Description Usage Arguments Details Value References Examples

Calculates the predation mortality for each species in each length class.

1 | ```
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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
# 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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