1 Advances in Ecological Research, Volume 37, 2005, 101-141 Nonlinear stochastic population dynamics: The flour beetle Tribolium as an effective tool of discovery R. F. Costantino, Robert A. Desharnais, J. M. Cushing, Brian Dennis, Shandelle M. Henson, and Aaron A. King When observation and theory collide, scientists turn to carefully designed experiments for resolution. Their motivation is especially high in the case of biological systems, which are typically far too complex to be grasped by observation and theory alone. The best procedure, as in the rest of science, is first to simplify the system, then to hold it more or less constant while varying the important parameters one or two at a time to see what happens. —Edward O. Wilson (2002) INTRODUCTION Prior to the seminal work of R. M. May in the 1970s, the prevailing paradigm viewed the unpredictable fluctuations in population time series data as random effects due to environmental variability and/or measurement errors. In the absence of environmental variability, according to this view, population numbers would either equilibrate or settle into regular periodic oscillations. May’s (1974) suggestion that simple deterministic rules might explain the complex fluctuations observed in animal abundances led to an intense search for chaos in extant population data. The results of the search were suggestive, but