calc_prefs: Calculate predator-prey size preferences
In LeMaRns: Length-Based Multispecies Analysis by Numerical Simulation

Description Usage Arguments Details Value References Examples

Calculates the size preference of each predator species in each length class for each prey species in each length class.

1	calc_prefs(pred_mu, pred_sigma, wgt, sc_Linf)

`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.

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)).

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.

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.

# 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

# Calculate predator-prey size preferences
prefs <- calc_prefs(pred_mu=-2.25, pred_sigma=0.5, wgt, sc_Linf)