Species coexistance by Chesson, Peter

Summary

Main Points

• Species coexistence is driven by the interplay between interspecies competition and intraspecies competition. As long as intraspecies competition is greater than interspecies competition the conditions exist for an equilibria which includes coexistence.

Environmental Dimensionality

Below we show the per capita abundance investigating the role of different relationships with inter and intra species competition. Here $a$ is taken as some growth rate for species 1 and 2 which is reduced by some additive factor based on the intraspecies competition (e.g., $a_{11}$) and the interspecies competition (e.g., $a{12}$).

$$\begin{align} \frac{1}{N1} \frac{dN_1}{dt} = a_1 - a_{11} N_1 - a_{12}N2 \newline \frac{1}{N2} \frac{dN_2}{dt} = a_2 - a_{22} N_2 - a_{21}N1 \end{align}$$

[!tip] Note that this can be placed into matrix notation and that matrix will have a range of two. The rank of this matrix tells us the dimensionality of the system as well as the dimensionality of the environment

Questions

Code/ Supplemental Data

Implications for Infectious Diseases

Summary

Under what conditions can species coexist? Species is the product of the interaction and dynamics of populations within the context of other species, predators, and resource availability.