Measuring age and sizedependent maturation probabilities

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Measuring age- and size-dependent maturation
probabilities

• Mikko Heino
• IMR, Bergen
• IIASA, Austria

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In collaboration with
Sébastien Barot, Ulf Dieckmann, Bruno Ernande,
Esben Olsen Adaptive Dynamics Network, IIASA,
Austria
Georg Engelhard, Olav Rune Godø Institute of
Marine Research, Bergen, Norway
Loretta OBrien Northeast Fisheries Science
Center, USA
George Lilly, Joanne Morgan Northwest Atlantic
Fisheries Science Center, Canada
Rob Grift, Adriaan Rijnsdorp Netherlands
Institute for Fisheries Research
presently at IRD-LEST, France
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Decline in age size at maturationin the
Barents Sea cod
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Does maturation matter in the context of stock
assessments?

• Maturation may have strong effects on survival
  and growth
• Maturation may influence the availability of fish
  to harvesting
• Spawning stock biomass and reproductive potential
  depend
• on maturity

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State vs. Process?

• Maturity refers to a state (immature/mature)
• Maturation refers to a process
• Maturity state is of ultimate interest in
  population models
• May be directly estimated from data
• Infered with a help of a statistical (regression)
  approach
• Infered with a help of a process-based model
• Process-based approach becomes particularly
  attractive in the context of stock projections
• ?maturation described by a transition probability
  dependent on the state variables of the model

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Probabilistic maturation reaction norm
probability that a juvenile matures, during a
certain season, as a function of its age and
size Maturation tendency is expressed as
conditional to having reached a certain age and
size (and still being immature) This
conditioning separates description of maturation
process from descriptions of growth and mortality
process (which is not true for maturity ogives)
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Probabilistic maturation reaction norm
probability that a juvenile matures, during a
certain season, as a function of its age and size
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Probabilistic maturation reaction norm
? maturity ogive Probability of being mature as
a function of age and size vs. Probability of
maturing as a function of age and size State
vs. Process
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Why to measure age- and size based maturation
probabilities?

• Element in process-based population models
• Description of maturation process
• Disentangling environmental and genetic effects
  on maturation
• Probabilistic reaction norm for age and size at
  maturation ?
• Age- and size-dependent maturation probability

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How to estimate the probabilistic reaction norm?
Method 1
Required data representative sample of immature
and newly-matured individuals, sized and
aged Estimation logistic regression
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Incomplete data
Representative data only on mature individuals -
data on immature individuals missing
Solution reconstruct missing data

• Barents Sea cod

• Norwegian Sea herring

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How to estimate the probabilistic reaction norm?
Method 2
Representative data on immature and mature
individuals, but newly-matured individuals cannot
be identified
Solution an alternative estimation method

• Almost all fish

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Estimation based on age- and size-based maturity
ogives
Ordinary age-based maturity ogive
where o(a) is ogive (proportion of mature at
age), a is age, s is size, and m(a) is
probability of maturing
simplifying assumptions
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The formula can be extended to account for age
and size
where is annual growth increment,
and m(a,s) is the reaction norm!
more simplifying assumptions
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How to estimate the probabilistic reaction norm?
Method 3
Representative data on individuals sampled
repeatedly, with maturity status recorded
Solution methods to analyse of longitudinal data

• Practical in e.g. salmonids

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Case study on Barents Sea cod
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Decline in age size at maturation
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Decline ? demographic change?

• Total mortality has increased
• Population dominated by younger cod
• ? Lower average age at maturation

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Decline ? phenotypic plasticity?

• Growth has accelerated (compensatory growth)
• Fast-growing cod mature earlier
• 1) 2) ? Earlier maturation

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Decline ? genetic change?

• Historical harvest regime targetting mostly
  mature cod
• ? Genetic selection for delayed maturation
• Modern harvest regime unselective
• ? Genetic selection for earlier maturation

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Results on NEA cod
Change in length at which probability of maturing
is 50 at age 7
logit(pmaturing)cohortilength
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Results on NEA cod
Predicted reaction norm midpoints for cohorts
1923-90
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Results on NEA cod
Change in the reaction norm midpoints
Age
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Other case studies
Grayling
Norway
Atlantic cod
American plaice
Newfoundland
Barents Sea, Georges Bank Gulf of Maine
Herring
Plaice
Norwegian Sea
North Sea
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Conclusions

• Conditional maturation probabilities are
  estimable from various kinds of data
• Maturation depends on length, age, condition etc.
• Maturation may evolve in decadal scale