mizer (version 3.4.0)

sizeIntegral: 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
)

Value

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

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.

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")]