Physiology
V
Von Bertalanffy Growth Function
Quick Definition
The standard mathematical model describing indeterminate fish growth: L(t) = L∞(1 − e^(−K(t−t₀))), where L∞ is asymptotic length and K is the growth rate.
📖 Full Definition
The von Bertalanffy Growth Function (VBGF) describes the typical pattern of fish growth: rapid early growth that progressively slows as fish approach their asymptotic maximum size (L∞). The model parameters are: L∞ (asymptotic length — the mean size the species would reach given unlimited time and food), K (Brody growth coefficient — the rate at which growth decelerates, per year), and t₀ (theoretical age at zero length). K is high (>0.5/yr) in short-lived fast-growing species (sardine, tilapia) and very low (<0.05/yr) in slow-growing longevous species (orange roughy, grouper). The VBGF is the foundation of yield-per-recruit analysis and most stock assessment models.
💡 Examples & Context
Atlantic cod: L∞ ≈ 132 cm, K ≈ 0.2/yr. Sooty grouper: L∞ ≈ 80 cm, K ≈ 0.07/yr — very slow growing, making it highly vulnerable to overfishing.
🧪 Scientific Usage
Growth parameters (L∞, K, t₀) are estimated by fitting the VBGF to length-at-age data. Walford plots (length at age t+1 vs length at age t) give linear estimates of L∞ and K.
✏️ Also Written As
Alternative spellings / forms
VBGF, von Bertalanffy growth model