rstar: R* model Model implementing the "R*" model, most closely...
In traitecoevo/Revolve: Adaptive Dynamics toolkit for R

R* model

Model implementing the "R*" model, most closely based on that presented by "Huisman, J., and Weissing, F.J. (2001). Biological conditions for oscillations and chaos generated by multispecies competition. Ecology 82, 2682-2695."

make_rstar_identity(k)

rstar_mat_1(x)

rstar_mat_2(x)

rstar_mat_2_tradeoff(x)

make_rstar_mat_constant(M)

rstar_matrices_fixed(K, C)

rstar_matrices(K, C)

`k`	number of resources
`x`	matrix of traits (for the `rstar_mat_` functions).
`M`	coumn matrix with K or C matrix that will be shared by all species.
`K`	Matrix of Monod constants
`C`	Matrix of consumption constants

Rstar(x): Compute equilibrium level of each resource (i.e. level it will reach when limiting. This is the resource level where the growth rate equals the mortality rate.
carrying_capacity(x): Compute the carrying capacity – the population size that a species with trait x will reach when alone.
dNdt(x, N, R): Change in density with respect to time (total, not per capita)
dRdt(x, N, R): Change in resources with respect to time
equilibrium(sys, ...): Given traits and initial densities as a system (sys) compute equilibirum numerically.
equilibrium_R(sys, ...): Given traits 'x' and initial densities 'y', compute the equilibrium. Return the equilibrium resource availability at the same time.
p(x, R): Specific growth rate at a particular resource level R
pinv(x, g): Resource level that would be required for particular growth rate g
single_equilibrium(x): Given species traits x, compute equilibrium system. If multiple species are given, the output will be multiple separate equilibira, rather than an actual community.
single_equilibrium_R(sys, force.numerical = FALSE): Solve for the equilibrium level of a resource, given a vector of densities (and species traits). Do do this, we solve dRdt == 0: $D (S - R) - c N p(R) == 0$ $D * (S - R) - c N r R / (K + R) == 0$ As a quadratic with respect to 'R': $-D * R^2 + (D (S - K) - c r N) * R + D K S == 0$