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Stage SizeStructured Models

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7-mature breeders. 458. Stage-Structured Models (Advantages and Disadvantages) Advantages: ... Some fisheries models keep track of age and whether an animal is mature ... – PowerPoint PPT presentation

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Title: Stage SizeStructured Models


1
Stage- / Size-Structured Models
  • Fish 458, Lecture 16

2
Stage-Structured Models
  • Why not always use age-structured models
  • Ageing is difficult (or impossible) for several
    types of organisms.
  • Division of the population into stages may be
    more natural than into ages (the most common
    type of stage is size-class).
  • Animals in a stage share demographically
    similar characteristics.
  • The data available to fit the model may be
    stage- based (e.g. the fraction of new-borns,
    juveniles, mature animals).

3
Stage-Structured Models(Examples of
Stage-structured Populations)
  • Trees seed, in the understory, in the canopy
  • Trees may spend decades in any of these stages
    and the age of a tree may have little to do with
    moving from one stage to another.
  • Insects eggs, larvae, pupae, adults.
  • Seabirds new borns, fledglings, juveniles,
    adults giving birth this year, adults resting
    between giving birth.

4
Modeling Stage-Structure-I(back to age-based
models)
5
Modeling Stage-Structure-II(differences from
age-based models)
  • The age-based model can be written
  • We now generalize this by
  • defining each row in N as the abundance of a
    stage (rather than an age-class)
  • allowing recruitment to occur to any stage
    (though usually recruitment only occurs to the
    first stage) and
  • allowing animals to move between any stages.

6
Modeling Stage-Structure-III(example Loggerhead
turtles)
1 first years 2 small juveniles 3 large
juveniles 4-subadults 5-novice breeders 6
first-year remigrants 7-mature breeders
7
Stage-Structured Models(Advantages and
Disadvantages)
  • Advantages
  • Highly flexible Some fisheries models keep track
    of age and whether an animal is mature and
    whether it is recruited to the fishery (i.e. each
    age is associated with four stages).
  • Realistic It is reasonably easy to build in
    assumptions regarding behavior that cannot be
    captured using standard age-structured models.

8
Stage-Structured Models(Advantages and
Disadvantages)
  • Disadvantages
  • The flexibility makes designing the model more
    difficult (how to select the stages?)
  • A stage-structured model may have many more
    (rather than fewer) parameters than the
    equivalent age-structured model.

9
Moving to Size-Structured Models
  • For these models, each stage is a size-class
    (usually all of equal width).
  • The general equation for these models is

10
expanded
Natural survival
Harvest survival
Growth
The matrix X is often constrained to prevent
negative growth (e.g. lobsters, abalone)
11
Fitting Size-Structured Models
  • The typical parameters of a size-structured model
    are
  • The numbers-at-size for the first year
    (analogously with age-structured models, one can
    assume that the population was in equilibrium at
    that time).
  • The recruitments.
  • The parameters that define vulnerability at size.
  • The parameters of the size-transition matrix (the
    growth parameters).

12
Estimating the Size-Transition Matrix
  • This can be the most data-demanding step of
    applying a size-structured model.
  • Typically, the size-transition matrix is
    estimated by postulating a growth curve
    (including its uncertainty) and fitting it to
    tagging data. A typical choice is the normal
    distribution

13
Estimating the Size-Transition Matrix
Size-increment information for Tasmanian rock
lobster (note the large fraction of zero
increments)
14
Fitting Size-Structured Models
Example rock lobster off Tasmania, Australia
Size-structured models are almost always fitted
to information on population (or catch)
size-structure in addition to some index of
abundance
15
Fitting Size-Structured Models
  • The likelihood function for the length-frequency
    data (often the fraction in each size-class) is
    usually assumed to be multinomial.

16
Size-structured models(Advantages and
Disadvantages)
  • Advantages
  • Requires no ability to age animals (crabs,
    abalone, rock lobsters).
  • Uses the data actually available
    (size-compositions).
  • Vulnerability / maturity are often functions of
    size and not age.

17
Size-structured models(Advantages and
Disadvantages)
  • Disadvantages
  • Potentially very many parameters that are
    difficult to estimate (e.g. the entries in the
    size-transition matrix).
  • Still needs an estimate of M (in years-1).
  • Computationally much more intensive that
    age-structured models.
  • Many of the animals to which these models are
    applied exhibit small-scale spatial differences
    in growth.

18
Readings
  • Burgman et al. (1993) Chapter 4.
  • Quinn and Deriso (1999) Chapter 9.
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