Developing Models to Better Understand Sea Otter Colonization in Glacier Bay

A sea otter seen through a spotting scope. NPS/Jamie Womble

By the early 1900s, sea otters were almost extirpated throughout much of their range due to commercial harvest. At that time, only a few remnant populations of sea otters remained in the North Pacific Ocean. In 1911, the International Fur Treaty provided the remaining populations with their first measure of protection. In the 1960s, just over 413 sea otters were translocated to several locations along the outer coast of southeastern Alaska and sea otters began to recover. Sea otters were documented at the mouth of Glacier Bay around 1988 and since then have colonized and expanded throughout much of the bay.

The study of sea otter colonization in Glacier Bay provides important insight into the ability of a species to recover from near extirpation, as well as the impact of recent deglaciation on their recovery. A model was developed that incorporates logistic growth to characterize colonization processes and abundance of sea otters across Glacier Bay over time. The logistic growth models assumes that the per capita growth rate declines as population size approaches a maximum. A hierarchical modeling framework was used that allows for the incorporation of data from multiple sources collected at different spatial scales. Given that sea otters have relatively small home ranges and high site fidelity, this model allows for the estimation of spatially varying local equilibrium abundance of sea otters in Glacier Bay.

Nonlinear reaction-diffusion process models improve inference for population dynamics

Abstract

Partial differential equations (PDEs) are a useful tool for modeling spatiotemporal dynamics of ecological processes. However, as an ecological process evolves, we need statistical models that can adapt to changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and logistic growth to characterize colonization processes of a population that establishes long-term equilibrium over a heterogeneous environment. We also developed a homogenization strategy to statistically upscale the PDE for faster computation and adopted a hierarchical framework to accommodate multiple data sources collected at different spatial scales. We highlighted the advantages of using a logistic reaction component instead of a Malthusian component when population growth demonstrates asymptotic behavior. As a case study, we demonstrated that our model improves spatiotemporal abundance forecasts of sea otters in Glacier Bay, Alaska. Furthermore,we predicted spatially varying local equilibrium abundances as a result of environmentally driven diffusion and density-regulated growth. Integrating equilibrium abundances over the study area in our application enabled us to infer the overall carrying capacity of sea otters in Glacier Bay, Alaska.

Lu, X., P. J. Williams, M. B. Hooten, J. A. Powell, J. N. Womble, and M. R. Bower. 2019. Nonlinear reaction–diffusion process models improve inference for population dynamics. Environmetrics :e2604.

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