set_scaling_model: Sets up parameters for a scale free trait-based model

Description Usage Arguments Details Value See Also Examples

View source: R/wrapper_functions.R

Description

This functions creates a MizerParams object so that scale free trait-based-type models can be easily set up and run. The scale free trait-based size spectrum model can be derived as a simplification of the general size-based model used in mizer. All the species-specific parameters are the same for all species, except for the egg size, maturity size and asymptotic size. These differ over the species, but the ratio of egg size to maturity size and the ratio of egg size to asymptotic size are the same for each species. The asymptotic sizes of the species are spread evenly on a logarithmic scale. See the mizer vignette and the Details section below for more details and examples of the scale free trait-based model.

Usage

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set_scaling_model(no_sp = 11, min_w_inf = 10, max_w_inf = 10^3,
  min_egg = 10^(-4), min_w_mat = 10^(0.4), no_w = log10(max_w_inf/min_egg)
  * 100 + 1, min_w_pp = min_egg/(beta * exp(5 * sigma)), n = 2/3, q = 3/4,
  lambda = 2 + q - n, r_pp = 0.1, kappa = 0.005, alpha = 0.4, ks = 4,
  h = 30, beta = 100, sigma = 1.3, f0 = 0.6, knife_edge_size = 100,
  gear_names = "knife_edge_gear", rfac = Inf, ...)

Arguments

no_sp

The number of species in the model. The default value is 11.

min_w_inf

The asymptotic size of the smallest species in the community. Default value is 10.

max_w_inf

The asymptotic size of the largest species in the community. Default value is 1000.

min_egg

The size of the the egg of the smallest species. Default value is 10^(-4).

min_w_mat

The maturity size of the smallest species. Default value is 10^(0.4),

no_w

The number of size bins in the community spectrum. Default value is such that there are 100 bins for each factor of 10 in weight.

min_w_pp

The smallest size of the background spectrum. Default value is min_egg/(beta*exp(5*sigma)) so that it covers the entire range of the feeding kernel of even the smallest fish larva.

n

Scaling of the intake. Default value is 2/3.

q

Exponent of the search volume. Default value is 3/4 unless lambda is provided, in which case this argument is ignored and q = lambda - 2 + n.

lambda

Exponent of the abundance power law. If supplied, this overrrules the q argument. Otherwise the default value is 2+q-n.

r_pp

Growth rate of the primary productivity. Default value is 0.1.

kappa

Coefficient in abundance power law. Default value is 0.005.

alpha

The assimilation efficiency of the community. The default value is 0.4.

ks

Standard metabolism coefficient. Default value is 4.

h

Maximum food intake rate. Default value is 30.

beta

Preferred predator prey mass ratio. Default value is 100.

sigma

Width of prey size preference. Default value is 1.3.

f0

Expected average feeding level. Used to set gamma, the coefficient in the search rate. The default value is 0.6.

knife_edge_size

The minimum size at which the gear or gears select species. Must be of length 1 or no_sp. Default value is 100.

gear_names

The names of the fishing gears. A character vector, the same length as the knife_edge_size parameter. Default value is "knife_edge_gear".

rfac

The factor such that Rmax = rfac * R, where Rmax is the maximum recruitment allowed and R is the steady-state recruitment. Thus the larger rfac the less the impact of the non-linear stock-recruitment curve. The default is Inf.

...

Other arguments to pass to the MizerParams constructor.

Details

The scale free trait-based model is similar to the standard trait-based model, with three main differences:

  1. We have an exact equation for a steady state of this system which is often stable, even when we include no extra stabilization effects like density dependence or stock recruitment relationships.

  2. The egg size is proportional to the maturity size for each species

  3. The parameters are chosen so that R_0 (the expected number of offspring produced by an individual over a lifetime) is close to 1 for each species.

The function has many arguments, all of which have default values. Of particular interest to the user are the number of species in the model and the minimum and maximum asymptotic sizes.

The characteristic weights of the different species are defined by min_egg, min_w_mat, min_w_inf, max_w_inf and no_sp, in the sense that the egg weights of the no_sp species are logarithmically evenly spaced, ranging from min_w=min_egg to max_w=max_w_inf. The maturity weights of the species can be obtained by muliplying the egg_weights by min_w_mat/min_egg. The asymptotic weights of the species can be obtained by multiplying the egg weights by min_w_inf/min_egg.

Although the scale free trait based model's default steady state is often stable without imposing a stock recruitment relationship, the function can set a Beverton-Holt type stock recruitment relationship that imposes a maximal reproduction rate that is a multiple of the recruitment rate at steady state. That multiple is set by the argument rfac.

In addition to setting up the parameters, this function also evaluates the analytic expression for a steady state of the scale free trait-based model and sets it as the initial condition.

The search rate coefficient gamma is calculated using the expected feeding level, f0.

The option of including fishing is given, but the steady state may lose its natural stability if too much fishing is included. In such a case the user may wish to include stablizing effects (like Rmax and chi) to ensure the steady state is stable. Fishing selectivity is modelled as a knife-edge function with one parameter, knife_edge_size, which is the size at which species are selected. Each species can either be fished by the same gear (knife_edge_size has a length of 1) or by a different gear (the length of knife_edge_size has the same length as the number of species and the order of selectivity size is that of the asymptotic size).

The resulting MizerParams object can be projected forward using project() like any other MizerParams object. When projecting the model it may be necessary to reduce dt to 0.1 to avoid any instabilities with the solver. You can check this by plotting the biomass or abundance through time after the projection.

Value

An object of type MizerParams

See Also

MizerParams

Examples

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## Not run: 
s_params <- set_scaling_model()
sim <- project(s_params, t_max=5, effort = 0)
plotSpectra(sim)

## End(Not run)

drfinlayscott/mizer documentation built on May 18, 2018, 9:20 a.m.