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# Implications of uncertainty: Bayesian modelling of aquatic invasive species spread

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

## Transcript

1. Implications of uncertainty: Bayesian
modelling of aquatic invasive species spread
Corey Chivers & Brian Leung
Dept. of Biology, McGill University

2. 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
– Noise and non-determinism

3. Prediction is very hard,
Prediction is very hard,
-Niels Bohr, physicist (1885-1962)
-Niels Bohr, physicist (1885-1962)

4. 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

5. 6
Why does uncertainty matter?
t=0 t=T
Probability
Density
Risk =( Probability) x(Consequence)

6. 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.

7. 8

8. 9

9. 10
O
O
O

10. 11
X
X
X
O
O
O

11. 12
X
X
X
O
O
O
?
? ?
?
?
?
?
?
?
? = Unknown
?

12. 13
X
X
X
O
O
O
?
? ?
?
?
?
?
?
?
? = Unknown
?

13. 14
X
X
X
O
O
O
?
? ?
?
?
?
?
?
?
? = Unknown
?

14. 15
X
X
X
O
O
O
?
? ?
?
?
?
?
?
?
? = Unknown
?

15. 16
311/1600 = 19% data coverage

16. 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

17. 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

18. 19
Results

19. 20

20. 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.

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

22. Thank you
Supervisors:
Dr. Brian Leung
Dr. Elena Bennett
Dr. Claire De Mazancourt
Dr. Gregor Fussman
300 Lakes Survey Team
Lab Mates: