www.csse.monash.edu.au/~jbernard/Project
By: James Bernard
Supervised By: Charles Todd (Department of Sustainability and Environment)
Simon Nicol (Department of Sustainability and Environment) Charles Twardy (Monash University)
David Green (Monash University)
Building Bayesian Models for the Analysis of Critical Knowledge Gaps in Australian Freshwater Fish
www.csse.monash.edu.au/~jbernard/Project
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Introduction
• Aim
• Growth Curves
• New Growth Curves
• New Curves using Data Clustering
• Future Work
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Aim
• Overall Goal (Big Picture):
– Predict the sustainability of the Murray Cod
> Growth Curves
> Survival Rate (Mortality)
> Population Modelling
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Growth Curves
• Considered various curves:– von Bertalanffy, Gompertz, Logistic
• Reviewed previous experts curves:– Anderson (1992)– Gooley (1995)– Rowland (1998)– Todd (unpublished)
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Existing Growth Curves: Rowland
Original Growth Curves
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35
Age
Len
gth
Rowland
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Original Growth Curves
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35
Age
Len
gth Rowland
Anderson
Existing Growth Curves: Anderson
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Existing Growth Curves: Todd
Original Growth Curves
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35
Age
Len
gth
Rowland
Anderson
Todd
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Existing Growth Curves: Gooley
Original Growth Curves
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35
Age
Len
gth Row land
Anderson
Todd
Gooley
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Existing Growth Curves (equations)
Rowland
Todd Anderson
1369 1307 1202
k 0.06 0.08 0.108
-5.209 -2.481 -0.832
Parameters:
Equation: (von Bertalanffy)
∞L
Ot
)))tk(texp((1LL 0t
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Original Growth Curves (0-5)
0
100
200
300
400
500
600
700
800
0 2 4 6 8
Age
Len
gth
Row land
Anderson
Todd
Difference (0-5)
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Difference (0-5) continued…
Rowland Todd Anderson
367.47 237.81 103.30
What happens to the differences between these curves if is set
to zero?
OL
Ot
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New Growth Curves
Rowland Todd Anderson
1161 1166 1210
k 0.1263 0.1393 0.10
(0) (0) (0)
Parameters:
Equation: (von Bertalanffy)
k(t)))exp((1LLt =0Note:
∞L
Ot
Ot
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New Growth Curves: Rowland
New Growth Curves
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35
Age
Leng
th
Row land to=00
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New Growth Curves: Anderson
New Growth Curves
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35
Age
Len
gth
Row land to=0
Anderson to=0
0
0
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New Growth Curves: Todd
New Growth Curves
0
200
400
600
800
1000
1200
1400
0 5 10 15 20 25 30 35
Age
Len
gth Row land to=0
Anderson to=0
Todd to=00
0
0
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Evaluating the New Curves
Original Curves vs New Curves
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50 60
Age
Le
ng
th
Anderson
Rowland
Todd
Anderson (to=0)
Rowland (to=0)
Todd (to=0)
Data
New Curves vs Old Curves
0
0
0
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New Growth Curves: Using Data Clustering
• New Data Set: Only lengths (no age)
• Data Clustering provides: Length-Classes– using Minimum Message Length (MML) approach
• Expert Knowledge: Assign approximate ages to the classes
• Results: Three New Growth Curves modelling different amounts of uncertainty
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New Growth Curves: Achieved by Data Clustering
•Class 1: Length: 50-150mm -> Age: 0-1
•Class 2: Length: 150-250mm -> Age: 1-2
•Class 3: Length: 250-600mm -> Age: 2-5
•Class 4: Length: 600-1000mm -> Age: 3-9
• Class 5: Length: 1000-1350mm -> Age 9+
Length (mm)
Nu
mb
er (
fish
in e
ach
cla
ss)
Data Clustering Murray Cod lengths
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New Growth Curves:Using Data Clustering
D/Clus 1
D/Clus 2 D/Clus 3
1362 1431 1585
k 0.10 0.08 0.06
-0.16 -0.56 -1.21
Parameters:
Equation: (von Bertalanffy)
)))tk(texp((1LL 0t
∞L
Ot
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New Growth Curves:Using Data Clustering
D/Clus 1
D/Clus 2 D/Clus 3
1330 1289 1199
k 0.1042 0.1026 0.1115
(0) (0) (0)
Parameters:
Equation: (von Bertalanffy)
k(t)))exp((1LLt =0Note:
∞L
Ot
Ot
www.csse.monash.edu.au/~jbernard/Project
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New Growth Curves:Using Data Clustering
Data Clustering curves Original Equation vs Setting = 0
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50 60
Age
Len
gth
D/Clus 1
D/Clus 2
D/Clus 3
D/Clus 1 (to=0)
D/Clus 2 (to=0)
D/Clus 3 (to=0)
Data
Ot
0
0
0
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Comparing Existing Curves to New Curves
Best Existing Curve (Todd) vs Best Data Clustering Curve (D/Clus 3)
0
200
400
600
800
1000
1200
1400
1600
0 10 20 30 40 50 60
Age
Leng
th
D/Clus 3
D/Clus 3 (to=0)
Todd
Todd (to=0)
Data0
0
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Summary
• Improved Existing Curves– Using old data sets
• Created New Curves– Using new data sets and data clustering– The curve modelling the most uncertainty
provided the best fit to otolith data– In all cases setting = 0 provided the best
fit to recapture dataOt
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Future Work
• We do plan on modelling the entire population– Our next step is developing a
Bayesian model for determining survival rates!
• Stay tuned:– http://www.csse.monash.edu.au/jbernard/
Project
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