powerFraction: Power Fraction Model

In MarioJose/nicheApport: Tokeshi's Niche Apportionment Species Abundance Distributions Models

Description

Simulate a ranked abundance distribution for Power Fraction, Random Fraction and MacArthur Fraction models. The total niche is sequential and randomly divided and probability p of selection of a fraction is related with fraction length or abundance x by w as a power function (p*x^w, where 0 <= emphw <= 1). First, total niche is divided randomly in two fraction. Then, one of this two fraction is selected, with probability of selection of each fraction emphp*x^w, and divided again in two fraction. One of this three fraction is selected, again with probability p*x^w for each fraction, and divided again in two fraction. This procedures is repeated until all species have a fraction of total niche.

Usage

  randFraction(N, S, count = FALSE)
  powerFraction(N, S, w = 0.2, count = FALSE)
  MacArthurFraction(N, S, count = FALSE)

Arguments

N	Total abundance. See 'Details' for more information.
S	Number of species.
w	Exponential parameter to weighting fraction selection by abundance. See 'Details' for more information.
count	Define if measure of abundance is number of individuals. See 'Details' for more information.

Details

Abundance is a measure of the amount of each species and can be represented by number of individuals or biomass, dry weight or cover (Pielou 1975). If the argument count is TRUE, then each specie will have amount of individual in accordance with model rules. Note that some species may have zero individual if model rules result in hight dominance. If count is FALSE (default), then each species will have a fraction of total abundance. The values randomly generated to represent amount of niche to be divided follow uniform distribution.

The Random Fraction and MacArthur Fraction models are special cases of Power fraction model. When w = 0, Power Fraction correspond to Random Fraction and the probability of selection of fractions are independently of fraction length (abundance). In this case all fraction have the same probability of selection. When w = 1, Power Fraction correspond to MacArthur Fraction and fractions have probability of selection weighted by their abundances. Values of w between 0 and 1 (Power Fraction), the probability selection of fractions are weighted by w as a power of their abundances (p*x^w). Tokesh (1996) proposed this model as alternative to species-rich communities in face of other model fit well in species-poor communities. The author verified that Power Fraction with w = 0.2 fit well to many species-rich communities analysed. The function randFraction and MacArthurFraction call powerFraction internally with respective w value (0 and 1).

Value

A vector of ranked species abundance from the most abundant (rank 1) to the least abundant (rank S).

Author(s)

Mario J. Marques-Azevedo

Maintainer: Mario J. Marques-Azevedo <[e-mail]>

References

Pielou, E. C. 1975. Ecological diversity. Wiley, New York.

Tokeshi, M. 1996. Power fraction: a new explanation of relative abundance patterns in species-rich assemblages. Oikos 75: 543-550.

See Also

For others models see dominanceDecay, dominancePreemp, MacArthurFraction, randFraction and randAssort.

For fit models see fitmodel and fitmodelCl to fit using parellel computation. To find best w parameter to powerFraction see findPFw.

Examples

  set.seed(42)
  randFraction(100, 10)
  
  powerFraction(100, 10, w = 0.2)
  
  MacArthurFraction(100, 10)

MarioJose/nicheApport documentation built on May 7, 2019, 2:52 p.m.