Prey-dependent assimilation rates

[gustavdelius]

Asta (@astaaudzi) suggested in #46 that we might like to have different assimilation efficiencies for different food sources. Currently mizer does not allow that, having a species parameter alpha[i] that depends on the predator species i only and does not depend on the prey species. The proposal is to introduce a slot alpha in the MizerParams class for a matrix alpha[i, j] depending on both predator and prey species.

Unfortunately there is an efficiency problem with this idea: due to the way satiation is handled in mizer it would require summing over prey species twice. Mizer first calculates the encountered food. This involves summing over all prey species, independently of how well the prey species biomass can be assimilated. That rate of food encounter is then used to calculate the feeding level that determines what proportion of the encountered food is actually consumed by a predator. If we now wanted to implement a prey-specific assimilation rate we would have to re-do the sum over all prey species j and this time multiply by alpha[i, j]. Not horrible, but a slightly larger change than we might be prepared to accept.

If we decided to go ahead with this we would still want to make it convenient for the user to set up the assimilation efficiency matrix via the species parameter data frame if they want to. One proposal would be to allow two species parameters alpha_prey and alpha_pred and then to set alpha[i, j] <- alpha_pred[i] * alpha_prey[j].

I suspect that in many cases the assimilation efficiency will depend more on the prey species than on the predator species. in which case the user would only specify alpha_prey and leave alpha_pred at its default value. So the user would not have to specify more parameters but rather would be allowed to specify the parameters they actually care about.