Build an ecosystem model
10. Mass balance
Mass balance is performed using a number of algorithms and a routine for matrix inversion, see the energy balance of a box for a description of these. Once the program has estimated the missing parameters, the system balances the input and output of each group, using respi- ration for adjustments. The relationship used is
Master Equation 1:
where, consumption is the total consumption for a group, i.e., biomass · (consumption / bio- mass). Respiration is the part of the consumption that is not used for production or recycled as egestion or excretion. Respiration is nonusable currency, i.e., it cannot be used by the other groups in the system. Autotrophs with Q/B = 0 and detritus have zero respiration. Unassim- ilated food is an input parameter expressing the fraction of food that is not assimilated, (i.e., is egested or excreted). For models whose currency is energy, the default is 0.20, i.e. 20% of consumption for all groups, though this is most applicable for finfish groups following Win- berg1. The non-assimilated food is directed to the detritus.
If the model currency is a nutrient, there is no respiration. Instead, the model is balanced such that the non- assimilated food equals the difference between consumption and production.
Some consumers are also producers, e.g., coral reefs can be a bit of both. We accommodate that by noting that production in the first Master Equation does not include primary production, i.e., it is defined as biomass · (production / bio- mass) · (1 – PP), where PP is the proportion of total production that can be attrib- uted to primary production. We thus have that (1 – PP) = 0 in plants, 1 in
heterotrophic consumers, and intermediate in the 0 to 1 range for e.g., corals or tridacnid clams.
An exhaustive set of guidelines for how a model should be balanced cannot be given. However, if it existed, such a set would include the following general guidelines
• Make sure to document what is done in the balancing process by entering remarks for all parameters and to extract these subsequently. A model where the balancing process is not appropriately documented is not likely to be publishable;
• Remember which data that are the more reliable and avoid changing these;
• Formulate assumptions and argumentation for changes: the ones easy to explain are likely to be the better assumptions;
• Start by looking at the estimated values. Are the EE values possible (less than 1)? Are the g (= P/Q) values physiologically realistic (0.1-0.3 for most groups, perhaps lower for top predators and higher for very small organisms, (e.g., up to 0.5 for bacteria). If not decide from where the problem is the biggest if you want to balance your model starting from the bottom (producers) or from the top down;
• Search out one group with a bigger problem and try to solve this. Are the P/B, Q/B and B values appropriate for this group? What would happen to, e.g., the g and the EE if you changed the parameters? If the problem is the consumption by predators, look at the Predation mortality form, and identify the quantitatively most important predators.
Check the diet compositions and B and Q/B values for these predators;
• Continue for as long as necessary, documenting carefully what changes are made. It may be a good idea to save the data file under a new name before/after making the set of changes;
• You may get warnings that the “Respiration cannot be negative”. If this happens the sec- ond master equation of Ecopath has been violated. We have:
Consumption = production + respiration + unassimilated food or
Q = P + R + U
Expressing this relative to consumption we have:
1 = P/Q + R/Q + U/Q
Of these P/Q is entered as the gross food conversion efficiency (g) (or estimated from entered P and Q) and U/Q is the proportion of food that is not assimilated. If g + U/Q exceeds unity, then R/Q and hence the respiration, R, has to be negative. You will need to reduce the production/consumption (g) ratio by lowering the production/biomass (P/B) ratio or increasing the consumption/biomass (Q/B) ratio, and/or reduce the pro- portion of unassimilated food;
• Examine the respiration/biomass (R/B) ratios for each group. Generally this ratio reflects activity level. For fish it should as a rule be in the range 1-10 year-1, for copepods perhaps around 50-100 year-1. Please consult physiology texts for more information. If the ratio seems high it may be necessary to change the (assumed) proportion of the food that is not assimilated on the basic input form;
• Examine the Electivity form. Do the preferences seem reasonable?
• Examine the predation mortalities at Ecopath > Output > Mortality rates > Mortalities, along with the predation mortality spreadsheet (Ecopath > Output > Mortality rates >
Predation mortality rates) to identify how important the various predators are for any group. Does this show what you expect? Are the predators shown to be the most impor- tant predators in accordance with what you expect? If not, re-evaluate your model’s diet compositions. The information on the mortality forms is very important!
• Noting how the energy balance of a group is formulated, it is clear that, for instance, increasing the proportion of the consumption that is not assimilated will leave less energy to respiration (production being unaffected). This will result in a lower R/B ratio and a larger flow to the detritus. The latter may be necessary to balance the model if
there is only little system surplus production.
Fixed Selectivity Principle for diets
When balancing a model there are often groups for which the information about diet has less detail than required in the model or is qualitative rather than quantitative.
You may for instance have a predator that feeds on “small fish”; blue heron could be an example.
A common assumption when defining the diet composition for such predators is to use a seemingly parsimonious assumption of “all equal”, i.e. for a start set the, e.g.,
“20% small fish” to 5% for each of the four potential prey groups. Such an assump- tion will very likely lead to the model not balancing.
For such predators, it is more reasonable to assume that they take prey in proportion to how common the prey is in the environment. We can quantify this using what we call the ‘fixed selectivity’ principle, assuming the prey preference for such predators when feeding on suitable prey should be comparable across species or functional groups.
When setting this up, consider that it’s not the biomass of a group that is eaten by a predator, it’s the production. Therefore, to use this principle, estimate the production (B x P/B) for each (i) of the potential prey groups (n) for a predator (j). Then assume that the proportion each contribute to the predator diet (DCji) is proportional to their production. We have,
We first used this principle for the Roberts Bank Terminal 2 ecosystem model2 to adjust the diet composition of pinnipeds, diving waterbirds, great blue heron, shore- birds, chinook adult, chinook juvenile, chum juvenile, dogfish, flatfish, large demer- sals, lingcod, rockfish, salmon juvenile, skate, and starry flounder. The total
contribution of “small fish” in the diet of these predators was maintained, but the dis- tribution among potential prey groups was estimated relative to prey productivity. In that model, the ‘fixed selectivity’ principle was also used to adjust the contribution of invertebrates in the diets of diving waterbirds, waterfowl, forage fish, herring, carniv- orous zooplankton, jellyfish, macrofauna, and polychaetes. Contribution of vegetation was also adjusted in a similar way in the diets of American wigeon, waterfowl, epifau- nal grazer, epifauna.
What was that warn- ing, again?
You can find warnings and messages in the Status panel at the lower left of the EwE form