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.
1 
J 
Size of community 
params 
A twoelement 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 
bins 
Boolean, with default 
give 
Boolean, with 
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.
Robin K. S. Hankin
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")

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