in which players are able to switch from a more cooperative behavior to a less cooperative one at some step of an n-step game. Payoffs are survival probabilities and lone individuals have to finish the game on their own. We explore the potential of these games to support cooperation, focusing on the case in which each single step is a Prisoner's Dilemma.

Bayesian Estimation of Population Size Changes by Sampling Tajima's Trees.

The large state space of gene genealogies is a major hurdle for inference methods based on Kingman's coalescent. Here, we present a new Bayesian approach for inferring past population sizes, which relies on a lower-resolution coalescent process that we refer to as "Tajima's coalescent." Tajima's coalescent has a drastically smaller state space, and hence it is a computationally more efficient model, than the standard Kingman coalescent.

Some topics in theoretical population genetics: Editorial commentaries on a selection of Marc Feldman's TPB papers.

This article consists of commentaries on a selected group of papers of Marc Feldman published in Theoretical Population Biology from 1970 to the present. The papers describe a diverse set of population-genetic models, covering topics such as cultural evolution, social evolution, and the evolution of recombination. The commentaries highlight Marc Feldman's role in providing mathematically rigorous formulations to explore qualitative hypotheses, in many cases generating surprising conclusions.

A two-player iterated survival game.

We describe an iterated game between two players, in which the payoff is to survive a number of steps. Expected payoffs are probabilities of survival. A key feature of the game is that individuals have to survive on their own if their partner dies.

Public goods games in populations with fluctuating size.

Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended Wright-Fisher process with variable population size. In such a scenario, it is possible that the entire population becomes extinct.

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.

Population structure and coalescence in pedigrees: Comparisons to the structured coalescent and a framework for inference.

Contrary to what is often assumed in population genetics, independently segregating loci do not have completely independent ancestries, since all loci are inherited through a single, shared population pedigree. Previous work has shown that the non-independence between gene genealogies of independently segregating loci created by the population pedigree is weak in panmictic populations, and predictions made from standard coalescent theory are accurate for populations that are at least moderately sized. Here, we investigate patterns of coalescence in pedigrees of structured populations.

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.

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.

Vulnerability to depression is associated with a failure to acquire implicit social appraisals.

Major depressive disorder (MDD) is associated with disrupted relationships with partners, family, and peers. These problems can precipitate the onset of clinical illness, influence severity and the prospects for recovery. Here, we investigated whether individuals who have recovered from depression use interpersonal signals to form favourable appraisals of others as social partners.

Leveraging Distant Relatedness to Quantify Human Mutation and Gene-Conversion Rates.

The rate at which human genomes mutate is a central biological parameter that has many implications for our ability to understand demographic and evolutionary phenomena. We present a method for inferring mutation and gene-conversion rates by using the number of sequence differences observed in identical-by-descent (IBD) segments together with a reconstructed model of recent population-size history. This approach is robust to, and can quantify, the presence of substantial genotyping error, as validated in coalescent simulations.

Bayesian Nonparametric Inference of Population Size Changes from Sequential Genealogies.

Sophisticated inferential tools coupled with the coalescent model have recently emerged for estimating past population sizes from genomic data. Recent methods that model recombination require small sample sizes, make constraining assumptions about population size changes, and do not report measures of uncertainty for estimates. Here, we develop a Gaussian process-based Bayesian nonparametric method coupled with a sequentially Markov coalescent model that allows accurate inference of population sizes over time from a set of genealogies.

A renewal theory approach to IBD sharing.

A long genomic segment inherited by a pair of individuals from a single, recent common ancestor is said to be identical-by-descent (IBD). Shared IBD segments have numerous applications in genetics, from demographic inference to phasing, imputation, pedigree reconstruction, and disease mapping. Here, we provide a theoretical analysis of IBD sharing under Markovian approximations of the coalescent with recombination.

Loss and recovery of genetic diversity in adapting populations of HIV.

The evolution of drug resistance in HIV occurs by the fixation of specific, well-known, drug-resistance mutations, but the underlying population genetic processes are not well understood. By analyzing within-patient longitudinal sequence data, we make four observations that shed a light on the underlying processes and allow us to infer the short-term effective population size of the viral population in a patient. Our first observation is that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time, as opposed to several changes simultaneously.

Preliminary evidence that sub-chronic citalopram triggers the re-evaluation of value in intimate partnerships.

Depression frequently involves disrupted inter-personal relationships, while treatment with serotonergic anti-depressants can interfere with libido and sexual function. However, little is known about how serotonin activity influences appraisals of intimate partnerships. Learning more could help to specify how serotonergic mechanisms mediate social isolation in psychiatric illness.

I want to help you, but I am not sure why: gaze-cuing induces altruistic giving.

Detecting subtle indicators of trustworthiness is highly adaptive for moving effectively amongst social partners. One powerful signal is gaze direction, which individuals can use to inform (or deceive) by looking toward (or away from) important objects or events in the environment. Here, across 5 experiments, we investigate whether implicit learning about gaze cues can influence subsequent economic transactions; we also examine some of the underlying mechanisms.