Both at its theoretical level and for practical reasons that shape public policy, researchers have investigated issues in life history and selection, evelutionary issues in sex-ratio, population structure and genetic structure, and the interaction of behavior and genetics.
The arthropods, particularly insects and spiders, make ideal test cases for research on these questions. These creatures are abundant in nature, often have high fecundity and their life cycles are short. More critically, they can be used as subjects in controlled experiments to test the hypotheses that emerge from the mathematical models. Beginning with the seminal work of Robert May and co-workers, the theory of discrete time dynamical systems has been a major mathematical tool to investigate population dynamics. Because dynamical systems can illustrate many fascinating properties that are easy to display on a personal computer, much of the biological motivation for their study has been lost in abstract mathematical theory and computer simulation.
One multidisciplinary research team (consisting of J. Cushing and co-workers) is dedicated to keeping the study of discrete time dynamical systems close to laboratory experiment through the study of the genus Tribolium ,the common flour beetle [1]. Under controlled conditions, these beetles can display highly fluctuation population dynamics. The beetle team's modeling program begins with the translation of life history into the language of mathematics. Mathematical analysis of the derived models couples with experimental design and statistical techniques are used to test the models. As the parameters in the model vary, it predicts regimes of periodic cycles, aperiodic orbits, multiple attractors, unstable equilibria with stable and unstable manifolds, and chaos [2]. This research team received considerable attention for its ability to produce "chaos in a bottle" [3]. These successes have allowed the team to move on to more subtle questions in population dynamics- the effects of saddle nodes, periodically fluctuating habitats, and metapopulations.
Several fundamental questions in population dynamics can studied effectively by joining ideas in population models and genetics models.
Because of their special population structure, social spiders are a large scale natural experiment amenable to mathematical modeling for which alternative hypotheses regrading fundamental questions in ecology can be tested. Based on more than 10 years of field work on social spiders in the tropical forests of Ecuador, L. Aviles and co-workers [4] have developed models designed to explain the course and consequences of social evolution and the evolution of life histories in meta-populations.
A decade ago, a team of entomologists at the Carl Hayden Bee Research Center were asked to analyze all the molecular population biology on honey bees. Because the Africanized honey bee was migrating northward at 400 miles per year, this was a substantial request. Invasion of species and the inheritance of complex characteristics are basic questions in ecology. Thus the Africanization of the European honey bee population, one of the great population genetics events of our time, provides a rare opportunity to study these basic questions. The team at the Bee Center took on this task - developing first a population dynamics model [5] then later a genetics model [6]. Their modeling strategy reached beyond its limit with the data on queen development time and the hypothsis that this development time is the key to understanding the Africanization of the honey bee population. Further progress required the active participation of a mathematician (J. Watkins)with expertise in probabilistic methods [7]. This multidisciplinary team (de-Granndi Hoffman, Watkins and co-workers) is now moving to studying relationships between behavior and genetics in queen development, in foraging behavior, and in the dynamics of swarms and migrations.
With an emphasis more directly on the genetics and evolutionary issues in insects, M. Kidwell works to improve our understanding of the genetics and mode of evolution of mobile genetic elements. These elements are found in almost all living organisms, including humans. Her studies have focused on insect transposable elements using the P element in Drosophila as a model system. Studies underway in her laboratory include aspects of horizontal transfer of transposable elements, transposable elements as genetic carriers in insect populations, and population surveys on the distribution and evolution of P elements in D. melonagaster and other insects [8,9]. Professor Kidwell's contribution have been recognized by her recent induction into the National Academy of Science.
Through the Flinn Foundation pilot projects, the research team has supported one fellow, Wade Leitner, who will complete his doctoral studies in 1998 in the Department of Ecology and Evolutionary Biology under the direction of Michael Rosenzweig. Leitner's thesis uses levels of ecological hierarchies. He applied his methods to create a model for the range size-abundance relationship which he compares to data from the North American Breeding Bird Survey. He also developed an individual-based stochastic model to determine extinction rates and mean times to extinction.