Expected frequency of species
Given a community size, biodiversity parameter $theta$, and an immigration rate $m$, returns the expected frequency of species with $n$ individuals, for $0
volkov(J, params, bins = FALSE, give = FALSE)
- Size of community
- A two-element vector with first element interpreted as
theta, the Fundamental biodiversity parameter and the second, m,
interpreted as the probability of immigration. This argument will
accept the output of
- Boolean, with default
FALSEmeaning to return the expected number of species with $1,2,...J$ individuals, and
FALSEmeaning to return the binned total, using a Preston-like binning system as used in
- Boolean, with
TRUEmeaning to return all the output of
integrate(), and default
FALSEmeaning to return just the value of the integral
Returns an object of class phi.
The method used is slightly inefficient: the terms to the left of the integral sign [in Volkov's equation 7] are integrated and this is, strictly, unnecessary as it is not a function of $y$. However, taking advantage of this fact results in messy code.
I. Volkov and others 2003. Neutral theory and relative species abundance in ecology. Nature, volume 424, number 28.
## Not run: # volkov(J=21457,c(theta=47.226, m=0.1)) # Example in figure 1 # ## End(Not run) volkov(J=20,params=c(theta=1,m=0.4)) data(butterflies) r <- plot(preston(butterflies,n=9,orig=TRUE)) ## Not run: jj <- optimal.params(butterflies) # needs PARI/GP jj <- c(9.99980936124759, 0.991791987473506) points(r,volkov(no.of.ind(butterflies), jj, bins=TRUE),type="b")