# Calculate growth increments Calculates the amount of food required for fish of a given species and length class to grow according to the von Bertalanffy growth curve in a time step. ```r calc_ration_growthfac( k, Linf, nsc, nfish, l_bound, u_bound, mid, W_a, W_b, phi_min, vary_growth = TRUE, growth_eff = 0.5, growth_eff_decay = 0.11 ) ``` ## 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. - `l_bound`: A numeric vector of length `nsc` representing the lower bounds of the length classes. - `u_bound`: A numeric vector of length `nsc` representing the upper bounds of the length classes. - `mid`: A numeric vector of length `nfish` representing the mid-point of the length classes. - `W_a`: A numeric vector of length `nfish` representing the parameter `a` in the length-weight conversion. See 'Details' for more information. - `W_b`: A numeric vector of length `nfish` representing the parameter `b` in the length-weight conversion. See 'Details' for more information. - `phi_min`: A numeric value representing the time step of the model. - `vary_growth`: A logical statement indicating whether growth efficiency should vary for each species (`vary_growth=TRUE`) or be fixed at the value given by `fixed_growth` (`vary_growth=FALSE`). The default is `FALSE`. - `growth_eff`: If `vary_growth==TRUE`, `growth_eff` is a numeric representing the growth efficiencies of a fish of length 0. If `vary_growth==FALSE`, `growth_eff` is a numeric value of length `1` representing a fixed growth efficiency for all fish. The default is 0.5. - `growth_eff_decay`: A numeric value specifying the rate at which growth efficiency decreases as length approaches `Linf`. The default is 0.11. ## Returns A list object containing `ration`, `sc_Linf`, `wgt` and `g_eff`. `ration` is a matrix with dimensions `nsc` and `nfish` representing the amount of food required for fish of a given species and length class to grow according to the von Bertalanffy growth curve in a time step. `sc_Linf` is a numeric vector of length `nfish` representing the length class at which each species reaches `Linf`. `wgt` is a matrix with dimensions `nsc` and `nfish` representing the weight of each species in each length class. `g_eff` is a matrix with dimensions `nsc` and `nfish` representing the growth efficiency of each species in each length class. ## Details The weight increments of the `i`th species in the `j`th length class is calculated by determining the amount an individual will grow in one time step, `phi_min`, if it were to follow the von Bertalanffy growth curve `L22=(Linf[i]-mid[j])*(1-exp(-k[i]*phi_min))`. The weight of a fish at the mid-point of the size class is calculated using the length-weight relationship `wgt[j,i] = a[i]*mid[j]^b[i]`, and similarly the expected change in weight of the the fish is calculated as `growth_inc = (W_a[i]*L22^W_b[i])`. It also has a growth efficiency `g_eff[j,i]=(1-(wgt[j,i]/(W_a[i]*Linf[i]^W_b[i]))^growth_eff_decay)*growth_eff` if `vary_growth==TRUE` or `g_eff[j, i]=growth_eff` otherwise. `ration` is then calculated by `growth_inc*(1/g_eff[j, i])`. ## 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). # 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$phi_min tmp <- calc_ration_growthfac(k, Linf, nsc, nfish, l_bound, u_bound, mid, W_a, W_b, phi_min) ration <- tmp$ration sc_Linf <- tmp$sc_Linf wgt <- tmp$wgt g_eff <- tmp$g_eff ``` ## References von Bertalanffy, L. (1957). Quantitative Laws in Metabolism and Growth. **The Quarterly Review of Biology**, 32:217-231

calc_ration_growthfac function