dvolkov {sads} | R Documentation |

Density, distribution function, quantile function and random generation for species abundances distribution in a neutral community with immigration as deduced by Volkov et al. (2003).

dvolkov( x, theta, m, J, order=96, log = FALSE ) pvolkov( q, theta, m , J, lower.tail = TRUE, log.p = FALSE ) qvolkov( p, theta, m, J, lower.tail = TRUE, log.p = FALSE ) rvolkov( n, theta, m, J) Svolkov( theta, m, J, order=96)

`x` |
vector of (non-negative integer) quantiles. In the context of species abundance distributions, this is a vector of abundance of species in a sample. |

`q` |
vector of (non-negative integer) quantiles. In the context of species abundance distributions, a vector of abundance of species in a sample. |

`n` |
number of random values to return. |

`p` |
vector of probabilities. |

`theta` |
positive real, theta > 0; Hubbell's ‘fundamental biodiversity number’. |

`order` |
order of the approximation for the numerical integration. The default of 96 usually gives a rounding error of 1e-8 for moderate dataset; orders greater than 128 are probably overkill |

`m` |
positive real, 0 <= m <= 1; immigration rate (see details). |

`J` |
positive integer; sample size. In the context of species abundance distributions, usually the number of individuals in a sample. |

`log, log.p` |
logical; if TRUE, probabilities p are given as log(p). |

`lower.tail` |
logical; if TRUE (default), probabilities are P[X <= x], otherwise, P[X > x]. |

Volkov *et al* (2003) proposed one of the analytic solutions for the
species abundance distributions (SADs)
for The Neutral Theory of Biodiversity (Hubbell 2001).

Their solution is deduced from a model of stochastic dynamics of a set of species where the following rules apply: (1) replacement of a dead individual by local offspring – with probability 1-m, individuals picked at random are replaced by the offspring of other individuals picked at random; (2) replacement of a dead individual by an immigrant – with probability m individuals picked at random are replaced by immigrants taken at random from a pool of potential colonizers (the metacommunity).

Volkov et al. (2003, eq.7) provide the stationary solution for
the expected number
of species with a given abundance.
A probability density function is easily calculated by taking
these expected values for abundances 1:J and dividing them
by the total number of
species.
`dvolkov`

performs the numerical integration of the
density function by means of Gaussian quadrature, using a
library by Pavel Holoborodko (http://www.holoborodko.com/pavel/?page_id=679).
The code is based on the `untb::volkov`

function (Hankin 2007).
`pvolkov`

provides CDF by
cumulative sum of density values, and `qvolkov`

use
a numeric interpolation with a step function (`approxfun`

)
to find quantiles.
Calculations can be slow for larger datasets.

A special function Svolkov is provided to estimate the expected community size from a Volkov distribution with parameters theta, m and J, but this function is deprecated. A more comprehensive function to estimate community sizes will be developed in the future.

`dvolkov`

gives the (log) density of the density, `pvolkov`

gives the (log)
distribution function, `qvolkov`

gives the (log) the quantile function.

Invalid values for parameters `J`

or `theta`

will result in return
values `NaN`

, with a warning.

Paulo I Prado prado@ib.usp.br, Andre Chalom and Murilo Dantas Miranda.

Hankin, R.K.S. 2007. Introducing untb, an **R** Package For Simulating Ecological Drift
Under the Unified Neutral Theory of Biodiversity. *Journal of Statistical Software 22* (12).

Hubbell, S. P. 2001. *The Unified Neutral Theory of Biodiversity*.
Princeton University Press.

Volkov, I., Banavar, J.R., Hubbell, S.P., Maritan, A. 2003.
Neutral theory and relative species abundance in ecology.
*Nature 424*:1035–1037

`fitvolkov`

for maximum likelihood fit,
`dmzsm`

for the distribution of abundances in the metacommunity,
`volkov`

in package untb.

## Volkov et al 2003 fig 1 ## But without Preston correction to binning method ## and only the line of expected values by Volkov's model data( bci ) bci.oct <- octav( bci, preston = FALSE ) plot( bci.oct ) CDF <- pvolkov( bci.oct$upper, theta = 47.226, m = 0.1, J = sum(bci) ) bci.exp <- diff( c(0,CDF) ) * length(bci) midpoints <- as.numeric( as.character( bci.oct$octave ) ) - 0.5 lines( midpoints, bci.exp, type="b" ) ## the same with Preston binning using octavpred plot(octav( bci, preston = TRUE )) bci.exp2 <- octavpred( bci, sad = "volkov", coef = list(theta = 47.226, m = 0.1, J=sum(bci)), preston=TRUE) lines( bci.exp2 )

[Package *sads* version 0.4.2 Index]