Mixed‐model splines for environmental time series: Fid-Bau Portal

Mixed‐model splines for environmental time series

Street, W. Scott IV / Edwards, Don / Feller, Robert J. / Coull, Bruce C. / Stancyk, Stephen E.

10.1002/env.609.abs

Eleven‐year biweekly time series of larval abundance of benthic fauna in a South Carolina salt marsh reveal, in the log scale, a clear annual pattern of alternating near‐linear growth and decay. The ecological processes governing these dynamics, particularly the dramatic year‐to‐year differences in annual maxima and minima, are mysterious. Traditional time series analyses (Fourier and ARIMA methods) can in some cases adequately mimic the patterns in these series, but they do little to enhance ecological understanding because they are not meaningfully parameterized. We model these series using floating‐knot linear splines in two ways: (i) as high‐dimensional non‐linear regression models with no forced similarity from year to year; and (ii) as a hierarchical spline model placing a probability distribution on annual maxima, minima, growth rate and decay rate across years, thereby enforcing some similarity in seasonal patterns. We discuss fitting and inference under both approaches; both yield excellent fits with ecologically interpretable results that can be used to shed light on governing processes. Results of a simulation study show that the hierarchical approach can yield substantial improvements in efficiency over the non‐linear regression approach, particularly for series with low interannual variability. Copyright © 2003 John Wiley & Sons, Ltd.