# Calculate predation mortality Calculates the predation mortality for each species in each length class. ```r calc_M2(N, ration, wgt, nfish, nsc, other, sc_Linf, suit_M2) ``` ## Arguments - `N`: A matrix with dimensions `nsc` and `nfish` representing the number of individuals in each length class for the current time step. - `ration`: 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. - `wgt`: A matrix with dimensions `nsc` and `nfish` representing the weight of each species in each length class. - `nfish`: A numeric value representing the number of species in the model. - `nsc`: A numeric value representing the number of length classes in the model. - `other`: A numeric value representing the amount of other food (g) available from prey that is not explicitly represented in the model. - `sc_Linf`: A numeric vector of length `nsc` representing the length class at which each species reaches its asymptotic length. - `suit_M2`: A list object of length `nfish`. Each element in the list is an array of dimensions `nsc`, `nsc` and `nfish` containing a value between zero and 1 representing prey preference and prey suitability for each species and length class. ## Returns A matrix with dimensions `nsc` and `nfish` representing the the predation mortality for each species in each length class. ## Details The predation mortality of the `i`th species in the `j`th length class is `sum_m(sum_n(I[j,i]*N[j,i]*suit_M2[[m]][n,j,i]/` `(sum_k(sum_l(suit_M2[[m]][n,l,k]wgt[l,k]N[l,k]))+other)))` where `sum_m` represents the sum over all `m`, `sum_n` represents the sum over all `n`, `sum_l` represents the sum over all `l` and `sum_k` represents the sum over all `k`. This equation corresponds to a Holling type-II functional response. See equation 8 of Hall et al. (2006) for more details. ## 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 <- tmp$phi phi_min <- tmp$phi_min # Calculate growth increments tmp <- calc_ration_growthfac(k, Linf, nsc, nfish, l_bound, u_bound, mid, W_a, W_b, phi_min) ration <- tmp$ration sc_Linf <- tmp$sc_Linf wgt <- tmp$wgt g_eff <- tmp$g_eff # Calculate predator-prey size preferences prefs <- calc_prefs(pred_mu=-2.25, pred_sigma=0.5, wgt, sc_Linf) # Calculate prey preference and prey suitability suit_M2 <- calc_suit_vect(nsc, nfish, sc_Linf, prefs, NS_tau) # Get an initial population N0 <- get_N0(nsc, nfish, mid, wgt, sc_Linf, intercept=1e10, slope=-5) # Calculate the predation mortality M2 <- calc_M2(N0, ration, wgt, nfish, nsc, other=1e12, sc_Linf, suit_M2) ``` ## 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.

calc_M2 function