Ecological Archives A018-069-A3

Jeffrey E. Moore and Andrew J. Read. 2008. A Bayesian uncertainty analysis of cetacean demography and bycatch mortality using age-at-death data. Ecological Applications 18:1914–1931.

Appendix C. Model-averaged estimates of age-specific mortality, survivorship, net reproductive rate, life expectancy, population age distribution (live animals), and death distribution.

TABLE C1. Model averaged estimates (medians and 90% Bayesian credible limits) of natural mortality, bycatch mortality and total mortality, from models 1 and 2. Median qtot(t)’s were calculated from qtot(t) estimates at each MCMC sample, rather than as the sum of median qnat(t) and median qbyc(t). Right-skewed posterior distributions and correlations between qnat(t) and qbyc(t) result in median values of qtot(t) that are slightly larger than the sum of medians from constituent mortality types.

Age

qnat(t)

5% CL

95% CL

qbyc(t)

5% CL

95% CL

qtot(t)

5% CL

95% CL


0

0.400

0.180

0.592

0.045

0.007

0.236

0.469

0.306

0.642

1

0.130

0.040

0.255

0.097

0.018

0.267

0.249

0.131

0.387

2

0.079

0.022

0.153

0.100

0.020

0.269

0.185

0.091

0.351

3

0.066

0.018

0.132

0.084

0.018

0.230

0.153

0.071

0.316

4

0.064

0.018

0.133

0.068

0.015

0.190

0.136

0.061

0.288

5

0.067

0.019

0.138

0.055

0.012

0.158

0.125

0.055

0.266

6

0.073

0.022

0.146

0.045

0.010

0.130

0.120

0.052

0.252

7

0.081

0.026

0.156

0.036

0.008

0.109

0.118

0.051

0.245

8

0.090

0.031

0.169

0.030

0.007

0.093

0.120

0.053

0.246

9

0.101

0.038

0.187

0.025

0.006

0.079

0.127

0.056

0.253

10

0.115

0.047

0.210

0.020

0.005

0.068

0.135

0.062

0.268

11

0.131

0.058

0.241

0.017

0.004

0.059

0.148

0.071

0.289

12

0.149

0.074

0.277

0.015

0.003

0.052

0.165

0.084

0.321

13

0.170

0.093

0.324

0.012

0.003

0.046

0.184

0.101

0.360

14

0.195

0.115

0.378

0.011

0.002

0.042

0.207

0.122

0.409

15

0.224

0.140

0.444

0.009

0.002

0.037

0.235

0.146

0.470

16

0.261

0.166

0.514

0.008

0.002

0.034

0.271

0.171

0.538

17

0.302

0.189

0.591

0.007

0.001

0.031

0.311

0.193

0.611

18

0.349

0.210

0.671

0.006

0.001

0.028

0.356

0.214

0.685

19

0.398

0.230

0.745

0.005

0.001

0.026

0.407

0.234

0.759

20

0.452

0.249

0.810

0.005

0.001

0.024

0.459

0.254

0.820

21

0.508

0.269

0.861

0.004

0.001

0.022

0.514

0.272

0.870

22

0.563

0.288

0.903

0.004

0.001

0.020

0.570

0.292

0.910

23

0.619

0.308

0.933

0.003

0.001

0.018

0.624

0.312

0.939

24

0.671

0.330

0.954

0.003

0.001

0.017

0.676

0.333

0.959


 

TABLE C2. Model averaged estimates (medians and 90% Bayesian credible limits) of natural and actual (natural + bycatch) survivorship, from models 1 and 2.


Age

lnat(t)

5% CL

95% CL

ltot(t)

5% CL

95% CL


0

1.000

1.000

1.000

1.000

1.000

1.000

1

0.600

0.408

0.820

0.531

0.358

0.694

2

0.509

0.340

0.752

0.392

0.246

0.575

3

0.465

0.309

0.701

0.315

0.172

0.509

4

0.430

0.289

0.665

0.264

0.125

0.462

5

0.398

0.270

0.632

0.227

0.092

0.423

6

0.366

0.251

0.603

0.198

0.070

0.394

7

0.336

0.231

0.575

0.174

0.054

0.367

8

0.307

0.208

0.546

0.153

0.042

0.342

9

0.277

0.182

0.517

0.135

0.032

0.318

10

0.247

0.155

0.486

0.118

0.025

0.297

11

0.218

0.128

0.451

0.102

0.018

0.273

12

0.187

0.102

0.412

0.087

0.013

0.248

13

0.157

0.078

0.371

0.072

0.009

0.223

14

0.129

0.056

0.325

0.058

0.006

0.196

15

0.102

0.036

0.277

0.045

0.004

0.168

16

0.078

0.021

0.227

0.034

0.002

0.137

17

0.057

0.011

0.179

0.025

0.001

0.107

18

0.040

0.005

0.134

0.017

0.000

0.080

19

0.027

0.002

0.095

0.011

0.000

0.056

20

0.017

0.000

0.063

0.007

0.000

0.038

21

0.010

0.000

0.040

0.004

0.000

0.024

22

0.005

0.000

0.024

0.002

0.000

0.015

23

0.002

0.000

0.014

0.001

0.000

0.009

24

0.001

0.000

0.009

0.000

0.000

0.005


 

TABLE C3. Model averaged estimates (medians and 90% Bayesian credible limits) of natural and actual (natural + bycatch) net reproductive rate (expected number of female calves an adult female of age t will have during the remainder of her life), from models 1 and 2.


Age

Rnat(t)

5% CL

95% CL

Rtot(t)

5% CL

95% CL


0

1.5

1.0

2.8

0.8

0.2

1.8

1

2.6

1.6

4.2

1.5

0.4

2.9

2

3.1

1.9

4.7

2.0

0.7

3.5

3

3.4

2.2

4.9

2.5

1.1

4.0

4

3.6

2.4

5.1

2.9

1.5

4.3

5

3.5

2.4

4.9

3.0

1.7

4.3

6

3.3

2.3

4.6

2.9

1.7

4.1

7

3.1

2.1

4.2

2.8

1.7

3.9

8

2.9

1.9

3.9

2.6

1.6

3.7

9

2.7

1.8

3.6

2.5

1.5

3.4

10

2.5

1.6

3.3

2.3

1.4

3.1

11

2.3

1.4

3.0

2.1

1.3

2.9

12

2.1

1.3

2.7

2.0

1.2

2.7

13

1.9

1.1

2.5

1.8

1.1

2.4

14

1.7

1.0

2.3

1.6

1.0

2.2

15

1.5

0.9

2.1

1.5

0.9

2.1

16

1.4

0.8

1.9

1.3

0.8

1.9

17

1.2

0.7

1.8

1.2

0.7

1.8

18

1.1

0.6

1.6

1.1

0.6

1.6

19

1.0

0.6

1.5

1.0

0.6

1.5

20

0.9

0.6

1.4

0.9

0.5

1.4

21

0.8

0.5

1.2

0.8

0.5

1.2

22

0.7

0.5

1.0

0.7

0.5

1.0

23

0.6

0.5

0.8

0.6

0.5

0.8

24

0.5

0.4

0.5

0.5

0.4

0.5


 

TABLE C4. Model averaged estimates (medians and 90% Bayesian credible limits) of natural and actual (natural + bycatch) life expectancy from models 1 and 2.


Age

LEnat(t)

5% CL

95% CL

LEtot(t)

5% CL

95% CL


0

5.5

4.1

8.9

3.5

1.9

6.3

1

8.1

5.8

11.9

5.3

2.6

8.8

2

8.5

5.8

12.0

5.9

2.8

9.3

3

8.2

5.5

11.5

6.1

3.1

9.4

4

7.7

5.2

10.9

6.2

3.2

9.2

5

7.2

4.9

10.2

6.0

3.3

8.9

6

6.7

4.5

9.4

5.8

3.3

8.5

7

6.2

4.1

8.7

5.6

3.2

8.0

8

5.8

3.8

8.0

5.2

3.0

7.4

9

5.3

3.4

7.3

4.9

2.9

6.9

10

4.8

3.0

6.6

4.5

2.6

6.3

11

4.4

2.7

6.0

4.2

2.4

5.8

12

4.0

2.3

5.4

3.8

2.1

5.2

13

3.6

2.0

4.8

3.4

1.9

4.7

14

3.2

1.7

4.4

3.1

1.6

4.3

15

2.8

1.5

4.0

2.7

1.4

3.9

16

2.5

1.3

3.6

2.4

1.2

3.6

17

2.2

1.1

3.3

2.1

1.1

3.3

18

1.9

0.9

3.0

1.9

0.9

3.0

19

1.7

0.8

2.7

1.7

0.8

2.6

20

1.5

0.7

2.3

1.4

0.7

2.3

21

1.2

0.7

1.9

1.2

0.6

1.9

22

1.0

0.6

1.5

1.0

0.6

1.5

23

0.7

0.5

0.8

0.7

0.5

0.8

24

5.5

4.1

8.9

3.5

1.9

6.3


 

TABLE C5. Model averaged estimates (medians and 90% Bayesian credible limits) of population age structure from models 1 and 2. fnat(t) is for an unexploited population. ftot(t) is for a population impacted by bycatch. Sum of age-specific medians is ~ 1.


Age

fnat(t)

5% CL

95% CL

ftot(t)

5% CL

95% CL


0

0.211

0.186

0.234

0.216

0.197

0.239

1

0.121

0.092

0.144

0.120

0.091

0.141

2

0.097

0.076

0.122

0.093

0.070

0.111

3

0.085

0.068

0.104

0.077

0.059

0.091

4

0.075

0.062

0.088

0.067

0.052

0.078

5

0.066

0.057

0.076

0.059

0.047

0.067

6

0.059

0.052

0.065

0.053

0.043

0.059

7

0.051

0.047

0.056

0.047

0.040

0.053

8

0.044

0.040

0.050

0.042

0.037

0.048

9

0.038

0.033

0.045

0.038

0.034

0.045

10

0.033

0.026

0.040

0.034

0.029

0.042

11

0.028

0.020

0.035

0.031

0.025

0.039

12

0.023

0.015

0.030

0.027

0.020

0.036

13

0.019

0.010

0.026

0.023

0.016

0.033

14

0.015

0.007

0.022

0.019

0.012

0.029

15

0.011

0.004

0.018

0.015

0.009

0.025

16

0.008

0.002

0.015

0.012

0.006

0.021

17

0.006

0.001

0.011

0.009

0.003

0.017

18

0.004

0.000

0.009

0.006

0.001

0.014

19

0.002

0.000

0.006

0.004

0.001

0.011

20

0.001

0.000

0.005

0.002

0.000

0.008

21

0.001

0.000

0.003

0.001

0.000

0.006

22

0.000

0.000

0.002

0.001

0.000

0.004

23

0.000

0.000

0.002

0.000

0.000

0.003

24

0.000

0.000

0.001

0.000

0.000

0.002


 

TABLE C6. Model averaged estimates (medians and 90% Bayesian credible limits) of death (strandings) age structure from models 1 and 2. Pnat(t) is for an unexploited population. Ptot(t) is for a population impacted by bycatch. Sum of age-specific medians is ~ 1.


Age

Pnat(t)

5% CL

95% CL

Ptot(t)

5% CL

95% CL


0

0.503

0.256

0.690

0.336

0.267

0.422

1

0.096

0.031

0.162

0.164

0.129

0.198

2

0.047

0.013

0.090

0.116

0.087

0.145

3

0.033

0.009

0.075

0.082

0.058

0.101

4

0.028

0.008

0.067

0.060

0.042

0.073

5

0.026

0.008

0.061

0.045

0.032

0.055

6

0.025

0.008

0.055

0.035

0.025

0.043

7

0.024

0.009

0.051

0.028

0.020

0.035

8

0.024

0.009

0.046

0.023

0.017

0.029

9

0.023

0.010

0.042

0.019

0.014

0.025

10

0.022

0.011

0.038

0.016

0.012

0.021

11

0.021

0.012

0.034

0.014

0.010

0.019

12

0.020

0.013

0.031

0.012

0.008

0.017

13

0.018

0.013

0.029

0.010

0.006

0.016

14

0.016

0.012

0.026

0.009

0.005

0.014

15

0.014

0.010

0.023

0.008

0.003

0.013

16

0.012

0.007

0.019

0.006

0.002

0.011

17

0.010

0.004

0.016

0.005

0.001

0.009

18

0.007

0.002

0.013

0.003

0.001

0.008

19

0.005

0.001

0.010

0.002

0.000

0.006

20

0.003

0.000

0.008

0.001

0.000

0.005

21

0.002

0.000

0.005

0.001

0.000

0.003

22

0.001

0.000

0.004

0.000

0.000

0.002

23

0.000

0.000

0.003

0.000

0.000

0.002

24

0.000

0.000

0.002

0.000

0.000

0.001



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