Interaction between intraspecific variability and species sampling - Phylogenetic Linear Regression

Performs analyses of sensitivity to species sampling by randomly removing species and detecting the effects on parameter estimates in a phylogenetic linear regression, while taking into account potential interactions with intraspecific variability.

intra_samp_phylm(
  formula,
  data,
  phy,
  n.sim = 10,
  n.intra = 3,
  breaks = seq(0.1, 0.5, 0.1),
  model = "lambda",
  Vy = NULL,
  Vx = NULL,
  distrib = "normal",
  y.transf = NULL,
  x.transf = NULL,
  track = TRUE,
  ...
)

Arguments

formula	The model formula
data	Data frame containing species traits with row names matching tips in `phy`.
phy	A phylogeny (class 'phylo') matching `data`.
n.sim	The number of times species are randomly deleted for each `break`.
n.intra	Number of datasets resimulated taking into account intraspecific variation (see: `"intra_phylm"`)
breaks	A vector containing the percentages of species to remove.
model	The phylogenetic model to use (see Details). Default is `lambda`. #' @param Vy Name of the column containing the standard deviation or the standard error of the response variable. When information is not available for one taxon, the value can be 0 or `NA`.
Vy	Name of the column containing the standard deviation or the standard error of the response variable. When information is not available for one taxon, the value can be 0 or `NA`.
Vx	Name of the column containing the standard deviation or the standard error of the predictor variable. When information is not available for one taxon, the value can be 0 or `NA`
distrib	A character string indicating which distribution to use to generate a random value for the response and/or predictor variables. Default is normal distribution: "normal" (function `rnorm`). Uniform distribution: "uniform" (`runif`) Warning: we recommend to use normal distribution with Vx or Vy = standard deviation of the mean.
y.transf	Transformation for the response variable (e.g. `"log"` or `"sqrt"`). Please use this argument instead of transforming data in the formula directly (see also details below).
x.transf	Transformation for the predictor variable (e.g. `"log"` or `"sqrt"`). Please use this argument instead of transforming data in the formula directly (see also details below).
track	Print a report tracking function progress (default = TRUE)
...	Further arguments to be passed to `phylolm`

Value

The function samp_phylm returns a list with the following components:

formula: The formula

full.model.estimates: Coefficients, aic and the optimised value of the phylogenetic parameter (e.g. lambda or kappa) for the full model without deleted species.

sensi.estimates: A data frame with all simulation estimates. Each row represents a model rerun with a given number of species n.remov removed, representing n.percent of the full dataset. Columns report the calculated regression intercept (intercept), difference between simulation intercept and full model intercept (DIFintercept), the percentage of change in intercept compared to the full model (intercept.perc) and intercept p-value (pval.intercept). All these parameters are also reported for the regression slope (DIFestimate etc.). Additionally, model aic value (AIC) and the optimised value (optpar) of the phylogenetic parameter (e.g. kappa or lambda, depending on the phylogenetic model used) are reported. Lastly we reported the standardised difference in intercept (sDIFintercept) and slope (sDIFestimate).

sign.analysis For each break (i.e. each percentage of species removed) this reports the percentage of statistically significant (at p<0.05) intercepts (perc.sign.intercept) over all repetitions as well as the percentage of statisticaly significant (at p<0.05) slopes (perc.sign.estimate).

data: Original full dataset.

Details

This function randomly removes a given percentage of species (controlled by breaks) from the full phylogenetic linear regression, fits a phylogenetic linear regression model without these species using phylolm, repeats this many times (controlled by n.sim), stores the results and calculates the effects on model parameters. This operation is repeated n.intra times for simulated values of the dataset, taking into account intraspecific variation. At each iteration, the function generates a random value for each row in the dataset using the standard deviation or errors supplied, and evaluates the effects of sampling within that iteration.

All phylogenetic models from phylolm can be used, i.e. BM, OUfixedRoot, OUrandomRoot, lambda, kappa, delta, EB and trend. See ?phylolm for details.

Currently, this function can only implement simple linear models (i.e. \(trait~ predictor\)). In the future we will implement more complex models.

Output can be visualised using sensi_plot.

Note

Please be aware that dropping species may reduce power to detect significant slopes/intercepts and may partially be responsible for a potential effect of species removal on p-values. Please also consult standardised differences in the (summary) output.

References

Paterno, G. B., Penone, C. Werner, G. D. A. sensiPhy: An r-package for sensitivity analysis in phylogenetic comparative methods. Methods in Ecology and Evolution 2018, 9(6):1461-1467

Werner, G.D.A., Cornwell, W.K., Sprent, J.I., Kattge, J. & Kiers, E.T. (2014). A single evolutionary innovation drives the deep evolution of symbiotic N2-fixation in angiosperms. Nature Communications, 5, 4087.

Ho, L. S. T. and Ane, C. 2014. "A linear-time algorithm for Gaussian and non-Gaussian trait evolution models". Systematic Biology 63(3):397-408.

Examples

if (FALSE) {
# Load data:
data(alien)
# Run analysis:
samp <- intra_samp_phylm(gestaLen ~ adultMass, phy = alien$phy[[1]],
                         y.transf = log,x.transf = NULL,Vy="SD_gesta",Vx=NULL,
                         data = alien$data, n.intra = 5, n.sim=10)
summary(samp)
head(samp$sensi.estimates)
# Visual diagnostics
sensi_plot(samp)
# You can specify which graph and parameter ("estimate" or "intercept") to print: 
sensi_plot(samp, graphs = 1)
sensi_plot(samp, graphs = 2)
}