Consumer-resource model

In theoretical ecology and nonlinear dynamics, consumer-resource models (CRMs) are a class of ecological models in which a community of consumer species compete for a common pool of resources. Instead of species interacting directly, all species-species interactions are mediated through resource dynamics. Consumer-resource models have served as fundamental tools in the quantitative development of theories of niche construction, coexistence, and biological diversity. These models can be interpreted as a quantitative description of a single trophic level.^[1][2]

A general consumer-resource model consists of M resources whose abundances are ${\displaystyle R_{1},\dots ,R_{M}}$ and S consumer species whose populations are ${\displaystyle N_{1},\dots ,N_{S}}$. A general consumer-resource model is described by the system of coupled ordinary differential equations,$${\displaystyle {\begin{aligned}{\frac {\mathrm {d} N_{i}}{\mathrm {d} t}}&=N_{i}g_{i}(R_{1},\dots ,R_{M}),&&\qquad i=1,\dots ,S,\\{\frac {\mathrm {d} R_{\alpha }}{\mathrm {d} t}}&=f_{\alpha }(R_{1},\dots ,R_{M},N_{1},\dots ,N_{S}),&&\qquad \alpha =1,\dots ,M\end{aligned}}}$$ where ${\displaystyle g_{i}}$, depending only on resource abundances, is the per-capita growth rate of species ${\displaystyle i}$, and ${\displaystyle f_{\alpha }}$ is the growth rate of resource ${\displaystyle \alpha }$. An essential feature of CRMs is that species growth rates and populations are mediated through resources and there are no explicit species-species interactions. Through resource interactions, there are emergent inter-species interactions.

Originally introduced by Robert H. MacArthur^[3] and Richard Levins,^[4] consumer-resource models have found success in formalizing ecological principles and modeling experiments involving microbial ecosystems.^[5][6]