# Calculate the proportion of individuals that leave each length class for each species each length class each time step. Calculate the proportion of individuals of each species that leave each length class at each time step. ```r 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`. ## Returns 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. ## 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. ## Examples ```r # 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 ``` ## 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.

calc_phi function