Crossing the borders of spatial analysis and modelling: A rethink
Date
2008
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Nova Science Publishers
Abstract
Understanding the mechanisms behind the spatial patterns of species distributions is
one of the major focuses in theoretical ecology. Spatial modelling techniques such as
lattice models and cellular automata bring numerous spatial patterns in ecology. Taking
spatial factors into account also helps to solve many puzzles in ecology, such as the
paradoxes of diversity, polymorphism and altruism. To analyze the numerous spatial
patterns, ecologists introduced the moment approximation from statistical physics.
Spatial analysis of species distributions can also finds its roots in the sampling statistics of ecology. Based on aggregation indicators (e.g. Lloyd’s indices and joint-count statistics), ecologists are able to distinguish the degree of non-randomness from spatially implicit and explicit perspectives, with over-dispersal and spatial autocorrelation as the synonyms of aggregation, respectively. Such sampling statistics also leads to the occupancy-abundance relationship with valuable applications in conservation. Although
both spatial modelling and spatial analysis aim to achieve a profound understanding of
species spatial patterns, they barely intersect. Through building the connections between sampling statistics and moment (pair) approximation, we unveil the relationship between the sampling density (mean abundance) and the colonization-extinction process. The intersection also solves the scaling pattern of species distribution by applying the pair
approximation and the Bayesian rule into the joint-count statistics. By a scaling
metapopulation model, we found that randomness is the bridge linking sampling statistics and spatial modelling, as well as the spatially implicit and explicit patterns. This intersection also sheds light on the occupancy-abundance relationship and the connection between spatial patterns and species life-history traits. In this exercise, we emphasize the importance and potential of bringing these two schools of knowledge together in understanding ecological complexity. Ten merging questions that require this intersection have been presented to expound on possible applications to the species distribution and
the community structure in the near future.
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Citation
Hui, C. (2008) Crossing the borders of spatial analysis and modelling: A rethink. In: Kelly, J.T. (ed.) Progress in Mathematical Biology Research, pp. 191-219. Nova Science Publishers, Inc., Hauppauge, NY, USA. ISBN: 978-1-604-56171-5