Publications

Book
Wakeley J. Coalescent Theory: An Introduction. Greenwood Village: Roberts & Company Publishers; 2009.Abstract
Not the abstract, but a note. This book is available from Macmillan. The title above links directly to their web site.
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Book Chapter
Wakeley J. Coalescent models. In: Human Population Genomics, K. E. Lohmueller, R. Nielsen (eds.). Springer Nature Switzerland AG ; 2021. Publisher's Version
Wakeley J, Wilton PR. Coalescent and models of identity by descent. In: Encyclopedia of Evolutionary Biology. Vol 1. Oxford: Academic Press ; 2016 :287-292. (pdf)
Wakeley J. Natural selection and coalescent theory. In: Evolution since Darwin: The First 150 Years. Sunderland, MA: Sinauer and Associates ; 2010 :119-149. short draft (pdf) long draft (pdf)
Wakeley J. Metapopulations and coalescent theory. In: Ecology, Genetics, and Evolution of Metapopulations. Amsterdam, Boston etc. Elsevier Academic Press ; 2004 :175-198.
Wakeley J. Inferences about the structure and history of populations: coalescents and intraspecific phylogeography. In: The Evolution of Population Biology - Modern Synthesis. Cambridge: Cambridge University Press ; 2002 :193-215. (pdf)
Wakeley J, Hey J. Testing speciation models with DNA sequence data. In: Molecular approaches to ecology and evolution. Basel, Boston & Berlin: Birkhauser ; 1998 :157-175.
Journal Article
Diamantidis D, Fan W-T, Birkner M, Wakeley J. Bursts of coalescence within population pedigrees whenever big families occur. Genetics. 2024 :iyae030. Accepted Manuscript
Wakeley J, Fan W-T, Koch E, Sunyaev S. Recurrent mutation in the ancestry of a rare variant. Genetics. 2023 :iyad049. Publisher's Version
McAvoy A, Wakeley J. Evaluating the structure-coefficient theorem of evolutionary game theory. Proceedings of the National Academy of Sciences, USA. 2022;119 :e2119656119. Publisher's Version
Harney É, Patterson N, Reich D, Wakeley J. Assessing the performance of qpAdm: a statistical tool for studying population admixture. Genetics. 2021;iyaa045.Abstract
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. We performed a simulation study to assess the behavior of qpAdm under various scenarios in order to identify areas of potential weakness and establish recommended best practices for use. We find that qpAdm is a robust tool that yields accurate results in many cases, including when data coverage is low, there are high rates of missing data or ancient DNA damage, or when diploid calls cannot be made. However, we caution against co-analyzing ancient and present-day data, the inclusion of an extremely large number of reference populations in a single model, and analyzing population histories involving extended periods of gene flow. We provide a user guide suggesting best practices for the use of qpAdm.
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Salagnac O, Wakeley J. The consequences of switching strategies in a two-player iterated survival game. Journal of Mathematical Biology. 2021;82 :17.Abstract
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.  We find that incentives for or against cooperation depend on the number of defections at the end of the game, as opposed to the number of steps in the game.  Broadly, cooperation is supported when the survival prospects of lone individuals are relatively bleak.  Specifically, we find three critical values or cutoffs for the loner survival probability which, in concert with other survival parameters, determine the incentives for or against cooperation.  One cutoff determines the existence of an optimal number of defections against a fully cooperative partner, one determines whether additional defections eventually become disfavored as the number of defections by the partner increases, and one determines whether additional cooperations eventually become favored as the number of defections by the partner increases.  We obtain expressions for these switch-points and for optimal numbers of defections against partners with various strategies.  These typically involve small numbers of defections even in very long games. We show that potentially long stretches of equilibria may exist, in which there is no incentive to defect more or cooperate more.  We describe how individuals find equilibria in best-response walks among n-step strategies.
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Wakeley J. Developments in coalescent theory from single loci to chromosomes. Theoretical Population Biology. 2020;133 :56-64. (pdf)
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.
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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.

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King L, Wakeley J, Carmi S. A non-zero variance of Tajima’s estimator for two sequences even for infinitely many unlinked loci. Theoretical Population Biology. 2018;122 :22-29.Abstract
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 (ˆθ), which is the average number of pairwise differences, does not vanish even as n → ∞. The non-zero variance of ˆθ 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 (Var [ˆθ]/θ2 ≈ O(N−1e)), it is important to recognize this feature of statistical population genetics, which runs counter to commonly held notions about unlinked loci.
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McAvoy A, Fraiman N, Hauert C, Wakeley J, Nowak MA. Public goods games in populations with fluctuating size. Theoretical Population Biology. 2018;121 :72-84.Abstract
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. Survival of the population may depend on which strategy prevails in the game dynamics. Studying cooperative dilemmas, it is a natural feature of such a model that cooperators enable survival, while defectors drive extinction. Although defectors are favored for any mixed population, random drift could lead to their elimination and the resulting pure-cooperator population could survive. On the other hand, if the defectors remain, then the population will quickly go extinct because the frequency of cooperators steadily declines and defectors alone cannot survive. In a mutation–selection model, we find that (i) a steady supply of cooperators can enable long-term population survival, provided selection is sufficiently strong, and (ii) selection can increase the abundance of cooperators but reduce their relative frequency. Thus, evolutionary game dynamics in populations with variable size generate a multifaceted notion of what constitutes a trait’s long-term success.
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Wilton PR, Baduel P, Landon MM, Wakeley J. Population structure and coalescence in pedigrees: Comparisons to the structured coalescent and a framework for inference. Theoretical Population Biology. 2017;115 :1-12.Abstract

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. We find that the pedigree creates deviations away from the predictions of the structured coalescent that persist on a longer timescale than in the case of panmictic populations. Nevertheless, we find that the structured coalescent provides a reasonable approximation for the coalescent process in structured population pedigrees so long as migration events are moderately frequent and there are no migration events in the recent pedigree of the sample. When there are migration events in the recent sample pedigree, we find that distributions of coalescence in the sample can be modeled as a mixture of distributions from different initial sample configurations. We use this observation to motivate a maximum-likelihood approach for inferring migration rates and mutation rates jointly with features of the pedigree such as recent migrant ancestry and recent relatedness. Using simulation, we show that our inference framework accurately recovers long-term migration rates in the presence of recent migration events in the sample pedigree.

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King L, Wakeley J. Empirical Bayes estimation of coalescence times from nucleotide sequence data. Genetics. 2016;204 :249-257.Abstract

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.

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