22 Mediation and time forcing

The basic Ecosim prediction for consumption or flow rate (unit: biomass/time, e.g., t km^-2 year^-1) of type i prey biomass to type j predator is of the functional form

[latex]\text{flow rate} = a_{ij} V_{ij} B_j \tag{1}[/latex]

where a_ij is a “rate of effective search” parameter, V_ij is vulnerable prey biomass, and B_j is effective predator abundance (for simple models B_j is just predator biomass; for multi-stanza groups it is the sum over ages in that group of numbers at age times body weight to the 2/3 power, an index of per-predator search rate). If vulnerable prey were randomly distributed over the modelled spatial area, and V, B_j were expressed as abundances per unit area, then a_ij would be interpretable as a volume or area swept per unit predator abundance (per B_j) per unit time, corrected for the proportion of time actually spent searching for food (foraging time and handling time adjustments reduce a_ij from its theoretical maximum value for a predator that searched all the time for food).

To understand how effects of habitat changes as represented through time forcing functions, and mediation effects as expressed through mediation functions of abundances of other organisms, are likely to affect trophic flow rates, we need to be a bit more careful about the a_ij parameter. In particular, we need to recognize that for most trophic interactions, predators search for prey only over restricted spatial foraging arenas, and hence V_ij is distributed only over such areas rather than at random over the whole system.

Suppose the (practically unmeasurable) restricted area where foraging by j on prey i takes place is A_ij per unit total model area. Suppose that while in this area, each unit of predator abundance (per B_j) searches an effective area [latex]a_{ij}^*[/latex] for prey. On average, each such area searched should result in capture of V_ij/A_ij prey, since this ratio is prey density in the arena area. In other words, the flow rate could be modelled more precisely (if we could measure A_ij) as

[latex]\text{flow rate}=a_{ij}^{*} A_{ij} V_{ij} B_j \tag{2}[/latex]

i.e., the basic Ecosim equation’s a_ij can be interpreted as a_ij =  a_ij* /A_ij. Expressed this way, we see that time forcing and/or mediation effects can influence the flow rate in at least three quite distinct ways:

• by altering the effective search rate a_ij* of the predator, for example by using a turbidity time forcing function or a mediation function of algal biomass that reduces a_ij* at high algal biomass.
• by altering the area A_ij over which vulnerable prey and/or predators are distributed, for example by a mediation effect where macrophyte or seagrass biomass limits the foraging area usable by small predatory fish, so increases in those plant biomasses should be represented as causing increases in A_ij for all prey i of the small fish as predator j. Another example would be restriction of A_ij for feeding on small fishes by pelagic birds caused by large pelagic fishes, which drive small fishes nearer to the surface where they are more available to the birds.
• by altering the vulnerability exchange rates v_ij that determine (along with a_ij* / A_ij) V_ij from total prey biomass B_i (the basic equation for V from B is V_ij = v_ij B_i / (v_ij + v_ij‘ + a_ij* /A_ij B_j). For example, if small fish respond to increased large plant biomass by occupying a larger area, the mixing rate (v_ij) of planktonic food organisms into that larger area will increase as well.

It is possible to apply multiple time forcing and/or mediation functions to each trophic flow (i,j) rate prediction, and to specify whether each function multiplies [latex]a_{ij}^*[/latex], A_ij, and/or v_ij. Using these forms, one can choose the parameter that is multiplied by each forcing or mediation function, i.e. one of the following choices:

• Multiply overall predator rate of effective search (a_i,j), for example to represent time-varying turbidity changes that affect predator search efficiency or mediation effects of algal biomass on search efficiency.
• Multiply vulnerability exchange rate (v_ij), for example to represent increased movement rates of prey into vulnerable behavioural state at times when water mixing rates are higher.
• Multiply area of foraging arenas (divide A_ij by multiplier), for example to represent increase in habitat area available for juvenile fish refuges.
• Multiply area (divide A_ij) and also multiply v_ij, for example to represent increase in safe foraging habitat available to a predator that feeds on prey that become available in foraging arenas through passive drift/mixing processes such that increasing area used by predator results in higher proportion of total prey population being available in foraging areas at any moment.

Forcing and trophic mediation functions in Ecosim can be set up at the Ecosim > Input > Forcing function; and Ecosim) > Input > Mediation forms.