Transcript Biodiversity of Fishes Growth Rainer Froese 04.12.2014 Most Species Grow Throughout their Lifes (Exception: birds and mammals) 0.9 Weight (relative to maximum weight) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.10 Age (in units of mean.

Biodiversity of Fishes
Growth
Rainer Froese
04.12.2014
Most Species
Grow Throughout their Lifes
(Exception: birds and mammals)
1
0.9
Weight (relative to maximum weight)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
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2
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4
5
Age (in units of mean adult life expectancy)
Fishes
Bivalve
Euphausiid
Trees
Newt
Squid
6
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
⅔ Versus ¾ Scaling
1
0.9
Weight (relative to maximum weight)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
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0
1
2
3
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5
6
Age (in units of mean adult life expectancy)
Fishes
Bivalve
Euphausiid
Trees
Newt
Squid
3/4
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
Understanding Linf
Linf is similar to maximum size (e.g. mean of three largest
specimens) reached in an unfished population
1
0.9
0.8
Length (L/Linf)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
2.5
Age (E)
3
3.5
4
4.5
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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
50
Length (cm)
40
30
20
10
0
-2
0
2
Age (years)
4
6
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
50
Length (cm)
40
30
20
10
t0
0
-2
0
2
Age (years)
4
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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
16000
14000
Weight (g)
12000
10000
8000
First maturity
6000
max dW/dt
4000
2000
0
0
5
10
Age (years)
15
20
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. (125 Thomson Reuters citations 11/2013)
Grow Fast, Die Young
Linf = 120
K = 0.13
tmax= 23
100
90
Linf = 88
K = 0.27
tmax= 11
80
Length (cm)
70
Linf = 64
K = 0.53
tmax= 5.6
60
Linf = 73
K = 0.4
tmax= 7.5
50
40
30
20
10
0
0
2
4
6
Age (years)
8
10
12
Interrelationship between K and Linf
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
ln(1 
tL  
K
Lt
)
L
 t0
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 tL
Time to Reach 200 g
Whale shark
200
White shark
White
Linf = 653
shark
K = 0.06
9.5tmax=
months
51
Whale
Linf = 14m
shark
K = 0.05
6.2
months
tmax=
60
180
Ø' = 5.0
Bluefin tuna
Bluefin
Linf
= 330
tuna
K = 0.1
tmax=
30
8.3 months
Ø' = 4.0
Ø' = 4.4
160
Length (cm)
140
120
100
80
Cod
Cod
Linfmonths
= 120
24
60
K = 0.13
tmax= 23
Ø' = 3.3
40
Anchovy
Anchovy
Linf = 20
Never
K = 1.2
50
g 2.5
tmax=
3Ø'years
= 2.7
20
0
0
2
4
6
Age (years)
8
10
12
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
ln(1 
tL  
K
Lt
)
L
 t0