calc_M2: Calculate predation mortality
In LeMaRns: Length-Based Multispecies Analysis by Numerical Simulation

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 `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.

The predation mortality of the ith species in the jth 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)