Theoretical Population Biology最新文献

{"title":"Duality and the well-posedness of a martingale problem","authors":"Andrej Depperschmidt , Andreas Greven , Peter Pfaffelhuber","doi":"10.1016/j.tpb.2024.07.003","DOIUrl":"10.1016/j.tpb.2024.07.003","url":null,"abstract":"<div><p>For two Polish state spaces <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span>, and an operator <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>, we obtain existence and uniqueness of a <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>-martingale problem provided there is a bounded continuous duality function <span><math><mi>H</mi></math></span> on <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>×</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>Y</mi></mrow></msub></mrow></math></span> together with a dual process <span><math><mi>Y</mi></math></span> on <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span> which is the unique solution of a <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>Y</mi></mrow></msub></math></span>-martingale problem. For the corresponding solutions <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span> and <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></math></span>, duality with respect to a function <span><math><mi>H</mi></math></span> in its simplest form means that the relation <span><math><mrow><msub><mrow><mi>E</mi></mrow><mrow><mi>x</mi></mrow></msub><mrow><mo>[</mo><mi>H</mi><mrow><mo>(</mo><msub><mrow><mi>X</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>]</mo></mrow><mo>=</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>y</mi></mrow></msub><mrow><mo>[</mo><mi>H</mi><mrow><mo>(</mo><mi>x</mi><mo>,</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow><mo>]</mo></mrow></mrow></math></span> holds for all <span><math><mrow><mrow><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo></mrow><mo>∈</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>X</mi></mrow></msub><mo>×</mo><msub><mrow><mi>E</mi></mrow><mrow><mi>Y</mi></mrow></msub></mrow></math></span> and <span><math><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></math></span>. While duality is well-known to imply uniqueness of the <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>X</mi></mrow></msub></math></span>-martingale problem, we give here a set of conditions under which duality also implies existence without using approximating sequences of processes of a different kind (e.g. jump processes to approximate diffusions) which is a widespread strategy for proving existence of solutions of martingale problems. Given the process <span><math><msub><mrow><mrow><mo>(</mo><msub><mrow><mi>Y</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>)</mo></mrow></mrow><mrow><mi>t</mi><mo>≥</mo><mn>0</mn></mrow></msub></mat","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"159 ","pages":"Pages 59-73"},"PeriodicalIF":1.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040580924000765/pdfft?md5=3a0d0ba95ef090a854236fc78278e994&pid=1-s2.0-S0040580924000765-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142001150","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"One hundred years of influenza A evolution","authors":"Bjarke Frost Nielsen ,&nbsp;Christian Berrig ,&nbsp;Bryan T. Grenfell ,&nbsp;Viggo Andreasen","doi":"10.1016/j.tpb.2024.07.005","DOIUrl":"10.1016/j.tpb.2024.07.005","url":null,"abstract":"<div><p>Leveraging the simplicity of nucleotide mismatch distributions, we provide an intuitive window into the evolution of the human influenza A ‘nonstructural’ (NS) gene segment. In an analysis suggested by the eminent Danish biologist Freddy B. Christiansen, we illustrate the existence of a continuous genetic “backbone” of influenza A NS sequences, steadily increasing in nucleotide distance to the 1918 root over more than a century. The 2009 influenza A/H1N1 pandemic represents a clear departure from this enduring genetic backbone. Utilizing nucleotide distance maps and phylogenetic analyses, we illustrate remaining uncertainties regarding the origin of the 2009 pandemic, highlighting the complexity of influenza evolution. The NS segment is interesting precisely because it experiences less pervasive positive selection, and departs less strongly from neutral evolution than e.g. the HA antigen. Consequently, sudden deviations from neutral diversification can indicate changes in other genes via the hitchhiking effect. Our approach employs two measures based on nucleotide mismatch counts to analyze the evolutionary dynamics of the NS gene segment. The <em>rooted Hamming map</em> of distances between a reference sequence and all other sequences over time, and the unrooted temporal Hamming distribution which captures the distribution of genotypic distances between simultaneously circulating viruses, thereby revealing patterns of nucleotide diversity and epi-evolutionary dynamics.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"159 ","pages":"Pages 25-34"},"PeriodicalIF":1.2,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141879655","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 Wright–Fisher graph model and the impact of directional selection on genetic variation","authors":"Ingemar Kaj ,&nbsp;Carina F. Mugal ,&nbsp;Rebekka Müller-Widmann","doi":"10.1016/j.tpb.2024.07.004","DOIUrl":"10.1016/j.tpb.2024.07.004","url":null,"abstract":"<div><p>We introduce a multi-allele Wright–Fisher model with mutation and selection such that allele frequencies at a single locus are traced by the path of a hybrid jump–diffusion process. The state space of the process is given by the vertices and edges of a topological graph, i.e. edges are unit intervals. Vertices represent monomorphic population states and positions on the edges mark the biallelic proportions of ancestral and derived alleles during polymorphic segments. In this setting, mutations can only occur at monomorphic loci. We derive the stationary distribution in mutation–selection–drift equilibrium and obtain the expected allele frequency spectrum under large population size scaling. For the extended model with multiple independent loci we derive rigorous upper bounds for a wide class of associated measures of genetic variation. Within this framework we present mathematically precise arguments to conclude that the presence of directional selection reduces the magnitude of genetic variation, as constrained by the bounds for neutral evolution.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"159 ","pages":"Pages 13-24"},"PeriodicalIF":1.2,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040580924000777/pdfft?md5=c7ea20aafbe501d42760b57841f9e368&pid=1-s2.0-S0040580924000777-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141635177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mean-field interacting multi-type birth–death processes with a view to applications in phylodynamics","authors":"William S. DeWitt ,&nbsp;Steven N. Evans ,&nbsp;Ella Hiesmayr ,&nbsp;Sebastian Hummel","doi":"10.1016/j.tpb.2024.07.002","DOIUrl":"10.1016/j.tpb.2024.07.002","url":null,"abstract":"<div><p>Multi-type birth–death processes underlie approaches for inferring evolutionary dynamics from phylogenetic trees across biological scales, ranging from deep-time species macroevolution to rapid viral evolution and somatic cellular proliferation. A limitation of current phylogenetic birth–death models is that they require restrictive linearity assumptions that yield tractable message-passing likelihoods, but that also preclude interactions between individuals. Many fundamental evolutionary processes – such as environmental carrying capacity or frequency-dependent selection – entail interactions, and may strongly influence the dynamics in some systems. Here, we introduce a multi-type birth–death process in mean-field interaction with an ensemble of replicas of the focal process. We prove that, under quite general conditions, the ensemble’s stochastically evolving interaction field converges to a <em>deterministic</em> trajectory in the limit of an infinite ensemble. In this limit, the replicas effectively decouple, and self-consistent interactions appear as nonlinearities in the infinitesimal generator of the focal process. We investigate a special case that is rich enough to model both carrying capacity and frequency-dependent selection while yielding tractable message-passing likelihoods in the context of a phylogenetic birth–death model.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"159 ","pages":"Pages 1-12"},"PeriodicalIF":1.2,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040580924000753/pdfft?md5=449649d0ee10fbb5ed718ac4824a76ef&pid=1-s2.0-S0040580924000753-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141635178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatial invasion of cooperative parasites","authors":"","doi":"10.1016/j.tpb.2024.07.001","DOIUrl":"10.1016/j.tpb.2024.07.001","url":null,"abstract":"<div><p>In this paper we study invasion probabilities and invasion times of cooperative parasites spreading in spatially structured host populations. The spatial structure of the host population is given by a random geometric graph on <span><math><msup><mrow><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></mrow></mrow><mrow><mi>n</mi></mrow></msup></math></span>, <span><math><mrow><mi>n</mi><mo>∈</mo><mi>N</mi></mrow></math></span>, with a Poisson<span><math><mrow><mo>(</mo><mi>N</mi><mo>)</mo></mrow></math></span>-distributed number of vertices and in which vertices are connected over an edge when they have a distance of at most <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> with <span><math><msub><mrow><mi>r</mi></mrow><mrow><mi>N</mi></mrow></msub></math></span> of order <span><math><msup><mrow><mi>N</mi></mrow><mrow><mrow><mo>(</mo><mi>β</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mo>/</mo><mi>n</mi></mrow></msup></math></span> for some <span><math><mrow><mn>0</mn><mo>&lt;</mo><mi>β</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>. At a host infection many parasites are generated and parasites move along edges to neighbouring hosts. We assume that parasites have to cooperate to infect hosts, in the sense that at least two parasites need to attack a host simultaneously. We find lower and upper bounds on the invasion probability of the parasites in terms of survival probabilities of branching processes with cooperation. Furthermore, we characterize the asymptotic invasion time.</p><p>An important ingredient of the proofs is a comparison with infection dynamics of cooperative parasites in host populations structured according to a complete graph, i.e. in well-mixed host populations. For these infection processes we can show that invasion probabilities are asymptotically equal to survival probabilities of branching processes with cooperation. Furthermore, we build on proof techniques developed in Brouard and Pokalyuk (2022), where an analogous invasion process has been studied for host populations structured according to a configuration model.</p><p>We substantiate our results with simulations.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"159 ","pages":"Pages 35-58"},"PeriodicalIF":1.2,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040580924000686/pdfft?md5=7baf961ab53e2f51f9344de949b836db&pid=1-s2.0-S0040580924000686-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141591851","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Temporal variability can promote migration between habitats","authors":"Harman Jaggi ,&nbsp;David Steinsaltz ,&nbsp;Shripad Tuljapurkar","doi":"10.1016/j.tpb.2024.06.005","DOIUrl":"10.1016/j.tpb.2024.06.005","url":null,"abstract":"<div><p>Understanding the conditions that promote the evolution of migration is important in ecology and evolution. When environments are fixed and there is one most favorable site, migration to other sites lowers overall growth rate and is not favored. Here we ask, can environmental variability favor migration when there is one best site on average? Previous work suggests that the answer is yes, but a general and precise answer remained elusive. Here we establish new, rigorous inequalities to show (and use simulations to illustrate) how stochastic growth rate can increase with migration when fitness (dis)advantages fluctuate over time across sites. The effect of migration between sites on the overall stochastic growth rate depends on the difference in expected growth rates and the variance of the fluctuating difference in growth rates. When fluctuations (variance) are large, a population can benefit from bursts of higher growth in sites that are worse on average. Such bursts become more probable as the between-site variance increases. Our results apply to many (<span><math><mo>≥</mo></math></span> 2) sites, and reveal an interplay between the length of paths between sites, the average differences in site-specific growth rates, and the size of fluctuations. Our findings have implications for evolutionary biology as they provide conditions for departure from the reduction principle, and for ecological dynamics: even when there are superior sites in a sea of poor habitats, variability and habitat quality across space determine the importance of migration.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"158 ","pages":"Pages 195-205"},"PeriodicalIF":1.2,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141460284","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":"Host control and species interactions jointly determine microbiome community structure","authors":"Eeman Abbasi,&nbsp;Erol Akçay","doi":"10.1016/j.tpb.2024.06.006","DOIUrl":"10.1016/j.tpb.2024.06.006","url":null,"abstract":"<div><p>The host microbiome can be considered an ecological community of microbes present inside a complex and dynamic host environment. The host is under selective pressure to ensure that its microbiome remains beneficial. The host can impose a range of ecological filters including the immune response that can influence the assembly and composition of the microbial community. How the host immune response interacts with the within-microbiome community dynamics to affect the assembly of the microbiome has been largely unexplored. We present here a mathematical framework to elucidate the role of host immune response and its interaction with the balance of ecological interactions types within the microbiome community. We find that highly mutualistic microbial communities characteristic of high community density are most susceptible to changes in immune control and become invasion prone as host immune control strength is increased. Whereas highly competitive communities remain relatively stable in resisting invasion to changing host immune control. Our model reveals that the host immune control can interact in unexpected ways with a microbial community depending on the prevalent ecological interactions types for that community. We stress the need to incorporate the role of host-control mechanisms to better understand microbiome community assembly and stability.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"158 ","pages":"Pages 185-194"},"PeriodicalIF":1.2,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141460283","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":"Unifying quantification methods for sexual selection and assortative mating using information theory","authors":"A. Carvajal-Rodríguez","doi":"10.1016/j.tpb.2024.06.007","DOIUrl":"10.1016/j.tpb.2024.06.007","url":null,"abstract":"<div><p>Sexual selection plays a crucial role in modern evolutionary theory, offering valuable insight into evolutionary patterns and species diversity. Recently, a comprehensive definition of sexual selection has been proposed, defining it as any selection that arises from fitness differences associated with nonrandom success in the competition for access to gametes for fertilization. Previous research on discrete traits demonstrated that non-random mating can be effectively quantified using Jeffreys (or symmetrized Kullback-Leibler) divergence, capturing information acquired through mating influenced by mutual mating propensities instead of random occurrences. This novel theoretical framework allows for detecting and assessing the strength of sexual selection and assortative mating.</p><p>In this study, we aim to achieve two primary objectives. Firstly, we demonstrate the seamless alignment of the previous theoretical development, rooted in information theory and mutual mating propensity, with the aforementioned definition of sexual selection. Secondly, we extend the theory to encompass quantitative traits. Our findings reveal that sexual selection and assortative mating can be quantified effectively for quantitative traits by measuring the information gain relative to the random mating pattern. The connection of the information indices of sexual selection with the classical measures of sexual selection is established.</p><p>Additionally, if mating traits are normally distributed, the measure capturing the underlying information of assortative mating is a function of the square of the correlation coefficient, taking values within the non-negative real number set [0, +∞).</p><p>It is worth noting that the same divergence measure captures information acquired through mating for both discrete and quantitative traits. This is interesting as it provides a common context and can help simplify the study of sexual selection patterns.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"158 ","pages":"Pages 206-215"},"PeriodicalIF":1.2,"publicationDate":"2024-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040580924000650/pdfft?md5=a22dea1ed5eeb299ff36e9cf8734d81b&pid=1-s2.0-S0040580924000650-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141452035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stochastic viability in an island model with partial dispersal: Approximation by a diffusion process in the limit of a large number of islands","authors":"Dhaker Kroumi ,&nbsp;Sabin Lessard","doi":"10.1016/j.tpb.2024.06.003","DOIUrl":"10.1016/j.tpb.2024.06.003","url":null,"abstract":"<div><p>In this paper, we investigate a finite population undergoing evolution through an island model with partial dispersal and without mutation, where generations are discrete and non-overlapping. The population is structured into <span><math><mi>D</mi></math></span> demes, each containing <span><math><mi>N</mi></math></span> individuals of two possible types, <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span>, whose viability coefficients, <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>s</mi></mrow><mrow><mi>B</mi></mrow></msub></math></span>, respectively, vary randomly from one generation to the next. We assume that the means, variances and covariance of the viability coefficients are inversely proportional to the number of demes <span><math><mi>D</mi></math></span>, while higher-order moments are negligible in comparison to <span><math><mrow><mn>1</mn><mo>/</mo><mi>D</mi></mrow></math></span>. We use a discrete-time Markov chain with two timescales to model the evolutionary process, and we demonstrate that as the number of demes <span><math><mi>D</mi></math></span> approaches infinity, the accelerated Markov chain converges to a diffusion process for any deme size <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. This diffusion process allows us to evaluate the fixation probability of type <span><math><mi>A</mi></math></span> following its introduction as a single mutant in a population that was fixed for type <span><math><mi>B</mi></math></span>. We explore the impact of increasing the variability in the viability coefficients on this fixation probability. At least when <span><math><mi>N</mi></math></span> is large enough, it is shown that increasing this variability for type <span><math><mi>B</mi></math></span> or decreasing it for type <span><math><mi>A</mi></math></span> leads to an increase in the fixation probability of a single <span><math><mi>A</mi></math></span>. The effect of the population-scaled variances, <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>A</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span> and <span><math><msubsup><mrow><mi>σ</mi></mrow><mrow><mi>B</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math></span>, can even cancel the effects of the population-scaled means, <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>A</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>μ</mi></mrow><mrow><mi>B</mi></mrow></msub></math></span>. We also show that the fixation probability of a single <span><math><mi>A</mi></math></span> increases as the deme-scaled migration rate increases. Moreover, this probability is higher for type <span><math><mi>A</mi></math></span> than for type <span><math><mi>B</mi></math></span> if the population-scaled geometric mean viability coefficient is higher for type <span><math><mi>A</mi></math></span> than for type <span><math><mi>B</mi></math></span>,","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"158 ","pages":"Pages 170-184"},"PeriodicalIF":1.2,"publicationDate":"2024-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141443582","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 coalescent in finite populations with arbitrary, fixed structure","authors":"Benjamin Allen ,&nbsp;Alex McAvoy","doi":"10.1016/j.tpb.2024.06.004","DOIUrl":"10.1016/j.tpb.2024.06.004","url":null,"abstract":"<div><p>The coalescent is a stochastic process representing ancestral lineages in a population undergoing neutral genetic drift. Originally defined for a well-mixed population, the coalescent has been adapted in various ways to accommodate spatial, age, and class structure, along with other features of real-world populations. To further extend the range of population structures to which coalescent theory applies, we formulate a coalescent process for a broad class of neutral drift models with arbitrary – but fixed – spatial, age, sex, and class structure, haploid or diploid genetics, and any fixed mating pattern. Here, the coalescent is represented as a random sequence of mappings <span><math><mrow><mi>C</mi><mo>=</mo><msubsup><mrow><mfenced><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>t</mi></mrow></msub></mrow></mfenced></mrow><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>∞</mi></mrow></msubsup></mrow></math></span> from a finite set <span><math><mi>G</mi></math></span> to itself. The set <span><math><mi>G</mi></math></span> represents the “sites” (in individuals, in particular locations and/or classes) at which these alleles can live. The state of the coalescent, <span><math><mrow><msub><mrow><mi>C</mi></mrow><mrow><mi>t</mi></mrow></msub><mo>:</mo><mi>G</mi><mo>→</mo><mi>G</mi></mrow></math></span>, maps each site <span><math><mrow><mi>g</mi><mo>∈</mo><mi>G</mi></mrow></math></span> to the site containing <span><math><mi>g</mi></math></span>’s ancestor, <span><math><mi>t</mi></math></span> time-steps into the past. Using this representation, we define and analyze coalescence time, coalescence branch length, mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity-by-state. For low mutation, we provide a recipe for computing identity-by-descent and identity-by-state probabilities via the coalescent. Applying our results to a diploid population with arbitrary sex ratio <span><math><mi>r</mi></math></span>, we find that measures of genetic dissimilarity, among any set of sites, are scaled by <span><math><mrow><mn>4</mn><mi>r</mi><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>r</mi><mo>)</mo></mrow></mrow></math></span> relative to the even sex ratio case.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"158 ","pages":"Pages 150-169"},"PeriodicalIF":1.2,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0040580924000649/pdfft?md5=a09fbbcdb9b66c124896eb3ccc9340db&pid=1-s2.0-S0040580924000649-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141332353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}