# Predicting Numbers of Hauled-out Harbour Seals: A Mathematical Model

Article

2-1-2005

## Keywords

Akaike information criterion, Census times, Current, Phoca vitulina, Prediction, Tide, Washington

## Abstract

1. It was once assumed that commercially important fish make up significant portions of seal diets. As a consequence, prior to the 1970s many seal populations were dramatically reduced by rampant slaughtering. Today, seals and other marine mammals are valued components of marine ecosystems and their numbers are carefully managed. To facilitate management, government statutes mandate the systematic monitoring of seal populations. Population estimates are based on counts of hauled-out seals obtained by aerial survey and radio and satellite telemetry; hence, considerable effort has been devoted to finding optimal times for such counts. We have developed a predictive mathematical model of seal haul-out to assist resource managers in the selection of optimal census times. 2. Haul-out depends on a number of environmental variables. Some of these variables, such as wind speed, can be obtained only as historical data or short-range predictions. Others, such as tide height, are deterministic and can be obtained as long-range predictions. 3. We used deterministic environmental variables to develop mathematical models that describe haul-out dynamics of harbour seals Phoca vitulina during the pupping season at a site in Washington, USA. A list of alternative hypotheses for environmental cues gave rise to a suite of competing models. We used information-theoretic model selection techniques to choose the best model. The selected model was a function of tide height and current direction, and explained 40% of the variability in hourly census data. 4. An assumption that the system recovers rapidly after disturbance introduced two time scales. This allowed the differential equation model to be reduced to an algebraic equation. 5. Synthesis and applications. This study demonstrates that resource managers can use a simple algebraic equation based on deterministic environmental variables to predict times at which to census maximal haul-out in harbour seals. At the Washington site, maximal daily haul-outs during pupping season are predicted to occur during receding tides, approximately midway between high and low tides. The largest maximal daily haul-outs during the pupping season are predicted to occur in the last week of July. The environmental factors correlated with haul-out are, however, site-specific; therefore the model developed for the Washington site will not necessarily hold for other haul-out areas. Managers should carry out the model selection procedure separately for each monitored haul-out site. The general methodology employed in this study can be used to make long-range predictions of diurnal movements for a variety of marine birds and mammals. © 2005 British Ecological Society.

## Journal Title

Journal of Applied Ecology

42

1

108

117

## DOI

10.1111/j.1365-2664.2005.00999.x

Biology

Mathematics

## Acknowledgements

Free access article retrieved March 22, 2021 from https://besjournals.onlinelibrary.wiley.com/doi/epdf/10.1111/j.1365-2664.2005.00999.x

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