# volkov: Expected frequency of species In untb: ecological drift under the UNTB

## 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<=J.

## Usage

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

## 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,...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

## Value

Returns an object of class “phi”.

## Note

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.

## Author(s)

Robin K. S. Hankin

## References

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

`phi`,`preston`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```## 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") ```