{"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":"2025-12-01","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 asymmetry between spite and altruism","authors":"Shun Kurokawa , Sabin Lessard","doi":"10.1016/j.tpb.2025.11.001","DOIUrl":"10.1016/j.tpb.2025.11.001","url":null,"abstract":"<div><div>Empirical evidence suggests that altruistic social behavior (helping others at a cost to oneself) is more common than spiteful behavior (harming others at a cost to oneself) in nature. Here, we provide a general mathematical explanation for this asymmetry based on fundamental constraints on the composition of social groups. Since both behaviors are costly to the actor, they require additional mechanisms to avoid being eliminated by natural selection, such as assortative interactions. When interactions tend to occur between similar individuals (positive assortment), altruism can evolve, whereas spite requires negative assortment. We use a linear game in groups of fixed size <em>n</em> to derive an index of assortativity, and we analyze evolution in both infinite and finite populations. We show that positive assortment faces no fundamental limits – complete segregation into homogeneous groups is always mathematically possible. In contrast, negative assortment is constrained, especially in larger groups and unbalanced populations. This asymmetry creates more opportunities for altruism to evolve than spite. Our results explain the empirical rarity of spiteful behavior without assuming any specific population structure or group formation mechanism, suggesting that the scarcity of spite may reflect fundamental mathematical constraints inherent to assortment patterns.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 107-115"},"PeriodicalIF":1.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145565999","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":"2025-12-01","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":"Computing tree size under dynamical models of diversification","authors":"Ailene MacPherson , Matt Pennell","doi":"10.1016/j.tpb.2025.10.003","DOIUrl":"10.1016/j.tpb.2025.10.003","url":null,"abstract":"<div><div>A phylogenetic tree has three types of attributes: size, shape (topology), and branch density. Phylodynamic studies are often motivated by questions regarding the size of clades, nevertheless, nearly all of the inference methods only make use of the other two attributes. In this paper, we ask whether there is additional information if we consider tree size more explicitly in phylodynamic inference methods. To address this question, we first needed to be able to compute the expected tree size distribution under a specified phylodynamic model; perhaps surprisingly, there is not a general method for doing so — it is known what this is under a Yule or constant rate birth–death model but not for the more complicated scenarios researchers are often interested in. We present three different solutions to this problem: using (i) the deterministic limit; (ii) master equations; and (iii) an ensemble moment approximation. Using simulations, we evaluate the accuracy of these three approaches under a variety of scenarios and alternative measures of tree size (i.e., sampling through time or only at the present; sampling ancestors or not). We then use the most accurate measures for the situation, to investigate the added informational content of tree size. We find that for two critical phylodynamic questions — (i) is diversification diversity dependent? and, (ii) can we distinguish between alternative diversification scenarios? — knowing the expected tree size distribution under the specified scenario provides insights that could not be gleaned from considering the expected shape and branch density alone. The contribution of this paper is both a novel set of methods for computing tree size distributions and a path forward for richer phylodynamic inference into the evolutionary and epidemiological processes that shape lineage trees.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 80-91"},"PeriodicalIF":1.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145402328","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}
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":"10.1016/j.tpb.2025.09.004","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 56-69"},"PeriodicalIF":1.3,"publicationDate":"2025-12-01","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":"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":"2025-12-01","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":"A decomposition of a phylogenetically-informed distance between species assemblages into basal and terminal components","authors":"Julia Fukuyama","doi":"10.1016/j.tpb.2025.10.002","DOIUrl":"10.1016/j.tpb.2025.10.002","url":null,"abstract":"<div><div>Ecologists seeking to quantify differences between species assemblages often rely on dissimilarity measures that incorporate both species composition and the phylogenetic relatedness among species. Although many variants of such distances are available, their statistical properties remain poorly understood. For instance, an analyst comparing species abundances in two types of sites might apply PERMANOVA with UniFrac as the dissimilarity measure and obtain one result, but using PERMANOVA with Rao’s dissimilarity coefficient could yield a different conclusion. In other contexts, the pattern of significance might be reversed. While such discrepancies are well documented empirically, the mathematical underpinnings of this phenomenon are not well understood. We analyze a phylogenetically-informed distance that has been described many times in the literature under different names. Specifically, it corresponds to Rao’s DISC (Radhakrishna, 1982) with a certain choice of distance between species, has also been referred to as <span><math><mi>H</mi></math></span> (Jérôme et al., 2007), <span><math><msup><mrow><mi>δ</mi></mrow><mrow><mi>C</mi><mi>O</mi></mrow></msup></math></span> (Sandrine et al., 2004), and is related to <span><math><msub><mrow><mi>P</mi></mrow><mrow><mi>S</mi><mi>T</mi></mrow></msub></math></span> (Olivier and Bruno, 2007). We show that we can decompose this distance into pieces that describe basal and terminal phylogenetic structure and show that it places an overwhelming amount of weight on the basal phylogenetic structure. We show that a related class of distances used in other contexts can be interpreted as modulating the influence of the basal structure, demonstrate how this modification can increase power for detecting phylogenetically-structured effects at different scales, and present examples using both simulated and real datasets.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 92-106"},"PeriodicalIF":1.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145477364","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":"Using mathematical constraints to explain narrow ranges for allele-sharing dissimilarities","authors":"Xiran Liu , Zarif Ahsan , Noah A. Rosenberg","doi":"10.1016/j.tpb.2025.05.002","DOIUrl":"10.1016/j.tpb.2025.05.002","url":null,"abstract":"<div><div>Allele-sharing dissimilarity (ASD) statistics are measures of genetic differentiation for pairs of individuals or populations. Given the allele-frequency distributions of two populations — possibly the same population — the expected value of an ASD statistic is computed by evaluating the expectation of the pairwise dissimilarity between two individuals drawn at random, each from its associated allele-frequency distribution. For each of two ASD statistics, which we term <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>D</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>, we investigate the extent to which the expected ASD is constrained by allele frequencies in the two populations; in other words, how is the magnitude of the measure bounded as a function of the frequency of the most frequent allelic type? We first consider dissimilarity of a population with itself, obtaining bounds on expected ASD in terms of the frequency of the most frequent allelic type in the population. We then examine pairs of populations that might or might not possess the same most frequent allelic type. Across the unit interval for the frequency of the most frequent allelic type, the expected allele-sharing dissimilarity has a range that is more restricted than the <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></math></span> interval. The mathematical constraints on expected ASD assist in explaining a pattern observed empirically in human populations, namely that when averaging across loci, allele-sharing dissimilarities between pairs of individuals often tend to vary only within a relatively narrow range.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 116-137"},"PeriodicalIF":1.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144486686","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":"2025-10-01","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}
{"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":"2025-10-01","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}