calc_phi {LeMaRns}

Calculate the proportion of individuals that leave each length class for each species each length class each time step.

Description

Calculate the proportion of individuals of each species that leave each length class at each time step.

Usage

calc_phi(
  k,
  Linf,
  nsc,
  nfish,
  u_bound,
  l_bound,
  calc_phi_min = FALSE,
  phi_min = 0.1
)

Arguments

k

A numeric vector of length nfish representing the von Bertalanffy growth parameter (1/yr) for each species.

Linf

A numeric vector of length nfish representing the asymptotic length of each species.

nsc

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

nfish

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

u_bound

A numeric vector of length nsc representing the upper bounds of the length classes.

l_bound

A numeric vector of length nsc representing the lower bounds of the length classes.

calc_phi_min

A logical statement indicating whether phi_min should be calculated within the function. The default is FALSE.

phi_min

A fixed numeric value of phi_min, which represents the time step of the model. This is only required if calc_phi_min=FALSE. The default is 0.1.

Details

Calculates the time (yrs) for an average fish to grow from the lower to the upper bound of a length class assuming von Bertalanffy growth. The values are scaled to the fastest growing fish and length class combination in order to calculate the proportion of individuals leaving each length class in a time step.

Value

A list object containing phi and phi_min. phi is a matrix of dimensions nsc and nfish representing the proportion of individuals of each species that leave each length class. phi_min is a numeric value representing the time step of the model.

References

Hilborn, R. & Walters, C.J. (1992). Quantitative Fisheries Stock Assessment. Springer.

von Bertalanffy, L. (1957). Quantitative Laws in Metabolism and Growth. The Quarterly Review of Biology, 32:217-231.

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).

# Calculate the proportion of individuals that leave each length class
# with and without a fixed value for 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

tmp <- calc_phi(k, Linf, nsc, nfish, u_bound, l_bound, calc_phi_min=TRUE) # without fixed phi_min
phi <- tmp$phi
phi_min <- tmp$phi_min