resource_logistic: Project resource using logistic model

In mizer: Dynamic Multi-Species Size Spectrum Modelling

Project resource using logistic model

Description

If you set your resource dynamics to use this function then the time evolution of the resource spectrum is described by a logistic equation

\frac{\partial N_R(w,t)}{\partial t} = r_R(w) N_R(w)\Big[ 1 - \frac{N_R(w,t)}{c_R (w)} \Big] - \mu_R(w, t) N_R(w,t)

Usage

resource_logistic(
  params,
  n,
  n_pp,
  n_other,
  rates,
  t,
  dt,
  resource_rate,
  resource_capacity,
  ...
)

balance_resource_logistic(params, resource_rate, resource_capacity)

Arguments

params	A MizerParams object
n	A matrix of species abundances (species x size)
n_pp	A vector of the resource abundance by size
n_other	A list with the abundances of other components
rates	A list of rates as returned by mizerRates()
t	The current time
dt	Time step
resource_rate	Resource replenishment rate
resource_capacity	Resource carrying capacity
...	Unused

Details

Here r_R(w) is the resource regeneration rate and c_R(w) is the carrying capacity in the absence of predation. These parameters are changed with setResource(). The mortality \mu_R(w, t) is due to predation by consumers and is calculate with getResourceMort().

This function uses the analytic solution of the above equation to calculate the resource abundance at time t + dt from all abundances and rates at time t, keeping the mortality fixed during the timestep.

To set your model to use logistic dynamics for the resource you do

params <- setResource(params, 
                      resource_dynamics = "resource_logistic", 
                      resource_level = 0.5)

where you should replace params with the name of the variable holding your MizerParams object. You can of course choose any value between 0 and 1 for the resource level.

The balance_resource_logistic() function is called by setResource() to determine the values of the resource parameters that are needed to make the replenishment rate at each size equal the consumption rate at that size, as calculated by getResourceMort(). It should be called with only one of resource_rate or resource_capacity should and will return a named list with the values for both.

Value

Vector containing resource spectrum at next timestep

See Also

Other resource dynamics: resource_constant(), resource_semichemostat()

mizer documentation built on Oct. 17, 2024, 9:07 a.m.