Www.csse.monash.edu.au/~jbernard/Project By: James Bernard Supervised By: Charles Todd (Department...

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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4

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• Reviewed previous experts curves:– Anderson (1992)– Gooley (1995)– Rowland (1998)– Todd (unpublished)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

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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