Estimate the expected species abundance distribution of both guilds using the guilds model, provided theta, alpha_x, alpha_y and J.

This function estimates the expected species abundance distribution of both guilds using the guilds model, provided theta, alpha_x, alpha_y and J. The expected species abundance distribution is approximated by first drawing px from a beta distribution (equation 4 in Janzen et al. 2015). Then, guild sizes are drawn using equation 3 in Janzen et al. 2015. Because the abundance distributions of the two guilds are independent, the distributions can now be obtained using equation 6 in Etienne and Alonso 2005. Because drawing from the beta distribution and equation 3 is inherently stochastic, this function returns the average over a specified number of replicates.

Usage

expected.SAD.Guilds(theta, alpha_x, alpha_y, J, n_replicates = 100)

Arguments

theta: Fundamental biodiversity number theta
alpha_x: Dispersal ability of guild X
alpha_y: Dispersal ability of guild Y
J: Total number of individuals in the local community, e.g. J = Jx + Jy
n_replicates: Number of replicates to use to estimate the abundance distributions.

Value

guildX: Vector containing the mean abundances of species in Guild X, binned into log2 bins
guildY: Vector containing the mean abundances of species in Guild Y, binned into log2 bins

References

Etienne, R.S., & Alonso, D. (2005). A dispersal-limited sampling theory for species and alleles. Ecology Letters, 8(100), 1147-1156.

Author

Thijs Janzen & Bart Haegeman

Examples

  SADs <- expected.SAD.Guilds(theta = 42, alpha_x = 0.01, alpha_y = 0.1, J = 1000, n_replicates = 3)
  par(mfrow=c(1,2));
  barplot(SADs$guildX,names.arg=0:(length(SADs$guildX)-1),
    xlab="Number of individuals (log2)",
    ylab="Number of Species",main="Guild X" )

  barplot(SADs$guildY,names.arg=0:(length(SADs$guildY)-1),
    xlab="Number of individuals (log2)",
    ylab="Number of Species",main="Guild Y" )