Multiple hysteretic patterns from elementary population models

Critical transitions whereby small changes in conditions can cause large and irreversible changes in ecosystem states are a cause of increasing concern in ecology. Here, we focus on the irreversibility of these transitions, formally known as hysteresis. We explore how simple correlations between parameters in Lotka-Volterra predator-prey equations result in a variety of complicated hysteretic patterns. These patterns include “unattainable” stable states that once lost may never be recovered. We suspect these patterns to be common in natural systems, where interactions between diverse assemblages are unavoidable. Thus, understanding underlying hysteretic structures may be necessary for rescuing lost ecosystem states and avoiding future losses.