Related papers: Population dynamics under random switching
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…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…
In a complex community, species continuously adapt to each other. On rare occasions, the adaptation of a species can lead to the extinction of others, and even its own. "Adaptive dynamics" is the standard mathematical framework to describe…
Most population models assume that individuals within a given population are identical, that is, the fundamental role of variation is ignored. Here we develop a general approach to modeling heterogeneous populations with discrete…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
Species extinction is a core process that affects the diversity of life on Earth. Competition between species in a population is considered by ecological niche-based theories as a key factor leading to different severity of species…
The processes and mechanisms underlying the origin and maintenance of biological diversity have long been of central importance in ecology and evolution. The competitive exclusion principle states that the number of coexisting species is…
We develop a landscape-flux framework to investigate observed frequency distributions of vegetation and the stability of these ecological systems under fluctuations. The frequency distributions can characterize the population-potential…
We study a model ecosystem by means of dynamical techniques from disordered systems theory. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally…
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…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
We are interested in modeling Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions. The population is modeled as a stochastic point process whose generator captures…
Stochastic thermodynamics and the associated fluctuation relations provide the means to extend the fundamental laws of thermodynamics to small scales and systems out of equilibrium. The fluctuating thermodynamic variables are usually…
We consider a class of piecewise-deterministic Markov processes where the state evolves according to a linear dynamical system. This continuous time evolution is interspersed by discrete events that occur at random times and change (reset)…
We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…
We consider two dimensional Lotka-Volterra systems in fluctuating environment. Relying on recent results on stochastic persistence and piecewise deterministic Markov processes, we show that random switching between two environments both…
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…
Population dynamics with complex biological interactions, accounting for uncertainty quantification, is critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the…
We study the evolutionary dynamics of a phenotypically structured population in a changing environment , where the environmental conditions vary with a linear trend but in an oscillatory manner. Such phenomena can be described by parabolic…
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. We revisit a…