Spatial complexity of ecological communities: Bridging the gap between probabilistic and non-probabilistic uncertainty measures

Recently, it has become well appreciated that disorder-based measures of biological diversity, such as Shannon's entropy, fail to adequately capture the structural complexity of an ecological community. The contributions of spatial complexity to community structure are however quantifiable if we consider, for example, the degree of spatial co-occurrence between species. The larger and more intricate these correlations, the more structurally complex the community. We suggest that Juhász-Nagy information-theoretical functions offer an adequate basis for the measurement of structural complexity of plant communities. However, whereas Juhász-Nagy's developed his model solely in terms of classical probabilistic uncertainty, we show that these functions are based both on traditional probabilistic concepts and on non-probabilistic elements borrowed from fuzzy set theory. Therefore, the proposed representation of community structure offers an interesting way for linking probabilistic uncertainty and fuzzy uncertainty. It also turns out that Juhász-Nagy information-theoretical functions fit previously established theoretical definitions of ecological complexity. We illustrate the utility of the proposed functions to the multi-scale analysis of disturbed and undisturbed plant communities.