Linear inverse ecosystem models (LIEM) are a powerful tool for integrating in situ rate and standing stock measurements with a priori knowledge of ecosystem structure and organismal constraints. LIEM work are typically constructed by specifying a set of three systems of equations. The first is a series of mass balance constraints that are typically constrained by the assumption of steady-state, but for time-series or Lagrangian studies can be forced by measured rates of change. The second system of equations is set by measured ecosystem rates (e.g. 14C-PP, protozoan grazing, and carbon export). The third is a system of inequalities that assimilate measurements of ecosystem standing stocks with assumptions about ecosystem efficiency (e.g. Equatorial Pacific e-ratios vary from 0.05 to 0.20) and organismal constraints (e.g. 0.1<GGE<0.4 or minimum respiration is a specificed function biomass).

 

Despite the amount of information that goes into an inverse ecosystem model, these models are still highly underconstrained. LIEM often have >60 ecosystem flows that they are trying to recover, but are constrained with only 10-15 rate measurement and mass balance constraints (combined with a much larger number of inequalities that often add little constraint to the model). The result is an incredibly broad solution space - in typical LIEM many flows remain almost completely unconstrained. Nevertheless, interpretation of LIEM requires some objective way of choosing between the infinite set of solutions that satisfy the underconstrained system of equations. The original technique used to choose between them was known as the least squares solution. The least squares method chose the particular solution that minimized the sum of squared flows through the ecosystem, but in the process it often chose solutions that were on the edge of the total solution space and hence may not have been representative. A new method, known as Markov Chain Monte Carlo (MCMC), developed by Kones et al. 2009, uses a random walk approach to randomly sample the full solution space, then reports the mean (or median) of all solutions as well as error bars that represent the uncertainty derived from the under-constrained nature of the model. Using field data from the CCE LTER program, I have shown that the MCMC method provides a more accurate picture of the ecosystem.

 

Most recently, we have developed a new approach for incorporating 15N isotopic data or varying C:N elemental stoichiometry into LIEM.  Our approach, published in PLOS ONE, uses a double Markov Chain Monte Carlo simulation approach to allow modeling of ecosystem compartments for which 15N isotopic values are unknown.  Our model code can be downloaded from GitHub or here.

 

Publications:

 

Stukel, M. R., M. Décima, T. B. Kelly (in press).   A new approach for incorporating 15N isotopic data into linear inverse ecosystem models with Markov Chain Monte Carlo sampling.  PLOS ONE.

 

Stukel, M. R., M. R. Landry, M. D. Ohman, R. Goericke, T. Samo, C. R. Benitez-Nelson.  2012.  Do inverse ecosystem models accurately reconstruct plankton trophic flows?  Comparing two solution methods using field data from the California Current.  Journal of Marine Systems 91:20-33  doi:10.1016/j.jmarsys.2011.09.004 Email PDF

 

Stukel, M. R., M. R. Landry.  2010.  Contribution of picophytoplankton to carbon export in the equatorial Pacific: A reassessment of food web flux inferences from inverse models.  doi: 10.4319/lo.2010.55.6.2669. Limnol. Oceanogr. 55:2669-2685 PDF