In genetics the Moran model describes the neutral evolution of a bi-allelic gene in a population of haploid individuals subjected to mutations. We show in this paper that this model can be mapped into an influence dynamical process on networks subjected to external influences. The panmictic case considered by Moran corresponds to fully connected networks and can be completely solved in terms of hypergeometric functions. Other types of networks correspond to structured populations, for which approximate solutions are also available. This new approach to the classic Moran model leads to a relation between regular networks based on spatial grids and the mechanism of isolation by distance. We discuss the consequences of this connection for topopatric speciation and the theory of neutral speciation and biodiversity. We show that the effect of mutations in structured populations, where individuals can mate only with neighbors, is greatly enhanced with respect to the panmictic case. If mating is further constrained by genetic proximity between individuals, a balance of opposing tendencies take place: increasing diversity promoted by enhanced effective mutations versus decreasing diversity promoted by similarity between mates. Stabilization occurs with speciation via pattern formation. We derive an explicit relation involving the parameters characterizing the population that indicates when speciation is possible.
The evolutionary and ecological processes behind the origin of species are among the most fundamental problems in biology. In fact, many theoretical hypothesis on different type of speciation have been proposed. In particular, models of sympatric speciation leading to the formation of new species without geographical isolation, are based on the niche hypothesis: the diversification of the population is induced by the competition for a limited set of the available resources. On the other hand, neutral models of evolution have shown that stochastic forces are sufficient to generate coexistence o…
In this article, a biallelic reversible mutation model with linear and quadratic selection is analyzed. The approach reconnects to one proposed by Kimura ( Possibility of extensive neutral evolution under stabilizing selection with special reference to nonrandom use of codons (PNAS,1981)), who starts from a diffusion model and derives its equilibrium distribution up to a constant. We use a boundary-mutation Moran model, which approximates a general mutation model for small effective mutation rates, and derive its equilibrium distribution for polymorphic and monomorphic variants in small to mod…
Geographic isolation is a central mechanism of speciation, but perfect isolation of populations is rare. Although speciation can be hindered if gene flow is large, intermediate levels of migration can enhance speciation by introducing genetic novelty in the semi-isolated populations or founding small communities of migrants. Here we consider a two island neutral model of speciation with continuous migration and study diversity patterns as a function of the migration probability, population size, and number of genes involved in reproductive isolation (dubbed as genome size). For small genomes, …
We study the evolution of the population genealogy in the classic neutral Moran Model of finite size and in discrete time. The stochastic transformations that shape a Moran population can be realized directly on its genealogy and give rise to a process with a state space consisting of the finite set of Yule trees of a certain size. We derive a number of properties of this process, and show that they are in agreement with existing results on the infinite-population limit of the Moran Model. Most importantly, this process admits time reversal, which gives rise to another tree-valued Markov Chain…
The evolutionary advantage of replacers in the Moran process
Computer Science Institute, Charles University（查尔斯大学计算机科学学院）；Department of Organismic and Evolutionary Biology, Harvard University（哈佛大学生物演化系）；Department of Mathematics, Harvard University（哈佛大学数学系）
Environmental variation can play an important role in ecological competition by influencing the relative advantage between competing species. Here, we consider such effects by extending a classical, competitive Moran model to incorporate an environment that fluctuates periodically in time. We adapt methods from work on these classical models to investigate the effects of the magnitude and frequency of environmental fluctuations on two important population statistics: the probability of fixation and the mean time to fixation. In particular, we find that for small frequencies, the system behaves…
We present a novel communication-free algorithm for individual-based probabilistic neutral biodiversity simulations. The algorithm transforms a neutral Moran ecosystem model into an embarrassingly parallel problem by trading off inter-process communication at the cost of some redundant computation. Specifically, by careful design of the random number generator that drives the simulation, we arrange for evolutionary parent-child interactions to be modelled without requiring knowledge of the interaction, its participants, or which processor is performing the computation. Critically, this means t…
The stationary sampling distribution of a neutral decoupled Moran or Wright-Fisher diffusion with neutral mutations is known to first order for a general rate matrix with small but otherwise unconstrained mutation rates. Using this distribution as a starting point we derive results for maximum likelihood estimates of scaled mutation rates from site frequency data under three model assumptions: a twelve-parameter general rate matrix, a nine-parameter reversible rate matrix, and a six-parameter strand-symmetric rate matrix. The site frequency spectrum is assumed to be sampled from a fixed size p…
Center for Interdisciplinary Research in Biology (CIRB), Collège de France, CNRS, INSERM, PSL Research University（跨学科生物学研究中心，法兰西学院，法国国家科学研究中心，法国国家健康与医学研究院，PSL研究大学）；Laboratoire de Probabilités, Statistique et Modélisation (LPSM), Sorbonne Université, CNRS（概率、统计与建模实验室，索邦大学，法国国家科学研究中心）；Institut de Systématique, Évolution, Biodiversité (ISYEB), MNHN, CNRS, Sorbonne Université（系统分类学、进化与生物多样性研究所，法国国家自然历史博物馆，法国国家科学研究中心，索邦大学）
Detecting interspecific and geographic differentiation patterns in two interfertile oak species (Quercus petraea (Matt.) Liebl. and Q. robur L.) using small sets of microsatellite markers
