Critical Transitions in Generalised Lotka-Volterra Systems With Random Interaction Strengths and Positive Self-Growth

Abstract

With better understanding of what causes complex systems to undergo critical transitions, unwanted consequences can be avoided or turned into opportunities [23]. In this thesis I add to that understanding by investigating criticality in an example complex system called the generalised Lotka-Volterra equations. Exploration of this system also adds nuance to May’s comment in the diversity-complexity debate [16]. I restrict myself to positive self-growth and random interactions between species and investigate how system behaviour changes as the average interaction strength increases, using computer simulations and analytical methods. In line with May’s thesis I find that large systems undergo critical transitions for lower than small systems, but the route to system instability or collapse goes through an intermediate state where species frequently go extinct and the system is dynamically close to instability. Structurally on the other hand, the system is resilient to changes to , except when roughly half of the initial amount of species has gone extinct, at which point either limit cycle behaviour sets in or system collapse occurs. The ecological realism of the model is difficult to justify, but as an example of a complex system exhibiting criticality it has many insights to offer.