Peterson-Wroblewski Natural Mortality Model — M_peterson

Computes weight-based natural mortality following Peterson & Wroblewski (1984). Mortality scales allometrically with body weight.

Usage

M_peterson_wroblewski(
  age,
  Linf,
  L0,
  k,
  lw_fun,
  growth_model = c("vb", "gompertz", "logistic")
)

Arguments

age: Numeric vector of ages at which to compute mortality.
Linf: Asymptotic length.
L0: Length at birth.
k: Growth coefficient (native to the fitted model).
lw_fun: Function mapping length to weight in grams: lw_fun(L).
growth_model: Character. Growth model for length prediction: "vb", "gompertz", or "logistic". Default "vb".

Value

Numeric vector of instantaneous mortality rates.

Details

The model expresses mortality as a power function of body weight: $$M(W) = 1.92 \cdot W^{-0.25}$$ where $W$ is body weight in grams.

This model is growth-model-agnostic: it only requires predicted body weight at age, which can be derived from any growth model via a length-weight relationship. The $-0.25$ exponent reflects metabolic scaling theory: metabolic rate scales approximately as $W^{0.75}$ (Kleiber's law), and mortality is assumed proportional to mass-specific metabolic rate, yielding a $W^{-0.25}$ dependence.

Because $k$ does not appear in the mortality equation itself, the native growth coefficient and native growth model should always be used for $L(t)$ prediction — no VB-equivalent conversion is needed.

References

Peterson, I., & Wroblewski, J. S. (1984). Mortality rate of fishes in the pelagic ecosystem. Canadian Journal of Fisheries and Aquatic Sciences, 41(7), 1117-1120.

Examples

if (FALSE) { # \dontrun{
lw_fun <- function(L) 0.0001 * L^3.1  # Length in cm, weight in g
ages <- seq(0.5, 30, by = 0.5)

M <- M_peterson_wroblewski(
  age = ages, Linf = 100, L0 = 25, k = 0.1,
  lw_fun = lw_fun, growth_model = "gompertz"
)
} # }