Fit and test a distance-decay model

Fits a nonlinear distance-decay model to the pairwise similarities from beta_decay() and tests it by permutation, as in betapart::decay.model() (Gómez-Rodríguez and Baselga 2018). Similarity is one minus the chosen dissimilarity component. The models are

Usage

beta_decay_model(
  x,
  model = c("exponential", "power"),
  component = c("total", "turnover", "nestedness"),
  permutations = 999
)

Arguments

x

A td_beta_decay tibble from beta_decay(). Its groups are kept and fitted separately.

model

"exponential" or "power".

component

Dissimilarity component turned into similarity: "total", "turnover" or "nestedness".

permutations

Number of permutations for the test; 0 skips it.

Value

A tibble with one row per group: model, component, n_pairs, a, b, half_distance (the distance over which similarity halves, \(\log 2 / b\) for the exponential model and the factor \(2^{1/b}\) for the power model), pseudo_r2, aic and p.value.

Details

• "exponential": \(S = a e^{-b d}\) (Nekola and White 1999), and

• "power": \(S = a d^{-b}\), which needs positive distances.

Here a is the similarity at distance zero (exponential) or one (power), and b is the rate of decay: positive values mean similarity falls with distance. The fit is by nonlinear least squares, and the fit statistic is the pseudo-\(R^2\), one minus the residual deviance over the deviance of a constant model.

Pairs of sites are not independent, so the test permutes site labels: rows and columns of the similarity matrix are shuffled together while the distances stay in place, as in a Mantel test, and the model is refitted each time. The p-value is \((1 + \#\{R^2_{perm} \ge R^2_{obs}\}) / (1 + B)\). betapart instead reports the proportion of permuted values strictly greater than the observed one, which can be zero; the version here cannot.

References

Nekola, J. C. and White, P. S. (1999). The distance decay of similarity in biogeography and ecology. Journal of Biogeography, 26, 867-878. doi:10.1046/j.1365-2699.1999.00305.x

Gómez-Rodríguez, C. and Baselga, A. (2018). Variation among European beetle taxa in patterns of distance decay of similarity suggests a major role of dispersal processes. Ecography, 41, 1825-1834. doi:10.1111/ecog.03693

Examples

decay <- beta_decay(png_ants, gradient = elevation, .by = season)
set.seed(1)
beta_decay_model(decay, permutations = 199)
#> # A tibble: 2 x 10
#>   season model    component n_pairs     a       b half_distance pseudo_r2    aic
#>   <chr>  <chr>    <chr>       <int> <dbl>   <dbl>         <dbl>     <dbl>  <dbl>
#> 1 dry    exponen~ total          10 0.257 7.50e-4          924.     0.143  -9.21
#> 2 wet    exponen~ total          10 0.897 2.36e-3          293.     0.694 -17.6 
#> # i 1 more variable: p.value <dbl>