Biodiversity of Fishes Growth Rainer Froese

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

Karl Ludwig von Bertalanffy 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 * 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

⅔ Versus ¾ Scaling

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

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

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

L inf as a Function of L max Froese, R. and C. Binohlan 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: log10L  = * log10(L max ) (n = 551, r 2 = 0.959)

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 t0t0

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

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

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 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: (125 Thomson Reuters citations 11/2013) Log10L m = * log10L inf r 2 = n=467

Grow Fast, Die Young

Interrelationship between K and L inf

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^((logW – 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 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