Biodiversity of Fishes Growth Rainer Froese 23 11

Biodiversity of Fishes Growth Rainer Froese 23. 11. 2017 GEOMAR, Kiel

Most Species Grow Throughout their Lifes (Exception: birds and mammals)

Karl Ludwig von Bertalanffy 1901 -1972 1934 -1948 Professor Uni Wien Later London, Canada, USA Concept of ‘Fließgleichgewicht’ (steady state of open systems)

von Bertalanffy Growth Von Bertalanffy’s (1934) Growth Function (VBGF) d. W/dt = H * Wt 2/3 – B * Wt where W = body weight, H W 2/3= total available energy (metabolism), B W = energy needed for processes other than growth, t = age, d. W/dt = growth rate at age t = energy available for growth at age t Solving the differential equation results in Wt = Winf (1 – e-K * t)3 Lt = Linf (1 - e-K * t) where Winf and Linf are asymptotic weight and length, and K describes how fast these are approached (the exponential decrease of the distance to Linf)

⅔ Versus ¾ Scaling The ¾ scaling often observed in metabolic comparisons across species (black curve) gives a similar but slightly less convincing fit than the 2/3 geometric scaling (red curve)

Using VBGF Lt = Linf (1 – exp(-K * (t – t 0))) Where Lt = length (cm) at age t (years) Linf = asymptotic length if t = infinite K = parameter indicating how fast Linf is approached (1/year) t 0 = hypothetical age at L = 0

Understanding K K describes the curvature of the growth curve, i. e. , how fast Linf is reached: K <= 0. 05 in large, long-lived fishes K > 1 in small, short-lived fishes 2. 996/K + to is the time needed to reach 0. 95 Linf which is a proxy for maximum age

Understanding Linf is similar to maximum size (e. g. mean of three largest specimens) reached in an unexploited population

Linf as a Function of Lmax log 10 L = 0. 044 + 0. 9841 * log 10(Lmax) (n = 551, r 2 = 0. 959) Froese, R. and C. Binohlan 2000. Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data. J. Fish Biol. 56: 758 -773.

Understanding t 0 • Age t = 0 is at hatching or birth, when newborns already have a length

Understanding t 0 • Age t = 0 is at hatching or birth, when newborns already have a length • t 0 is used to account for that and improve the fit of the curve by moving it to the left t 0

Understanding t 0 • t 0 is thus the hypothetical age at L=0 if VBGF applies (not for larvae) • t 0 is usually small and negative • t 0 moves the curve left (t 0 is typically negative) without changing K or Linf • Growth curves without t 0 give length at ‘relative’ age; for true age add t 0

Growth and Maturity • VBGF in weight has an inflection point at 0. 3 Winf = 2/3 Linf (if growth is isometric with b ~ 3) • Fish mature before or at that size First maturity max d. W/dt

Length at Maturity vs Linf Log 10 Lm = 0. 8979 * log 10 Linf -0. 0782 r 2= 0. 888 n=467 Relationship between length at first maturity and asymptotic length for all records representing 265 species of fish. Regression lines are for females (----) and males ( ). Froese, R. and C. Binohlan 2000. Empirical relationships to estimate asymptotic length, length at first maturity and length at maximum yield per recruit in fishes, with a simple method to evaluate length frequency data. J. Fish Biol. 56: 758 -773. (173 Web of Science citations 11/2015)

Grow Fast, Die Young

Interrelationship between K and Linf Largemouth black bass, freshwater North America

How to Compare Growth K is NOT a growth-per-time indicator: Example: Anchovy K >1. 0 reach 20 cm in second year Cod K ~ 0. 13 reaches 30 cm in second year

How to Compare Growth Compare the time needed to reach a certain length Compare the time needed to reach a certain weight 1. find corresponding length from length-weight relationship L = 10^((log. W – log a) / b) 2. find corresponding age from t. L

Time to Reach 200 g Whale shark 6. 2 months White shark 9. 5 months Bluefin tuna 8. 3 months Cod 24 months Anchovy Never 50 g 3 years

Exercises • Find a species with at least 5 growth studies • Discuss the variability of Linf and K and the value of t 0 • Select a study that describes growth well and justify your selection • How long will it take to reach 200 g? W = a Lb