Food web dynamics in the ocean. I. Best-estimates of flow networks using inverse methods

Abstract

We describe the application of inverse methods to the estimation of food web fluxes in undersampled ocean environments. The general objective is to deduce the flow networks that conserve mass, satisfy basic biological constraints, and are compatible with the observed structure of the food web. Given inevitable gaps in the observational data, a number of different networks will fit these requirements. In this paper, we estimate the simplest possible flow structure, that is, the network that minimizes (1) the sum total of the rate constants that relate flux to stock and (2) the differences among the constants. We present a general framework for the application of the inverse algorithm: (1) a linear compartmental model of the oceanic food web that initially includes all the possible inter-compartmental fluxes, and (2) a set of constraints on the flow estimates that reflect contemporary knowledge of the limits and efficiencies of ecophysiological processes. The methodology is applied to detailed observations of food web structure and dynamics in 2 areas off the English coast. The inverse solutions are discussed in terms of current concepts of the role of the microbial loop in the pelagic marine ecosystem.

An inverse model for the analysis of the Venice lagoon food web

“…Savenkoff et al (2004Savenkoff et al ( , 2007a extended it to the whole ecosystem network. Details on the solution algorithm are reported in Vézina and Platt (1988) and Savenkoff et al (2004). This section focuses on equations and constraints used within the present work, which differ slightly from those employed in previous studies (Savenkoff et al, 2004(Savenkoff et al, , 2007a.…”

“…The mass balance equations computed through the optimization algorithm has not to be exactly balanced, that is, the sum of the inputs and outputs for each compartment does not necessarily equal zero. The differences are termed residuals, and are represented by the error term ε. Residuals are assumed to be randomly and independently distributed with uniform variance (Vézina and Platt, 1988). The general mass balance equation for individual compartments can be written as:…”

“…This method was initially adapted from physical sciences by Vézina and Platt (1988) for the reconstruction of planktonic food webs. Savenkoff et al (2004Savenkoff et al ( , 2007a extended it to the whole ecosystem network.…”

“…The food web model was constructed using a method belonging to the class of so-called Inverse Model, IM (Vézina and Platt, 1988), according to which the trophic network is balanced, under a set of constraints, on the basis of an objective least-squares criterion for the minimization of the residuals, i.e. of the differences between the left hands and the right hands of the steady-state mass balance equations.…”

Quantifying Food Web Flows Using Linear Inverse Models

“…Firstly, an improved LIM procedure has been proposed in the field of marine ecology. This LIM procedure solves multiple mass balances simultaneously and directly deals with the underdetermined matrix equation (Klepper and Van de Kamer 1987;Vé zina and Platt 1988). Rather than artificially upgrading the data set, one uses the incomplete and/or uncertain data set as such, and selects a ''best'' solution from the infinite set of food web structures.…”