Related papers: Stochastic differential equations for evolutionary…
Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
The dynamics of a general structured population is modelled using a general stochastic differential equation (SDE) with an infinite decomposability property. This property allows the population to be divided into an arbitrary number of…
Evolutionary game theory has traditionally employed deterministic models to describe population dynamics. These models, due to their inherent nonlinearities, can exhibit deterministic chaos, where population fluctuations follow complex,…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
Traditionally, frequency dependent evolutionary dynamics is described by deterministic replicator dynamics assuming implicitly infinite population sizes. Only recently have stochastic processes been introduced to study evolutionary dynamics…
We study how environmental stochasticity influences the long-term population size in certain one- and two-species models. The difficulty is that even when one can prove that there is persistence, it is usually impossible to say anything…
Strong positive feedback is considered a necessary condition to observe abrupt shifts of ecosystems. A few previous studies have shown that demographic noise -- arising from the probabilistic and discrete nature of birth and death processes…
We study the phenomenon of cyclic dominance in the paradigmatic Rock--Paper--Scissors model, as occurring in both stochastic individual-based models of finite populations and in the deterministic replicator equations. The mean-field…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
Many models of population dynamics are formulated as deterministic iterated maps although real populations are stochastic. This is justifiable in the limit of large population sizes, as the stochastic fluctuations are negligible then.…
Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
Neutral dynamics, where taxa are assumed to be demographically equivalent and their abundance is governed solely by the stochasticity of the underlying birth-death process, has proved itself as an important minimal model that accounts for…
We propose a formal framework based on collective coordinates to reduce infinite-dimensional stochastic partial differential equations (SPDEs) with symmetry to a set of finite-dimensional stochastic differential equations which describe the…
We use analytical techniques based on an expansion in the inverse system size to study the stochastic evolutionary dynamics of finite populations of players interacting in a repeated prisoner's dilemma game. We show that a mechanism of…
Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
Over the past century, nonlinear difference and differential equations have been used to understand conditions for species coexistence. However, these models fail to account for random fluctuations due to demographic and environmental…