Motivations
The ecological patterns observed in nature have traditionally been explained by postulating niches into which the differentially endowment of individuals permits each species to evolve. In contrast, 'neutral theory' assumes the equivalence of individuals belonging to trophycally similar species and explains species composition simply by the drift due to the stochasticity in birth, death and dispersal. Neutral theory has provided an explanation of many of the observed ecological patterns without the need of further mechanisms, such as suitability to their environment. However, it has been shown recently that it fails to explain some important facts, for example some of the spatial features of ecological systems such as beta-diversity, i. e. the change in species composition from place to place.Why the AB model?
In the past, the logistic equation has been used to describe the growth of a population. The AB model is a discrete and spatially extended version of the logistic equation. Its behavior is dramatically different from the one obtained in the continuum case and brings new insights into the whole theory. Moreover, the AB model is suitable for a "neutral" extension, Ã la Hubbell. Its particular spatial features, if preserved in the extension, will be essentially new in the whole panorama of the neutral theory.Models
We will assume a basic knowledge on the AB model. Like in Hubbell, we assume that there is an external source (mainland) that assures the survival of biodiversity in our system (the island). For the moment we'll neglect the species composition on the mainlaind and we'll assume different distribution for it; when the project will be in a more advanced state, we'll need to discuss this point. With this assumption, our model becomes essentially a multispecies AB modelTeX Embedding failed! birth
TeX Embedding failed! death
TeX Embedding failed! diffusion
TeX Embedding failed! immigration
TeX Embedding failed! A diffusion .
Depending on the competition mechanism, one can have different models :
global ceiling TeX Embedding failed!
local ceiling TeX Embedding failed!
global competitions TeX Embedding failed! where TeX Embedding failed! (logistic-equation type)
local competition TeX Embedding failed! as above, but TeX Embedding failed!
where TeX Embedding failed! and TeX Embedding failed! are the maximum numbers of B individuals that the island and a site can contain, respectively.
Bibliography
Sthephen Hubbell The Unified Neutral Theory of Biodiversity and Biogeography Princeton University Press, 2001.Graham Bell Neutral Macroecology Science, 293, 2413-2418, 2001.
Nadav M. Snherb, Y. Louzon, E. Bettelhelm and S. Solomon The importance of being discrete: Life always wins on the surface PNAS, 97(19), 10322-10324, 2000.
