Biodiversity of Fishes: LifeHistory Allometries and Invariants

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Biodiversity of FishesLife-History Allometries
and Invariants

• Rainer Froese
• 22.01.09

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What is Life History?

• The stages of life an organism passes through
  from birth to death
• The study of the timing of life cycle events such
  as maturity, growth and death.
• Keywords life span, longevity, mortality,
  survival, reproduction, fecundity, eggs, larvae,
  juveniles, adults, natural selection of adaptive
  traits

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Life History Allometries

• Typically a power function describing how one
  trait changes in relation to another.
• Example How body weight scales with length
• W a Lb
• where a is a proportionality factor and b 3

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Body Weight Allometries

• Y a W 0.75
• where Y is a whole body rate such as oxygen
  consumption, production, ingestion, blood flow
• Y a W 1
• where Y is another weight or volume such as
  weight at maturity, gonad weight, heart volume
• Y a W 0.25 W1-gt
  Y1, W1000-gtY5.6
• where Y is age such as age at maturity, life
  span, longevity
• Y a W -0.25
• where Y is a rate per year such as natural
  mortality, annual reproductive rate, growth rate
  (individual and population)

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The von Bertalanffy Growth Function

• dW/dt H W 2/3 k W 1
• where H W 2/3 stands for anabolism assumed
  proportional to resorbing surfaces scaling as 2/3
  0.666 with weight
• and k W 1 stands for catabolism scaling
  proportional to weight
• Integrating, rearranging and simplifying gives
• Wt W8 (1 e-K(t to))3
• where W8 is proportional to H/k and K 3 k.

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Western Baltic Cod Life History
max age
max reproductive biomass
max growth
maturity
average adult life span
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Life History InvariantsMaximum growth is
obtained at

• 0.296 Winf
• if b3
• 0.667 Linf

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Average Adult Life Expectancy
where Ex is the average life expectancy after
reaching age x and l are the probabilities of
reaching x and subsequent ages y. If mortality is
constant then
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Mortality and Growth

• In species that grow throughout their lives,
  maximum size is determined by life span
• Life span is determined by mortality
• Therefore
• Maximum size and growth is determined by
  mortality
• K 2/3 M

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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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M observed vs M 1.5 K
M from 1.5 K
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Life History InvariantsMaximum Reproductive
Biomass
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Life History Invariantsa M number
Assuming a topt then
topt M 1.65
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Variability in Maturity
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Longevity as Size Invariant

• Taylor (1958) suggests maximum age is reached at
  95 Linf -gt tmax 3/K

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Longevity vs Age at 96 Linf
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Summary

• Growth, average adult lifespan, maximum
  reproductive biomass, and longevity have
  co-evolved so that maximum reproductive output is
  reached as fast as possible and maximum lifespan
  is reached near maximum size.
• Maturity may start before Lopt if successful
  reproduction is uncertain.

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Exercise

• Find species with growth and maturity data and
  high versus low fecundity
• Compare Lm/Linf with 0.67 and discuss differences