Catastrophic regime shifts in model ecological communities are true phase transitions

Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in external conditions. Usual models introduce nonlinearities in the macroscopic dynamics of the ecosystem that lead to different stable attractors among which the shift takes place. Here we propose an alternative explanation of catastrophic regime shifts based on a recent model that pictures ecological communities as systems in continuous fluctuation, according to certain transition probabilities, between different microstates in the phase space of viable communities. We introduce a spontaneous extinction rate that accounts for gradual changes in external conditions, and upon variations on this control parameter the system undergoes a regime shift with similar features to those previously reported. Under our microscopic viewpoint we recover the main results obtained in previous theoretical and empirical work (anomalous variance, hysteresis cycles, trophic cascades). The model predicts a gradual loss of species in trophic levels from bottom to top near the transition. But more importantly, the spectral analysis of the transition probability matrix allows us to rigorously establish that we are observing the fingerprints, in a finite size system, of a true phase transition driven by background extinctions. Submitted to: J. Stat. Mech. ‡ [email protected] § [email protected] ar X iv :1 00 8. 03 35 v2 [ qbi o. PE ] 7 S ep 2 01 0 Catastrophic regime shifts in model ecological communities are true phase transitions 2