Related papers: Large fluctuations in stochastic population dynami…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
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…
The abundance of a species' population in an ecosystem is rarely stationary, often exhibiting large fluctuations over time. Using historical data on marine species, we show that the year-to-year fluctuations of population growth rate obey a…
The time evolution of the Partridge-Barton model in the presence of the pleiotropic constraint and deleterious somatic mutations is exactly solved for arbitrary fecundity in the context of a matricial formalism. Analytical expressions for…
In this paper we introduce a class of stochastic population models based on "patch dynamics". The size of the patch may be varied, and this allows one to quantify the departures of these stochastic models from various mean field theories,…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
Stochastic exponential growth is observed in a variety of contexts, including molecular autocatalysis, nuclear fission, population growth, inflation of the universe, viral social media posts, and financial markets. Yet literature on…
The methodology based on the random walk processes is adapted and applied to a comprehensive analysis of the statistical properties of the probability fluxes. To this aim we define a simple model of the Markovian stochastic dynamics on a…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
A stochastic model for behavioral changes by imitative pair interactions of individuals is developed. `Microscopic' assumptions on the specific form of the imitative processes lead to a stochastic version of the game dynamical equations.…
We study the interplay of population growth and evolutionary dynamics using a stochastic model based on birth and death events. In contrast to the common assumption of an independent population size, evolution can be strongly affected by…
In recent years non-demographic variability has been shown to greatly affect dynamics of stochastic populations. For example, non-demographic noise in the form of a bursty reproduction process with an a-priori unknown burst size, or…
This paper deals with extinction of an isolated population caused by intrinsic noise. We model the population dynamics in a "refuge" as a Markov process which involves births and deaths on discrete lattice sites and random migrations…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
Markov Population Model is a commonly used framework to describe stochastic systems. Their exact analysis is unfeasible in most cases because of the state space explosion. Approximations are usually sought, often with the goal of reducing…
We present an application of the theory of stochastic processes to model and categorize non-equilibrium physical phenomena. The concepts of uniformly continuous probability measures and modular evolution lead to a systematic hierarchical…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
A novel approach to moment closure problem is used to derive low dimensional laws for the dynamics of the moments of the membrane potential distribution in a population of spiking neurons. Using spectral expansion of the density equation we…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
This paper analyzes the stationary distributions of populations governed by the discrete stochastic logistic and Ricker difference equations at equilibrium examines with the gamma distribution. We identify mathematical relationships between…