Goodbye K, Welcome M The Interrelationship between Life Span, Growth and Reproduction

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Goodbye K, Welcome MThe Interrelationship
between Life Span, Growth and Reproduction

• Rainer Froese
• IFM-GEOMAR
• Kiel, Germany

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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

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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

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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

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Gill Area vs Body Weight
log GA 0.65 0.91 log BW r2 0.93
Megamouth 0.8 tons 57 m2
Goby 0.02 g 0.2 cm2
Data for 118 species of fishes, from FishBase
11/2006
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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)

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Size of prey vs predator
4,453 cases for 1,743 species of fishes, data
from FishBase 11/2006
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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)

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Approaching the Problem

• Growth is constrained by oxygen
• Lifespan is determined by mortality rate
• Maximum size is determined by lifespan

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Maximum Size is Determined by Lifespan
largest water-breathers
fastest growth warm water
longest lifespan cold water
smallest vertebrates
Based on growth data for 6,418 populations of
fishes in FishBase 11/2006
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Maximum Size is Determined by Lifespan
Empirical within species Linf C tmax0.41
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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)

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Approaching the Problem

• Growth is constrained by oxygen
• Lifespan is determined by mortality rate
• Maximum size is determined by lifespan
• K 2/3 M

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The von Bertalanffy Growth Equation
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Growth and Mortality
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Growth and Mortality
Winf
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Growth and Mortality
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Growth and Mortality
M/K gt 3/2 Peak left and smaller
M/K lt 3/2 Peak right and smaller
M/K 3/2
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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)

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Growth, Mortality and Fecundity
M/K 3/2 maximizes fitness
Expected fecundity
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Empirical Evidence for M/K 3/2
Based on growth and mortality data for 272
populations of 181 species, FishBase 11/2006
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The New Growth Equations
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More Evidence
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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

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The Most Important Point in Life

• Where growth is maximum
• Where expected fecundity is maximum

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Growth and Maturity
low fecundity, low dependence on environment
high fecundity, high dependence on environment
Maturity data for 672 populations of 351 species
from FishBase 11/2006
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Framework forLifespan, Growth and Reproduction
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Framework forLifespan, Growth and Reproduction
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Framework forLifespan, Growth and Reproduction
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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

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Implications for Management
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Implications for Management
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Implications for Management
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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

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Thank You