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= Consumer-resource model = In theoretical ecology and nonlinear dynamics, consumer-resource models (CRMs), also known as resource-competition models, are a class of dynamical systems which the abundances of a community of consumer species which compete for a common pool of resources. Consumer-resource models have served as fundamental tools in the quantitative development of theories of niche construction, coexistence, and biological diversity.

A general consumer-resource model consists of $M$ resources whose abundances are $$R_1,\dots,R_M$$ and $S$ consumer species whose populations are $$N_1,\dots,N_S$$. A general consumer-resource model is described by the system of coupled ordinary differential equations,

\begin{align} \frac{\mathrm dN_i}{\mathrm dt} &= 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_\alpha,N_1,\dots,N_S), &&\qquad \alpha = 1,\dots,M \end{align} $$ where $$g_i$$, depending only on resource abundances, is the per-capita growth rate of species $$i$$, and $$f_\alpha$$, depending only on the abundance of resource $$\alpha$$ and species populations, is the growth rate of resource $$\alpha$$. Some essential features of CRMs that can be seen in these equations are:


 * Species growth rates and populations are mediated through resources and there are no explicit species-species interactions
 * Resource abundances growth rates explicitly depend on the populations of all species
 * The growth rate of a resource depends explicitly only on its own present abundance and not on the abundances of other resources

Despite explicit dependence of certain quantities on others being disallowed, there remains implicit dependence due to the interacting nature of the system.

Niche models
Niche models are a notable class of CRMs which are described by the system of coupled ordinary differential equations,

\begin{align} \frac{\mathrm dN_i}{\mathrm dt} &= N_i g_i(\mathbf R), &&\qquad i =1,\dots,S,\\ \frac{\mathrm dR_\alpha}{\mathrm dt} &= h_\alpha(\mathbf R) - \sum_{i=1}^S N_i q_{i\alpha}(\mathbf R), &&\qquad \alpha = 1,\dots,M, \end{align} $$ where $$\mathbf R \equiv (R_1,\dots,R_M)$$ is a vector abbreviation for resource abundances, $$g_i$$ is the per-capita growth rate of species $$i$$, $$h_\alpha$$ is the growth rate of species $$\alpha$$ in the absence of consumption, and $$q_{i\alpha}$$ is the rate per unit species population that species $$i$$ depletes the abundance of resource $$\alpha$$ through consumption. In this class of CRMs, consumer species' impacts on resources are not explicitly coordinated; however, there are implicit interactions.

MacArthur consumer resource model (MCRM)
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Externally-supplied resources model
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Tilman consumer resource model
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Interacting self-regulation
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Microbial consumer resource model
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Alternative cross-feeding model
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Liebig’s Law
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Interactively-essential resources
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Multi-trophic Model
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