All Publications

  • Cultural transmission of move choice in chess. Proceedings. Biological sciences Lappo, E., Rosenberg, N. A., Feldman, M. W. 2023; 290 (2011): 20231634


    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.

    View details for DOI 10.1098/rspb.2023.1634

    View details for PubMedID 37964528

  • Concordance of spatial graphs CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES Lappo, E. 2023; 66 (4): 1091-1108
  • Conformity and anti-conformity in a finite population. Journal of theoretical biology Lappo, E., Denton, K. K., Feldman, M. W. 2023: 111429


    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.

    View details for DOI 10.1016/j.jtbi.2023.111429

    View details for PubMedID 36746297

  • Approximations to the expectations and variances of ratios of tree properties under the coalescent. G3 (Bethesda, Md.) Lappo, E., Rosenberg, N. A. 2022


    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.

    View details for DOI 10.1093/g3journal/jkac205

    View details for PubMedID 35951748

  • A compendium of covariances and correlation coefficients of coalescent tree properties. Theoretical population biology Alimpiev, E., Rosenberg, N. A. 2021


    Gene genealogies are frequently studied by measuring properties such as their height ( H), length (L), sum of external branches (E), sum of internal branches (I), and mean of their two basal branches (B), and the coalescence times that contribute to the other genealogical features (T). These tree properties and their relationships can provide insight into the effects of population-genetic processes on genealogies and genetic sequences. Here, under the coalescent model, we study the 15 correlations among pairs of features of genealogical trees: Hn, Ln, En, In, Bn, and Tk for a sample of size n, with 2≤k≤n. We report high correlations among Hn, Ln, In, and Bn, with all pairwise correlations of these quantities having values greater than or equal to 6[6zeta(3)+6-pi2]/(pi18+9pi2-pi4)0.84930 in the limit as n, where zeta is the Riemann zeta function. Although En has expectation 2 for all n and Hn has expectation 2 in the n limit, their limiting correlation is 0. The results contribute toward understanding features of the shapes of coalescent trees.

    View details for DOI 10.1016/j.tpb.2021.09.008

    View details for PubMedID 34757022

  • Enumeration of coalescent histories for caterpillar species trees and p-pseudocaterpillar gene trees. Advances in applied mathematics Alimpiev, E., Rosenberg, N. A. 2021; 131


    For a fixed set X containing n taxon labels, an ordered pair consisting of a gene tree topology G and a species tree topology S bijectively labeled with the labels of X possesses a set of coalescent histories-mappings from the set of internal nodes of G to the set of edges of S describing possible lists of edges in S on which the coalescences in G take place. Enumerations of coalescent histories for gene trees and species trees have produced suggestive results regarding the pairs (G, S) that, for a fixed n, have the largest number of coalescent histories. We define a class of 2-cherry binary tree topologies that we term p-pseudocaterpillars, examining coalescent histories for non-matching pairs (G, S) in the case in which S has a caterpillar shape and G has a p-pseudocaterpillar shape. Using a construction that associates coalescent histories for (G, S) with a class of "roadblocked" monotonic paths, we identify the p-pseudocaterpillar labeled gene tree topology that, for a fixed caterpillar labeled species tree topology, gives rise to the largest number of coalescent histories. The shape that maximizes the number of coalescent histories places the "second" cherry of the p-pseudocaterpillar equidistantly from the root of the "first" cherry and from the tree root. A symmetry in the numbers of coalescent histories for p-pseudocaterpillar gene trees and caterpillar species trees is seen to exist around the maximizing value of the parameter p. The results provide insight into the factors that influence the number of coalescent histories possible for a given gene tree and species tree.

    View details for DOI 10.1016/j.aam.2021.102265

    View details for PubMedID 34483422