volkov: Expected frequency of species

Description

Given a community size, biodiversity parameter \(\theta\), and an immigration rate \(m\), returns the expected frequency of species with \(n\) individuals, for \(0<n\leq J\).

Usage

volkov(J, params, bins = FALSE, give = FALSE)

Value

Returns an object of class “phi”.

Arguments

J: Size of community
params: 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 optimal.params()
bins: Boolean, with default FALSE meaning to return the expected number of species with \(1,2,\ldots,J\) individuals, and FALSE meaning to return the binned total, using a Preston-like binning system as used in preston()
give: Boolean, with TRUE meaning to return all the output of integrate(), and default FALSE meaning to return just the value of the integral

Author

Robin K. S. Hankin

References

I. Volkov and others 2003. “Neutral theory and relative species abundance in ecology”. Nature, volume 424, number 28.

Examples

Run this code

if (FALSE) {
  volkov(J=21457,c(theta=47.226, m=0.1)) # Example in figure 1
} 

volkov(J=20,params=c(theta=1,m=0.4))

 data(butterflies)
 r <- plot(preston(butterflies,n=9,orig=TRUE))

 if (FALSE)   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")

Run the code above in your browser using DataCamp Workspace