Abstract
Functional regression is a natural tool for exploring the potential impact of the physical environment (continuously monitored) on biological processes (often only assessed annually). This paper explores the potential use of functional regression analysis and the closely related functional principal component analysis for studying the relationship between river flow (continuously monitored) and salmon abundance (measured annually). The specific example involves a depressed sockeye salmon population in Rivers Inlet, BC. Particular attention is given to (i) the role of subject matter expertise and cross-validation techniques in guiding decisions on basis functions and smoothing parameters, and (ii) the importance of restricting the time domain for the continuously monitored variable to a scientifically meaningful period of time. In addition, we derive a joint confidence region for the functional regression coefficient function and discuss its use relative to the more commonly used pointwise confidence intervals. The analysis points to a substantial negative correlation between early spring river flow and marine survival of the sockeye salmon that subsequently migrate down the inlet.
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Research was supported by the Natural Sciences and Engineering Research Council of Canada, the Research and National Program on Complex Data Structures and the Tula Foundation.
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Ainsworth, L.M., Routledge, R. & Cao, J. Functional Data Analysis in Ecosystem Research: The Decline of Oweekeno Lake Sockeye Salmon and Wannock River Flow. JABES 16, 282–300 (2011). https://doi.org/10.1007/s13253-010-0049-z
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DOI: https://doi.org/10.1007/s13253-010-0049-z