Dr. Craig Jackson (Department of Mathematics and Computer Science)

Ecological stability is an important feature of ecosystems given the increasing rate of global change and human-induced disturbances. 'Ecological stability' is a term that encompasses many different aspects of stability, including the resistance and resilience of ecosystems to disturbances, the temporal variability of populations and communities, species’ persistence in ecosystems through time, and ecosystem resistance to invasion or extinction. Because ecological stability is such an important and valued aspect of ecosystems, ecologists are keenly interested in understanding what features of ecosystems lead to more stable ecosystems.

Ecological stability can be defined in both experimental and theoretical contexts. However, even within a particular context there may be several different definitions of ecological stability and it is not always clear how these various definitions are related. Hence, there is an emerging interest among both theoretical and observational ecologists in reaching a more integrated understanding of ecological stability.

One important abstraction that is often found in discussions on stability is the so-called 'community matrix.' In a modeling context, the community matrix determines how an ecological system behaves near an equilibrium. There are several methods by which community matrices can be estimated from population data. On the other hand, a given community matrix will produce any number of simulated data sets when forced by a noise signal. Because of this, when trying to understand the relation between theoretical and observational definitions of stability, the community matrix is a natural place to look.  In fact, theoretical definitions of stability are often derived directly from the community matrix itself which means that they do not depend on the shape of the noise signal driving the system. Of course, the same cannot always be said for the temporal variability of real or simulated ecological systems.

The student selected for this project will study the relationship between temporal variability and theoretical notions of stability. In particular, we seek relations which are qualitatively invariant under changes in noise. We will bring computer simulation, statistical techniques, and pure mathematics to bear on this problem. Good knowledge of linear algebra is required. Knowledge of intermediate statistics and decent experience with scientific computing would be helpful, but is not required.