Many defoliating forest lepidopterans cause predictable periodic deforestation. Several of these species exhibit geographical variation in both the strength of periodic behavior and the frequency of cycles. The mathematical models used to describe the population dynamics of such species commonly predict that gradual variation in the underlying ecological mechanisms may lead to punctuated (subharmonic) variation in outbreak cycles through period-doubling cascades. Gypsy moth, Lymantria dispar, in its recently established range in the northeastern United States may represent an unusually clear natural manifestation of this phenomenon. In this study we introduce a new statistical spatial-smoothing method for estimating outbreak periodicity from space–time defoliation data collected with spatial error. The method statistically confirms the existence of subharmonic variation in cyclicity among different forest types. Some xeric forest types exhibit a statistical 4–5 year period in outbreak dynamics, some mesic forest types a 9–10 year period, and some intermediate forest types a dominant 9–10 year period with a 4–5 year subdominant superharmonic. We then use a theoretical model involving gypsy moth, pathogens, and predators to investigate the possible role of geographical variation in generalist predator populations as the cause of this variation n dynamics. The model predicts that the period of gypsy moth oscillations should be positively associated with predator carrying capacity and that variation in the carrying capacity provides a parsimonious explanation of previous reports of geographical variation in gypsy moth periodicity. Furthermore, a two-patch spatial extension of the model shows that, in the presence of spatial coupling, subharmonic attractors can coexist whereas nonharmonic attractors (i.e., where the cycle lengths are not integer multiples of one another) cannot.