We study a random community model by means of theoretical techniques from statistical physics [1]. The model describes a set of species subject to competitive interactions through a background of resources, which they feed upon. Additionally direct interaction between species may occur through a random matrix, including predations, competitions, mutualisms, decompositions, etc. We focus on the effects of variability of resources, level of symmetry of the interaction matrix, strength of direct interactions between species and intraspecific competition, dilution or connectivity of the direct interactions on the stability, the diversity and the species abundance distribution (SAD) [2] of the community. It is shown that resources can be exploited optimally only in the low limit of the intraspecific competition or direct interactions. The theory also predicts that the variance of SAD becomes larger, the higher the variety of resources and the level of the symmetry of the interaction matrix.

[1] Yoshino, Galla and Tokita, "Statistical mechanics and stability of a model eco-system", Journal of Statistical Mechanics (2007) P09003.

[2] Tokita, "Statistical mechanics of relative species abundance", Ecological Informatics 1 (2006) 315-324.