Lopt

Lopt, the length at which a cohort achives its maximum biomass, can be used as a reference point to identify growth over- or underfishing. Since taking fish below or above this size results in potential loss of yield. The total biomass of a cohort changes through time as a result of gains due to an increase in mean size-at-age and losses due to natural mortality. Lopt can therefore be estimated from the natural mortality and weight-at-age vectors.

# S4 method for FLPar
lopt(
  params,
  m = function(length, params) exp(0.55) * (length^-1.61) %*% (params["linf"]^1.44)
    %*% params["k"],
  growth = FLife::vonB,
  ...
)

Arguments

params

an FLPar object with parameter values for the natural mortality and growth functions, and the exponent b of the length/weight relationship.

m

natural mortality function, by default Gislason

growth

length or weight-at-age function, by default von Bertalanffy

...

any other arguments

Value

FLPar with $L_opt$ the length at which a cohort achives its maximum biomass

Details

Lopt is a function of growth and natural mortality-at-age and there are several approximations such as \(2/3 L_{\infty}\) and \(L_{\infty}\frac{3}{3+k/m}\). If the life history parameters and relationships are known then $L_opt$ can be found by finding the time (t) and hence length at which the maximum biomass is achieved i.e. \(L(T)^a e^{\int_0^T m(t)}\) where \(m(t)\) can be found from the relationship of mortality at length using the relationship of Gislason, assuming the von Bertalanffy growth curve.

See also

gislason, vonB, lhRef, lhPar, lhEql,

Examples

if (FALSE) {
params=lhPar(FLPar(linf=100,k=0.1,t0=-0.1,b=3))
lopt(params)
}