1. Biodiversity of Fishes Growth Rainer Froese 04.12.2014

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

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

4. von Bertalanffy Growth Von Bertalanffy’s (1934) Growth Function (VBGF) dW/dt = H * W t 2/3 – B * W t where W = body weight, H W 2/3 = 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 W t = W inf (1 – e -K * t ) 3 L t = L inf (1 - e -K * t ) where W inf and L inf are asymptotic weight and length, and K describes how fast these are approached

5. ⅔ Versus ¾ Scaling

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

7. Understanding K K describes the curvature of the growth curve, i.e., how fast L inf is reached: K <= 0.05 in large, long-lived fishes K > 1 in small, short-lived fishes

8. Understanding L inf L inf is similar to maximum size (e.g. mean of three largest specimens) reached in an unfished population

9. L inf as a Function of L max 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. log10L  = 0.044 + 0.9841 * log10(L max ) (n = 551, r 2 = 0.959)

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

11. 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 t0t0

12. 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 L inf Growth curves without t 0 give length at ‘relative’ age; for true age add t 0

13. Growth and Maturity VBGF in weight has an inflection point at 0.3 W inf = 2/3 L inf (if growth is isometric with b ~ 3) Fish mature before or at that size max dW/dt First maturity

14. Length at Maturity vs Linf 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. (125 Thomson Reuters citations 11/2013) Log10L m = 0.8979 * log10L inf -0.0782 r 2 = 0.888 n=467

15. Grow Fast, Die Young

16. Interrelationship between K and L inf

17. 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

18. 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^((logW – log a) / b) 2. find corresponding age from t L

19. 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

20. Exercises Find a species with at least 5 growth studies Discuss the variability of L inf 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 L b