# Calculate predator-prey size preferences Calculates the size preference of each predator species in each length class for each prey species in each length class. ```r calc_prefs(pred_mu, pred_sigma, wgt, sc_Linf) ``` ## Arguments - `pred_mu`: A numeric value representing the preferred predator-prey mass ratio. - `pred_sigma`: A numeric value representing the width of the weight preference function. - `wgt`: A matrix with dimensions `nsc` and `nfish` representing the weight of each species in each length class. - `sc_Linf`: A numeric vector of length `nsc` representing the length class at which each species reaches its asymptotic length. ## Returns An array of dimensions `nsc`, `nfish`, `nsc` and `nfish`. The first and second dimensions represent the prey species whereas the third and fourth dimensions represent the predator species. ## Details A predator of species `i` in length class `j` has a size preference for species `k` in length class `l` equal to `exp(-(log10(wgt[l, k]/wgt[j, i])-pred_mu)^2/(2*pred_sigma))`. ## 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$phi_min # Calculate growth increments tmp <- calc_ration_growthfac(k, Linf, nsc, nfish, l_bound, u_bound, mid, W_a, W_b, phi_min) sc_Linf <- tmp$sc_Linf wgt <- tmp$wgt prefs <- calc_prefs(pred_mu=-2.25, pred_sigma=0.5, wgt, sc_Linf) ``` ## 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. Ursin, E. (1973). On the prey size preferences of cod and dab. **Meddelelser fra Danmarks Fiskeri-og Havundersgelser**, 7:85-98.

calc_prefs function