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

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

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

Diurnal habitat occupancy dynamics of Glaucous-winged Gulls were evaluated in a system of six habitats on and around Protection Island, Washington. Data were collected on the rates of gull movement between habitat patches, and from these data the probabilities of transitions between habitats were estimated as functions of tide height and time of day. A discrete-time matrix model based on the transition probabilities was used to generate habitat occupancy predictions, which were then compared to hourly census data. All model parameters were estimated directly from data rather than through model fitting. The model made reasonable predictions for two of the six habitats and explained 45% of the variability in the data from 2003. The construction and testing of mathematical models that predict occupancies in multiple habitats may play increasingly important roles in the understanding and management of animal populations within complex environments. © 2005 Rocky Mountain Mathematics Consortium

Identifying Environmental Determinants of Diurnal Distribution in Marine Birds and Mammals

Marine birds and mammals move between various habitats during the day as they engage in behaviors related to resting, sleeping, preening, feeding, and breeding. The per capita rates of movement between these habitats, and hence the habitat occupancy dynamics, often are functions of environmental variables such as tide height, solar elevation, wind speed, and temperature. If the system recovers rapidly after disturbance, differential equation models of occupancy dynamics can be reduced to algebraic equations on two time scales. Identification of environmental factors that influence movement between habitats requires time series census data collected in both the absence and presence of disturbance. © Society for Mathematical Biology 2006