Invasion dynamics in generalized MacArthur's consumer resource models

A fundamental problem in community ecology is to identify the principles governing ecosystem evolution due to invasions by new species. By studying the MacArthur's consumer resource model (MCRM) with renewable resources, we show that a successful invasions (almost) always increases the total power consumption of an ecosystem. We show that this is generally true even when we include more complicated dynamics such as nonlinear response functions and cross feeding, suggesting there exists a maximum energy utilization efficiency principle underlying successful invasions in ecosystems with renewable resources. As a test of this idea, we show that this principle can be used to predict the success of an invasion with high probability. Furthermore in simulations where we repeatedly invade ecosystems, we show that ecosystems eventually reach an approximate steady-state dynamic where the probability of successful invasion drops dramatically. We argue that this is the analogue of a jamming transition in 'species packing' and can be naturally explained in terms of glass physics.