Algae dynamics

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

Usage

algae_dynamics(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 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.

See also

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