Description Usage Arguments Details Value References Examples

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

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`k` |
A numeric vector of length |

`Linf` |
A numeric vector of length |

`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 |

`l_bound` |
A numeric vector of length |

`calc_phi_min` |
A logical statement indicating whether |

`phi_min` |
A fixed numeric value of |

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.

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.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 | ```
# 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
``` |

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