calc_M1 {LeMaRns}

Calculate background mortality

Description

Calculates the background mortality of each species in each length class per time step.

Usage

calc_M1(
  nsc,
  sc_Linf,
  phi_min,
  natmort_opt = rep("std_RNM", length(sc_Linf)),
  Nmort = rep(0.8, length(sc_Linf)),
  prop = rep(0.75, length(sc_Linf))
)

get_M1(nsc, sc_Linf, natmort_opt, Nmort, prop)

calc_M1_stdRNM(nsc, sc_Linf, Nmort = 0.8, prop = 0.75)

calc_M1_lin(nsc, sc_Linf, Nmort = 0.8)

calc_M1_constRNM(nsc, sc_Linf, Nmort = 0.8)

Arguments

nsc

A numeric value representing the number of length classes in the model.

sc_Linf

A numeric vector of length nfish for calc_M1 and 1 for get_M1, calc_M1_stdRNM, calc_M1_constRNM and calc_M1_lin, representing the length class at which each species reaches its asymptotic length.

phi_min

A numeric value representing the time step of the model.

natmort_opt

A character vector of length nfish for calc_M1 and 1 for get_M1, describing the mortality function to be used for each species. By default, natmort_opt takes the value "std_RNM", but it can also take "constant" or "linear". See 'Details' for more information.

Nmort

A numeric vector of length nfish representing the maximum background mortality of each species. The default is 0.8 for all species.

prop

A numeric vector of length nfish representing the proportion of length classes that have a non-zero background mortality. This parameter is required only when the natmort_opt mortality function is used. The default is 0.75.

Details

The background mortality is defined as the number of individuals that die per year, but not from predation or fishing

N*exp(-M1)

where N is the total number of individuals. This function allows three different models for background mortality: (1) "constant", which gives M1=Nmort for all length classes up to and including the sc_Linf-th class; (2) "std_RNM", which gives M1=Nmort for all length classes between floor(sc_Linf*prop) and the sc_Linf-th class and M1=0 for the rest; and (3) "linear", which gives M1=0 for the first length class, followed by a linear increase in M1 up to and including the sc_Linf-th length class M1=Nmort and M1=0 for the rest.

Value

calc_M1 returns a matrix of dimensions nsc and nfish representing the background mortality of each species for each length class.

get_M1 returns a numeric vector of length nsc representing the background mortality for each length class.

calc_M1_stdRNM returns a numeric vector of length nsc representing the background mortality for each length class. M1=Nmort for all length classes between floor(sc_Linf*prop) and the sc_Linf-th class and M1=0 for the rest.

calc_M1_lin returns a numeric vector of length nsc representing the background mortality for each length class. M1=0 for the first length class. M1 then increases linearly up to and including the sc_Linf-th length class. For all length classes above sc_Linf, M1=0.

calc_M1_constRNM returns a numeric vector of length nsc representing the background mortality for each length class. M1=Nmort for all length classes up to and including the sc_Linf-th class. For all length classes above sc_Linf, M1=0.

References

Thorpe, R.B., Jennings, S., Dolder, P.J. (2017). Risks and benefits of catching pretty good yield in multispecies mixed fisheries. ICES Journal of Marine Science, 74(8):2097-2106.

Examples

# Set up the inputs to the function - species-independent parameters
nfish <- nrow(NS_par)
nsc <- 32
maxsize <- max(NS_par$Linf)*1.01 # the biggest size is 1% bigger than the largest Linf
l_bound <- seq(0, maxsize, maxsize/nsc); l_bound <- l_bound[-length(l_bound)]
u_bound <- seq(maxsize/nsc, maxsize, maxsize/nsc)
mid <- l_bound+(u_bound-l_bound)/2

# Set up the inputs to the function - species-specific parameters
Linf <- NS_par$Linf # the von-Bertalanffy asymptotic length of each species (cm).
W_a <- NS_par$W_a # length-weight conversion parameter.
W_b <- NS_par$W_b # length-weight conversion parameter.
k <- NS_par$k # the von-Bertalnaffy growth parameter.
Lmat <- NS_par$Lmat # the length at which 50\% of individuals are mature (cm).

# Get phi_min
tmp <- calc_phi(k, Linf, nsc, nfish, u_bound, l_bound, calc_phi_min=FALSE,
                  phi_min=0.1) # fixed phi_min
phi_min <- tmp$phi_min

# Calculate growth increments
tmp <- calc_ration_growthfac(k, Linf, nsc, nfish, l_bound, u_bound, mid, W_a, W_b, phi_min)
sc_Linf <- tmp$sc_Linf

# Calculate background mortality with natmort_opt="std_RNM", Nmort=0.8 and prop=0.75 for all species
M1 <- calc_M1(nsc, sc_Linf, phi_min)

# Get background mortality with natmort_opt="std_RNM", Nmort=0.8 and prop=0.75 for all species
natmort_opt <- "std_RNM"
Nmort <- 0.8
prop <- 0.75
get_M1(nsc, sc_Linf, natmort_opt, Nmort, prop)

# Calculate standard residual background mortality
M1_stdRNM <- calc_M1_stdRNM(nsc, sc_Linf)

# Calculate linear background mortality
M1_lin <- calc_M1_lin(nsc, sc_Linf,Nmort=0.3)

# Calculate constant residual background mortality
M1_constRNM <- calc_M1_constRNM(nsc, sc_Linf)