1. Energy balance models
Chris Harvey, John Field, Chris Legault, Sarah Gaichas, Kerim Aydin, Frank Parrish, Clay Porch, Howard Townsend, Joan Browder, and John Carlson

2. All mass and energy is conserved.
Bioenergetics models--Introduction
Objectives:
To characterize a fish energy budget, w.r.t. species, temperature, body size, prey quality
To predict growth or consumption under different environmental scenarios
To predict uptake and accumulation of other currencies (e.g., contaminants)
R, SDA C D
B, G
F, U
DB = C – R – SDA – F – U – G
Each term represents a non-linear, temperature- and mass-dependent function.
All mass and energy is conserved.

3. Bioenergetics models—data requirements
Mass-specific rates of:
Consumption
VO2 (resting and active)
Q10 for C, R
Thermal tolerances
Energy densities (J/g)
Seasonal, ontogenetic diets
“Other”
Core demographic data for model fitting
R, SDA C D
B, G
F, U
DB = C – R – SDA – F – U – G
“other” could include increased respiration for live-bearers, salinity impacts, migration activity, etc.

4. Bioenergetics models—data gaps
Parameter sets available for relatively few marine species
Activity multiplier for respiration
Diet information
Other than diets, gaps not a big part of most monitoring plans
But, temperature, growth, diet, maturation are probably the right places to invest monitoring effort
R, SDA C D
B, G
F, U
DB = C – R – SDA – F – U – G

5. Relative % change in per capita
Bioenergetics models—pros and cons
Fishery sectors have age-specific effects on blue shark survival and predation (Schindler et al. 2002)
The Good:
Basis: thermodynamics
Rapid, robust, flexible
Can link to other models
Useful applications
The Bad:
Some parameters don’t scale well from lab to field
Key parameters difficult to estimate (ACT, p)
Shortcuts
The Ugly:
Parameter borrowing
1933-
1946
1947-
1958
1959-
1969
1970-
1977
1978-
1996
Climate period 10 5 -5
-10
Relative % change in per capita
salmonids consumed
Effects of climate regime on salmon predation below Bonneville Dam (Petersen and Kitchell 2001)
R, SDA C D
B, G
F, U
DB = C – R – SDA – F – U – G

6. Bioenergetics models—status
Vast literature, >100 yrs, 60+ spp; many reviews, critiques, sensitivity analyses
Portable, easy to code or use in spreadsheet
Used by NOAA scientists in every region—fish, bivalves, turtles, mammals, birds; local to LME scales
Future:
Work out data gaps, abuses
Forge links w/ other models
↑ creativity
# citations in ISI database:
Winberg (1956): 545 hits
Kitchell et al. (1977): 435 hits
Jobling (1994): 489 hits
R, SDA C D
B, G
F, U
DB = C – R – SDA – F – U – G

7. ≈ P/B ≈ Q/B ≈ link to other spp.
R, SDA C D
B, G
F, U
DB = CA · WCB · CVCX · e (CX · (1 – CV)) · EDdiet / ED
– RA · WRB · RVRX · e (RX · (1 – RV)) · ACT · oxycal · ED
– (SDA + U) · (C – F) – F – W · (GSImax – GSImin)
segue to ecopath
≈ P/B
≈ Q/B
≈ link to
other spp.

8. Ecopath mass balance ecosystem models
Ecopath is a steady-state ecosystem model that integrates rates of production and consumption of marine populations and functional groups In doing so, the model provides a template for integrating a wide range of biological and fisheries information from stock assessments, survey data, bioenergetics models, food habits studies, and fisheries statistics As such, it allows for both explicit examination of predator/prey relationships, as well as providing a means for smaller-scale research or model results to be viewed in the context of the ecosystem as a whole
Origins in Laevastu (Ryther, Steele, etc)
Enabled by Allen (PB=Z)
Operationalized in Polovina’s French Frigate Shoals model (1984, above),
Made widely available by Christensen and Pauly (1992,

9. What are the data requirements?
For each functional group, you must supply diet composition (DC) information, and three out of the following four parameters:
Total standing biomass (B)
The production to biomass (P/B) ratio
The consumption to biomass (Q/B) ratio,
The ecotrophic efficiency (EE), which represents the fraction of P used within the system (must be between 0 and 1)
Each functional group can have one “unknown” that is estimated by solving a set of linear equations. Ideally this is EE, but can be any of the 4
Additional options include biomass accumulation terms (to represent disequilibrium), and the fraction of consumed biomass that is not assimilated (generally default values).
Estimate of catches and/or discards for exploited species are necessary.
Units can be dry weight, wet weight, carbon, other- almost always need to make some flawed assumptions here (a kg of jellyfish <> a kg of herring)

10. What are the key data gaps?
For each functional group, you must supply diet composition (DC) information, and three out of the following four parameters:
Total standing biomass (B)
The production to biomass (P/B) ratio
The consumption to biomass (Q/B) ratio,
The ecotrophic efficiency (EE), which represents the fraction of P used within the system (must be between 0 and 1)
Each functional group can have one “unknown” that is estimated by solving a set of linear equations. Ideally this is EE, but can be any of the 4
Additional options include biomass accumulation terms (to represent disequilibrium), and the fraction of consumed biomass that is not assimilated (generally default values).
Estimate of catches and/or discards for exploited species are necessary.
Units can be dry weight, wet weight, carbon, other- almost always need to make some flawed assumptions here (a kg of jellyfish <> a kg of herring)

11. Consumption by predators
The basics, equations
Consumption by predators
New production

12. What are the strengths of the model
Basic bookkeeping- allows us to make extensive use of data and to evaluate whether what we believe about a system adds up. Understanding an imbalance can be the most educational part of model development
Improve estimates of changes in predation mortality resulting from fishing or other ecosystem changes
Model output can be used to derive a suite of properties and metrics from the single species (partitioning of mortality) to community and ecosystem levels. Such outputs are beginning to find their way into both single species and ecosystem assessments.
Tools for visualizing and communicating significance of trophic relationships and ecosystem interactions

13. Example- balancing the Pribilof Archipelago
Balancing models can be informative
Ciannelli et al. (2004) used mass balance models to evaluate predatory demand by fur seals around the Pribilof Islands. They found that a circle of 100 nm enclosed the area of highest energy balance and lowest biomass import.
This was also the mean distance from the breeding site to locations recorded at sea for breeding females, indicating that additional factors likely motivated foraging ranges.

14. Example- partitioning mortality
Pollock’s biggest mortality sources are halibut and arrowtooth in the GOA, fisheries in the EBS

15. What are the weaknesses of the model
Severe data limitations, most parameters very poorly defined, food habits data often limited in time and space
Balancing the model can be informative, however doing so does not necessarily infer confidence in the ultimate results
Extensive degree of aggregation into functional groups for widely diverse and complex communities, difficulty addressing ontogenetic changes
The inadequacy in which many key processes in a typical model are understood with respect to energy flow
There are significant difficulties associated with adequately reflecting uncertainty
Models are typically constrained by equilibrium processes, while ecosystems are often thought to be characterized by thresholds and “flips” between states
The ease-of-use of Ecopath makes it easy for a novice developer to ignore the limitations of the model

16. Table 2: Qualitative Confidence Limits in Model Parameters
There are significant difficulties associated with adequately reflecting uncertainty
Table 2: Qualitative Confidence Limits in Model Parameters
(green = high confidence, yellow= moderate confidence, red = low confidence)

17. The balanced model suggests that this ecosystem could sustain a small population of top-level predators with a total biomass on the order of 5.5 metric tons. Interestingly, this is near the center of the range suggested by the transfer efficiency studies of Sheldon and Kerr (1972).
Sheldon and Kerr, The population density of monsters in Loch Ness. Limnology and Oceanography 17:

18. A slightly more rigorous way to contemplate food web impacts using simple mass balance models
Assign data-quality based levels of uncertainty on parameters
Draw 10000s of random ecosystems from uniform distributions around suites of point estimates for B, PB, QB, DC (resulting systems not necessarily in equilibrium, but have some thermodynamic constraints)
Evaluate range of impacts in perturbed v. baseline for variations on the base model, calculate percentiles and confidence intervals around direction of change
Now appearing in NPFMC Stock Assessment Documents
Figure from: Kock K-H, 2000, Understanding CCAMLR’s Approach to Management

19. Has the model been published in the peer reviewed literature?
Answer: yes, to the extent that there have been concerns raised regarding an impending Ecopocalypse, or even an Eco-epidemic!
The model and software have also been subject to literature reviews, and their strengths and weaknesses evaluated in workshops and working groups, and other external reviews
The package is very portable, there is at least one parallel software package available (AFSC), model development is ongoing on many levels

20. Has/is/will the model outputs be used in LMR management?
The interpretation of results is challenging, despite widespread application of the approach - how can we use the results to inform or guide management decisions?
The bar, “To contribute to practical advice, a multispecies modeling approach should provide at least qualitative, and ideally defensible quantitative guidance as to the modifications in annual catch levels deemed necessary because of the predicted effects that fishing on a target species will have on other components of the ecosystem” (Plagányi and Butterworth 2004)
The reality, we’re not quite there yet, although the results of mass balance models are increasingly useful in visualizing and understanding trophic interactions, supplementing single species model outputs for decisionmakers…

21. Indicators and metrics- are we fishing down the food web. (Pauly et al
Or through the food web (Essington et al. 2006)

22. Energy or mass balance models more generally-
We have focused on two of the many flavors, there are more! Example, carbon cycle models, mass balance of nitrogen in the Mississippi Basin