# 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<=J*.

### Usage

1 |

### 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 |

`bins` |
Boolean, with default |

`give` |
Boolean, with |

### 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.

### See Also

`phi`

,`preston`

### Examples

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")
``` |