R: Gadget3 suitability formulae

suitability {gadget3}

R Documentation

Gadget3 suitability formulae

Description

Formula-returning functions describing length suitability relationships.

Usage

g3_suitability_exponentiall50(
    alpha = g3_parameterized("alpha", by_stock = by_stock, by_predator = by_predator),
    l50 = g3_parameterized("l50", by_stock = by_stock, by_predator = by_predator),
    by_stock = TRUE,
    by_predator = TRUE)

g3_suitability_andersen(p0, p1, p2, p3 = p4, p4, p5 = ~predstock__midlen)

g3_suitability_andersenfleet(
        p0 = g3_parameterized('andersen.p0', value = 0, optimise = FALSE,
                              by_stock = by_stock),
        p1 = g3_parameterized('andersen.p1', value = log(2),
                              by_stock = by_stock, by_predator = by_predator),
        p2 = g3_parameterized('andersen.p2', value = 1, optimise = FALSE,
                              by_stock = by_stock),
        p3 = g3_parameterized('andersen.p3', value = 0.1, exponentiate = exponentiate,
                              by_stock = by_stock, by_predator = by_predator),
        p4 = g3_parameterized('andersen.p4', value = 0.1, exponentiate = exponentiate,
                              by_stock = by_stock, by_predator = by_predator),
        p5 = quote( stock__maxmidlen ),
        by_stock = TRUE,
        by_predator = TRUE,
        exponentiate = TRUE)

g3_suitability_gamma(alpha, beta, gamma)

g3_suitability_exponential(alpha, beta, gamma, delta)

g3_suitability_straightline(alpha, beta)

g3_suitability_constant(alpha)

g3_suitability_richards(p0, p1, p2, p3, p4)

Arguments

`alpha`, `beta`, `gamma`, `delta`, `l50`, `p0`, `p1`, `p2`, `p3`, `p4`, `p5`	formula substituted into calcuations, see below.
`by_stock`	Change the default parameterisation (e.g. to be by 'species'), passed through to default calls to `g3_parameterized`.
`by_predator`	Change the default parameterisation (e.g. to be by 'fleet'), passed through to default calls to `g3_parameterized`.
`exponentiate`	Exponentiate parameters,passed through to default calls to `g3_parameterized`.

Details

When using these to describe a predator/prey relationship, the stock midlength l will refer to the prey midlength.

Value

All functions return a formula for use in g3a_predate_fleet's suitabilities argument:

g3_suitability_exponentiall50

A logarithmic dependence on the length of the prey as given by the following equation (note that the prey length dependence is actually dependant on the difference between the length of the prey and l_{50}):

\frac{1}{ 1 + e^{-\alpha (l - l_{50})} }

l: Vector of stock midlength for each lengthgroup
l_{50}: Length of the stock with a 50% probability of predation, from parameter l50

g3_suitability_andersen

This is a more general suitability function that is dependant on the ratio of the predator length to the prey length as given by the following equation:

If p_3 = p_4:

p_0 + p_2 e^{-\frac{(x - p_1)^2}{p_4}}

Otherwise:

p_0 + p_2 e^{-\frac{(x - p_1)^2}{p_4}} * \min(\max(p_1 - x, 0), 1) + p_2 e^{-\frac{(x - p_1)^2}{p_3}} * \min(\max(x, 0), 1)

...i.e if \log\frac{L}{l} <= p_1 then p_3 used in place of p_4.

x: \log\frac{p_5}{l}
L: Vector of predator midlength for each lengthgroup
l: Vector of stock midlength for each lengthgroup
p_0 .. p_4: Function parameter p0 .. p4
p_5: Function parameter p5, if unspecified uses L, Vector of predator midlength for each lengthgroup.

NB: Specifying p_5 is equivalent to using the andersenfleet function in gadget2.

g3_suitability_andersenfleet

A simplified version of g3_suitability_andersen, suitable for predation by fleets, as the defaults do not rely on the predator's length.

g3_suitability_gamma

This is a suitability function that is more suitable for use when considering the predation by a fleet, where the parameter \gamma would represent the size of the mesh used by the fleet (specified in centimetres).

(\frac{l}{(\alpha - 1)\beta\gamma}) ^ {(\alpha - 1) e^{\alpha - 1 - \frac{l}{\beta\gamma}}}

l: Vector of stock midlength for each lengthgroup
\alpha: Function parameter alpha
\beta: Function parameter beta
\gamma: Function parameter gamma

g3_suitability_exponential

This is a suitability function that has a logarithmic dependence on both the length of the predator and the length of the prey as given by the following equation:

\frac{\delta}{1 + e^{-\alpha - \beta l - \gamma L}}

L: Vector of predator midlength for each lengthgroup
l: Vector of stock midlength for each lengthgroup
\alpha: Function parameter alpha
\beta: Function parameter beta
\gamma: Function parameter gamma
\delta: Function parameter delta

g3_suitability_straightline

Returns a formula for use in predation function's suitabilities argument:

\alpha + \beta l

l: Vector of stock midlength for each lengthgroup
\alpha: Function parameter alpha
\beta: Function parameter beta

g3_suitability_constant

Returns a formula for use in predation function's suitabilities argument:

\alpha

\alpha: Function parameter alpha

g3_suitability_richards

Returns a formula for use in predation function's suitabilities argument:

{\big( \frac{p_3}{1 + e^{-p_0 - p_1 l - p_2 L}} \big)}^{\frac{1}{p_4}}

L: Vector of predator midlength for each lengthgroup
l: Vector of stock midlength for each lengthgroup
p_0 .. p_4: Function parameter p0 .. p4

This is an extension to g3_suitability_exponential.

Examples


ling_imm <- g3_stock(c(species = 'ling', 'imm'), seq(20, 156, 4)) %>% g3s_age(3, 10)
ling_mat <- g3_stock(c(species = 'ling', 'mat'), seq(20, 156, 4)) %>% g3s_age(5, 15)
igfs <- g3_fleet('igfs')

igfs_landings <-
  structure(expand.grid(year=1990:1994, step=2, area=1, total_weight=1),
            area_group = list(`1` = 1))

# Generate a fleet predation action using g3_suitability_exponentiall50
predate_action <- g3a_predate_fleet(
    igfs,
    list(ling_imm, ling_mat),
    suitabilities = list(
        ling_imm = g3_suitability_exponentiall50(
            g3_parameterized('lln.alpha', by_stock = 'species'),
            g3_parameterized('lln.l50', by_stock = 'species')),
        ling_mat = g3_suitability_exponentiall50(
            g3_parameterized('lln.alpha', by_stock = 'species'),
            g3_parameterized('lln.l50', by_stock = 'species'))),
    catchability = g3a_predate_catchability_totalfleet(
        g3_timeareadata('igfs_landings', igfs_landings)))

# You can use g3_eval to directly calculate values for a stock:
g3_eval(
    g3_suitability_exponentiall50(alpha = 0.2, l50 = 60),
    stock = g3_stock('x', seq(0, 100, 10)) )

## Plots
suit_plot <- function (
    fn,
    stock = g3_stock('x', seq(0, 100, 10)),
    predstock__midlen = 140 ) {
  cols <- rainbow(5)
  par(mar = c(2,2,2,2), cex.main = 1)

  plot(
    g3_stock_def(stock, 'midlen'),
    seq(0, 1, length.out = length(g3_stock_def(stock, 'midlen'))),
    main=deparse1(body(fn)),
    type = "n")
  for (a in seq_along(cols)) lines(
    g3_stock_def(stock, 'midlen'),
    g3_eval(fn(a), stock = stock, predstock__midlen = predstock__midlen),
    type = "o", col = cols[[a]] )
}

suit_plot(function (a) g3_suitability_exponentiall50(alpha = a * 0.1, l50 = 50))
suit_plot(function (a) g3_suitability_andersen(0, log(2), 1, p3 = a * 0.1, 0.1, 140))
suit_plot(function (a) g3_suitability_andersen(0, log(2), 1, 0.1, p4 = a * 0.1, 140))
suit_plot(function (a) g3_suitability_gamma(alpha = 2 + a * 0.1, beta = 1, gamma = 40))
suit_plot(function (a) g3_suitability_exponential(0, 0.01 * a, 0, 1))
suit_plot(function (a) g3_suitability_straightline(alpha = 0.1, beta = 0.01 * a))
suit_plot(function (a) g3_suitability_constant(a * 0.1))
suit_plot(function (a) g3_suitability_richards(0, 0.05, 0, 1, 0.1 * a))

[Package gadget3 version 0.11-1 Index]

Gadget3 suitability formulae

Description

Usage

Arguments

Details

Value

g3_suitability_exponentiall50

g3_suitability_andersen

g3_suitability_andersenfleet

g3_suitability_gamma

g3_suitability_exponential

g3_suitability_straightline

g3_suitability_constant

g3_suitability_richards

See Also

Examples