A stage-explicit expression of the von Bertalanffy growth model for understanding age at first reproduction of Great Lakes fishes

Abstract

An initial annual growth rate of body length and its regular decrease with increasing age has general linkages with age at first reproduction (tR). We clarify their combinations and develop predictive functions. We use a complete Ford–Walford plot with yearling size (L1) on the y axis and show a slope transition between the relative yearling growth rate (ρy) and the Ford–Walford slope (ρ). The three stage-specific variables define a complete body-length trajectory over ages, including all von Bertalanffy growth parameters and the Ford–Walford intercept (Lint). The difference between asymptotic length (Linf) and yearling length is growth potential after the first annulus. Yearling growth is a transition period, so growth potential can be adjusted as ρLinf or Linf – Lint. Changes in the three life-stage variables have contrasting effects on growth potential and von Bertalanffy growth parameters, so they have contrasting relations with tR. For most invertebrate-eating fishes in the Laurentian Great Lakes, dominant changes in growth trajectories were reflected in ρ, so tR was predicted by the von Bertalanffy growth coefficient, K. For walleye (Stizostedion vitreum) populations around the Great Lakes, dominant changes in growth trajectories were from yearling size or yearling growth, so tR was predicted using Lint. Our results have clear implications for understanding fish population dynamics.