Set up parameters for a general multispecies model

Sets up a multi-species size spectrum model by filling all slots in the MizerParams object based on user-provided or default parameters. There is a long list of arguments, but almost all of them have sensible default values. The only required argument is the species_params data frame. All arguments are described in more details in the sections below the list.

Usage

newMultispeciesParams(
  species_params,
  interaction = NULL,
  no_w = 100,
  min_w = 0.001,
  max_w = NA,
  min_w_pp = NA,
  pred_kernel = NULL,
  search_vol = NULL,
  intake_max = NULL,
  metab = NULL,
  p = 0.7,
  ext_mort = NULL,
  z0pre = 0.6,
  z0exp = n - 1,
  ext_encounter = NULL,
  maturity = NULL,
  repro_prop = NULL,
  RDD = "BevertonHoltRDD",
  kappa = 1e+11,
  n = 2/3,
  resource_rate = 10,
  resource_capacity = kappa,
  lambda = 2.05,
  w_pp_cutoff = 10,
  resource_dynamics = "resource_semichemostat",
  gear_params = NULL,
  selectivity = NULL,
  catchability = NULL,
  initial_effort = NULL,
  info_level = 3,
  z0 = deprecated(),
  r_pp = deprecated()
)

Arguments

species_params

A data frame of species-specific parameter values.

interaction

Optional interaction matrix of the species (predator species x prey species). By default all entries are 1. See "Setting interaction matrix" section below.

no_w

The number of size bins in the consumer spectrum.

min_w

Sets the size of the eggs of all species for which this is not given in the w_min column of the species_params dataframe.

max_w

The largest size of the consumer spectrum. By default this is set to the largest w_max specified in the species_params data frame.

min_w_pp

The smallest size of the resource spectrum. By default this is set to the smallest value at which any of the consumers can feed.

pred_kernel

Optional. An array (species x predator size x prey size) that holds the predation coefficient of each predator at size on each prey size. If not supplied, a default is set as described in section "Setting predation kernel".

search_vol

Optional. An array (species x size) holding the search volume for each species at size. If not supplied, a default is set as described in the section "Setting search volume".

intake_max

Optional. An array (species x size) holding the maximum intake rate for each species at size. If not supplied, a default is set as described in the section "Setting maximum intake rate".

metab

Optional. An array (species x size) holding the metabolic rate for each species at size. If not supplied, a default is set as described in the section "Setting metabolic rate".

p

The allometric metabolic exponent. This is only used if metab is not given explicitly and if the exponent is not specified in a p column in the species_params.

ext_mort

Optional. An array (species x size) holding the external mortality rate. If not supplied, a default is set as described in the section "Setting external mortality rate".

z0pre

If z0, the mortality from other sources, is not a column in the species data frame, it is calculated as z0pre * w_max ^ z0exp. Default value is 0.6.

z0exp

If z0, the mortality from other sources, is not a column in the species data frame, it is calculated as z0pre * w_max ^ z0exp. Default value is n-1.

ext_encounter

Optional. An array (species x size) holding the external encounter rate. If not supplied, the external encounter rate is left unchanged. Initially is is set to 0.

maturity

Optional. An array (species x size) that holds the proportion of individuals of each species at size that are mature. If not supplied, a default is set as described in the section "Setting reproduction".

repro_prop

Optional. An array (species x size) that holds the proportion of consumed energy that a mature individual allocates to reproduction for each species at size. If not supplied, a default is set as described in the section "Setting reproduction".

RDD

The name of the function calculating the density-dependent reproduction rate from the density-independent rate. Defaults to "BevertonHoltRDD()".

kappa

The coefficient of the initial resource abundance power-law.

n

The allometric growth exponent. This can be overruled for individual species by including a n column in the species_params.

resource_rate

Optional. Vector of resource intrinsic birth rates or coefficient in the power-law for the birth rate, see Details. Must be strictly positive.

resource_capacity

Optional. Vector of resource intrinsic carrying capacities or coefficient in the power-law for the capacity, see Details. The resource capacity must be larger than the resource abundance.

lambda

Used to set power-law exponent for resource capacity if the resource_capacity argument is given as a single number.

w_pp_cutoff

The upper cut off size of the resource spectrum power law used only if resource_capacity is given as a single number.

resource_dynamics

Optional. Name of the function that determines the resource dynamics by calculating the resource spectrum at the next time step from the current state.

gear_params

A data frame with gear-specific parameter values.

selectivity

Optional. An array (gear x species x size) that holds the selectivity of each gear for species and size, \(S_{g,i,w}\).

catchability

Optional. An array (gear x species) that holds the catchability of each species by each gear, \(Q_{g,i}\).

initial_effort

Optional. A number or a named numeric vector specifying the fishing effort. If a number, the same effort is used for all gears. If a vector, must be named by gear.

info_level

Controls the amount of information messages that are shown when the function sets default values for parameters. Higher levels lead to more messages.

z0

Use ext_mort instead. Not to be confused with the species_parameter z0.

r_pp

. Use resource_rate argument instead.

Value

An object of type MizerParams

Species parameters

The only essential argument is a data frame that contains the species parameters. The data frame is arranged species by parameter, so each column of the parameter data frame is a parameter and each row has the values of the parameters for one of the species in the model.

There are two essential columns that must be included in the species parameter data.frame and that do not have default values: the species column that should hold strings with the names of the species and the w_max column with the maximum sizes of the species in grams. (You could alternatively specify the maximum length in cm in an l_max column.)

The species_params dataframe also needs to contain the parameters needed by any predation kernel function (size selectivity function). This will be mentioned in the appropriate sections below.

For all other species parameters, mizer will calculate default values if they are not included in the species parameter data frame. They will be automatically added when the MizerParams object is created. For these parameters you can also specify values for only some species and leave the other entries as NA and the missing values will be set to the defaults. So the species_params data frame saved in the returned MizerParams object will differ from the one you supply because it will have the missing species parameters filled in with default values.

If you are not happy with any of the species parameter values used you can always change them later with species_params<-().

All the parameters will be mentioned in the following sections.

Setting initial values

The initial values for the species number densities are set using the function get_initial_n(). These are quite arbitrary and not very close to the steady state abundances. We intend to improve this in the future.

The initial resource number density \(N_R(w)\) is set to a power law with coefficient kappa (\(\kappa\)) and exponent -lambda (\(-\lambda\)): $$N_R(w) = \kappa\, w^{-\lambda}$$ for all \(w\) less than w_pp_cutoff and zero for larger sizes.

Size grid

A size grid is created so that the log-sizes are equally spaced. The spacing is chosen so that there will be no_w fish size bins, with the smallest starting at min_w and the largest starting at max_w. For the resource spectrum there is a larger set of bins containing additional bins below min_w, with the same log size. The number of extra bins is such that min_w_pp comes to lie within the smallest bin.

Units in mizer

Mizer uses grams to measure weight, centimetres to measure lengths, and years to measure time.

Mizer is agnostic about whether abundances are given as

1. numbers per area,

2. numbers per volume or

3. total numbers for the entire study area.

You should make the choice most convenient for your application and then stick with it. If you make choice 1 or 2 you will also have to choose a unit for area or volume. Your choice will then determine the units for some of the parameters. This will be mentioned when the parameters are discussed in the sections below.

Your choice will also affect the units of the quantities you may want to calculate with the model. For example, the yield will be in grams/year/m^2 in case 1 if you choose m^2 as your measure of area, in grams/year/m^3 in case 2 if you choose m^3 as your unit of volume, or simply grams/year in case 3. The same comment applies for other measures, like total biomass, which will be grams/area in case 1, grams/volume in case 2 or simply grams in case 3. When mizer puts units on axes in plots, it will choose the units appropriate for case 3. So for example in plotBiomass() it gives the unit as grams.

You can convert between these choices. For example, if you use case 1, you need to multiply with the area of the ecosystem to get the total quantity. If you work with case 2, you need to multiply by both area and the thickness of the productive layer. In that respect, case 2 is a bit cumbersome. The function scaleModel() is useful to change the units you are using.

Setting interaction matrix

You do not need to specify an interaction matrix. If you do not, then the predator-prey interactions are purely determined by the size of predator and prey and totally independent of the species of predator and prey.

The interaction matrix \(\theta_{ij}\) modifies the interaction of each pair of species in the model. This can be used for example to allow for different spatial overlap among the species. The values in the interaction matrix are used to scale the encountered food and predation mortality (see on the website the section on predator-prey encounter rate and on predation mortality). The first index refers to the predator species and the second to the prey species.

The interaction matrix is used when calculating the food encounter rate in getEncounter() and the predation mortality rate in getPredMort(). Its entries are dimensionless numbers. If all the values in the interaction matrix are equal then predator-prey interactions are determined entirely by size-preference.

This function checks that the supplied interaction matrix is valid and then stores it in the interaction slot of the params object.

The order of the columns and rows of the interaction argument should be the same as the order in the species params data frame in the params object. If you supply a named array then the function will check the order and warn if it is different. One way of creating your own interaction matrix is to enter the data using a spreadsheet program and saving it as a .csv file. The data can then be read into R using the command read.csv().

The interaction of the species with the resource are set via a column interaction_resource in the species_params data frame. By default this column is set to all 1s.

Setting predation kernel

Kernel dependent on predator to prey size ratio

If the pred_kernel argument is not supplied, then this function sets a predation kernel that depends only on the ratio of predator mass to prey mass, not on the two masses independently. The shape of that kernel is then determined by the pred_kernel_type column in species_params.

The default for pred_kernel_type is "lognormal". This will call the function lognormal_pred_kernel() to calculate the predation kernel. An alternative pred_kernel type is "box", implemented by the function box_pred_kernel(), and "power_law", implemented by the function power_law_pred_kernel(). These functions require certain species parameters in the species_params data frame. For the lognormal kernel these are beta and sigma, for the box kernel they are ppmr_min and ppmr_max. They are explained in the help pages for the kernel functions. Except for beta and sigma, no defaults are set for these parameters. If they are missing from the species_params data frame then mizer will issue an error message.

You can use any other string for pred_kernel_type. If for example you choose "my" then you need to define a function my_pred_kernel that you can model on the existing functions like lognormal_pred_kernel().

When using a kernel that depends on the predator/prey size ratio only, mizer does not need to store the entire three dimensional array in the MizerParams object. Such an array can be very big when there is a large number of size bins. Instead, mizer only needs to store two two-dimensional arrays that hold Fourier transforms of the feeding kernel function that allow the encounter rate and the predation rate to be calculated very efficiently. However, if you need the full three-dimensional array you can calculate it with the getPredKernel() function.

Kernel dependent on both predator and prey size

If you want to work with a feeding kernel that depends on predator mass and prey mass independently, you can specify the full feeding kernel as a three-dimensional array (predator species x predator size x prey size).

You should use this option only if a kernel dependent only on the predator/prey mass ratio is not appropriate. Using a kernel dependent on predator/prey mass ratio only allows mizer to use fast Fourier transform methods to significantly reduce the running time of simulations.

The order of the predator species in pred_kernel should be the same as the order in the species params dataframe in the params object. If you supply a named array then the function will check the order and warn if it is different.

Setting search volume

The search volume \(\gamma_i(w)\) of an individual of species \(i\) and weight \(w\) multiplies the predation kernel when calculating the encounter rate in getEncounter() and the predation rate in getPredRate().

The name "search volume" is a bit misleading, because \(\gamma_i(w)\) does not have units of volume. It is simply a parameter that determines the rate of predation. Its units depend on your choice, see section "Units in mizer". If you have chosen to work with total abundances, then it is a rate with units 1/year. If you have chosen to work with abundances per m^2 then it has units of m^2/year. If you have chosen to work with abundances per m^3 then it has units of m^3/year.

If the search_vol argument is not supplied, then the search volume is set to $$\gamma_i(w) = \gamma_i w^q_i.$$ The values of \(\gamma_i\) (the search volume at 1g) and \(q_i\) (the allometric exponent of the search volume) are taken from the gamma and q columns in the species parameter dataframe. If the gamma column is not supplied in the species parameter dataframe, a default is calculated by the get_gamma_default() function. Note that only for predators of size \(w = 1\) gram is the value of the species parameter \(\gamma_i\) the same as the value of the search volume \(\gamma_i(w)\).

Setting maximum intake rate

The maximum intake rate \(h_i(w)\) of an individual of species \(i\) and weight \(w\) determines the feeding level, calculated with getFeedingLevel(). It is measured in grams/year.

If the intake_max argument is not supplied, then the maximum intake rate is set to $$h_i(w) = h_i w^{n_i}.$$ The values of \(h_i\) (the maximum intake rate of an individual of size 1 gram) and \(n_i\) (the allometric exponent for the intake rate) are taken from the h and n columns in the species parameter dataframe. If the h column is not supplied in the species parameter dataframe, it is calculated by the get_h_default() function.

If \(h_i\) is set to Inf, fish of species i will consume all encountered food.

Setting metabolic rate

The metabolic rate is subtracted from the energy income rate to calculate the rate at which energy is available for growth and reproduction, see getEReproAndGrowth(). It is measured in grams/year.

If the metab argument is not supplied, then for each species the metabolic rate \(k(w)\) for an individual of size \(w\) is set to $$k(w) = k_s w^p + k w,$$ where \(k_s w^p\) represents the rate of standard metabolism and \(k w\) is the rate at which energy is expended on activity and movement. The values of \(k_s\), \(p\) and \(k\) are taken from the ks, p and k columns in the species parameter dataframe. If any of these parameters are not supplied, the defaults are \(k = 0\), \(p = n\) and $$k_s = f_c h \alpha w_{mat}^{n-p},$$ where \(f_c\) is the critical feeding level taken from the fc column in the species parameter data frame. If the critical feeding level is not specified, a default of \(f_c = 0.2\) is used.

Setting external mortality rate

The external mortality is all the mortality that is not due to fishing or predation by predators included in the model. The external mortality could be due to predation by predators that are not explicitly included in the model (e.g. mammals or seabirds) or due to other causes like illness. It is a rate with units 1/year.

The ext_mort argument allows you to specify an external mortality rate that depends on species and body size. You can see an example of this in the Examples section of the help page for setExtMort().

If the ext_mort argument is not supplied, then the external mortality is assumed to depend only on the species, not on the size of the individual: \(\mu_{ext.i}(w) = z_{0.i}\). The value of the constant \(z_0\) for each species is taken from the z0 column of the species parameter data frame, if that column exists. Otherwise it is calculated as $$z_{0.i} = {\tt z0pre}_i\, w_{inf}^{\tt z0exp}.$$

Setting external encounter rate

The external encounter rate is the rate at which a predator encounters food that is not explicitly modelled. It is a rate with units mass/year.

The ext_encounter argument allows you to specify an external encounter rate that depends on species and body size. You can see an example of this in the Examples section of the help page for setExtEncounter().

Setting reproduction

For each species and at each size, the proportion \(\psi\) of the available energy that is invested into reproduction is the product of two factors: the proportion maturity of individuals that are mature and the proportion repro_prop of the energy available to a mature individual that is invested into reproduction. There is a size w_repro_max at which all the energy is invested into reproduction and therefore all growth stops. There can be no fish larger than w_repro_max. If you have not specified the w_repro_max column in the species parameter data frame, then the maximum size w_max is used instead.

Maturity ogive

If the the proportion of individuals that are mature is not supplied via the maturity argument, then it is set to a sigmoidal maturity ogive that changes from 0 to 1 at around the maturity size: $${\tt maturity}(w) = \left[1+\left(\frac{w}{w_{mat}}\right)^{-U}\right]^{-1}.$$ (To avoid clutter, we are not showing the species index in the equations, although each species has its own maturity ogive.) The maturity weights are taken from the w_mat column of the species_params data frame. Any missing maturity weights are set to 1/4 of the maximum weight in the w_max column.

The exponent \(U\) determines the steepness of the maturity ogive. By default it is chosen as \(U = 10\), however this can be overridden by including a column w_mat25 in the species parameter dataframe that specifies the weight at which 25% of individuals are mature, which sets \(U = \log(3) / \log(w_{mat} / w_{mat25}).\)

The sigmoidal function given above would strictly reach 1 only asymptotically. Mizer instead sets the function equal to 1 already at a size taken from the w_repro_max column in the species parameter data frame, if it exists, or otherwise from the w_max column. Also, for computational simplicity, any proportion smaller than 1e-8 is set to 0.

Investment into reproduction

If the the energy available to a mature individual that is invested into reproduction is not supplied via the repro_prop argument, it is set to the allometric form $${\tt repro\_prop}(w) = \left(\frac{w}{w_{\tt{repro\_max}}}\right)^{m-n}.$$ Here \(n\) is the scaling exponent of the energy income rate. Hence the exponent \(m\) determines the scaling of the investment into reproduction for mature individuals. By default it is chosen to be \(m = 1\) so that the rate at which energy is invested into reproduction scales linearly with the size. This default can be overridden by including a column m in the species parameter dataframe. The maximum sizes are taken from the w_repro_max column in the species parameter data frame, if it exists, or otherwise from the w_max column.

The total proportion of energy invested into reproduction of an individual of size \(w\) is then $$\psi(w) = {\tt maturity}(w){\tt repro\_prop}(w)$$

Reproductive efficiency

The reproductive efficiency \(\epsilon\), i.e., the proportion of energy allocated to reproduction that results in egg biomass, is set through the erepro column in the species_params data frame. If that is not provided, the default is set to 1 (which you will want to override). The offspring biomass divided by the egg biomass gives the rate of egg production, returned by getRDI(): $$R_{di} = \frac{\epsilon}{2 w_{min}} \int N(w) E_r(w) \psi(w) \, dw$$

Density dependence

The stock-recruitment relationship is an emergent phenomenon in mizer, with several sources of density dependence. Firstly, the amount of energy invested into reproduction depends on the energy income of the spawners, which is density-dependent due to competition for prey. Secondly, the proportion of larvae that grow up to recruitment size depends on the larval mortality, which depends on the density of predators, and on larval growth rate, which depends on density of prey.

Finally, to encode all the density dependence in the stock-recruitment relationship that is not already included in the other two sources of density dependence, mizer puts the the density-independent rate of egg production through a density-dependence function. The result is returned by getRDD(). The name of the density-dependence function is specified by the RDD argument. The default is the Beverton-Holt function BevertonHoltRDD(), which requires an R_max column in the species_params data frame giving the maximum egg production rate. If this column does not exist, it is initialised to Inf, leading to no density-dependence. Other functions provided by mizer are RickerRDD() and SheperdRDD() and you can easily use these as models for writing your own functions.

Setting fishing

Gears

In mizer, fishing mortality is imposed on species by fishing gears. The total per-capita fishing mortality (1/year) is obtained by summing over the mortality from all gears, $$\mu_{f.i}(w) = \sum_g F_{g,i}(w),$$ where the fishing mortality \(F_{g,i}(w)\) imposed by gear \(g\) on species \(i\) at size \(w\) is calculated as: $$F_{g,i}(w) = S_{g,i}(w) Q_{g,i} E_{g},$$ where \(S\) is the selectivity by species, gear and size, \(Q\) is the catchability by species and gear and \(E\) is the fishing effort by gear.

Selectivity

The selectivity at size of each gear for each species is saved as a three dimensional array (gear x species x size). Each entry has a range between 0 (that gear is not selecting that species at that size) to 1 (that gear is selecting all individuals of that species of that size). This three dimensional array can be specified explicitly via the selectivity argument, but usually mizer calculates it from the gear_params slot of the MizerParams object.

To allow the calculation of the selectivity array, the gear_params slot must be a data frame with one row for each gear-species combination. So if for example a gear can select three species, then that gear contributes three rows to the gear_params data frame, one for each species it can select. The data frame must have columns gear, holding the name of the gear, species, holding the name of the species, and sel_func, holding the name of the function that calculates the selectivity curve. Some selectivity functions are included in the package: knife_edge(), sigmoid_length(), double_sigmoid_length(), and sigmoid_weight(). Users are able to write their own size-based selectivity function. The first argument to the function must be w and the function must return a vector of the selectivity (between 0 and 1) at size.

Each selectivity function may have parameters. Values for these parameters must be included as columns in the gear parameters data.frame. The names of the columns must exactly match the names of the corresponding arguments of the selectivity function. For example, the default selectivity function is knife_edge() that a has sudden change of selectivity from 0 to 1 at a certain size. In its help page you can see that the knife_edge() function has arguments w and knife_edge_size. The first argument, w, is size (the function calculates selectivity at size). All selectivity functions must have w as the first argument. The values for the other arguments must be found in the gear parameters data.frame. So for the knife_edge() function there should be a knife_edge_size column. Because knife_edge() is the default selectivity function, the knife_edge_size argument has a default value = w_mat.

The most commonly-used selectivity function is sigmoid_length(). It has a smooth transition from 0 to 1 at a certain size. The sigmoid_length() function has the two parameters l50 and l25 that are the lengths in cm at which 50% or 25% of the fish are selected by the gear. If you choose this selectivity function then the l50 and l25 columns must be included in the gear parameters data.frame.

In case each species is only selected by one gear, the columns of the gear_params data frame can alternatively be provided as columns of the species_params data frame, if this is more convenient for the user to set up. Mizer will then copy these columns over to create the gear_params data frame when it creates the MizerParams object. However changing these columns in the species parameter data frame later will not update the gear_params data frame.

Catchability

Catchability is used as an additional factor to make the link between gear selectivity, fishing effort and fishing mortality. For example, it can be set so that an effort of 1 gives a desired fishing mortality. In this way effort can then be specified relative to a 'base effort', e.g. the effort in a particular year.

Catchability is stored as a two dimensional array (gear x species). This can either be provided explicitly via the catchability argument, or the information can be provided via a catchability column in the gear_params data frame.

In the case where each species is selected by only a single gear, the catchability column can also be provided in the species_params data frame. Mizer will then copy this over to the gear_params data frame when the MizerParams object is created.

Effort

The initial fishing effort is stored in the MizerParams object. If it is not supplied, it is set to zero. The initial effort can be overruled when the simulation is run with project(), where it is also possible to specify an effort that varies through time.

Setting resource dynamics

You would usually set the resource dynamics only after having finished the calibration of the steady state. Then setting the resource dynamics with this function will preserve that steady state, unless you explicitly choose to set balance = FALSE. Your choice of the resource dynamics only affects the dynamics around the steady state. The higher the resource rate or the lower the resource capacity the less sensitive the model will be to changes in the competition for resource.

The resource_dynamics argument allows you to choose the resource dynamics function. By default, mizer uses a semichemostat model to describe the resource dynamics in each size class independently. This semichemostat dynamics is implemented by the function resource_semichemostat(). You can change that to use a logistic model implemented by resource_logistic() or you can use resource_constant() which keeps the resource constant or you can write your own function.

Both the resource_semichemostat() and the resource_logistic() dynamics are parametrised in terms of a size-dependent rate \(r_R(w)\) and a size-dependent capacity \(c_R\). The help pages of these functions give the details.

The resource_rate argument can be a vector (with the same length as w_full(params)) specifying the intrinsic resource growth rate for each size class. Alternatively it can be a single number, which is then used as the coefficient in a power law: then the intrinsic growth rate \(r_R(w)\) at size \(w\) is set to $$r_R(w) = r_R w^{n-1}.$$ The power-law exponent \(n\) is taken from the n argument.

The resource_capacity argument can be a vector specifying the intrinsic resource carrying capacity for each size class. Alternatively it can be a single number, which is then used as the coefficient in a truncated power law: then the intrinsic growth rate \(c_R(w)\) at size \(w\) is set to $$c(w) = \kappa\, w^{-\lambda}$$ for all \(w\) less than w_pp_cutoff and zero for larger sizes. The power-law exponent \(\lambda\) is taken from the lambda argument.

The values for lambda, n and w_pp_cutoff are stored in a list in the resource_params slot of the MizerParams object so that they can be re-used automatically in the future. That list can be accessed with resource_params(). It also holds the coefficient kappa that describes the steady-state resource abundance.

See also

Other functions for setting up models: newCommunityParams(), newSingleSpeciesParams(), newTraitParams()

Examples

params <- newMultispeciesParams(NS_species_params)
#> Because you have n != p, the default value for `h` is not very good.
#> Because the age at maturity is not known, I need to fall back to using
#> von Bertalanffy parameters, where available, and this is not reliable.
#> No ks column so calculating from critical feeding level.
#> Using z0 = z0pre * w_max ^ z0exp for missing z0 values.
#> Using f0, h, lambda, kappa and the predation kernel to calculate gamma.