Detritus dynamics

Calculates the detritus biomass at the next time step based on the current detritus biomass.

Usage

detritus_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 vector giving the detritus spectrum at the next time step.

Details

The time evolution of the detritus biomass \(B\) is described by

$$dB_D/dt = P_D - c_D \cdot B_D $$

where \(c_D\) is the mass-specific rate of consumption, calculated with detritus_consumption()and \(P_D\) is the rate at which the rest of the system produces detritus biomass, calculate with getDetritusProduction().

The dynamical equation is solved analytically to

$$B_D(t+dt) = B(t)\exp(-c_D \cdot dt) + \frac{P_D}{c_D} (1-\exp(-c_D \cdot dt)).$$

This avoids the stability problems that would arise if we used the Euler method to solve the equation numerically.

See also

algae_dynamics(), detritus_consumption(), getDetritusConsumption(), getDetritusProduction()