calc_mature {LeMaRns}

Calculate the proportion of mature individuals

Description

Calculates the proportion of individuals that are mature for each species and length class.

Usage

calc_mature(Lmat, nfish, mid, kappa, sc_Linf, eps = 1e-05, force_mature = TRUE)

Arguments

Lmat

A numeric vector of length nfish representing the length at which 50% of individuals are mature for each species.

nfish

A numeric value representing the number of species in the model.

mid

A numeric vector of length nfish representing the mid-point of the length classes in the model.

kappa

A numeric vector of length nfish representing the rate of change from immaturity to maturity for each species.

sc_Linf

A numeric vector of length nsc representing the length class at which each species reaches its asymptotic length.

eps

A numeric value specifying a numerical offset. The default is 1e-5.

force_mature

A logical statement indicating whether to force all fish in the largest length class to be mature. The default is TRUE.

Details

The proportion of individuals in the jth length class of the ith species that are mature is described by a logistic model

1/(1+exp(-kappa[i]*(mid[j]-Lmat[i])))

Value

A matrix with dimensions nsc and nfish and elements in the range 0-1 representing the proportion of individuals that are mature for each species and length class.

References

Hall, S. J., Collie, J. S., Duplisea, D. E., Jennings, S., Bravington, M., & Link, J. (2006). A length-based multispecies model for evaluating community responses to fishing. Canadian Journal of Fisheries and Aquatic Sciences, 63(6):1344-1359.

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 <- tmp$phi
phi_min <- tmp$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 the proportion of mature individuals
mature <- calc_mature(Lmat, nfish, mid, kappa=rep(10, nfish), sc_Linf)