Simulate a static metacommunity — simulate

Draws species abundances directly from unimodal responses to an environmental gradient, without population dynamics, competition or dispersal. The expected abundance of species j at site i is r_max[j] * exp(-(env[i] - optimum[j])^2 / (2 * sigma[j]^2)), the Gaussian response of Dray & Legendre (2008), also used by Peres-Neto et al. (2012). By default, observed abundances are Poisson counts with that mean, as in Peres-Neto & Kembel (2015) and Duarte et al. (2016), where r_max lies between 0 and 30. In the two earlier studies r_max lies between 0.5 and 1, abundances are the expected values (sampling = "expected"), and Dray & Legendre (2008) draw presences from a binomial distribution with the expected value as the probability (sampling = "binomial"). Because nothing but the gradient structures the data, this is a baseline for simulate_metacommunity() and a fast generator for evaluating methods.

Usage

simulate_static(
  traits,
  env,
  incidence = FALSE,
  sampling = c("poisson", "binomial", "expected")
)

Arguments

traits: Data frame from species_traits(), or any data frame with columns optimum, sigma and r_max, or a list of them, one per gradient, with the same species. Here r_max is the maximum expected abundance, not a growth rate, so set rmax_range accordingly. With several gradients the maxima multiply, so a range such as c(1, 1) in all but one of them keeps abundances on the scale of the first.
env: Value of the gradient at each site, or a list or data frame with one gradient per element, in the order of traits.
incidence: Return presences and absences instead of Poisson counts? A species is present where its count is positive. Only for sampling = "poisson".
sampling: How to obtain the data from the expected values: "poisson" draws counts, "binomial" draws presences and absences, which needs expected values of at most 1, and "expected" returns the expected values.

Value

List of class mc_sim with abundance, a matrix with one row per site and one column per species, plus env and traits. Sites and species with no individuals are kept, so remove them if a method requires it.

Details

With several gradients, for example an environmental and a spatial one, each species has its own response to each gradient and the expected abundance is the product of the responses, as in Peres-Neto et al. (2012).

References

Dray, S., & Legendre, P. (2008). Testing the species traits-environment relationships: the fourth-corner problem revisited. Ecology, 89, 3400–3412. doi:10.1890/08-0349.1

Duarte, L. D. S., et al. (2016). Dissecting phylogenetic fuzzy weighting: theory and application in metacommunity phylogenetics. Methods in Ecology and Evolution, 7, 937–946. doi:10.1111/2041-210X.12547

Peres-Neto, P. R., & Kembel, S. W. (2015). Phylogenetic gradient analysis: environmental drivers of phylogenetic variation across ecological communities. Plant Ecology, 216, 709–724. doi:10.1007/s11258-014-0405-0

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 <- treeshapesim::sim_tree_shape(20)
traits <- species_traits(tr, lambda = 1, optima_range = c(-1, 101),
                         rmax_range = c(0, 30))
sim <- simulate_static(traits, env = runif(100, 0, 100))
sim
#> <mc_sim> 100 sites x 20 species
#> species persisting: 19 of 20 
#> mean local richness: 8.35 

# an environmental and a spatial gradient
space <- species_traits(tr, lambda = 1, optima_range = c(-1, 101),
                        rmax_range = c(1, 1))
gradients <- data.frame(env = runif(100, 0, 100), space = 1:100)
simulate_static(list(traits, space), gradients)
#> <mc_sim> 100 sites x 20 species
#> species persisting: 18 of 20 
#> mean local richness: 4.01