Mathematics, Department of



Bo DengFollow

Date of this Version



The Open Ecology Journal, 2010, 3, 95-110


© Bo Deng; Licensee Bentham Open. This is an open access article licensed under the terms of the Creative Commons Attribution Non-Commercial License ( 3.0/), which permits unrestricted, non-commercial use, distribution & reproduction in any medium, provided the work is properly cited.


The purpose of this paper is to incorporate well-established ecological principles into a foodweb model consisting of four trophic levels --- abiotic resources, plants, herbivores, and carnivores. The underlining principles include Kimura's neutral theory of genetic evolution, Liebig's Law of the Minimum for plant growth, Holling's functionals for herbivore foraging and carnivore predation, the One-Life Rule for all organisms, and Lotka-Volterra's model for intraand interspecific competitions. Numerical simulations of the model led to the following statistical findings: (a) particular foodwebs can give contradicting observations on biodiversity and productivity, in particular, all known functional forms -- - positive, negative, sigmoidal, and unimodal correlations are present in the model; (b) drifting stable equilibria should be expected for ecosystems regardless of their size; (c) resource abundance and specific competitions are the main determining factors for biodiversity, with intraspecific competition enhancing diversity while interspecific competition impeding diversity; (d) endangered species are expected always and loss in lower trophic endangered species are expected at trophication, i.e. the establishment of a higher trophic level of a community. These findings may shed lights on some ongoing debates on biodiversity. In particular, finding (a) implies that the diversity vs. ecosystems functioning debate is most likely the result of incompatible particular observations each cannot be generalized. In particular, general causality should not be expected between diversity and productivity. Finding (b) does not support May's theory that large ecosystems are inherently unstable nor Eton's theory that stability requires diversity. However, it lends a strong support to the energetic theory for the latitudinal diversity gradient. Finding (c) supports Darwin's observation on the effect of interspecific competition on diversity. Finding (d) implies that loss of diversity is inevitable with the appearance of a super species like the human race. Our method and result also suggest that although the evolution of particular species cannot be predicted, some general statistic patterns appear to persist. In addition to the aforementioned findings, these persisting patterns include: the trophic succession, the trophic biomass separation in orders of magnitude, the upper bounds in biodiversity in relationship to the intensities of specific competitions despite the enormous possible number of species allowed by genetic mutations.