Related papers: The general theory of species abundance distributi…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
We look at the interaction of dispersal and environmental stochasticity in $n$-patch models. We are able to prove persistence and extinction results even in the setting when the dispersal rates are stochastic. As applications we look at…
The consistency of the species abundance distribution across diverse communities has attracted widespread attention. In this paper, I argue that the consistency of pattern arises because diverse ecological mechanisms share a common symmetry…
Taylor's power law is one of the mostly widely known empirical patterns in ecology discovered in the 20th century. It states that the variance of species population density scales as a power-law function of the mean population density.…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
Near the beginning of the century, Wright and Fisher devised an elegant, mathematically tractable model of gene reproduction and replacement that laid the foundation for contemporary population genetics. The Wright-Fisher model and its…
We revisit the problem of influencing the sex ratio of a population by subjecting reproduction of each family to some stopping rule. As an easy consequence of the strong law of large numbers, no such modification is possible in the sense…
According to the competitive exclusion principle, in a finite ecosystem, extinction occurs naturally when two or more species compete for the same resources. An important question that arises is: when coexistence is not possible, which…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics. Diversity can be intended as the count of different items, animals, or, more generally, interactions. There are two…
Whether or not biodiversity dynamics tend toward stable equilibria remains an unsolved question in ecology and evolution with important implications for our understanding of diversity and its conservation. Phylo/population genetic models…
Understanding the influence of an environment on the evolution of its resident population is a major challenge in evolutionary biology. Great progress has been made in homogeneous population structures while heterogeneous structures have…
The problem of natural selection in dispersal-structured populations consisting of individuals characterized by different diffusion coefficients is studied. The competition between the organisms is taken into account through the assumption…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference…
One of the fundamental problems in biology concerns the method by which a cluster of organisms can regulate the proportion of individuals that perform various roles or modes as if each individual knows a whole situation without a leader. A…
Vortex singularities in speckle patterns formed from random superpositions of waves are an inevitable consequence of destructive interference and are consequently generic and ubiquitous. Singularities are topologically stable, meaning they…
Fifty years ago, Robert MacArthur showed that stable equilibria optimize quadratic functions of the population sizes in several important ecological models. Here, we generalize this finding to a broader class of systems within the framework…
Starting from the well-known field theory for directed percolation, we describe an evolving population, near extinction, in an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the…