Mapping diversity indices: not a trivial issue

Mapping diversity indices, that is estimating values in all locations of a given area from some sampled locations, is central to numerous research and applied fields in ecology. Two approaches are used to map diversity indices without including abiotic or biotic variables: (i) the indirect approach, which consists in estimating each individual species distribution over the area, then stacking the distributions of all species to estimate and map a posteriori the diversity index, (ii) the direct approach, which relies on computing a diversity index in each sampled locations and then to interpolate these values to all locations of the studied area for mapping. For both approaches, we document drawbacks from theoretical and practical viewpoints and argue about the need for adequate interpolation methods. First, we point out that the indirect approach is problematic because of the high proportion of rare species in natural communities. This leads to zero-inflated distributions, which cannot be interpolated using standard statistical approaches. Secondly, the direct approach is inaccurate because diversity indices are not spatially additive, that is the diversity of a studied area (e.g. region) is not the sum of the local diversities. Therefore, the arithmetic variance and some of its derivatives, such as the variogram, are not appropriate to ecologically measure variation in diversity indices. For the direct approach, we propose to consider the β-diversity, which quantifies diversity variations between locations, by the mean of a β-gram within the interpolation procedure. We applied this method, as well as the traditional interpolation methods for comparison purposes on different faunistic and floristic data sets collected from scientific surveys. We considered two common diversity indices, the species richness and the Rao's quadratic entropy, knowing that the above issues are true for complementary species diversity indices as well as those dealing with other biodiversity levels such as genetic diversity. We conclude that none of the approaches provided an accurate mapping of diversity indices and that further methodological developments are still needed. We finally discuss lines of research that may resolve this key issue, dealing with conditional simulations and models taking into account biotic and abiotic explanatory variables.