Algae dynamics with carrying capacity

Calculates the algae biomass at the next time step from the current algae biomass

Usage

algae_dynamics_cc(params, n, n_other, rates, dt, ...)

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

...

Unused

Value

A single number giving the algae biomass at next time step

Details

The time evolution of the algae biomass \(B_A(t)\) is described by

$$ \frac{dB_A}{dt} = P_A\left( 1 - \frac{B_A}{K_A} \right) - c_A \, B_A $$

where \(K_A\) is the system's carrying capacity for algae in grams/ year, \(c_A\) 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

$$B_A(t + dt) = B_A(t) \cdot e^{-\frac{dt}{K_A}(P_A+ K_A \, c_A)} + \frac{K_A \, P_A}{P_A+ K_A \, c_A} \left(1- e^{-\frac{dt}{K_A}(P_A+ K_A \, c_A)}\right) $$

See also

detritus_dynamics(), algae_consumption(), getAlgaeConsumption(), getAlgaeProduction()