We study ecology from a population dynamic perspective with a focus on stochastic processes. Our research is characterized by the combination of field intensive studies with mathematical modeling, focused particularly on demography of structured populations in variable environments. This conceptual arena includes the development and application of new parameters (e.g. environment-specific elasticity) and encompasses an array of topics from biology of aging and evolution of life span to spatial population dynamics of both native and exotic species, and has exciting applications to plant-animal interactions, forest dynamics, as well as disturbance, global change and invasion biology.
Understanding how vital rates determine emergent properties of populations, including changes in population size, density, structure and spatial extent, comprises the fundamental issue of demography. This is also the fundamental issue of invasion biology: understanding why some species increase in number and spread more rapidly in populations that are introduced into a new region of the world than they do in populations located in their native range. Management of invasive species also depends upon understanding how different components of the life-cycle impact the dynamics of population growth and spread. Models of population dynamics and their sensitivity analyses are key for addressing this issue.
All life on earth is affected by interactions with other living organisms. Interspecific interactions are shaped over time by selection and play a critical role in the in the structuring of natural communities. We focus on the interactions between plants and animals (e.g. seed predation, seed dispersal, herbivory, pollination) and work to determine the outcome of these interactions in the currency of fitness. Plant-animal interactions range from mutualism to exploitation, the cost/benefits of which can be measured in terms of the average lifetime fitness, which integrates changes in growth, survival, reproduction for either the plant or the animal.
Spatial Population Dynamics
Most organisms move across the landscape at one point or another of their lives. We are interested in structured populations, so we study how far individuals are likely to move when they make transitions over time from one stage to another. Expansion of space occupied by a population depends upon all movements made by all stages. We collect data on these movements (in plants it is usually the seed stage that moves) and study models that combine survival, growth and reproduction with movement.
Forest Light Dynamics
Image borrowed from: http://eebweb.arizona.edu/faculty/saleska/Ecol596L/P1000016.JPG
Within tropical forests, light from the tree canopy is a dynamic resource that changes over space and time. Gaps in the canopy will form when trees fall or lose their leaves, and slowly close as trees grow up and into these gaps. Past and current members of this lab have studied the myriad of ways that plants respond to forest light availability. We use integral projection models (IPM's) to study how light relates to demography of Calathea and Heliconia. Demographic data coupled with measures of light availability experienced by each individual allow us to evaluate both stage dynamics and environmental dynamics and the feedback between organism and environment.
Evolution of Lifespan and Life History
Individuals are dynamic and stochastic in socio-economic status over their life-times, and the survival probability associated with a given status changes with age. To gather these observations into a single theory we developed a stochastic two stage and a stochastic multi-stage Markov model at each age and a stage-by-age matrix model of a cohort of individuals experiencing dynamic heterogeneity over their lifetimes. We elucidated the consequences of changing marital status and income level on cohort dynamics and individual variability in lifespan and other first passage times.