Thursday, August 11, 2022

New preprint out: Incorporating sampling bias into permutation tests for niche and distribution models

I'm happy to announce that I have a new preprint out in collaboration with Jamie Kass, Ale Casadei-Ferreira, and Evan Economo.  I think this one is pretty important for anyone who's using ENMTools for hypothesis tests.

Using simulations, we demonstrate that hypothesis tests that use geographic randomization can be severely misled if the real occurrence data is subject to spatial sampling biases that are not included in the replicates used for constructing null distributions.  This reinforces a recent result by Osborne et al. showing that failing to include spatial autocorrelation in geographic randomization tests could have serious negative effects.  In both cases the result is an unacceptably high level of Type 1 error, leading users to conclude that test results were significant when they should not be.  In our case we showed that spatial sampling bias could be enough to generate statistically significant results on its own, even when the species being modeled was completely unaffected by the environmental predictors used for modeling.  This affects the ENMTools background test, the Raes and ter Steege-style (RTS) tests of model significance (and presumably the Bohl et al. 2019 test as well), and the bias assessment method demonstrated in our recent paper about Australian Pokemon (Warren et al. 2021).

To be completely frank this is one of those situations where we were in the middle of a study and were somewhat scooped - the excellent Osborne et al. study already demonstrates many of the same points we're making and was published right as we were getting our final simulation results back.  However, we think there are some important differences that make publishing this study still quite valuable.  

Most importantly, the Osborne et al. study includes all spatial autocorrelation in occurrence data into the pseudoreplicate data sets, while we focus on spatial sampling bias alone.  That means the Osborne et al. approach would be most useful in cases where it can be assumed that all spatial autocorrelation is a statistical artifact, while ours may be more useful in cases where you only want to correct for spatial autocorrelation due to spatial sampling bias while leaving the rest intact.  To the extent that spatial autocorrelation reflects individuals responding independently to a spatially autocorrelated environment, the spatial autocorrelation in the data set should arguably not be considered a statistical artifact as doing so would result in increased Type II error (erroneously failing to reject the null). Which one of these is a better idea will therefore vary by data set and requires a decent amount of thought (see Kühn and Dormann 2012 and Hawkins 2012 for a detailed discussion).  

However, our method requires a raster or set of points representing spatial sampling bias.  Any use of a sampling bias estimate comes with a large number of assumptions, and an inaccurate bias estimate will probably not fully correct for the inflated Type I error rate we demonstrate here (depending on exactly how wrong it is and exactly how it's wrong, if you get the distinction).  We discuss these issues in detail in the manuscript, and they are not trivial.

One thing is clear from both studies, however; using uniformly distributed points for pseudoreplicates makes a very strong assumption about spatial sampling bias and autocorrelation, and if those assumptions aren't met the result is an unacceptable rate of false positives.  I would highly recommend that people consider using one or the other of these methods (or both) for any geographic randomization tests in the future.

The good news from the ENMTools front is that this can already be done without modifying ENMTools.  You only need to provide the background points manually for the species objects, because the geographic randomization tests will sample from those automatically if they're available.  

I've had issues sampling in proportion to grid cell values using the functionality in the raster package before, so here's a quick function to get you started:

bias.sample <- function(bias.raster, npoints, replace = TRUE, biased = TRUE){
  # Convert the raster to a set of points
  bias.points <- data.frame(rasterToPoints(bias.raster))
  if(biased == TRUE){
    # Sampling is biased
    bias.points <- bias.points[sample(nrow(bias.points), 
                                      size = npoints, 
                                      prob = bias.points[,3],
                                      replace = replace),]
  } else {
    # Sampling is unbiased
    bias.points <- bias.points[sample(nrow(bias.points), 
                                      size = npoints, 
                                      replace = replace),]

To perform an RTS-style test of model significance with a bias layer you'd just sample your background manually from that layer and stuff it into the background points in the species object.  Let's say you already have a species object and have a bias layer named "bias.layer".  To do an RTS test that incorporates spatial sampling bias, you'd just do this:

this.species$background.points <- bias.sample(bias.layer, npoints)
this.species <- check.species(this.species) <- enmtools.maxent(this.species, env,
                             bg.source = "points",
                             rts.reps = 100)

Applying the correction to the background test is essentially the same, but for both species.  You'll want to crop your bias layer to the range of each species before sampling background for it, though, otherwise the background will be drawn from the entire area of the bias raster.  

Bohl, Corentin L., Jamie M. Kass, and Robert P. Anderson. 2019. “A New Null Model Approach to Quantify Performance and Significance for Ecological Niche Models of Species Distributions.” Journal of Biogeography 46 (6): 1101–11.

Hawkins, Bradford A. 2012. “Eight (and a Half) Deadly Sins of Spatial Analysis.” Journal of Biogeography 39 (1): 1–9.

Kühn, Ingolf, and Carsten F. Dormann. 2012. “Less than Eight (and a Half) Misconceptions of Spatial Analysis.” Journal of Biogeography 39 (5): 995–98.

Osborne, Owen G., Henry G. Fell, Hannah Atkins, Jan van Tol, Daniel Phillips, Leonel Herrera-Alsina, Poppy Mynard, et al. 2022. “Fauxcurrence: Simulating Multi-species Occurrences for Null Models in Species Distribution Modelling and Biogeography.” Ecography, April.

Warren, Dan L., Alex Dornburg, Katerina Zapfe, and Teresa L. Iglesias. 2021. “The Effects of Climate Change on Australia’s Only Endemic Pokémon: Measuring Bias in Species Distribution Models.” Methods in Ecology and Evolution / British Ecological Society 12 (6): 985–95.

Warren, Dan L., Jamie M. Kass, Alexandre Cassadei-Ferreira, and Evan P. Economo.  2022 (preprint). Incorporating sampling bias into permutation tests for niche and distribution models.  biorXiv.

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