Interannual variability in a plankton time series

Abstract

SUMMARYTemporal changes in a plankton time series are examined, with an emphasis on interannual variability. A stochastic cycle model is used which describes an annual cycle with a fixed frequency, but a randomly varying amplitude and phase. A state space representation is used with the Kalman filter, and associated fixed-interval smoother, to provide estimation of the time-varying state. Parameter estimation relies on maximum likelihood methods. A data set is considered comprised of an irregularly sampled time series of plankton (dinoflagellate) abundance over a 12 year period in the Bay of Fundy, off the east coast of Canada. Analysis of the log 10 -transformed data indicated timing changes in the seasonal cycle of up to 23 days. Significant variations in abundance relative to the mean cycle were found for some highly sampled summer periods. Case deletion diagnostics identified two influential observations, one of which has a large impact on the estimated system noise. Examination of the sampling protocol, or monitoring design, indicates the need to reduce the observation error variance in order to improve detection of interannual variations in plankton abundance.

A Bayesian approach to the ecosystem inverse problem

“…It also means that the variance of M t , P t , and D t scales with their respective time-varying mean population level. This feature has been observed for both phytoplankton (Dowd et al, 2003) and individual shellfish weight (Gangnery et al, 2001). Here, we assume that σ 2 x = 0.05 gC 2 m −6 .…”

“…Such model errors and stochastic forcing are collectively known as system noise. Measurements for ecological state variables (populations numbers or biomass) are often sparse, noisy, and have distributions which are far from Gaussian (Soudant et al, 1997;Dowd et al, 2003).…”

Extraction of interannual trends in seasonal events for ecological time series

“…Cyclical state space models allow for adaptive seasonal cycles, and models of this nature have been used (Harvey 1990;Haywood and Wilson 2000), especially in econometrics (Harvey, 1985). In Dowd et al (2003Dowd et al ( , 2004 is a variable that has no actual interpretation but allows for the cycle to adapt to the observations (the r and i superscripting refers to the real and imaginary parts in a complex valued state formulation). Each element of the state vector has a corresponding system noise term denoted by n r t and n i t , respectively.…”

“…There is a corresponding need for robust statistical approaches that identify and detect interannual changes in abundance and species composition from such data (Jassby and Powell 1990;Dowd et al 2003;Ikeda et al 2008). Furthermore, there is a desire to identify phenological changes in key biological events (Edwards and Richardson 2004).…”

“…In previous studies (Dowd et al 2003(Dowd et al , 2004, an approach to treating nonstationary seasonal cycles was introduced and applied to plankton monitoring data. It was based on a cyclical state space model, and explicitly allowed for abundance…”