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 q_tot(t)’s were calculated from q_tot(t) estimates at each MCMC sample, rather than as the sum of median q_nat(t) and median q_byc(t). Right-skewed posterior distributions and correlations between q_nat(t) and q_byc(t) result in median values of q_tot(t) that are slightly larger than the sum of medians from constituent mortality types.

Age	q_nat(t)	5% CL	95% CL	q_byc(t)	5% CL	95% CL	q_tot(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	l_nat(t)	5% CL	95% CL	l_tot(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	R_nat(t)	5% CL	95% CL	R_tot(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	LE_nat(t)	5% CL	95% CL	LE_tot(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. f_nat(t) is for an unexploited population. f_tot(t) is for a population impacted by bycatch. Sum of age-specific medians is ~ 1.

Age	f_nat(t)	5% CL	95% CL	f_tot(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. P_nat(t) is for an unexploited population. P_tot(t) is for a population impacted by bycatch. Sum of age-specific medians is ~ 1.

Age	P_nat(t)	5% CL	95% CL	P_tot(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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