getTrophicLevel: Get trophic level of individuals at size

In mizer: Dynamic Multi-Species Size Spectrum Modelling

Get trophic level of individuals at size

Description

Calculates the trophic level of individuals of each species at each size, assuming the system is in a steady state. The trophic level of an individual is defined as 1 more than the consumption-rate-weighted average trophic level of all the prey it has consumed during its lifetime up to the current size. The resource is given a size-dependent trophic level (see below).

Usage

getTrophicLevel(
  params,
  n = initialN(params),
  n_pp = initialNResource(params),
  n_other = initialNOther(params),
  w_R = 1e-10,
  beta_R = 1000,
  ...
)

Arguments

params	A MizerParams object.
n	A matrix of species abundances (species x size). Defaults to the initial abundances stored in params.
n_pp	A vector of the resource abundance by size. Defaults to the initial resource abundance stored in params.
n_other	A named list of the abundances of other dynamical components. Defaults to the initial values stored in params.
w_R	An average size (in grams) of primary producers in the resource spectrum, used to set the size-dependent resource trophic level. Defaults to 1e-10.
beta_R	An average predator/prey mass ratio for the resource spectrum, used to set the size-dependent resource trophic level. Must be greater than 1. Defaults to 1000.
...	Unused

Details

In the traditional non-size-resolved approach, all individuals of a species have the same diet composition D_{ij}, defined as the proportion of total biomass intake of species i that comes from species j. The trophic levels then satisfy

T_i = 1 + \sum_j D_{ij}\,T_j,

which is solved as a linear system (I - D)\,\mathbf{T} = \mathbf{1}.

In mizer, diet composition changes as an individual grows, so we must integrate over the individual's lifetime. Assuming a steady state so that the growth rate g_i(w) and prey densities depend only on size and not on time, we can replace the integral over time since birth by an integral over weight using dt = dw / g_i(w). The trophic level T_i(w) of an individual of species i at weight w is then

T_i(w) = 1 + \frac{ \int_{w_0}^{w} \frac{1}{g_i(w')} \sum_j \int r_{ij}(w', w_p)\, T_j(w_p)\, dw_p\, dw' }{ \int_{w_0}^{w} \frac{1}{g_i(w')} \sum_j \int r_{ij}(w', w_p)\, dw_p\, dw' },

where w_0 is the egg size and r_{ij}(w, w_p) is the rate at which a predator of species i at weight w consumes biomass from prey species j at weight w_p:

r_{ij}(w, w_p) = \theta_{ij}\,\gamma_i(w)\,(1 - f_i(w))\,\phi_i(w/w_p)\, N_j(w_p)\,w_p.

The sum over j runs over all species and the resource. The resource is assigned a size-dependent trophic level

T_R(w) = \max\left(1,\; 1 + \frac{\log(w / w_R)}{\log(\beta_R)}\right),

where w_R is an average size of primary producers (which therefore have trophic level 1) and \beta_R is an average predator/prey mass ratio for the resource (for example zooplankton). This adds one trophic level for each factor of \beta_R increase in resource size, with a floor at 1 so that the resource trophic level never drops below the primary-producer level. Both the numerator and the denominator (which equals the total biomass consumed over the predator's lifetime from egg size to current weight w) therefore include the resource.

This equation can be viewed as a linear system (I - D)\,\mathbf{T} = \mathbf{1} in which the entries of \mathbf{T} are indexed by (i, w) and the matrix D encodes the lifetime-integrated diet composition. The system is solved iteratively from small to large sizes, exploiting the fact that prey are typically much smaller than the predator (large predator-to-prey mass ratio), so that the trophic levels of all relevant prey sizes are already known when computing T_i(w).

Value

An ArraySpeciesBySize object (species x size) with the trophic level of individuals at each size. Entries below the egg size of each species are NA.

See Also

getTrophicLevelBySpecies()

Other summary functions: getBiomass(), getDiet(), getGrowthCurves(), getN(), getSSB(), getSteadyResidual(), getTrophicLevelBySpecies(), getYield(), getYieldGear()

Examples

tl <- getTrophicLevel(NS_params)
plot(tl)

mizer documentation built on Aug. 31, 2026, 5:08 p.m.