Transcript Biodiversity of Fishes Growth Rainer Froese Fish Grow Forever von Bertalanffy Growth • Search FishBase, FishBase Book, Population Dynamics, The POPGROWTH Table, Fig.

Biodiversity of Fishes
Growth
Rainer Froese
Fish Grow Forever
von Bertalanffy Growth
•
Search FishBase, FishBase Book, Population Dynamics, The POPGROWTH Table,
Fig. 20
• Von Bertalanffy’s Growth Function (VBGF)
dW / dt = A * W2/3 – B * W
where W=weight, A ~ anabolism, B ~ catabolism
• Solving the differential equation results in
Wt = Winf (1 – e-k * t)3
Lt = Linf(1 - e-k * t)
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 steepness 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
Understanding Linf
Linf is similar to maximum size (e.g. mean of
three largest specimens) reached in an
unfished population
Linf = Lmax / 0.95
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
• Fish larvae do not grow as VBGF
• t0 is used to correct for that and improve
the fit of the curve by moving it to the left
• t0 is thus the hypothetical age at L=0 if
VBGF would apply to larvae
• t0 does not change K or Linf
• Growth curves without t0 give length at
‘relative’ age
Interrelationship between k and Linf
k and Linf are inversely correlated
-> FishBase, Micropterus salmoides, Growth,
Auximetric graph
K is NOT a growth-per-time indicator:
Anchovy k >1.0 reaches 20 cm in first year
Mola mola k ~ 0.2 reaches 30 cm in first year
Growth Indicator Ø’
Ø’ = log k + 2 * log Linf
Unit: Size per time
For example:
Anchovy has Ø’ of 2.7
Mola mola has Ø’ of 4.5
Growth of Mola mola in the first year is
about 60% faster than in Anchovy.
Growth and Maturity
• VBGF in weight has an inflection point at
1/3 Winf, ~ 2/3 Linf
• Many fish mature at that size
Length at Maturity vs Linf
3
Length at first maturity (L
m; log cm)
Log10Lm = 0.8979 * log10Linf -0.0782
r2= 0.888 n=467
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
Asymptotic length (Loo; log cm)
3
3.5
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.
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