Simulate presences and absences from logistic responses — simulate

The two-gradient simulation of Appendix C of Peres-Neto et al. (2012), after Ives & Helmus (2011). The probability that species j occurs at site t along gradient x is plogis(a[j] + b[j] * x[t]), where a is a normal deviate and the slope b evolves on the tree. With several gradients, each with its own a and b, the probabilities multiply. A value drawn for each site from reduction then reduces them, which adds noise.

Usage

simulate_logistic(
  tree,
  gradients,
  intercept_mean = 0,
  intercept_sd = 0.5,
  slope_sd = 1,
  lambda = 1,
  reduction = c(0.5, 1),
  draw = c("uniform", "normal")
)

Arguments

tree: A phylo tree with branch lengths. Appendix C uses a fully balanced tree with 32 species.
gradients: Value of the gradient at each site, or a list or data frame with one gradient per element, such as logistic_gradients(). Gradients are centred.
intercept_mean, intercept_sd: Mean and standard deviation of a. Appendix C does not give these values, and the defaults are those of the code of Ives & Helmus (2011).
slope_sd: Standard deviation of the slopes b among the species of the tree, as in the code of Ives & Helmus (2011). Appendix C does not give this value.
lambda: Pagel's lambda of the slopes.
reduction: Range of the uniform distribution of the site reduction.
draw: Distribution of the value compared with each probability.

Value

List of class mc_sim with abundance, a 0/1 matrix with one row per site and one column per species; probability, the matrix of probabilities; env, the gradients; and traits, a list with the matrices intercept and slope, with one row per species and one column per gradient.

Details

Appendix C says that a species is present when a normally generated value is smaller than its probability. Taken literally, a species with a probability near zero is present half of the time, so the default is a uniform value (a Bernoulli draw), and draw = "normal" follows the text.

References

Ives, A. R., & Helmus, M. R. (2011). Generalized linear mixed models for phylogenetic analyses of community structure. Ecological Monographs, 81, 511–525. doi:10.1890/10-1264.1

Peres-Neto, P. R., Leibold, M. A., & Dray, S. (2012). Assessing the effects of spatial contingency and environmental filtering on metacommunity phylogenetics. Ecology, 93, S14–S30. doi:10.1890/11-0494.1

Examples

set.seed(1)
tr <- ape::compute.brlen(ape::stree(32, "balanced"), method = "Grafen")
simulate_logistic(tr, logistic_gradients(1)[c("x", "y")])
#> <mc_sim> 31 sites x 32 species
#> species persisting: 32 of 32 
#> mean local richness: 5.65