We are devoted to the study of theoretical population genetics. The goal of population genetics is to identify and understand the forces that produce and maintain genetic variation in natural populations. These forces include mutation (also recombination and gene conversion), natural selection, various kinds of population structure (e.g. subdivision with migration), and the random fluctuations of gene frequencies through time known as genetic drift. We study these forces mathematically, using both analysis and computation. We also develop statistical methods to make inferences about these forces from DNA sequences or other kinds of genetic data. For more information about specific areas of research, follow the leads to lab members.


Edelman NB, Frandsen PB, Miyagi M, et al. Genomic architecture and introgression shape a butterfly radiation. Science. 2019;366 (6465) :594-599. Publisher's VersionAbstract
We used 20 de novo genome assemblies to probe the speciation history and architecture of gene flow in rapidly radiating Heliconius butterflies. Our tests to distinguish incomplete lineage sorting from introgression indicate that gene flow has obscured several ancient phylogenetic relationships in this group over large swathes of the genome. Introgressed loci are underrepresented in low-recombination and gene-rich regions, consistent with the purging of foreign alleles more tightly linked to incompatibility loci. Here, we identify a hitherto unknown inversion that traps a color pattern switch locus. We infer that this inversion was transferred between lineages by introgression and is convergent with a similar rearrangement in another part of the genus. These multiple de novo genome sequences enable improved understanding of the importance of introgression and selective processes in adaptive radiation.
Palacios JA, Veber A, Cappello L, et al. Bayesian Estimation of Population Size Changes by Sampling Tajima’s Trees. Genetics. 2019;213 :967-986.Abstract
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. We provide a new algorithm for efficient and exact likelihood calculations for data without recombination, which exploits a directed acyclic graph and a correspondingly tailored Markov Chain Monte Carlo method. We compare the performance of our Bayesian Estimation of population size changes by Sampling Tajima’s Trees (BESTT) with a popular implementation of coalescent-based inference in BEAST using simulated and human data. We empirically demonstrate that BESTT can accurately infer effective population sizes, and it further provides an efficient alternative to the Kingman’s coalescent. The algorithms described here are implemented in the R package phylodyn, which is available for download at https://github.com/JuliaPalacios/phylodyn.
Wakeley J, Nowak M. A two-player iterated survival game. Theoretical Population Biology. 2019;125 :38–55.Abstract

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. We consider individuals with hardwired, unconditional behaviors or strategies. When both players are present, each step is a symmetric two-player game. The overall survival of the two individuals forms a Markov chain. As the number of iterations tends to infinity, all probabilities of survival decrease to zero. We obtain general, analytical results for n-step payoffs and use these to describe how the game changes as n increases. In order to predict changes in the frequency of a cooperative strategy over time, we embed the survival game in three different models of a large, well-mixed population. Two of these models are deterministic and one is stochastic. Offspring receive their parent’s type without modification and fitnesses are determined by the game. Increasing the number of iterations changes the prospects for cooperation. All models become neutral in the limit (n ). Further, if pairs of cooperative individuals survive together with high probability, specifically higher than for any other pair and for either type when it is alone, then cooperation becomes favored if the number of iterations is large enough. This holds regardless of the structure of pairwise interactions in a single step. Even if the single-step interaction is a Prisoner’s Dilemma, the cooperative type becomes favored. Enhanced survival is crucial in these iterated evolutionary games: if players in pairs start the game with a fitness deficit relative to lone individuals, the prospects for cooperation can become even worse than in the case of a single-step game.