The Bayesian Metabolic Model (BaMM)
The Bayesian Metabolic Model simulates diel dissolved oxygen dynamics in aquatic ecosystems as a function of water temperature and light. From this, ecosystem metabolism can be calculated including both instantaneous and 24 hour integrated gross primary productivity (GPP), ecosystem respiration (ER), and gas exchange with the atmosphere (G). The model can incorporate measure light data (PAR: photosynthetically active radiation) or can generate a modeled the light curve based on geographic parameters. Key metabolic parameters such as the gas transfer velocity (k), photosynthesis-irradiance relationship (P-I curve), and respiration at a standardized temperature (R20) are estimated as part of the modeling process.
The Original BaMM model was publishing by Holtgrieve et al. in 2010. This model is able to predict and utilized dissolved oxygen isotope data (18O:16O) in addition to bulk dissolved oxygen for estimating ecosystem metabolism. Holtgrieve et al. found that this can be particularly useful when ER >> GPP resulting in dampened diel dynamics. The Original BaMM also has a fixed coefficient for temperature sensitivity that is based on literature values. Schindler et al. (2017) describes a new “Two-Stage R” version of BaMM. This version of the model differs from the original in three main ways: 1) temperature sensitivity of respiration is a variable parameter that can be estimated from the data, 2) there is the option to model respiration as a two-stage process, with a constant background rate of ER and short-term added ER that is a function of previous GPP; and 3) no ability to use dissolved oxygen isotope data.
The choice of which BaMM to use depends on a number of factors specific to data at hand and the questions being asked. However, in short, the Original BaMM is the simpler model and has the ability to use isotope data if available, but makes some assumptions about temperature sensitivity that sometimes limits its ability to reproduce diel dynamics fully. The Two Stage BaMM has adjustable temperature sensitivity and simulates respiration of two hypothetical carbon pools (constant and production-dependent); this later feature can be turn off to simulate a single constant ER if desired.
Both versions of BaMM are written in AD Model Builder. ADMB is the gold standard for parameter estimation by optimization and is the go-to program for complex fisheries models. The main advantage of ADMB is it contains methods to find the single optimal solution (i.e., the maximum likelihood estimate) and has can deal with large number of sometime highly correlated parameters. Correlation among parameters can be a problem with metabolism models. Its main disadvantages are the user interface is through the command line and the Bayesian MCMC algorithm can take awhile to run. ADMB is based on C++ programming.
You do not need to install ADMB to use BaMM with the default set of options. I have provided an R script for each version of BaMM to help with the user interface. It’s by no means perfect, however.
Holtgrieve, GW, DE Schindler, TA Branch, and ZT A’Mar. 2010. Simultaneous quantification of aquatic ecosystem metabolism and re-aeration using a Bayesian statistical model of oxygen dynamics. Limnology and Oceanography 55 (3): 1047–1063.
ADMB executable file formatted to run on Mac OS
ADMB executable file formatted to run on MS Windows OS
R interface Script
A hopefully helpful R script to interface with the BaMM executable file. The script will load data from a data file, write control files based on user inputs, provide basic MCMC diagnostics, and write simple summary files. See comments at the beginning for details.