Calculates the algal biomass at the next time step from the current algae biomass
Arguments
- params
A MizerParams object
- n
A matrix of current species abundances (species x size)
- n_other
Other dynamic components.
- rates
A list of rates as returned by
getRates()- dt
Time step size
- t
The current time, used to determine the post-bleaching algae growth boost, if any (see
getAlgaeBoost()). Defaults to0, which is always before any bleaching event.- ...
Unused
Details
The time evolution of the algal biomass \(B\) is described by
$$dB_A/dt = P_A - c_A \cdot B_A$$
where \(c_A\) is the mass-specific rate of consumption calculated
with algae_consumption() and \(P_A\) is the rate at which algae
grows, calculated with getAlgaeProduction().
The dynamical equation is solved analytically to
$$B_A(t+dt) = B_A(t) e^{(- c_A \cdot dt)} +\frac{P_A}{c_A} (1- e^{(-c_A \cdot dt)}).$$
This avoids the stability problems that would arise if we used the Euler method to solve the equation numerically.
B_A(t+dt) above is a convex combination of B_A(t) and P_A/c_A, and
is therefore guaranteed non-negative only when P_A >= 0. P_A (from
getAlgaeProduction()) is a fixed, literature-informed production rate
representing real algal primary production, which is not driven by
consumer demand: it is set once (by setAlgaeParams()/newReefParams())
and does not respond to the changing fish abundances of a live,
non-frozen simulation, or get retuned to match consumption – only the
algae biomass moves, converging on P_A/c_A as c_A (and therefore
grazing pressure) changes. tuneUR()/tuneUR_cc() tune the algae
biomass to this same fixed point for a chosen set of abundances, rather
than tuning P_A. Production is floored at zero
(production <- max(production, 0)) before it enters the analytic
update above, so that this non-negativity guarantee holds even if some
future/degraded parameterisation ever drove P_A negative. This has no
effect at any steady state tuned by tuneUR()/tuneUR_cc() (there,
P_A is a literature-informed constant and is non-negative by
construction) – it only ever engages away from that steady state.