calc_M2 | R Documentation |
Calculates the predation mortality for each species in each length class.
calc_M2(N, ration, wgt, nfish, nsc, other, sc_Linf, suit_M2)
N |
A matrix with dimensions |
ration |
A matrix with dimensions |
wgt |
A matrix with dimensions |
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 |
suit_M2 |
A list object of length |
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.
A matrix with dimensions nsc
and nfish
representing the the predation mortality for each species in each length class.
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.
# 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)
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