Quantifying the effects of dynamical noise on the predictability of a simple ecosystem model

Abstract

SUMMARYThe need to understand the effects of anthropogenic perturbations on ocean biology has renewed interest in ecosystem and biogeochemical models in recent years. We develop a nonlinear time series approach to quantify the effects of different types of noise on ecosystem dynamics. Different types of noise can alter the local predictability of the system, induce qualitative regime shifts in model dynamics, and destroy (create) internal nonlinear oscillations and chaos. The ecosystem model we use in our article is a model of plankton dynamics and nitrogen cycling. It is a compartmental model (NPZD) consisting of compartments for nitrogen (N), phytoplankton (P), zooplankton (Z), and detritus (D). The flows or intercompartmental exchanges are modeled as a nonlinear system of four first-order differential equations. The types of noise of interest are both independent and correlated. Because the noise is an integral part of the system's dynamics, a nonlinear time series approach is used to quantify the dynamics and predictability of the system. This involves fitting neural network models and estimating dynamical system quantities of interest such as global and local Lyapunov exponents, along with measures of uncertainty for these estimates.

A sequential Monte Carlo approach for marine ecological prediction

“…Its standard deviation is 0:01 Â X Ã , where X Ã is one of P Ã , Z Ã , N Ã and D Ã . These values are the same order of magnitude as those of Bailey et al (2004).…”

“…Stochastic environmental and biological variability was included through the following processes: (i) photosynthetic production is described by the daily averaged growth rate parameter . This was considered here as a stochastic dynamic parameter driven by changes in surface and underwater light field (clouds, water properties), as well as the interaction of phytoplankton photosynthetic physiology with light and mixed layer physics (Denman and Gargett, 1983;Cullen and Lewis, 1988); (ii) dynamical noise occurs due from turbulent mixing and associated mass fluxes; these were included as an additive error term for each of (1)-(4) (Bailey et al, 2004;Monahan and Denman, 2004). Note that the remaining static parameters are assumed fixed and known, with their values taken from field and lab studies (cf.…”

Variance decompositions of nonlinear time series using stochastic simulation and sensitivity analysis

“…This class includes linear time series models, nonlinear autoregressive moving average (NARMA) models, Hammerstein and Wiener systems, random coefficient models, switching models such as SETAR and neural networks (Fan and Yao 2005;Granger and Teräsvirta 1993;Leontaritis and Billings 1985;Pearson 1999;Tong 1990). Also included are linear systems with multiplicative noise, which have seen widespread application in areas such as chemistry, biology, ecology and economics (Bailey and Lima 2004;Stachurski 2003). Although the identification of nonlinear stochastic systems described by (1) has been studied in some depth in the control community, the statistical analysis of these models is still in its infancy.…”

Diversity of the marine cyanobacterium Trichodesmium : characterization of the Woods Hole culture collection and quantification of field populations

“…Rates of competition increase with cell size and abundance, so in the oligotrophic ocean where abundance is low, competitive exclusion may take so many generations that other factors such as nutrient pulses or changes in physical properties become more important in population dynamics than competition (Siegel, 1998). Stochastic perturbations (noise) from the environment can cause shifts in model dynamics and decrease the predictability of a system (Bailey et al, 2004). Episodic events such as dust deposition, mesoscale eddies, and turbulent mixing can affect community dynamics of Trichodesmium.…”