Estimate the Beverton-Holt and hockey-stick stock recruitment relationships from data of spawning stock biomass (SBy) and recruits (Ry) with a give steepness (h) value.

Est_SR estimates the coefficients (i.e. alpha and beta) of the BH relationship from data of spawning stock biomass (SBy) and recruits (Ry).

Usage

Est_SR(
  SBy,
  Ry,
  h,
  h_fix = T,
  inits = c(1, 1),
  ref.year = c(1970:2019),
  SB0_max = max(SBy) * 100,
  M,
  w,
  g,
  A = 6,
  method
)

Arguments

SBy

A vector of spawning biomass at year. The vector should be named with years. The length should be the same as that of ref.year

Ry

A vector of recruits at year. The vector should be named with years. The length should be the same as that of ref.year

h

A value of steepness to be fixed.

h_fix

A logical value deciding whether the steepness is fixed. Default is TRUE. FALSE is allowed only for the BH relationship at this stage.

inits

A vector of initial values of the parameters search (alpha, beta) for BH. Although default is c(1, 1), searching for the suitable sets is recommended.

ref.year

A vector of years to be referred for the estimation. Default is c(1970:2019)

SB0_max

Maximum value of SB0 values to be searched for parameter estimation. Default is max(SBy)*100.

M

A vector of natural mortality rate at age a. The length should be A+1.

w

A vector of weight at age a. The length should be A+1.

g

A vector of maturity at age a. The length should be A+1.

A

Plus group age. Default is 6.

method

The type of the stock-recruitment relationship. At this stage, "BH" (Beverton-Holt) or "HS" (Hockey-stick) is allowed.

Fish_mort

Fishing mortality to calculate SBR. Should be provided with a numeric value.

Value

Values of alpha and beta coefficients for the BH relationships or a value of SB0 for the HS relationships. As for the BH, when h is not fixed (i.e. h_fix = T), the output from the optim() function is shown.