Simulates a fluctuating environment over time, and two species' responses to the environment, after Chesson (1994).
1 2 3 
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. 
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^(EC). type = 1
causes e^C
= alpha[i] N[J,i], that is, a
speciesspecific fixed fraction of juveniles that depends on each
species response to competition. This is illustrated in a forloop 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.
Returns a list of length one, for use with ode
in the deSolve
package.
Component 1 
vector of the state variables, y. 
Hank Stevens <HStevens@muohio.edu>
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.
succniche
1 2 3 4 5 6 7 8 9 10  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="Densityindependent reproduction")
matplot(out[["env"]], out[["Rs"]], xlab="Environment",
ylab="Annual growth rate")

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