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We study a discrete time, structured population dynamic model that is motivated by recent field observations concerning certain life history strategies of colonial-nesting gulls, specifically the glaucouswinged gull (Larus glaucescens). The model focuses on mechanisms hypothesized to play key roles in a population's response to degraded environment resources, namely, increased cannibalism and adjustments in reproductive timing. We explore the dynamic consequences of these mechanics using a juvenile-adult structure model. Mathematically, the model is unusual in that it involves a high co-dimension bifurcation at R 0 = 1 which, in turn, leads to a dynamic dichotomy between equilibrium states and synchronized oscillatory states. We give diagnostic criteria that determine which dynamic is stable. We also explore strong Allee effects caused by positive feedback mechanisms in the model and the possible consequence that a cannibalistic population can survive when a non-cannibalistic population cannot. ARTICLE HISTORY

Wildlife populations are often affected by natural or artificial disasters that reduce their vital rates leading to drastic fluctuations in population dynamics. We use a stagestructured matrix model to study the recovery process of a population given an environmental disturbance. We focus on the time it takes the population to recover to its pre-event level and develop general formulas to calculate the sensitivity and elasticity of the recovery time to changes in the initial population, vital rates, and event severity. Our results suggest that the recovery time is independent of the initial population size but it is sensitive to the initial structure.Moreover, the recovery time is more sensitive to reductions in vital rates than to the duration of the impact of the event.We explore an application of the model to the sperm whale population in Gulf of Mexico following a disturbance such as the Deepwater Horizon oil spill. Recommendations for Resource Managers• Understanding a population's recovery process following a disturbance is important for management and conservation decisions.

Recently, Constantinescu and Ilie proved a variant of the wellknown periodicity theorem of Fine and Wilf in the case of two relatively prime abelian periods and conjectured a result for the case of two nonrelatively prime abelian periods. In this paper, we answer some open problems they suggested. We show that their conjecture is false but we give bounds, that depend on the two abelian periods, such that the conjecture is true for all words having length at least those bounds and show that some of them are optimal. We also extend their study to the context of partial words, giving optimal lengths and describing an algorithm for constructing optimal words.