Related papers: Coexisting Stable Equilibria in a Multiple-allele …
Adaptation in response to selection on polygenic phenotypes may occur via subtle allele frequencies shifts at many loci. Current population genomic techniques are not well posed to identify such signals. In the past decade, detailed…
We provide a problem definition of the stable marriage problem for a general number of parties $p$ under a natural preference scheme in which each person has simple lists for the other parties. We extend the notion of stability in a natural…
We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many…
A single-column model run under the weak temperature gradient approximation, a parameterization of large-scale dynamics appropriate for the tropical atmosphere, is shown to have multiple stable equilibria. Under conditions permitting…
In this paper, we consider the steady state classification problem of the Allee effect system for multiple tribes. First, we reduce the high-dimensional model into several two-dimensional and three-dimensional algebraic systems such that we…
Coevolution is expected to follow two alternative dynamics, often called trench warfare and arms races in plant-pathogen systems. Trench warfare situations are stable cycles of allele frequencies at the coevolving loci of both host and…
We study a model of selection acting on a diploid population (one in which each individual carries two copies of each gene) living in one spatial dimension. We suppose a particular gene appears in two forms (alleles) $A$ and $a$, and that…
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed $k$, the method finds a convex polytope with $k$ vertices, called archetype points, such that the polytope is…
We present a model for evolving population which maintains genetic polymorphism. By introducing random mutation in the model population at a constant rate, we observe that the population does not become extinct but survives, keeping…
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables,…
We study the large population limit of a stochastic individual-based model which describes the time evolution of a diploid hermaphroditic population reproducing according to Mendelian rules. In [Neukirch, Bovier, 2016] it is proved that…
Local coexistence of species in large ecosystems is traditionally explained within the broad framework of niche theory. However, its rationale hardly justifies rich biodiversity observed in nearly homogeneous environments. Here we consider…
When a population inhabits an inhomogeneous environment, the fitness value of traits can vary with the position in the environment. Gene flow caused by random mating can nevertheless prevent that a sexually reproducing population splits…
This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions…
Natural flocks need to cope with various forms of heterogeneities, for instance, their composition, motility, interaction, or environmental factors. Here, we study the effects of such heterogeneities on the flocking dynamics of the…
Deriving emergent patterns from models of biological processes is a core concern of mathematical biology. In the context of partial differential equations (PDEs), these emergent patterns sometimes appear as local minimisers of a…
We show that the ratio of matched individuals to blocking pairs grows linearly with the number of propose--accept rounds executed by the Gale--Shapley algorithm for the stable marriage problem. Consequently, the participants can arrive at…
In this paper we explore the eco-evolutionary dynamics of a predator-prey model, where the prey population is structured according to a certain life history trait. The trait distribution within the prey population is the result of interplay…
This article is concerned with the long time behavior of neutral genetic population models, with fixed population size. We design an explicit, finite, exact, genealogical tree based representation of stationary populations that holds both…
In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the…