# volkov

0th

Percentile

##### 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 $0<n\leq J$.

Keywords
math
##### Usage
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 $1,2,\ldots,J$ 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

##### 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.

##### References

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

phi,preston

• volkov
##### Examples
# NOT RUN {
volkov(J=21457,c(theta=47.226, m=0.1)) # Example in figure 1
# }
# 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)
# }
# NOT RUN {
# needs PARI/GP

jj <- c(9.99980936124759, 0.991791987473506)

points(r,volkov(no.of.ind(butterflies), jj, bins=TRUE),type="b")

# }

Documentation reproduced from package untb, version 1.7-4, License: GPL

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