Daniel A Rickert, Louis Wai-Tong Fan, Matthew W Hahn
{"title":"Inconsistency of parsimony under the multispecies coalescent.","authors":"Daniel A Rickert, Louis Wai-Tong Fan, Matthew W Hahn","doi":"10.1016/j.tpb.2025.09.004","DOIUrl":"https://doi.org/10.1016/j.tpb.2025.09.004","url":null,"abstract":"<p><p>While it is known that parsimony can be statistically inconsistent under certain models of evolution due to high levels of homoplasy, the consistency of parsimony under the multispecies coalescent (MSC) is less well studied. Previous studies have shown the consistency of concatenated parsimony (parsimony applied to concatenated alignments) under the MSC for the rooted 4-taxa case under an infinite-sites model of mutation; on the other hand, other work has also established the inconsistency of concatenated parsimony for the unrooted 6-taxa case. These seemingly contradictory results suggest that concatenated parsimony may fail to be consistent for trees with more than 5 taxa, for all unrooted trees, or for some combination of the two. Here, we present a technique for computing the expected internal branch lengths of gene trees under the MSC. This technique allows us to determine the regions of the parameter space of the species tree under which concatenated parsimony fails for different numbers of taxa, for rooted or unrooted trees. We use our new approach to demonstrate that while parsimony succeeds in the unrooted 5-taxa case, there are regions of statistical inconsistency for concatenated parsimony for rooted 5+-taxa cases and unrooted 6+-taxa cases. Our results therefore suggest that parsimony is not generally dependable under the MSC.</p>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":" ","pages":""},"PeriodicalIF":1.3,"publicationDate":"2025-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145193680","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Dynamics of the distribution of fitness effects during adaptation","authors":"Tenoch Morales, Abigail Kushnir, Lindi M. Wahl","doi":"10.1016/j.tpb.2025.09.003","DOIUrl":"10.1016/j.tpb.2025.09.003","url":null,"abstract":"<div><div>Empirical measures of the distribution of fitness effects of new mutations (the DFE) have been increasingly successful, and have recently highlighted the fact that the DFE changes during adaptation. Here, we analyze these dynamic changes to the DFE during a simplified adaptive process: an adaptive walk across an additive fitness landscape. First, we derive analytical approximations for the underlying fitness distributions of alleles present in the genotype and available through mutation and use these to derive expressions for the DFE at each step of the adaptive walk. We then confirm these predictions with independent simulations that relax several simplifying assumptions made in the analysis. As expected, our analysis predicts that as adaptation proceeds, the DFE is reshaped dynamically throughout the walk by a decrease in the beneficial fraction of mutations (a shift to the left). Surprisingly, different mechanisms drive this change depending on the number of alleles available per site: for a small number of available alleles, we observe a depletion of high-fitness alleles available through mutation as expected, however for a large number of alleles we observe that adaptation may be more limited by the availability of low-fitness alleles to be replaced, rather than by the availability of high-fitness alleles to replace them.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 44-55"},"PeriodicalIF":1.3,"publicationDate":"2025-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145139211","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An equal-tempered measure of linkage disequilibrium","authors":"Mark M. Tanaka","doi":"10.1016/j.tpb.2025.09.002","DOIUrl":"10.1016/j.tpb.2025.09.002","url":null,"abstract":"<div><div>Linkage disequilibrium (LD), the association of alleles at two loci, is defined in multiple ways. Because LD measures depend on allele frequencies, it is difficult to compare LD values between populations or loci with different allele frequencies. Here, I consider a geometric interpretation of a commonly used LD measure <span><math><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> which suggests a modification that is frequency-independent in the sense that equal evolutionary forces lead to the same effect at different frequencies. This new measure is a very simple expression that is known elsewhere as the Hamann coefficient and the G index of agreement; it is a linear transformation of the simple matching coefficient. I explore properties of this quantity in comparison with <span><math><mi>D</mi></math></span> and <span><math><msup><mrow><mi>r</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>, and discuss its interpretation, advantages and disadvantages.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 36-43"},"PeriodicalIF":1.3,"publicationDate":"2025-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145066188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Tikhonov–Fenichel reductions and their application to a novel modelling approach for mutualism","authors":"Johannes Apelt, Volkmar Liebscher","doi":"10.1016/j.tpb.2025.08.004","DOIUrl":"10.1016/j.tpb.2025.08.004","url":null,"abstract":"<div><div>When formulating a model there is a trade-off between model complexity and (biological) realism. In the present paper we demonstrate how model reduction from a precise mechanistic “super model” to simpler conceptual models using Tikhonov–Fenichel reductions, an algebraic approach to singular perturbation theory, can mitigate this problem. Compared to traditional methods for time scale separations (Tikhonov’s theorem, quasi-steady state assumption), Tikhonov–Fenichel reductions have the advantage that we can compute a reduction directly for a separation of rates into slow and fast ones instead of a separation of components of the system. Moreover, we can find all such reductions algorithmically.</div><div>In this work we use Tikhonov–Fenichel reductions to analyse a mutualism model tailored towards lichens with an explicit description of the interaction. We find: (1) the implicit description of the interaction given in the reductions by interaction terms (functional responses) varies depending on the scenario, (2) there is a tendency for the mycobiont, an obligate mutualist, to always benefit from the interaction while it can be detrimental for the photobiont, a facultative mutualist, depending on the parameters, (3) our model is capable of describing the shift from mutualism to parasitism, (4) via numerical analyis, that our model experiences bistability with multiple stable fixed points in the interior of the first orthant. To analyse the reductions we formalize and discuss a mathematical criterion that categorizes two-species interactions. Throughout the paper we focus on the relation between the mathematics behind Tikhonov–Fenichel reductions and their biological interpretation.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 16-35"},"PeriodicalIF":1.3,"publicationDate":"2025-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145058685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The Feller diffusion conditioned on a single ancestral founder","authors":"Conrad J. Burden , Robert C. Griffiths","doi":"10.1016/j.tpb.2025.09.001","DOIUrl":"10.1016/j.tpb.2025.09.001","url":null,"abstract":"<div><div>We examine the distributional properties of a Feller diffusion <span><math><msub><mrow><mrow><mo>(</mo><mrow><mi>X</mi><mrow><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow><mrow><mi>τ</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>]</mo></mrow></mrow></msub></math></span> conditioned on the current population <span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> having a single ancestor at time zero. The approach is novel and is based on an interpretation of Feller’s original solution according to which the current population is comprised of a Poisson number of exponentially distributed families, each descended from a single ancestor. The distribution of the number of ancestors at intermediate times and the joint density of coalescent times is determined under assumptions of initiation of the process from a single ancestor at a specified time in the past, including infinitely far in the past, and for the case of a uniform prior on the time since initiation. Also calculated are the joint distribution of the time since the most recent common ancestor of the current population and the contemporaneous population size at that time under different assumptions on the time since initiation. In each case exact solutions are given for supercritical, critical and subcritical diffusions. For supercritical diffusions asymptotic forms of distributions are also given in the limit of unbounded exponential growth.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 1-15"},"PeriodicalIF":1.3,"publicationDate":"2025-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145056113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The distribution of the number of mutations in the genealogy of a sample from a single population","authors":"Yun-Xin Fu","doi":"10.1016/j.tpb.2025.08.001","DOIUrl":"10.1016/j.tpb.2025.08.001","url":null,"abstract":"<div><div>The number <span><math><mi>K</mi></math></span> of mutations in the genealogy of a sample of <span><math><mi>n</mi></math></span> sequences from a single population is one essential summary statistic in molecular population genetics and is equal to the number of segregating sites in the sample under the infinite-sites model. Although its expectation and variance are the most widely utilized properties, its sampling formula (i.e., probability distribution) is the foundation for all explorations related to <em>K</em>. Despite existence of an analytic sampling formula, its numerical application is limited due to susceptibility to error propagation. This paper presents a new sampling formula for <span><math><mi>K</mi></math></span> in a random sample of DNA sequences from a neutral locus without recombination, taken from a single population evolving according to the Wright–Fisher model with a constant effective population size, or the constant-in-state model, which allows the effective population size to vary across different coalescent states. The new sampling formula is expressed as the sum of the probabilities of the various ways mutations can manifest in the sample genealogy and achieves simplicity by partitioning mutations into hypothetical atomic clusters that cannot be further divided. Under the Wright–Fisher model with a constant effective population size, the new sampling formula is closely analogous to the celebrated Ewens’ sampling formula for the number of distinct alleles in a sample. Numerical computation using the new sampling formula is accurate and is limited only by the burden of enumerating a large number of partitions of a large <em>K</em>. However, significant improvement in efficiency can be achieved by prioritizing the enumeration of partitions with a large number of parts.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"165 ","pages":"Pages 72-78"},"PeriodicalIF":1.3,"publicationDate":"2025-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144922640","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Laurel Fogarty , Stephen Zhang , Marcus W. Feldman
{"title":"Gene-culture association and coevolution","authors":"Laurel Fogarty , Stephen Zhang , Marcus W. Feldman","doi":"10.1016/j.tpb.2025.08.003","DOIUrl":"10.1016/j.tpb.2025.08.003","url":null,"abstract":"<div><div>The genetic evolution of cultural species can be altered by the dynamic interaction of their genes with their cultural traits. In humans, examples of gene-culture interactions are common and a deeper theoretical understanding of gene-culture coevolution is a necessary precursor to recognizing the effects of culture on human evolution. Although there are a large number of empirical studies of gene-culture coevolutionary phenomena and a large amount of verbal theory, our theoretical understanding of gene-culture co-evolution, of what kinds of cultural traits are relevant, and of the quantitative nature of cultural interactions with genes remains incomplete. Two models of gene-culture coevolution in which there are interactions between cultural transmission biases, viability selection, and genetic evolution are presented. We show that gene-culture coevolution can occur in the absence of selection on the cultural trait, that some parameters can lead to internal equilibria in which all genetic and cultural types are polymorphic, that gene-culture association may be maintained, and that gene-culture coevolutionary systems have rich and unexpected dynamics.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"165 ","pages":"Pages 62-71"},"PeriodicalIF":1.3,"publicationDate":"2025-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144904250","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Prevalence of social parasitism in ant populations: Modeling energetics, demography and space in the Polyergus/Formica system","authors":"Patrick J. Talley , Frederick R. Adler","doi":"10.1016/j.tpb.2025.08.002","DOIUrl":"10.1016/j.tpb.2025.08.002","url":null,"abstract":"<div><div>Obligatory interspecific brood raiding is a unique form of parasitism in which one ant species steals pupae from another species and raises them into workers to perform duties within its nest. Although this strategy can support very large colonies, the relative species abundance of these social parasites is always low. Using fully parameterized mathematical models of the growth and reproduction of the well-studied interaction between brood raider <em>Polyergus</em> and its hosts in the genus <em>Formica</em>, we aim to discover the mechanisms that limit brood raider abundance. These mathematical models explain the range of observed relative species abundance of these social parasites and provide a criterion for <em>Polyergus</em> persistence within a patch of hosts. In particular, <em>Polyergus</em> colony survival depends on the number of host colonies between 23 and 73 meters from their nest—close enough to raid but distant enough to survive raiding. The number sets the upper bound of <em>Polyergus</em> abundance to be less than 10% of the community. Furthermore, we quantify the fitness costs imposed by brood raiding on nearby host colonies, which can be effectively castrated by the constant drain on their worker resources. These findings provide a mechanistic framework for understanding the ecological constraints on social parasitism, its role in shaping ant community dynamics and its connection to the evolution of host defense strategies.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"165 ","pages":"Pages 45-61"},"PeriodicalIF":1.3,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144849470","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maximillian Newman , John Wakeley , Wai-Tong (Louis) Fan
{"title":"Conditional gene genealogies given the population pedigree for a diploid Moran model with selfing","authors":"Maximillian Newman , John Wakeley , Wai-Tong (Louis) Fan","doi":"10.1016/j.tpb.2025.05.003","DOIUrl":"10.1016/j.tpb.2025.05.003","url":null,"abstract":"<div><div>We introduce a stochastic model of a population with overlapping generations and arbitrary levels of self-fertilization versus outcrossing. We study how the global graph of reproductive relationships, or population pedigree, influences the genealogical relationships of a sample of two gene copies at a genetic locus. Specifically, we consider a diploid Moran model with constant population size <span><math><mi>N</mi></math></span> over time, in which a proportion of offspring are produced by selfing. We show that the conditional distribution of the pairwise coalescence time at a single locus given the random pedigree converges to a limit law as <span><math><mi>N</mi></math></span> tends to infinity. The distribution of coalescence times obtained in this way predicts variation among unlinked loci in a sample of individuals. Traditional coalescent analyses implicitly average over pedigrees and generally make different predictions. We describe three different behaviors in the limit depending on the relative strengths, from large to small, of selfing versus outcrossing: partial selfing, limited outcrossing, and negligible outcrossing. In the case of partial selfing, coalescence times are related to the Kingman coalescent, similar to what is found in traditional analyses. In the case of limited outcrossing, the retained pedigree information forms a random graph, with coalescence times given by the meeting times of random walks on this graph. In the case of negligible outcrossing, which represents complete or nearly complete selfing, coalescence times are determined entirely by the fixed times to common ancestry of diploid individuals in the pedigree.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"165 ","pages":"Pages 29-44"},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144602077","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Identity-by-descent segments in large samples","authors":"Seth D. Temple , Elizabeth A. Thompson","doi":"10.1016/j.tpb.2025.06.003","DOIUrl":"10.1016/j.tpb.2025.06.003","url":null,"abstract":"<div><div>If two haplotypes share the same alleles for an extended gene tract, these haplotypes are likely to be derived identical-by-descent from a recent common ancestor. Identity-by-descent segment lengths are correlated via unobserved ancestral tree and recombination processes, which commonly presents challenges to the derivation of theoretical results in population genetics. We show that the proportion of detectable identity-by-descent segments around a locus is normally distributed when the sample size and the scaled population size are large. We generalize this central limit theorem to cover flexible demographic scenarios, multi-way identity-by-descent segments, and multivariate identity-by-descent rates. The regularity conditions on sample size and scaled population size are unlikely to hold in genetic data from real populations, but provide intuition for when the Gaussian distribution may be a reasonable approximate model for the IBD rate. We use efficient simulations to study the distributional behavior of the detectable identity-by-descent rate. One consequence of non-normality in finite samples is that a genome-wide scan looking for excess identity-by-descent rates may be subject to anti-conservative control of family-wise error rates.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"165 ","pages":"Pages 10-21"},"PeriodicalIF":1.2,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144585410","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}