I use this "gallery" as a place to post talks that I have given.
To perist or not to persist? On the mathematics of species coexistence: One of the most fundamental questions in population biology is "what are the minimal condiditions to ensure the long-term persistence of an ecological community?" I have worked on the development of mathematical theory to address this question for the past 15 years. This work has culminated in a general criterion for coexistence that holds for models including an arbitrary number of species, nonlinear feedbacks, environemental stochasticity, and population structure (e.g. spatial, genetic, or size). I gave an overview of this work in this plenary talk in Gothenburg, Sweden for the 9th European Conference in Mathematical and Theoretical Biology
Evolution of allocation strategies in the face of multiscale variation: When population fitness is an increasing and saturating function of resource avability, stochastic variation in resource availability reduces mean population fitness and, consequently, natural selection may favor allocation strategies that mitigate against this reduction in mean fitness. Bet-hedging or risk aversion are examples of such strategies. Most theoretical work has focused on a single scale of variation. However, populations are often structured and experience environmental variation at multiple scales. Understanding how species evolve allocation strategies in response to this multi-scale variation and the ensuing ecological consequences is the focus of one of my NSF grants. Here is a talk that I gave in Oregon State's Integrative Biology seminar on this topic. Relevant papers are "Parental optimism versus parental pessimism in plants", "Evolutionary and Ecological Consequences of Multiscale Variation in Pollen Receipt for Seed Production", "Evolution of patch selection in stochastic environments" and "Protected polymorphisms and evolutionary stability of patch-selection strategies in stochastic environments."
Establishment and spread in the face of uncertainty: When a population arrives in a novel environment (e.g. pathogen arriving in a new host species, a species transported to a novel habitat), demographic stochasticity and environmental heterogeneity may determine whether the population successfully establishes and, upon establishment, the rate at which is spreads across the landscape. This talk at University of Chicago (Feb. 25, 2013) attempts to synthesize some of my work in the past few years on the question of establishment and spread in the presence of demographic or environmental stochasticity.
Metastability: all populations eventually go extinct. However, the time to extinction may be exceptionally long and be preceeded by transient dynamics that exhibit a regular statistical pattern. For stochastic models in population biology, these duration of these transients often depends on size of the system (e.g. the carrying capacity of a population). For example, the above figure compares and constrasts the stochastic dynamics (in red) and the mean field dynamics (in black) of a host-parasitoid model; lower subfigures correspond to higher host carrying capacities. These figures suggest that as the system size increases, the attractors of the mean field model (a period four orbit) should provide a good description of the metastable behavior of the stochastic model. In collaboration with Mathieu Faure, we have proven tha this correspondence holds for a general class of Markov chains. Furthermore, we provide estimates of how time to extinction time scales with system system size. Here is a somewhat technical talk that I gave at Berkeley's Analysis and PDE seminar (Nov. 19th, 2012) on this topic. You can read about the nitty gritty mathematical details here. .
Eco-evo feedbacks: Ecological communities consist of complex webs of interacting species, each of which contain phenotypically diverse individuals. Species interactions drive ecological dynamics, while the genetic variation within species provides the raw material for natural selection. While ecological and evolutionary processes were traditionally not studied together, there is mounting evidence that feedbacks between the ecological and evolutionary processes (eco-evo feedbacks) occur over commensurate time scales (e.g. tens to thousands of generations instead of hundreds of thousands of generations). This raises the possibility that one can not be considered without the other. Dan Bolnick, Reinhard Burger and I studied these feedbacks for species sharing a predator with phenotypic variation in its ability to attack either prey species. Here is talk that I gave about some of our results at ESA in 2011.
Hedging your bets: All populations experience variability in environmental conditions (e.g. temperature, percipitation) across time or space. Since these environmental conditions influnence the propensity to survive, grow, and reproduce, populations can hedge their bets by distributing individuals across time and space. Understanding the evolution of these bet-hedging strategies and their ecological consequences continues to be one of the focii of my research. Here is a talk that I gave to students at the US Naval Academy (Nov. 27, 2012) introducing them to the world of bet-hedging. Some of my contributions to this theory include evolution of patch selection in stochastic environments, stochastic growth rates of populations in spatially and temporally variable environments, and upcoming work on the evolution of reproductive strategies of plants experiencing pollen variability.