A quixotic view of spatial bias in modelling the distribution of species and their diversity

Abstract

Ecological processes are often spatially and temporally structured, potentially leading to autocorrelation either in environmental variables or species distribution data. Because of that, spatially-biased in-situ samples or predictors might affect the outcomes of ecological models used to infer the geographic distribution of species and diversity. There is a vast heterogeneity of methods and approaches to assess and measure spatial bias; this paper aims at addressing the spatial component of data-driven biases in species distribution modelling, and to propose potential solutions to explicitly test and account for them. Our major goal is not to propose methods to remove spatial bias from the modelling procedure, which would be impossible without proper knowledge of all the processes generating it, but rather to propose alternatives to explore and handle it. In particular, we propose and describe three main strategies that may provide a fair account of spatial bias, namely: (i) how to represent spatial bias; (ii) how to simulate null models based on virtual species for testing biogeographical and species distribution hypotheses; and (iii) how to make use of spatial bias - in particular related to sampling effort - as a leverage instead of a hindrance in species distribution modelling. We link these strategies with good practice in accounting for spatial bias in species distribution modelling.

Fig. 1. Plant species occurrences over the globe available in GBIF (https://www.gbif.org, latest access: December 2021).

The cartogram or density-equalizing map as proposed by Dorling and Gastner and Newman) shows a bias on species occurrences towards continents with higher sampling effort. To generate the cartogram, a geographical grid of 10 degrees was superimposed on the dataset and the grid cells were further distorted according to the amount of plant species occurrences.

Fig. 2. The procedure used to generate virtual species and colorist-based community distribution.

First of all, the climatic variables are selected (a) and the species response functions of each environmental variable are set (b). The environmental suitability of the virtual species distribution is generated in conformity with the response functions (c). Then, a logistic conversion transforms it into presences and absences (d) and presence and absence points are sampled according to the sample prevalence value (e). Furthermore, a collinearity test is performed and the correlated variables are removed (f). Once the statistical model has been calibrated, the climatic variables for the prediction are selected (g) and—among them—those which are correlated are deleted (h). Eventually, multiple virtual species distributions are combined together in colorist R package to map community distribution (i). Results are shown in Fig. 3. The complete code to generate virtual species and final maps is available in both Appendix 1 and at the following GitHub repository link: https://github.com/ducciorocchini/Virtual_species_SDM/.

Fig. 3. Virtual species can be built to form a virtual community.

Starting from colours of single virtual species distributions and relying on the colorist package, it is possible to spatially merge colours and their overlaps in a final gamut which account for single species colour intensity.

Fig. 4. Boxplots of the β coefficients in three different models using a different prior on sampling effort.

Each box represents the 1st and 3rd quartiles of a coefficient distribution, the black horizontal line the distribution median, the whiskers the limits of the 1.5*interquartile range, while the filled circles represent the outlying points. We showed in red the boxplots reporting the distribution of the β coefficient of the sampling effort. Relying on Bayesian statistics it is possible to set three priors on sampling effort: not considering its effect, considering its effect in a mild manner, or in a strong manner. Sampling effort can be measured as an example by the number of revisiting dates. The precision of sampling effort increased passing from the model with an uninformative prior on sampling effort, through that with a mild prior, reaching its highest value in the model with a strong prior. Controlling sampling effort bias using a strongest prior could lead to the comparability of models related to species with opposite degrees of sampling effort in an area. See the main text for additional information. From Rocchini et al.: License Number: 5495740269939, License date: Feb 25th 2023, Licensed Content Publisher: Elsevier.