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Growth is computed on start-of-year biomass and a year of fishing removes B (1 - exp(-F)), so equilibrium is B/K = 1 - h/r with harvest rate h = 1 - exp(-F), hmsy = r/2 and B/Bmsy = 2 - h/hmsy exactly. ffmsy() returns h/hmsy. (Using r/2 for instantaneous F overstates F/Fmsy for fast stocks: for r = 1.4, Fmsy = -log(1 - r/2) = 1.2, not 0.7.)

Usage

ffmsy(F, r, h = FALSE)

Arguments

F

instantaneous annual F (vector, or matrix with stocks in columns).

r

intrinsic growth rate(s), one per stock.

h

if TRUE, F is already a harvest rate.

Value

h / hmsy, same shape as F.

Examples

ffmsy(-log(1 - 0.7), r = 1.4)   # 1: fished at MSY
#> [1] 1