sizeIntegral: Integrate a quantity over the size spectrum

In mizer: Dynamic Multi-Species Size Spectrum Modelling

Integrate a quantity over the size spectrum

Description

Calculates

\int_{w_{min}}^{w_{max}} N_i(w)\, K_i(w)\, dw

for each species i, using the quadrature scheme that the model is actually using. This is the recommended way to write your own summary or indicator function: it selects the size range, applies the bin-averaging appropriate to the model's second_order_w() setting and wraps the result in the appropriate mizer array class, so that none of those rules need to be remembered. The built-in summary functions like getBiomass(), getN(), getSSB() and getYield() are all implemented with it.

Usage

sizeIntegral(
  object,
  weighting = 1,
  n = NULL,
  ...,
  value_name = NULL,
  units = NULL
)

Arguments

object	A MizerParams or a MizerSim object.
weighting	The weighting factor K(w) of the integral, evaluated on the size grid. See the section "The weighting factor" below. Defaults to 1.
n	The abundance density. Either a species x size matrix or a time x species x size array. Defaults to the initial abundance initialN(object) for a MizerParams object and to the saved abundances object@n for a MizerSim object.
...	Arguments passed to get_size_range_array() to select the size range to integrate over, i.e. min_w, max_w, min_l and max_l.
value_name	A string giving a human-readable name for the value, used when the result is wrapped in a mizer array class.
units	A string giving the units of the result, used when the result is wrapped in a mizer array class.

Value

The value of the integral, see the section "Shape of the result" above.

The weighting factor

The weighting factor K(w) is supplied already evaluated on the size grid. It can be

• a single number (the default weighting = 1 integrates the abundance density itself, giving numbers),

• a vector with one value for each size bin, which is then used for all species,

• a matrix (species x size), for example params@maturity,

• an array with further dimensions in front, for example the gear x species x size array returned by getFMortGear() or the time x species x size array returned by getFMort(sim). Those extra dimensions are carried through to the result.

If the weighting factor is a product of several size-dependent factors, pass the whole product: bin-averaging is applied to the product as a single weighting factor, which is not the same as averaging the factors separately.

Do not include the bin widths params@dw in the weighting factor and do not bin-average it yourself; sizeIntegral() does both.

Shape of the result

The size dimension is integrated out. The remaining dimensions are those of n together with any extra dimensions of weighting, so

• with a MizerParams object and a species x size weighting the result is a named vector with one value per species,

• with a MizerSim object it is an ArrayTimeBySpecies object (time x species),

• with a gear x species x size weighting the extra gear dimension is kept, giving a gear x species array (or time x gear x species for a MizerSim).

Dimensions of weighting other than the last two are matched to the dimensions of n by the names of their dimnames, so a weighting whose first dimension is named "time" is lined up with the times of the simulation rather than producing an outer product.

See Also

get_size_range_array(), bin_average_weight(), second_order_w()

Examples

# The biomass of each species, i.e. what getBiomass() does
sizeIntegral(NS_params, weighting = NS_params@w)

# ... restricted to a size range
sizeIntegral(NS_params, weighting = NS_params@w, min_w = 10, max_w = 1000)

# The numbers of individuals larger than 10g
sizeIntegral(NS_params, min_w = 10)

# Spawning stock biomass: the weighting is the product maturity * w
K <- sweep(NS_params@maturity, 2, NS_params@w, "*")
sizeIntegral(NS_params, weighting = K)

# An indicator through time, ready to plot
biomass <- sizeIntegral(NS_sim, weighting = NS_params@w,
                        value_name = "Biomass", units = "g")
biomass[c("1972", "2010"), c("Herring", "Cod")]

mizer documentation built on Aug. 24, 2026, 9:08 a.m.