To assess bias related to sampling effort, we use one of the most widely used datasets for studying biodiversity at large spatial extents: the GBIF dataset. GBIF data comprise a large range of species occurrence observations collected using a variety of sampling approaches. The data span from well-established plot censuses to direct observations collected during field trips. Consequently, some of the data points are at the centre of sampled grids (each point comprises the species located at a specific-size quadrant) or correspond to a single observation of at least one individual of the same species. These differences also depend on the methodologies used to observe/record occurrences per taxon. Plots and transects are common practices in vegetation censuses, while transects, point counts, and live traps are preferred in the case of animals. Moreover, the variation in factors—such as per country biodiversity monitoring schemes, funding schemes, focal ecosystems, and accessibility to remote areas—add another source of variation, especially at multinational scales (Barbosa et al. 2013).

We aimed to quantify and map the uncertainty derived from variations in observations due to differences in sampling efforts. Cartograms were used to illustrate uncertainty, in which the shape of objects (countries) correlates with the level of uncertainty. Cartograms build on the standard treatment of diffusion, in which the current density is given by:

\documentclass[12pt]{standalone} \usepackage{varwidth} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage{amsmath, amssymb, graphics, setspace} \newcommand{\mathsym}[1]{{}} \newcommand{\unicode}[1]{{}} \newcounter{mathematicapage} \begin{document} \begin{varwidth}{50in} \begin{equation*} J = v(r, t) \rho(r, t) \end{equation*} \end{varwidth} \end{document}

where \documentclass[12pt]{standalone} \usepackage{varwidth} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage{amsmath, amssymb, graphics, setspace} \newcommand{\mathsym}[1]{{}} \newcommand{\unicode}[1]{{}} \newcounter{mathematicapage} \begin{document} \begin{varwidth}{50in} \begin{equation*} v(r, t) \end{equation*} \end{varwidth} \end{document} and \documentclass[12pt]{standalone} \usepackage{varwidth} \usepackage[utf8x]{inputenc} \usepackage[T1]{fontenc} \usepackage{lmodern} \usepackage{amsmath, amssymb, graphics, setspace} \newcommand{\mathsym}[1]{{}} \newcommand{\unicode}[1]{{}} \newcounter{mathematicapage} \begin{document} \begin{varwidth}{50in} \begin{equation*} \rho(r, t) \end{equation*} \end{varwidth} \end{document} are the velocity and density at a given position (r) and time (t) (Gastner and Newman 2004). The cartograms are created using ScapeToad, a free and open source software, that uses as an input a set of polygons (e.g. countries) with values (e.g., number of observations) and modifies the size of the polygons based on the density of observations contained (see Fig. 1). The shape and final area of the countries will derive from the difference between the actual size of the country and the size of the sampling (i.e., the number of observations).

In the proposed method, uncertainty is shown at the country level and corresponds with the deformation of the original country area. In other words, countries bigger than their original size require strategies to reduce the effect of oversampling on the products derived from the GBIF data, while countries smaller than their original sizes require more sampling effort. Future developments will include the visualization of species distribution model predictions combined with the maps of uncertainty presented here.