The two main topics in my current research are scale-specific inference using wavelets and estimation and analysis of spatial network models.
The goal of scale-specific inference is to understand causal relationships in hierarchically structured data. Hierarchical patterns are common in complex systems ranging from biochemical systems to ecological communities to global biodiversity patterns. There is a need for a rigorous statistical methodology to extract scale-specific patterns from data and to build statistical models that relate these patterns in biological systems to same-scale patterns in environmental covariates. We are focusing on species distributions in landscapes and patterns of biological diversity across large spatial scales. The scale-specific approach will allow us to refine our understanding of the relationship between diversity and ecosystem properties like productivity, temperature and topography. If we can elucidate key processes controlling biodiversity and different scales, we can then begin to build a more comprehensive theory of diversity.
The other area of research is in landscape networks. These models are extremely useful in quantifying connectivity among populations and communities. We are researching how to estimate rates of movement between different ecological zones using hierarchical modeling methods. We are also modeling from first principles how network structure influences diversity patterns in communities. Another aspect of this work is identifying critical "key stone" patches in a landscape network where ecological and evolutionary processes may be occurring on more rapid time scales because of high rates of immigration from neighboring regions. The network approach is leading us towards a more comprehensive theory of population and community structure in heterogeneous environments.
Check the publications page for more information.