The distance decay of similarity in tropical rainforests. A spatial point processes analytical formulation

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

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. 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. 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). 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. 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 slopes. Our results suggest that the degree of equilibrium decreases from marine to terrestrial realms, and is markedly different between vertebrates and beetles. This has profound implications on the expected ability of different groups to track their suitable climates, and thus on the impact of climate change on biodiversity.

Replicated point processes with application to population dynamics models

In this paper we study spatially clustered distribution of individuals using point process theory. In particular we discuss the spatially explicit neutral model of population dynamics of Shimatani (2010) which extends previous works on Malécot theory of isolation by distance. We reformulate Shimatani model of replicated Neyman-Scott process to allow for a general dispersal kernel function and we show that the random migration hypothesis can be substituted by the long dispersal distance property of the kernel. Moreover, the extended framework presented here is fit to handle spatially explicit statistical estimators of genetic variability like Moran autocorrelation index or Sørensen similarity index. We discuss the pivotal role of the choice of dispersal kernel for the above estimators in a toy model of dynamic population genetics theory.