Species in an ecological community with similar characteristics often compete with each other for available nutrients/resources. The Competition Exclusion Principle (CEP) predicts that the fittest species outcompetes the others to survive1 . MacArthur’s consumer-resource model successfully explains the validity of this competitive exclusion principle, i.e., the number of coexisting species competing for available resources is bounded by the number of resources themselves2 . On the contrary, we still observe rich biodiversity, where several species coexist in nearby regions3. So far, several explanations via different modeling techniques have been proposed to understand this rich biodiversity, but a definite answer in this direction is still not available4,5. In this talk, I will introduce an effective resource competition model for species coexistence that is obtained by performing spatial coarse-graining 6. With this new model, I will show when many species can coexist and violate CEP, and I will discuss the conditions under which an invading species can outcompete coexisting species. Furthermore, I will show that the distribution of population sizes of species has a power-law tail, which decays with an exponent of -2. The analytical calculations and numerical simulations correctly predict the empirical species abundance distribution calculated from plankton community data. At the end of my talk, I will discuss some of the open problems.

1 G. Hardin, The competitive exclusion principle, Science 131, 1292 (1960).

2 P. Chesson, Macarthur’s consumer-resource model, Theor. Popul. Biol. 37, 26 (1990).

3 G. E. Hutchinson, The paradox of the plankton, Am. Nat. 95, 137 (1961).

4 A. Posfai, T. Taillefumier, and N. S. Wingreen, Metabolic Trade-Offs Promote Diversity in a Model Ecosystem, Phys. Rev. Lett. 118, 028103 (2017).

5 S. Roy and J. Chattopadhyay, The stability of ecosystems: A brief overview of the paradox of enrichment, J. Biosci. 32, 421 (2007).

6 D. Gupta, S. Garlaschi, S. Suweis, S. Azaele, and A. Maritan, Effective Resource-Competition Model for Species Coexistence, Phys. Rev. Lett. 127, 208101 (2021).