Stable Bifurcations in Semelparous Leslie Models

In this paper, we consider nonlinear Leslie models for the dynamics of semelparous age-structured populations. We establish stability and instability criteria for positive equilibria that bifurcate from the extinction equilibrium at R0=1. When the bifurcation is to the right (forward or super-critical), the criteria consist of inequalities involving the (low-density) between-class and within-class competition intensities. Roughly speaking, stability (respectively, instability) occurs if between-class competition is weaker (respectively, stronger) than within-class competition. When the bifurcation is to the left (backward or sub-critical), the bifurcating equilibria are unstable. We also give criteria that determine whether the boundary of the positive cone is an attractor or a repeller. These general criteria contribute to the study of dynamic dichotomies, known to occur in lower dimensional semelparous Leslie models, between equilibration and age-cohort-synchronized oscillations. © 2012 Copyright J.M. Cushing

Socially Induced Ovulation Synchrony and its Effect on Seabird Population Dynamics

Spontaneous oscillator synchrony is a form of self-organization in which populations of interacting oscillators ultimately cycle together. This phenomenon occurs in a wide range of physical and biological systems. In rats and humans, oestrous/menstrual cycles synchronize through social stimulation with pheromones acting as synchronizing signals. In previous work, we showed that glaucous-winged gulls (Larus glaucescens) can lay eggs synchronously on an every-other-day schedule, and that synchrony increases with colony density. We posed a discrete-time mathematical model for reproduction during the breeding season based on the hypothesis that pre-ovulatory luteinizing hormone surges synchronize by means of visual, auditory and/or olfactory cues. Here, we extend the seasonal model in order to investigate the effect of ovulation synchrony on population dynamics across reproductive seasons. We show that socially stimulated ovulation synchrony can enhance total population size and allow the population to persist at lower birth rates than would otherwise be possible. © 2011 Taylor & Francis

Foraging-Related Activity of Bald Eagles at a Washington Seabird Colony and Seal Rookery

From 1980 to 1998, Washington\u27s Bald Eagle (Haliaeetus leucocephalus) population increased at an annual rate of 10. Over the same time period, foraging activity of Bald Eagles at marine bird breeding colonies also increased. From 1993 to 2008, we observed foraging-related behavior of Bald Eagles on Violet Point, Protection Island. This island hosts more than 70 of the breeding seabirds in Washington\u27s inner seaways and serves as an important rookery for harbor seals (Phoca vitulina). We found that (1) eagles landed more frequently in seal haul-out (beach) areas than in gull-nesting (non-beach) areas of Violet Point, and that subadult eagles were more likely to land in gull-nesting areas than were adult eagles; (2) the presence of eagles on the beach was positively related to the presence of harbor seals on the beach; (3) a greater-than-expected number of adult eagles as compared with subadult eagles preyed on gull chicks; (4) subadult and adult eagles that attempted prey capture were equally successful at snatching gull chicks from the gull colony; (5) eagles were more likely to prey on gull eggs in tall grass than on gull eggs in sparse vegetation. Prey remains beneath one eagle nest on the island did not accurately reflect the range and relative frequencies of observed eagle predation events. Although seal afterbirths and dead pups constitute a major component of the diet of Bald Eagles on the island, the effect of eagles on live seals is probably negligible. In contrast, direct predation and indirect effects of eagle activity on Glaucous-winged Gull (Larus glaucescens) reproductive success may be substantial and may have been partly responsible for a 44 decrease in the number of gull nests in the colony from 19932008. © 2010 The Raptor Research Foundation, Inc

P-46 A Periodic Matrix Model of Seabird Behavior and Population Dynamics

Rising sea surface temperatures (SSTs) in the Pacific Northwest lead to food resource reductions for surface-feeding seabirds, and have been correlated with several marked behavioral changes. Namely, higher SSTs are associated with increased egg cannibalism and egg-laying synchrony in the colony. We study the long-term effects of climate change on population dynamics and survival by considering a simplified, cross-season model that incorporates both of these behaviors in addition to density-dependent and environmental effects. We show that cannibalism can lead to backward bifurcations and strong Allee effects, allowing the population to survive at lower resource levels than would be possible otherwise

Habitat Patch Occupancy Dynamics of Glaucous-winged Gulls (larus glaucescens) ii: A Continuous-time Model

The diurnal distribution and abundance dynamics of loafing Glaucous-winged Gulls (Larus glaucescens) were examined at Protection Island National Wildlife Refuge, Strait of Juan de Fuca, Washington. Asynchronous movement of gulls among three habitat patches dedicated to loafing was modeled as a function of environmental variables using differential equations. Multiple time scale analysis led to the derivation of algebraic models for habitat patch occupancy dynamics. The models were parameterized with hourly census data collected from each habitat patch, and the resulting model predictions were compared with observed census data. A four-compartment model explained 41% of the variability in the data. Models that predict the dynamics of organism distribution and abundance enhance understanding of the temporal and spatial organization of ecological systems, as well as the decision-making process in natural resource management. © 2005 Rocky Mountain Mathematics Consortium

Socially Induced Synchronization of Every-other-day Egg Laying in a Seabird Colony

Spontaneous oscillator synchrony has been documented in a wide variety of electrical, mechanical, chemical, and biological systems, including the menstrual cycles of women and estrous cycles of Norway Rats (Rattus norvegicus). In temperate regions, many colonial birds breed seasonally in a time window set by photoperiod; some studies have suggested that heightened social stimulation in denser colonies can lead to a tightened annual reproductive pulse. It has been unknown, however, whether the analog of menstrual synchrony occurs in birdsthat is, whether avian ovulation cycles can synchronize on a daily timescale within the annual breeding pulse. We report every-other-day clutch-initiation and egg-laying synchrony in a breeding colony of Glaucous-winged Gulls (Larus glaucescens) and show that the level of synchrony declined with decreasing colony density. We also pose a mathematical model based on the hypothesis that preovulatory luteinizing hormone surges synchronize through social stimulation. Model predictions are consistent with observations. Finally, we suggest a procedure for identifying synchronous egg laying in other colonies and species. © 2010 by The American Ornithologists\u27 Union. All rights reserved

Modeling the Daily Activities of Breeding Colonial Seabirds: Dynamic Occupancy Patterns in Multiple Habitat Patches

We constructed differential equation models for the diurnal abundance and distribution of breeding glaucous-winged gulls (Larus glaucescens) as they moved among nesting and non-nesting habitat patches. We used time scale techniques to reduce the differential equations to algebraic equations and connected the models to field data. The models explained the data as a function of abiotic environmental variables with R2=0.57. A primary goal of this study is to demonstrate the utility of a methodology that can be used by ecologists and wildlife managers to understand and predict daily activity patterns in breeding seabirds