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) dW/dt = H * Wt 2/3 – B * Wt where W = body weight, H W2/3= total available energy (metabolism), B W = energy needed for processes other than growth, t = age, dW/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 – t0))) Where Lt = length (cm) at age t (years) Linf = asymptotic length if t = infinite K = parameter indicating how fast Linf is approached (1/year) t0 = 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 Linf is similar to maximum size (e.g. mean of three largest specimens) reached in an unexploited population

Linf as a Function of Lmax log10L = 0.044 + 0.9841 * log10(Lmax) (n = 551, r2 = 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 t0 Age t = 0 is at hatching or birth, when newborns already have a length

Understanding t0 Age t = 0 is at hatching or birth, when newborns already have a length t0 is used to account for that and improve the fit of the curve by moving it to the left t0

Understanding t0 t0 is thus the hypothetical age at L=0 if VBGF applies (not for larvae) t0 is usually small and negative t0 moves the curve left (t0 is typically negative) without changing K or Linf Growth curves without t0 give length at ‘relative’ age; for true age add t0

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 dW/dt

Length at Maturity vs Linf Log10Lm = 0.8979 * log10Linf -0.0782 r2= 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 find corresponding length from length-weight relationship L = 10^((logW – log a) / b) 2. find corresponding age from tL

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 t0 Select a study that describes growth well and justify your selection How long will it take to reach 200 g? W = a Lb