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Implications of uncertainty: Bayesian modelling of aquatic invasive species spread

Implications of uncertainty: Bayesian modelling of aquatic invasive species spread

Talk given at the International Aquatic Invasive Species (ICAIS) conference on April 23rd, 2013.

Corey Chivers

April 23, 2013
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  1. Implications of uncertainty: Bayesian
    modelling of aquatic invasive species spread
    Corey Chivers & Brian Leung
    Dept. of Biology, McGill University
    http://madere.biol.mcgill.ca/cchivers/

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  3. 3
    Difficulties in forecast
    modelling of invasive species

    Limited Data
    – Finite resources
    – Rare events – Long Distance Dispersal
    – Large scale phenomena

    Incomplete knowledge of how the processes work
    – How well is 'reality' captured through our abstraction?

    Stochasticity
    – Invasion/spread are probabilistic phenomena
    – Noise and non-determinism

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  4. Prediction is very hard,
    Prediction is very hard,
    especially about the future
    especially about the future
    -Niels Bohr, physicist (1885-1962)
    -Niels Bohr, physicist (1885-1962)

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  5. 5
    Why does uncertainty matter?

    Rather than a single estimate about a future
    state of nature, a forecast should be a
    probability distribution over the range of
    possible future states.
    t=0 t=T
    Probability
    Density

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  6. 6
    Why does uncertainty matter?
    t=0 t=T
    Probability
    Density
    Risk =( Probability) x(Consequence)

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  7. Outcome A
    Outcome B
    Outcome C
    Outcome E
    Outcome F
    Do A
    Do B
    Do C
    Do D
    Do
    Nothing
    t = 0 t = T
    Time
    In a changing world,
    not making a decision
    has consequences,
    intended or otherwise.

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  8. 8
    Forecasting aquatic species spread

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  9. 9

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  10. 10
    O
    O
    O
    O = known uninvaded

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  11. 11
    X
    X
    X
    O
    O
    O
    X = known invaded
    O = known uninvaded

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  12. 12
    X
    X
    X
    O
    O
    O
    ?
    ? ?
    ?
    ?
    ?
    ?
    ?
    ?
    X = known invaded
    O = known uninvaded
    ? = Unknown
    ?

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  13. 13
    X
    X
    X
    O
    O
    O
    ?
    ? ?
    ?
    ?
    ?
    ?
    ?
    ?
    X = known invaded
    O = known uninvaded
    ? = Unknown
    ?

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  14. 14
    X
    X
    X
    O
    O
    O
    ?
    ? ?
    ?
    ?
    ?
    ?
    ?
    ?
    X = known invaded
    O = known uninvaded
    ? = Unknown
    ?

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  15. 15
    X
    X
    X
    O
    O
    O
    ?
    ? ?
    ?
    ?
    ?
    ?
    ?
    ?
    X = known invaded
    O = known uninvaded
    ? = Unknown
    ?

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  16. 16
    311/1600 = 19% data coverage

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  17. 17
    Bayesian modelling of dispersal
    and environmental suitability
    Non-equilibrium species distribution modelling
    Q
    it
    E
    it
    α
    i
    GM X
    i
    β
    αi
    =−log(1−p
    i
    ),
    P
    i
    =
    1
    1+e−z
    i
    , z
    i

    0
    +∑
    j=1
    E
    β
    j
    X
    ij
    .
    E(Q
    it
    ,αi
    )=1−e−(α
    i
    Q
    it
    )c
    ,
    Q
    it
    = propagule pressure generated by
    underlying dispersal network
    c > 1 indicates an Allee effect
    α
    i
    = habitat suitability
    X
    ij
    = Environmental condition j at site i.
    β
    j
    = Estimated coefficients

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  18. 18
    Environmental Variables:
    Sodium (mg/L)
    Potassium (mg/L)
    Magnesium (mg/L)
    Calcium (mg/L)
    Total Phosphorus (μg/L)
    SiO3 (mg/L as Si)
    Dissolved Organic Carbon
    (mg/L)
    True Colour (TCU)
    Total inflection point alkalinity
    (mg/L as CaCO3)
    Total fixed end point alkalinity
    to pH 4.5 (mg/L as CaCO3)
    pH
    Conductivity @ 25*C (μS/cm)
    Secchi Depth

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  19. 19
    Results

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  20. 20

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  21. 21
    Validation

    We can evaluate the performance of this
    model using AUC. (~0.85)

    What we really want to know are probabilities.
    – Expressions of uncertainty

    Ongoing work into a validation metric which
    assesses model performance in terms of
    probability across the entire prediction range.

    Will use 102 new sample points from 2010.

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  22. Code available on Github
    https://github.com/cjbayesian/grav_mod

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  23. Thank you
    Supervisors:
    Dr. Brian Leung
    Dr. Elena Bennett
    Dr. Claire De Mazancourt
    Dr. Gregor Fussman
    300 Lakes Survey Team
    Lab Mates:
    Johanna Bradie
    Paul Edwards
    Kristina Marie Enciso
    Andrew Sellers
    Lidia Della Venezia
    Erin Gertzen

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