Related papers: Conditions for growth and extinction in matrix mod…
Environment plays a fundamental role in the competition for resources, and hence in the evolution of populations. Here, we study a well-mixed, finite population consisting of two strains competing for the limited resources provided by an…
Dispersal is an important strategy that allows organisms to locate and exploit favorable habitats. The question arises: given competition in a spatially heterogeneous landscape, what is the optimal rate of dispersal? Continuous population…
We consider an exponentially growing population of cells undergoing mutations and ask about the effect of reproductive fluctuations (genetic drift) on its long-term evolution. We combine first step analysis with the stochastic dynamics of a…
This article is concerned with a version of the contact process with sexual reproduction on a graph with two levels of interactions modeling metapopulations. The population is spatially distributed into patches and offspring are produced in…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
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…
An organism that is newly introduced into an existing population has a survival probability that is dependent on both the population density of its environment and the competition it experiences with the members of that population.…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
Microorganisms live in environments that inevitably fluctuate between mild and harsh conditions. As harsh conditions may cause extinctions, the rate at which fluctuations occur can shape microbial communities and their diversity, but we…
We propose a stochastic model for evolution. Births and deaths of species occur with constant probabilities. Each new species is associated with a fitness sampled from the uniform distribution on [0,1]. Every time there is a death event…
A wide range of stochastic processes that model the growth and decline of populations exhibit a curious dichotomy: with certainty either the population goes extinct or its size tends to infinity. There is a elegant and classical theorem…
Many species live in colonies that thrive for a while and then collapse. Upon collapse very few individuals survive. The survivors start new colonies at other sites that thrive until they collapse, and so on. We introduce spatial and…
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…
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…
We consider a population spreading across a finite number of sites. Individuals can move from one site to the other according to a network (oriented links between the sites) that vary periodically over time. On each site, the population…
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…
Community ecology has traditionally relied on the competitive exclusion principle, a piece of common wisdom in conceptual frameworks developed to describe species assemblages. Key concepts in community ecology, such as limiting similarity…
The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log-abundances of species, with…
The intensification and increased frequency of weather extremes is emerging as one of the most important aspects of climate change. We use Monte Carlo simulation to understand and predict the consequences of variations in trends (i.e.,…
We present a model for evolution and extinction in large ecosystems. The model incorporates the effects of interactions between species and the influences of abiotic environmental factors. We study the properties of the model by approximate…