Goodbye K, Welcome M The Interrelationship between Life Span, Growth and Reproduction Rainer Froese...
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Transcript of Goodbye K, Welcome M The Interrelationship between Life Span, Growth and Reproduction Rainer Froese...
Goodbye K, Welcome MThe Interrelationship between
Life Span, Growth and Reproduction
Rainer FroeseIFM-GEOMAR
Kiel, Germany
The Interrelationship between Lifespan, Growth and Reproduction
• Relationship between lifespan and reproduction:– In stable populations, on average, every adult
produces ONE new adult during its lifetime
• Relationship between growth and reproduction:– In species with indeterminate growth, fecundity
increases proportional to body weight (GSI is constant)
• Relationship between lifespan and growth:– Currently none – Size at age is a function of maximum size and a
parameter (K) indicating how fast it is reached
Approaching the Problem
• Growth is constrained by oxygen• Lifespan is determined by mortality rate• Maximum size is determined by lifespan• K = 2/3 M• The most important point in life• Growth and maturity• Framework for lifespan, growth & reproduction• Implications for managment
Growth is Constrained by Oxygen
• Growth needs food and energy for assimilation
• The oxygen-temperature window restricts growth (Pörtner, Science 2004)
• Water-breathing is energy-demanding
• Physics determine gill-area
Gill Area vs Body Weight
0.1
1
10
100
1000
10000
100000
1000000
10000000
0.01 0.1 1 10 100 1000 10000 100000 1000000
Body weight (g)
Gill
are
a (
cm
2 )
Megamouth0.8 tons57 m2
Goby0.02 g0.2 cm2
log GA = 0.65 + 0.91 log BWr2 = 0.93
Data for 118 species of fishes, from FishBase 11/2006
Lifespan is Determined by Mortality Rate
• M is constant during adult life– Intrinsic mortality rate increases (wear & tear, mutations
acting late in life) – Extrinsic mortality decreases (with size and growing
experience in predator avoidance)
Size of prey vs predator
1
10
100
1000
1 10 100 1000
Length of predator (cm TL)
Len
gth
of
pre
y (c
m T
L)
1 : 1
4,453 cases for 1,743 species of fishes, data from FishBase 11/2006
Lifespan is Determined by Mortality Rate
• M is constant during adult life– Intrinsic mortality rate increases (wear & tear, mutations acting late in
life) – Extrinsic mortality decreases (with size and growing experience in
predator avoidance)
– Intrinsic and extrinsic mortality balance each other, resulting in constant adult mortality
– Confirmed by 168 studies fitting a linear regression to (log) numbers at age (data in FishBase 11/2006)
• If adult mortality is constant, then mean adult life expectancy E = 1/M (from continuous life table analysis)
Approaching the Problem
• Growth is constrained by oxygen
• Lifespan is determined by mortality rate
• Maximum size is determined by lifespan
Maximum Size is Determined by Lifespan
Based on growth data for 6,418 populations of fishes in FishBase 11/2006
1
10
100
1000
10000
0.1 1 10 100 1000
Maximum age (years)
To
tal
len
gth
(cm
)
smallestvertebrates
fastest growth warm water
largest water-breathers
longest lifespancold water
Maximum Size is Determined by Lifespan
1
10
100
1000
10000
0.1 1 10 100 1000
Maximum life span (years)
Max
imu
m l
eng
th (
cm)
Carcharhinus acronotus Pleuronectes platessa Stolephorus indicus
Empiricalwithin species:Linf = C tmax
0.41
Slope of Linf-tmax trade-off
The slope is not significantly different in
• Taxonomic groups (Class, Order, Families)
• Salinity (marine, freshwater, diadromous)
• Deep waters
• Climate zones (temperate, subtropical, tropical)
Approaching the Problem
• Growth is constrained by oxygen
• Lifespan is determined by mortality rate
• Maximum size is determined by lifespan
• K = 2/3 M
The von Bertalanffy Growth Equation
ttt kWHW
dt
dW 3
2
3)1( Ktt eWW
)1( Ktt eLL
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
max. growth rate
Winf
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Probabilityof survival
max. growth rate
Growth and Mortality
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Probabilityof survival
max. growth rate
Expected weight
M/K = 3/2
M/K > 3/2Peak left and smaller
M/K < 3/2Peak right and smaller
Growth and Mortality
• Empirical slope of Linf-tmax trade-off is
0.41 (95% CL 0.35 – 0.48)
• Theoretical slope of Linf-tmax trade-off that results in overlap of maximum growth rate with maximum expected body weight is 0.45 (i.e., not significantly different from empirical value)
Growth, Mortality and Fecundity
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10 12 14 16 18 20 22 24
Age (years)
Weight
Probabilityof survival
max. growth rate
Expected weightExpected fecundity M/K = 3/2 maximizes fitness
Empirical Evidence for M/K = 3/2
0.01
0.1
1
10
100
0.01 0.1 1 10 100
M = 1.5 K
M o
bse
rved
1 : 1
Based on growth and mortality data for 272 populations of 181 species, FishBase 11/2006
The New Growth Equations
)1()1( )(667.03
)(2
0
0ttME
tt
t eLeLL
bttMbE
tt
t eWeWW )1()1( )(667.03
)(2
0
0
E
W
E
W
dt
dW flt 296.0max
More Evidence
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5
Age (E )
We
igh
t (W
/Win
f)
Fishes Bivalve Euphausiid Trees Newt Squid
33
)(2
)1(0
E
tt
t eWW
Approaching the Problem
• Growth is constrained by oxygen
• Lifespan is determined by mortality rate
• Maximum size is determined by lifespan
• K = 2/3 M
• The most important point in life
The Most Important Point in Life
LeLLopt 667.0)1( 3
265.1
WeWWopt 296.0)1( 33
265.1
EMM
topt 65.1648.1
2
)3ln(3
• Where growth is maximum
• Where expected fecundity is maximum
Growth and Maturity
1
10
100
1000
10000
1 10 100 1000 10000
L∞ (cm)
Lm
(cm
)
L∞
0.67 L∞
0.35 L∞
Maturity data for 672 populations of 351 species from FishBase 11/2006
low fecundity,low dependenceon environment
high fecundity,high dependenceon environment
Framework forLifespan, Growth and Reproduction
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4
Relative age (t/E )
Rel
ativ
e si
ze
L/L ∞=0.667
W/W ∞=0.296
0.65 1.65 2.65
t opt
Framework forLifespan, Growth and Reproduction
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4
Relative age (t/E )
Rel
ativ
e si
ze
spawners
L/L ∞=0.667
W/W ∞=0.296
old spawners
E
L/L ∞=0.83
0.65 1.65 2.65
t opt
W/W ∞=0.57
Framework forLifespan, Growth and Reproduction
0.0
0.2
0.4
0.6
0.8
1.0
0 1 2 3 4
Relative age (t/E )
Re
lati
ve
siz
e
spawnersearly spawners /
juvenilesjuveniles
L/L ∞=0.667
W/W ∞=0.296
old spawners
E
L/L ∞=0.35
L/L ∞=0.83
0.65 1.65 2.65
t opt
W/W ∞=0.57
Approaching the Problem
• Growth is constrained by oxygen• Lifespan is determined by mortality rate• Maximum size is determined by lifespan• K = 2/3 M• The most important point in life• Growth and maturity• Framework for lifespan, growth & reproduction• Implications for managment
Implications for Management
0.0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4
Relative age (t/E )
Pro
ba
bili
ty o
f s
urv
iva
l (lt
)
spawnersearly spawners /
juveniles old spawnersjuveniles
0.65 1.65 2.65
Implications for Management
0.0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4
Relative age (t/E )
Pro
ba
bili
ty o
f s
urv
iva
l (lt
)
spawnersearly spawners /
juveniles
current fishing
old spawnersjuveniles
0.65 1.65 2.65
t opt fishing
t opt+E fishing
Implications for Management
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0 1 2 3 4
Relative age (t/E )
Rel
ativ
e b
iom
ass
(B/N
o)
old spaw nersspaw nersearly spaw ners /
juvenilesjuveniles
current f ishing t opt f ishing
t opt +Ef ishing
no fishing
0.65 1.65 2.65
Conclusions• Growth is determined by mean adult life
expectancy, which is the inverse of the mortality rate
• At Lopt = 2/3 Linf, growth rate and expected fecundity are maximum
• Maturity is reached between topt -1 and topt, depending on life history strategy
• Ignoring the relationships between growth, mortality and reproduction may contribute to widespread failure of fisheries management
Thank You