Related papers: A host-parasite multilevel interacting process and…
Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field…
We consider a discrete-time host-parasite model for a population of cells which are colonized by proliferating parasites. The cell population grows like an ordinary Galton-Watson process, but in reflection of real biological settings the…
Self-organisation of individuals within large collectives occurs throughout biology. Mathematical models can help elucidate the individual-level mechanisms behind these dynamics, but analytical tractability often comes at the cost of…
We study an ecology-inspired model for a population of bounded size, whose dynamics is governed by random birth, death, and immigration events. Stochastic fluctuations in the number of individuals give rise to a succession of alternating…
Genetic data are often used to infer demographic history and changes or detect genes under selection. Inferential methods are commonly based on models making various strong assumptions: demography and population structures are supposed…
Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been…
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…
An infinite population of point entities dwelling in the habitat $X=\mathds{R}^d$ is studied. Its members arrive at and depart from $X$ at random. The departure rate has a term corresponding to a logistic-type interaction between the…
Population dynamics and in particular microbial population dynamics, though they are complex but also intrinsically discrete and random, are conventionally represented as deterministic differential equations systems. We propose to revisit…
Several theoretical frameworks have been proposed to explain observed biodiversity patterns, ranging from the classical niche-based theories, mainly employing a continuous formalism, to neutral theories, based on statistical mechanics of…
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics.…
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
Population structure induced by both spatial embedding and more general networks of interaction, such as model social networks, have been shown to have a fundamental effect on the dynamics and outcome of evolutionary games. These effects…
This paper is mainly devoted to lay an empirical foundation for further research on complex spatial dynamics of two-population interaction. Based on the US population census data, a rural and urban population interaction model is developed.…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
We suggest a novel approach to treating symbiotic relations between biological species or social entities. The main idea is the characterisation of symbiotic relations of coexisting species through their mutual influence on their respective…
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)…
Motivated by the study of a parasite infection in a cell line, we introduce a general class of Markov processes for the modelling of population dynamics. The population process evolves as a diffusion with positive jumps whose rate is a…