Assessing the equilibrium between assemblage composition and climate: A directional distance-decay approach

1. The variation of assemblage composition in space is characterised by the decrease in assemblage similarity with spatial distance. Climatic constraint and dispersal limitation are major drivers of distance-decay of similarity. Distance-decay of similarity is usually conceptualised and modelled as an isotropic pattern, that is, assuming that similarity decays with the same rate in all directions. 2. Because climatic gradients are markedly anisotropic, that is, they have different strength in different directions, if species distributions were in equilibrium with climate, the decay of assemblage similarity should be anisotropic in the same direction as the climatic gradient, that is, faster turnover in the direction that maximises the climatic gradient. Thus, deviations from equilibrium between assemblage composition and climatic conditions would result in differences in anisotropy between distance-decay of similarity and climatic gradients. 3. We assessed anisotropy in distance-decay patterns in marine plankton assemblages, terrestrial vertebrates and European beetles, using two procedures: (a) measuring the correlation between the residuals of a distance-decay model and the angle in which pairs of sites are separated and (b) computing two separate distance-decay models for each dataset, one using only pairwise cases that are separated on North-South direction and another one using pairwise cases separated on East-West direction. We also analysed whether the degree of anisotropy in distance-decay is related to dispersal ability (proportion of wingless species and body size) and ecological niche characteristics (main habitat and trophic position) by assessing these relationships among beetle taxonomic groups (n = 21). 4. Anisotropy varied markedly across realms and biological groups. Despite climatic gradients being steeper in North-South direction than in East-West direction in all datasets, North-South distance-decays tended to be steeper than East-West distance-decays in plankton and most vertebrate assemblages, but flatter in European amphibians and most beetle groups. 5. Anisotropy also markedly varied across beetle groups depending on their dispersal ability, as the proportion of wingless species explained 60% of the variance in the difference between North-South and East-West distance-decay slopesThis research was supported by the Spanish Ministerio de Ciencia, Innovación y Universidades and the European Regional Development Fund (ERDF) through grant CGL2016-76637-PS

Spatial non-stationarity and anisotropy of compositional turnover in eastern Australian Myrtaceae species

<div><p>Knowledge of species compositional turnover, the rate of change in the number of species shared between locations along geographic and environmental gradients, is important for conservation planning. Spatially global models relating species and environmental turnover are well established. However, to date there has been no explicit assessment of the effects of geographical variation in parameters (spatial non-stationarity) and directional dependence (anisotropy) on these models. Such processes are well known to affect other geospatial analyses. Here, we assess how these affect the shape, goodness of fit and composition of species turnover–environment relationships. We use the eastern Australian distribution of species in the Myrtaceae, an important family of vascular plants in the region. We obtained distribution data for Myrtaceae species from herbarium records and corresponding environmental attributes (mean of 1 km gridded cell values aggregated to 10 km grid cells). Species compositional turnover was quantified using the Sørensen pairwise dissimilarity index. The turnover–environment relationship was analysed using generalised dissimilarity modelling (GDM), a purpose-designed statistical regression technique. The data were divided into three sets of spatially local subsamples: 27 rectangular east–west-aligned coastal–inland bands, 8 north–south coastally aligned bands and 12 symmetrical omnidirectional blocks. A separate GDM was fitted to each spatially local subsample. The results display marked evidence of spatial variation in the shape, goodness of fit and composition of local species turnover–environment relationships, with this variation appearing strongly directional. The observed spatial structure of local biodiversity–environment relationships, expressed as species compositional turnover, is unsurprising considering both the steep east–west environmental gradients associated with Australia's eastern ranges and the known decreasing sampling intensity in the same direction. Local spatial non-stationarity and anisotropy are expected outcomes irrespective of the chosen turnover index, study taxa or statistical model used. Currently, it is difficult to separate genuine biogeographic effects from data bias. Future analyses could better account for the observed spatial structure of both biodiversity–environment relationships and data bias by incorporating directionality in data subsampling strategies and explicit biogeographic predictors in model design.</p> </div