Species Packing with Generalized Resource Dynamics*

An important question in ecology is to understand how species assemble under different resource dynamics. Here we explored generalized MacArthur's resource models with two different resource dynamics: self-renewing(original MacArthur's) and external-supplied resource dynamics. A statistical physics inspired cavity method is used to solve two resource dynamics analytically. Surprisingly, we find that two resource dynamics have different upper bounds of species packing. We show that external-supplied resource dynamics can introduce higher order competition between species and affect coexistence patterns dramatically.