Myriad influences shape the patterns of evolution, timing, behavior and ecology of living organisms. These influences range from biochemical cues to configurations of temperature, space and light, to interactions with other organisms. This one-year program focuses on connecting influence to pattern for processes involving plants and insects.
How do biotic and abiotic influences affect patterns of plants and insects? We investigate this complex question quantitatively, by focusing on specific areas where there has been recent growth, simultaneously in mathematical and statistical theories and in biological data and experiment. We propose to couple the mathematics and biology in new ways, allowing for innovative growth of both science and mathematics.
The year is based around the following workshops: (i) Mathematical modeling of plant development, (ii) Circadian clocks in plants and fungi, (iii) Insect self-organization and swarming, (iv) Ecology and control of invasive species, including insects, and (v) Coevolution and the ecological structure of plant-insect communities. Our mathematical investigation of these processes will rely upon a diverse array of quantitative theory, including geometry, control, optimization, pattern formation, spatial dynamics, evolution and data-model interaction.
The plant development workshop will connect biochemical mechanisms to geometric patterns, while simultaneously investigating the selection pressure for the geometric patterns. Circadian clocks will be evaluated both from the perspective of design features for feedback and control, and of robustness of these features to perturbation. Insect self-organization and swarming will employ dual perspectives of emergent self-organization properties arising from individual interactions, and optimal design of artificial swarms using diffuse (decentralized) information with implications for robotics and decentralized computer algorithms. Biological invasions will be understood, not only in terms of predictable forecasting of future invasions, but in terms of optimal control of the invasion processes. Finally, the physical and behavioral mechanisms involved in coevolution of plant-insect communities will be understood in terms of fitness advantages incurred evolution and adaptation.
Thus the underlying feature throughout the workshops is simultaneous investigation of mechanism and optimality: What mechanisms give rise to observed patterns? What is the fitness or optimality associated with observed patterns? It is through this simultaneous study of mechanism and optimality in plants and insects that the workshops will provide general insight to the processes of evolution, synchronization and environmental interactions.
The goals of the year program are (i) to develop, analyze and apply new mathematical models for processes of evolution, timing, behavior and ecology of living organisms that are tailored to investigate both mechanisms underlying the processes and optimality of associated patterns; and (ii) train interdisciplinary quantitative researchers at a variety of levels (graduate, postdoctoral and faculty) in the area of evolution, synchronization and environmental interactions for biological systems.