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Mean length and its spread at a set of real ages

get_laa_curve.Rd

Schnute-form von Bertalanffy growth: L1 is the mean length at age A1, L2 the mean length at age A2, and K the growth rate, so $$L_\infty = L_1 + \frac{L_2 - L_1}{1 - e^{-K(A_2 - A_1)}}$$ and \(L(x) = L_\infty + (L_1 - L_\infty) e^{-K(x - A_1)}\) for real ages \(x \ge A_1\). Below A1 growth is linear from L0 at age zero, \(L(x) = L_0 + (x / A_1)(L_1 - L_0)\), the linear phase. L2_asymptote = 1 reads L2 as the asymptote directly, with no second reference age to solve it from.

Usage

get_laa_curve(
  x,
  L0,
  L1,
  L2,
  K,
  CV1,
  CV2,
  A1,
  A2,
  cv_type = 0,
  sd_type = 0,
  A2_cv = NULL,
  rho = 1,
  cv_ref = NULL,
  L2_asymptote = 0
)

Arguments

x

Numeric vector of real ages (data, not parameters).

L0

Length at age zero, the anchor of the linear phase.

L1, L2, K, CV1, CV2

Growth parameters, natural scale, possibly AD.

A1, A2

Reference ages for L1 and L2. Ignored for the asymptote under L2_asymptote, though A2 still bounds the CV interpolation.

cv_type

Integer, 0 interpolate the CV on length, 1 scale by age.

sd_type

Integer, 0 the CV parameters scale the mean, 1 they are SDs.

A2_cv

Age at and above which CV2 applies. Defaults to A2. Under L2_asymptote there is no second reference age, so Setup_Mod_Biologicals sets A2 to the accumulator age and the interpolation runs to there.

rho

Richards coefficient, natural scale, possibly AD. One (the default) is the von Bertalanffy curve.

cv_ref

Optional vector of the coefficient of variation at each element of x, used in place of the one this curve implies. Holds the spread at age at a reference year's while the mean moves, which is the convention for a time-varying growth curve.

L2_asymptote

Integer, 0 (default) solves \(L_\infty\) from L1 and L2 at their reference ages, 1 reads L2 as \(L_\infty\) itself. Set from growth_A2 = "Linf" in Setup_Mod_Biologicals.

Value

List with L (mean length), sd (spread), Linf and cv.

Details

With a Richards coefficient rho other than one the curve is the Richards generalization, which applies the same form to the lengths raised to that power, $$L(x)^\rho = L_\infty^\rho + (L_1^\rho - L_\infty^\rho) e^{-K(x - A_1)}$$ with \(L_\infty^\rho = L_1^\rho + (L_2^\rho - L_1^\rho) / (1 - e^{-K(A_2 - A_1)})\) when A2 is a real age. rho = 1 is the von Bertalanffy curve.

The coefficient of variation is CV1 below A1, CV2 at and above A2, and in between interpolates linearly on mean length (cv_type = 0) or on age (cv_type = 1). The spread is CV * L under sd_type = 0 and the parameter itself under sd_type = 1.