Mathematical Biology Seminar Roy Wright U C Davis Friday Jan. 25, 2008 3:05pm in LCB 225 "Mathematical Methods for Connecting Ecological Scales " b Abstract: The idea of scale is relevant in many fields of applied mathematics, with particular and fundamental importance to mathematical ecology. Time scales are a natural feature of ecological systems because interacting species often have life cycles of radically differing length. Examples include the interaction of herbivores with plants -- especially trees, pathogens with their hosts, and some prey species with their predators. Spatial scales become relevant when individuals of distinct species have differing levels of movement. For example, a predator population may habitually hunt over an area wide enough to include several less mobile prey populations, or a flightless insect may be victimized by a highly mobile winged exploiter. Another issue of scale is the connection of individual-level behavior with population-level phenomena through the modeling process. This occurs in nearly all fields; one prominent example is the derivation of the Ideal Gas Law from assumptions about individual gas atoms. But in ecology, the connection between a model and the individual actions from which it is derived takes on a greater importance, since organisms are far less predictable than atoms and do not exist in populations as large as Avogadro's number. In this talk I will describe some of the mathematical tools that have been and continue to be used to better understand ecological problems in which scale issues play an important role.