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Abstract:
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Partial differential equations (PDEs) are a useful tool for modeling spatial-temporal ecological processes. As an ecological process evolves, we seek a model that can reflect changing dynamics as new data are collected. We developed a model that combines an ecological diffusion equation and a logistic function to characterize realistic colonization processes of a population that establishes long-term stationarity over a heterogeneous environment. We highlighted advantages of using a logistic reaction component instead of a Malthusian reaction component when population growth demonstrates asymptotic behavior. As a case study, we made inference on overall carrying capacity of sea otters in Glacier Bay, Alaska, and illustrated spatially-varying effective carrying capacity as a result of environmentally-driven diffusion. We 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 showed that our model improves inference on spatio-temporal abundance of sea otters in Glacier Bay, Alaska.
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