On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations

L Korobenko1, E Braverman

  • 1Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB, T2N 1N4, Canada.

Summary

Carrying capacity driven diffusion is an evolutionarily stable strategy. Species using this strategy can invade and outcompete randomly diffusing populations, leading to the extinction of the native species.

Related Concept Videos

Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.
23.2K
Speciation Rates01:07

Speciation Rates

Overview
18.8K
Distribution and Dispersion00:54

Distribution and Dispersion

To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...
20.9K
Competition02:34

Competition

When organisms require the same limited resources within an environment, they may have to compete for them. Competition is a net-negative interaction. Even if two competing individuals or populations do not interact directly, the overall fitness of both competitors is lowered as a result of not having full access to the limited resource.
21.4K
Mutation, Gene Flow, and Genetic Drift01:09

Mutation, Gene Flow, and Genetic Drift

In a population that is not at Hardy-Weinberg equilibrium, the frequency of alleles changes over time. Therefore, any deviations from the five conditions of Hardy-Weinberg equilibrium can alter the genetic variation of a given population. Conditions that change the genetic variability of a population include mutations, natural selection, non-random mating, gene flow, and genetic drift (small population size).
53.2K
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
336