chesson {primer}

Two-species model of the storage effect

Description

Simulates a fluctuating environment over time, and two species' responses to the environment, after Chesson (1994).

Usage

chesson(
  alpha = c(1.1 * 1e-05, 1e-05),
  d = 0.1,
  years = 10,
  N0 = c(1000, 1e+05),
  w = c(0.6, 1),
  env.var = 1,
  specialization = 1,
  spread = 0.67,
  type = 1
)

Arguments

alpha

a vector of length 2; the negative effects of all individuals (of both species) on each population – typically different among species.

d

disturbance rate; the proportion of all individuals killed at each time step.

years

numbers of time steps

N0

vector of length 2; initial abundances.

w

vector of length 2; average fitnesses for each species.

env.var

degree of environmental variability.

specialization

determines the narrowness of each species fitness response.

spread

determines how far apart the peak fitness responses are.

type

determines the form of C, the negative effect of competition.

Details

The argument type controls the value of e^C, the effect of competition on reproduction, where the annual finite rate of increase is R=e^{E-C}. type = 1 causes e^C = \alpha_i N_{J,i}, that is, a species-specific fixed fraction of juveniles that depends on each species response to competition. This is illustrated in a for-loop in Stevens (2009, Ch. 9, Storage Effect, Simulating Dynamics). Any other value for type results in the same negative effect on both species that depends on the number of juveniles and the disturbance rate.

Value

Returns a list of length one, for use with ode in the deSolve package.

Component 1

vector of the state variables, y.

Author(s)

Hank Stevens ([e-mail])

References

Chesson, P.L. (1994) Multispecies competition in variable environments. Theoretical Population Biology, 45, 227–276.

Stevens. M.H.H. (2009) A Primer of Ecology with R. Use R! Series. Springer.

See Also

succniche

Examples

out <- chesson(years=50)
layout(matrix(1:4, nc=2))
matplot(out[["time"]], out[["Ns"]], type='l', lty=c(1:3),
        xlab="Time", ylab="N", log="y")
plot(out[["time"]][-1], out[["env"]], type='l',
     xlab="Time", ylab="Environment")
matplot(out[["env"]], out[["Es"]], xlab="Environment",
 ylab="Density-independent reproduction")
matplot(out[["env"]], out[["Rs"]], xlab="Environment",
 ylab="Annual growth rate")