Continuously fluctuating selection reveals fine granularity of adaptation.

Temporally fluctuating environmental conditions are a ubiquitous feature of natural habitats. Yet, how finely natural populations adaptively track fluctuating selection pressures via shifts in standing genetic variation is unknown1,2. Here we generated genome-wide allele frequency data every 1-2 generations from a genetically diverse population of Drosophila melanogaster in extensively replicated field mesocosms from late June to mid-December (a period of approximately 12 total generations). Adaptation throughout the fundamental ecological phases of population expansion, peak density and collapse was underpinned by extremely rapid, parallel changes in genomic variation across replicates. Yet, the dominant direction of selection fluctuated repeatedly, even within each of these ecological phases. Comparing patterns of change in allele frequency to an independent dataset procured from the same experimental system demonstrated that the targets of selection are predictable across years. In concert, our results reveal a fitness relevance of standing variation that is likely to be masked by inference approaches based on static population sampling or insufficiently resolved time-series data. We propose that such fine-scaled, temporally fluctuating selection may be an important force contributing to the maintenance of functional genetic variation in natural populations and an important stochastic force impacting genome-wide patterns of diversity at linked neutral sites, akin to genetic draft.

A lattice structure for ancestral configurations arising from the relationship between gene trees and species trees.

To a given gene tree topology G and species tree topology S with leaves labeled bijectively from a fixed set X, one can associate a set of ancestral configurations, each of which encodes a set of gene lineages that can be found at a given node of the species tree. We introduce a lattice structure on ancestral configurations, studying the directed graphs that provide graphical representations of lattices of ancestral configurations. For a matching gene tree topology and species tree topology G=S, we present a method for defining the digraph of ancestral configurations from the tree topology by using iterated cartesian products of graphs. We show that a specific set of paths on the digraph of ancestral configurations is in bijection with the set of labeled histories - a well-known phylogenetic object that enumerates possible temporal orderings of the coalescences of a tree. For each of a series of tree families, we obtain closed-form expressions for the number of labeled histories by using this bijection to count paths on associated digraphs. Finally, we prove that our lattice construction extends to nonmatching tree pairs, and we use it to characterize pairs (G,S) having the maximal number of ancestral configurations for a fixed G. We discuss how the construction provides new methods for performing enumerations of combinatorial aspects of gene and species trees.

Cultural transmission of move choice in chess.

The study of cultural evolution benefits from detailed analysis of cultural transmission in specific human domains. Chess provides a platform for understanding the transmission of knowledge due to its active community of players, precise behaviours and long-term records of high-quality data. In this paper, we perform an analysis of chess in the context of cultural evolution, describing multiple cultural factors that affect move choice. We then build a population-level statistical model of move choice in chess, based on the Dirichlet-multinomial likelihood, to analyse cultural transmission over decades of recorded games played by leading players. For moves made in specific positions, we evaluate the relative effects of frequency-dependent bias, success bias and prestige bias on the dynamics of move frequencies. We observe that negative frequency-dependent bias plays a role in the dynamics of certain moves, and that other moves are compatible with transmission under prestige bias or success bias. These apparent biases may reflect recent changes, namely the introduction of computer chess engines and online tournament broadcasts. Our analysis of chess provides insights into broader questions concerning how social learning biases affect cultural evolution.

Conformity and anti-conformity in a finite population.

Conformist and anti-conformist cultural transmission have been studied both empirically, in several species, and theoretically, with population genetic models. Building upon standard, infinite-population models (IPMs) of conformity, we introduce finite-population models (FPMs) and study them via simulation and a diffusion approximation. In previous IPMs of conformity, offspring observe the variants of n adult role models, where n is often three. Numerical simulations show that while the short-term behavior of the FPM with n=3 role models is well approximated by the IPM, stable polymorphic equilibria of the IPM become effective equilibria of the FPM at which the variation persists prior to fixation or loss, and which produce plateaus in curves for fixation probabilities and expected times to absorption. In the FPM with n=5 role models, the population may switch between two effective equilibria, which is not possible in the IPM, or may cycle between frequencies that are not effective equilibria, which is possible in the IPM. In all observed cases of 'equilibrium switching' and 'cycling' in the FPM, model parameters exceed O(1/N), required for the diffusion approximation, resulting in an over-estimation of the actual times to absorption. However, in those cases with n=5 role models that have one effective equilibrium and stable fixation states, even if conformity coefficients exceed O(1/N), the diffusion approximation matches closely the numerical simulations of the FPM. This suggests that the robustness of the diffusion approximation depends not only on the magnitudes of coefficients, but also on the qualitative behavior of the conformity model.

Solving the Arizona search problem by imputation.

An "Arizona search" is an evaluation of the numbers of pairs of profiles in a forensic-genetic database that possess partial or complete genotypic matches; such a search assists in establishing the extent to which a set of loci provides unique identifications. In forensic genetics, however, the potential for performing Arizona searches is constrained by the limited availability of actual forensic profiles for research purposes. Here, we use genotype imputation to circumvent this problem. From a database of genomes, we impute genotypes of forensic short-tandem-repeat (STR) loci from neighboring single-nucleotide polymorphisms (SNPs), searching for partial STR matches using the imputed profiles. We compare the distributions of the numbers of partial matches in imputed and actual profiles, finding close agreement. Despite limited potential for performing Arizona searches with actual forensic STR profiles, the questions that such searches seek to answer can be posed with imputation-based Arizona searches in increasingly large SNP databases.

Approximations to the expectations and variances of ratios of tree properties under the coalescent.

Properties of gene genealogies such as tree height (H), total branch length (L), total lengths of external (E) and internal (I) branches, mean length of basal branches (B), and the underlying coalescence times (T) can be used to study population-genetic processes and to develop statistical tests of population-genetic models. Uses of tree features in statistical tests often rely on predictions that depend on pairwise relationships among such features. For genealogies under the coalescent, we provide exact expressions for Taylor approximations to expected values and variances of ratios Xn/Yn, for all 15 pairs among the variables {Hn,Ln,En,In,Bn,Tk}, considering n leaves and 2≤k≤n. For expected values of the ratios, the approximations match closely with empirical simulation-based values. The approximations to the variances are not as accurate, but they generally match simulations in their trends as n increases. Although En has expectation 2 and Hn has expectation 2 in the limit as n→∞, the approximation to the limiting expectation for En/Hn is not 1, instead equaling π2/3-2≈1.28987. The new approximations augment fundamental results in coalescent theory on the shapes of genealogical trees.