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Estimate the expected species abundance distribution of both guilds using the guilds model, provided theta, alpha_x, alpha_y, conditional on the size of guild X, Jx and the size of guild Y, Jy.

expected.SAD.Guilds.Conditional.Rd

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 equation 9. 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.Conditional(theta, alpha_x, alpha_y, Jx, Jy, n_replicates = 100)

Arguments

theta

Fundamental biodiversity number theta

alpha_x

Dispersal ability of guild X

alpha_y

Dispersal ability of guild Y

Jx

Total number of individuals in guild X

Jy

Total number of individuals in guild Y

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.Conditional(theta = 42,
                                          alpha_x = 0.01,
                                          alpha_y = 0.1,
                                          Jx = 100,
                                          Jy = 200,
                                          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" )