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.
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, ...)The number of species in the model. The default value is 11.
The asymptotic size of the smallest species in the community. Default value is 10.
The asymptotic size of the largest species in the community. Default value is 1000.
The size of the the egg of the smallest species. Default value is 10^(-4).
The maturity size of the smallest species. Default value is 10^(0.4),
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.
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.
Scaling of the intake. Default value is 2/3.
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.
Exponent of the abundance power law. If supplied, this
overrules the q argument. Otherwise the default value is 2+q-n.
Growth rate of the primary productivity. Default value is 0.1.
Coefficient in abundance power law. Default value is 0.005.
The assimilation efficiency of the community. The default value is 0.4.
Standard metabolism coefficient. Default value is 4.
Maximum food intake rate. Default value is 30.
Preferred predator prey mass ratio. Default value is 100.
Width of prey size preference. Default value is 1.3.
Expected average feeding level. Used to set gamma, the
coefficient in the search rate. The default value is 0.6.
The minimum size at which the gear or gears select species. Must be of length 1 or no_sp. Default value is 100.
The names of the fishing gears. A character vector, the same length as the knife_edge_size parameter. Default value is "knife_edge_gear".
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.
An object of type MizerParams
The scale free trait-based model is similar to the standard trait-based model, with three main differences:
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.
The egg size is proportional to the maturity size for each species
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 multiplying 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 stabilizing 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.
# NOT RUN {
s_params <- set_scaling_model()
sim <- project(s_params, t_max=5, effort = 0)
plotSpectra(sim)
# }
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