Toby is from Yorkshire in the UK. He was a philosophy and maths undergraduate and got his PhD in maths from Warwick University. Since then he has been an itinerant mathematician, working on “Coupled Cell Systems” at the University of Houston (2003-2005) and adaptive radiation and “Pod Systems” at the University of British Columbia (2005-2007). He is currently trying to understand resilience in coupled social-ecological systems using the theories of singularities and bifurcations.
In this talk I will present an overview of a number of themes relating to hysteresis and its role in the theory of social and ecological resilience. First, I will set hysteresis in its proper context, and show how this expanded view of regime shifts can lead to novel management strategies based on the notion of a “meta-threshold”. Second, I will present a model that describes the dynamics of occupations in a community, and specifically, how the number of people in the fishing industry can change with changes in fish stocks. Unsurprisingly, this model exhibits hysteresis (along with more complicated behaviour), and leads to the natural question; What happens when a hysteretic social system is coupled to a hysteretic ecosystem? The answer (which involves the notion of a “mirage regime”) raises important problems for managers of these systems, to which I will attempt to provide some general solutions. Finally, I will present a simple extension to a model describing the dynamics of coral cover on a grazed reef ecosystem to study the effects that recruitment of both beneficial and detrimental elements can have on the structure of regimes and the possibilities for sudden transitions.