Related papers: How trait distributions evolve in heterogeneous po…
Models in evolutionary game theory traditionally assume symmetric interactions in homogeneous environments. Here, we consider populations evolving in a heterogeneous environment, which consists of patches of different qualities that are…
We study the response of a quantitative trait to exponential directional selection in a finite haploid population at the genetic and the phenotypic level. We assume an infinite sites model, in which the number of new mutations per…
In ecology and population dynamics, gene-flow refers to the transfer of a trait from one population to another. This phenomenon appears in studying the evolution of social features, such as languages. From the mathematical point of view,…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a…
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…
The modeling of time series is becoming increasingly critical in a wide variety of applications. Overall, data evolves by following different patterns, which are generally caused by different user behaviors. Given a time series, we define…
We consider a multitype Galton-Watson process that allows for the mutation and reversion of individual types in discrete and continuous time. In this setting, we explicitly compute the time evolution of quantities such as the mean and…
We consider the evolutionary trajectories traced out by an infinite population undergoing mutation-selection dynamics in static, uncorrelated random fitness landscapes. Starting from the population that consists of a single genotype, the…
A study of time homogeneous, real valued Markov processes with a special property and a non-atomic initial distribution is provided. The new notion of a function of evolution of distribution which determines the dependency between one…
The time taken for gene expression varies not least because proteins vary in length considerably. This paper uses an abstract, tuneable Boolean regulatory network model to explore gene expression time variation. In particular, it is shown…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as…
This article analyzes the problem of estimating the time until an event occurs, also known as survival modeling. We observe through substantial experiments on large real-world datasets and use-cases that populations are largely…
We consider a neutral haploid population whose generations are not overlapping and whose size is large and constantly of $N$ individuals. Any generation is replaced by a new one and any individual has a single parent. We do not choose the…
Large sets of genotypes give rise to the same phenotype because phenotypic expression is highly redundant. Accordingly, a population can accept mutations without altering its phenotype, as long as thegenotype mutates into another one on the…
In the presence of persistent payoff heterogeneity, the evolution of the aggregate strategy hugely depends on the underlying strategy composition under many evolutionary dynamics, while the aggregate dynamic under the standard BRD reduces…
In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as…
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and…
Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a…