Implications of uncertainty: Bayesian modelling of aquatic invasive species spread

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

Transcript

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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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
    =β
    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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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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