nicheROVER (version 1.1.2)

overlap: Monte Carlo calculation of niche region overlap metrics.

Description

Calculates the distribution of a niche region overlap metric for each pairwise species combination and user-specified niche region sizes.

Usage

overlap(
  niche.par,
  nreps,
  nprob,
  alpha = 0.95,
  species.names,
  norm.redraw = TRUE
)

Value

Returns an array of size c(nspecies, nspecies, nreps, nlevels), where nlevels is the number of alpha levels at which to calculate the overlap metric. For each of the last two dimensions of the output array, the first two dimensions form an nspecies by nspecies matrix giving each pairwise calculation of overlap metric between two species for given \(\Theta_A\), \(\Theta_B\), and alpha. In each of these matrices, Species \(A\) is along the rows of this matrix and Species \(B\) is along the columns.

Arguments

niche.par

A list with nspecies = length(niche.par), each element of which in turn is a list with elements mu and Sigma. See Details.

nreps

The number of overlap metric calculations for each species. Defaults to the smallest number of parameter samples supplied by niche.par. See 'Details'.

nprob

The number of normal draws for each Monte Carlo overlap metric calculation. See 'Details'.

alpha

Scalar or vector of niche region sizes for calculating the niche overlap metric. Defaults to 0.95.

species.names

Names of the species. Defaults to names(niche.par).

norm.redraw

Logical. If FALSE, the same nprob*nspecies iid \(N(0,1)\) draws are used for each calculation of the overlap metric. This increases the Monte Carlo error, but the procedure is about 1.5x faster. Defaults to TRUE.

Details

The overlap metric is the probability that a randomly drawn individual from species \(A\) will be found within the niche region of species \(B\) (for a given niche region size, e.g., alpha = .95). It is a single number which is a function of the parameters for each species, \(\Theta_A = (\mu_A, \Sigma_A)\) and \(\Theta_B = (\mu_B, \Sigma_B)\). This number is difficult to calculate directly, but easy to approximate stochastically by generating nprob draws from the distribution of species \(A\) and counting the fraction of them which fall in the niche region of species \(B\).

Typically the true values of \(\Theta_A\) and \(\Theta_B\) are unknown and must be estimated from the data. Thus, the overlap metric is calculated for nreps combinations of samples from \(p(\Theta_A | X)\) and \(p(\Theta_B | X)\) which are supplied in niche.par.

See Swanson et al. (2015) for a detailed description of niche overlap and its calculation.

References

Swanson, H.K., Lysy, M., Stasko, A.D., Power, M., Johnson, J.D., and Reist, J.D. "A new probabilistic method for quantifying n-dimensional ecological niches and niche overlap." Ecology: Statistical Reports 96:2 (2015): 318-324. tools:::Rd_expr_doi("10.1890/14-0235.1").

See Also

overlap.plot(), niw.post(), niiw.post().

Examples

# fish data
data(fish)

# generate parameter draws from the "default" posteriors of each fish
nsamples <- 500
system.time({
  fish.par <- tapply(1:nrow(fish), fish$species,
                     function(ii) niw.post(nsamples = nsamples, X = fish[ii,2:4]))
})

# overlap calculation. use nsamples = nprob = 1e4 for more accurate results.
system.time({
  over <- overlap(fish.par, nreps = nsamples, nprob = nsamples,
                  alpha = c(.95, .99))
})

# posterior expectations of overlap metrics
over.mean <- apply(over*100, c(1:2, 4), mean)
round(over.mean)

# posterior 95% credible intervals of overlap metrics
over.cred <- apply(over*100, c(1:2, 4), quantile,
                   prob = c(.025, .975), na.rm = TRUE)
round(over.cred[,,,1]) # display alpha = .95 niche region