Related papers: Reflections on the extinction-explosion dichotomy

Standard neutral population genetics theory with a strictly fixed population size has important limitations. An alternative model that allows independently fluctuating population sizes and reproduces the standard neutral evolution is…

We study the biodiversity problem for resource competition systems with extinctions and self-limitation effects. Our main result establishes estimates of biodiversity in terms of the fundamental parameters of the model. We also prove the…

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…

The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…

A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…

Anthropic reasoning often begins with the premise that we should expect to find ourselves typical among all intelligent observers. However, in the infinite universe predicted by inflation, there are some civilizations which have spread…

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…

Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…

A phenomenological theory of growth of the population of humankind is proposed. The theory based on the assumption about a multifractal nature of the set of number of people in temporal axis and contains control parameters. In particular…

The biological theory of adaptive dynamics proposes a description of the long-term evolution of a structured asexual population. It is based on the assumptions of large population, rare mutations and small mutation steps, that lead to a…

Time-dependent distribution of the global extinction of megafauna is compared with the growth of human population. There is no correlation between the two processes. Furthermore, the size of human population and its growth rate were far too…

We study a pure death process. At each discrete time every individual dies or not independently of each other with a constant probability. We give examples showing that in a certain limit extinction happens along a path where one and only…

We finely describe the speed of "coming down from infinity" for birth and death processes which eventually become extinct. Under general assumptions on the birth and death rates, we firstly determine the behavior of the successive hitting…

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,…

The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…

Fluctuations in diversity and extinction sizes are discussed and compared for two different, individual-based models of biological coevolution. Both models display power-law distributions for various quantities of evolutionary interest,…

We consider asymptotic orbit-counting problems for certain expansive actions by commuting automorphisms of compact groups. A dichotomy is found between systems with asymptotically more periodic orbits than the topological entropy predicts,…

We review recent work aimed at modeling species extinction over geological time. We discuss a number of models which, rather than dealing with the direct causes of particular extinction events, attempt to predict overall statistical trends,…

How diversity is maintained in natural ecosystems is a long-standing question in Theoretical Ecology. By studying a system that combines ecological dynamics, heterogeneous interactions and spatial structure, we uncover a new mechanism for…

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…