{"title":"Towards more realistic models of genomes in populations: The Markov-modulated sequentially Markov coalescent","authors":"J. Dutheil","doi":"10.4171/ecr/17-1/18","DOIUrl":"https://doi.org/10.4171/ecr/17-1/18","url":null,"abstract":"The development of coalescent theory paved the way to statistical inference from population genetic data. In the genomic era, however, coalescent models are limited due to the complexity of the underlying ancestral recombination graph. The sequentially Markov coalescent (SMC) is a heuristic that enables the modelling of complete genomes under the coalescent framework. While it empowers the inference of detailed demographic history of a population from as few as one diploid genome, current implementations of the SMC make unrealistic assumptions about the homogeneity of the coalescent process along the genome, ignoring the intrinsic spatial variability of parameters such as the recombination rate. Here, I review the historical developments of SMC models and discuss the evidence for parameter heterogeneity. I then survey approaches to handle this heterogeneity, focusing on a recently developed extension of the SMC.","PeriodicalId":298855,"journal":{"name":"Probabilistic Structures in Evolution","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133084108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Ancestral lines under recombination","authors":"E. Baake, M. Baake","doi":"10.4171/ecr/17-1/17","DOIUrl":"https://doi.org/10.4171/ecr/17-1/17","url":null,"abstract":"Solving the recombination equation has been a long-standing challenge of emph{deterministic} population genetics. We review recent progress obtained by introducing ancestral processes, as traditionally used in the context of emph{stochastic} models of population genetics, into the deterministic setting. With the help of an ancestral partitioning process, which is obtained by letting population size tend to infinity (without rescaling parameters or time) in an ancestral recombination graph, we obtain the solution to the recombination equation in a transparent form.","PeriodicalId":298855,"journal":{"name":"Probabilistic Structures in Evolution","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116313522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The symbiotic branching model: Duality and interfaces","authors":"J. Blath, Marcel Ortgiese","doi":"10.4171/ECR/17-1/15","DOIUrl":"https://doi.org/10.4171/ECR/17-1/15","url":null,"abstract":"The symbiotic branching model describes the dynamics of a spatial two-type population, where locally particles branch at a rate given by the frequency of the other type combined with nearest-neighbour migration. This model generalizes various classic models in population dynamics, such as the stepping stone model and the mutually catalytic branching model. We are particularly interested in understanding the region of coexistence, i.e. the interface between the two types. In this chapter, we give an overview over our results that describe the dynamics of these interfaces at large scales. One of the reasons that this system is tractable is that it exhibits a rich duality theory. So at the same time, we take the opportunity to provide an introduction to the strength of duality methods in the context of spatial population models.","PeriodicalId":298855,"journal":{"name":"Probabilistic Structures in Evolution","volume":"523 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133699160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Stochastic models for adaptive dynamics: Scaling limits and diversity","authors":"Anton Bovier","doi":"10.4171/ecr/17-1/7","DOIUrl":"https://doi.org/10.4171/ecr/17-1/7","url":null,"abstract":"I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations together with appropriate time rescaling. In particular, one derives the trait substitution sequence, polymorphic evolution sequence, and the canonical equation of adaptive dynamics. In addition, I show how the escape from an evolutionary stable conditions can occur as a metastable transition. This is a review paper that will appear in \u0000\"Probabilistic Structures in Evolution\", ed. by E. Baake and A. Wakolbinger.","PeriodicalId":298855,"journal":{"name":"Probabilistic Structures in Evolution","volume":"436 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122876390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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