Ecological Archives E094-217-A2
Tamar Lok, Otto Overdijk, Joost M. Tinbergen, Theunis Piersma. 2013. Seasonal variation in density dependence in age-specific survival of a long-distance migrant. Ecology 94:2358–2369. http://dx.doi.org/10.1890/12-1914.1
Appendix B. Annual survival: model selection results, shrunken estimates of true survival, and maximum-likelihood estimates of other parameters of the full Barker model.
Table B1. Model selection results to investigate whether fidelity (F), resighting (p, R and R') and recovery (r) probabilities are more parsimoniously modelled with between-year variation (t), as a linear function of population size (Nlin, only for fidelity) or as constant (.). Survival is modeled as S0(t) S1(t) S2(t) S≥3(t).
Parameterization |
K |
ΔQDev |
ΔQAICc |
||||
F012(t) Fad(t) |
p1(t) p2(t) p≥3(t) |
r(.) |
R(t) |
R'(t) |
223 |
0.00* |
4.26 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(t) |
R(t) |
R'(t) |
209 |
36.25 |
11.95 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(t) |
R(t) |
R'(.) |
188 |
101.96 |
34.88 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(t) |
R(.) |
R'(t) |
188 |
337.64 |
270.56 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(t) |
R(.) |
R'(.) |
167 |
408.53 |
298.76 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(.) |
R(t) |
R'(t) |
188 |
67.08 |
0.00** |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(.) |
R(t) |
R'(.) |
167 |
135.49 |
25.72 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(.) |
R(.) |
R'(t) |
167 |
367.99 |
258.22 |
F012(Nlin) Fad(Nlin) |
p1(t) p2(t) p≥3(t) |
r(.) |
R(.) |
R'(.) |
146 |
442.06 |
289.67 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(t) |
R(t) |
R'(t) |
172 |
150.32 |
50.71 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(t) |
R(t) |
R'(.) |
151 |
208.61 |
66.37 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(t) |
R(.) |
R'(t) |
151 |
450.45 |
308.20 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(t) |
R(.) |
R'(.) |
130 |
514.94 |
330.14 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(.) |
R(t) |
R'(t) |
151 |
182.22 |
39.98 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(.) |
R(t) |
R'(.) |
130 |
247.12 |
62.33 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(.) |
R(.) |
R'(t) |
130 |
489.80 |
305.00 |
F012(Nlin) Fad(Nlin) |
(p1, p2, p≥3)(t) |
r(.) |
R(.) |
R'(.) |
109 |
554.44 |
327.18 |
K = number of parameters. The best-supported (full) model is shown in bold. Results are adjusted for overdispersion (ĉ = 1.16, see Methods). Note that the fully time-dependent model (the first model in the list) was run using the simulated annealing optimization routine.
*QDeviance = 24479.92
**QAICc = 56977.74
Table B2. Model selection results for reduced fixed and random effects models of age-specific survival and fidelity, starting from the full model.
Table B3. Shrunken estimates (mean ± SE) for age-specific survival from the best-supported random effects parameterization per age class (Nquad, σ² for S0 and Nlin, σ² for S1, S2, and S≥3, see Table B2). For fidelity, the maximum- likelihood estimates of the full Barker model are shown which were modeled as a linear function of population size.
Year |
Population size |
|
F012 |
F≥3 |
||||
1988 |
415 |
0.46 ± 0.04 |
n.a. |
n.a. |
n.a. |
0.94 ± 0.008 |
n.a. |
|
1989 |
492 |
0.43 ± 0.04 |
1.00 ± 0.00 |
n.a. |
n.a. |
0.94 ± 0.007 |
n.a. |
|
1990 |
438 |
0.39 ± 0.04 |
0.96 ± 0.04 |
0.96 ± 0.05 |
n.a. |
0.94 ± 0.007 |
n.a. |
|
1991 |
527 |
0.52 ± 0.04 |
0.95 ± 0.03 |
0.99 ± 0.03 |
1.00 ± 0.00 |
0.93 ± 0.007 |
0.99 ± 0.004 |
|
1992 |
560 |
0.52 ± 0.03 |
0.91 ± 0.05 |
1.00 ± 0.00 |
0.88 ± 0.06 |
0.93 ± 0.007 |
0.99 ± 0.004 |
|
1993 |
593 |
0.57 ± 0.03 |
0.97 ± 0.02 |
1.00 ± 0.00 |
0.91 ± 0.02 |
0.93 ± 0.007 |
0.99 ± 0.004 |
|
1994 |
661 |
0.68 ± 0.03 |
0.99 ± 0.02 |
0.98 ± 0.02 |
0.91 ± 0.02 |
0.93 ± 0.007 |
0.99 ± 0.004 |
|
1995 |
810 |
n.a. |
0.97 ± 0.02 |
0.97 ± 0.02 |
0.90 ± 0.02 |
0.92 ± 0.006 |
0.99 ± 0.004 |
|
1996 |
847 |
0.65 ± 0.03 |
n.a. |
0.96 ± 0.02 |
0.89 ± 0.02 |
0.92 ± 0.006 |
0.99 ± 0.004 |
|
1997 |
1122 |
0.63 ± 0.03 |
0.88 ± 0.03 |
n.a. |
0.88 ± 0.02 |
0.91 ± 0.005 |
0.98 ± 0.003 |
|
1998 |
1270 |
0.69 ± 0.03 |
0.87 ± 0.04 |
0.93 ± 0.02 |
0.85 ± 0.02 |
0.90 ± 0.005 |
0.98 ± 0.003 |
|
1999 |
1038 |
0.69 ± 0.03 |
0.86 ± 0.04 |
0.95 ± 0.02 |
0.90 ± 0.02 |
0.92 ± 0.005 |
0.98 ± 0.003 |
|
2000 |
1043 |
0.66 ± 0.03 |
0.90 ± 0.02 |
0.90 ± 0.05 |
0.88 ± 0.02 |
0.92 ± 0.005 |
0.98 ± 0.003 |
|
2001 |
1165 |
0.67 ± 0.03 |
0.89 ± 0.03 |
0.98 ± 0.02 |
0.90 ± 0.02 |
0.91 ± 0.005 |
0.98 ± 0.003 |
|
2002 |
1534 |
0.56 ± 0.03 |
0.95 ± 0.02 |
0.93 ± 0.02 |
0.87 ± 0.02 |
0.89 ± 0.007 |
0.97 ± 0.004 |
|
2003 |
1293 |
0.62 ± 0.03 |
0.96 ± 0.03 |
0.95 ± 0.02 |
0.88 ± 0.02 |
0.90 ± 0.005 |
0.98 ± 0.003 |
|
2004 |
1699 |
0.51 ± 0.03 |
0.84 ± 0.03 |
0.90 ± 0.03 |
0.84 ± 0.02 |
0.88 ± 0.009 |
0.96 ± 0.006 |
|
2005 |
1443 |
0.58 ± 0.03 |
0.85 ± 0.03 |
1.00 ± 0.00 |
0.88 ± 0.01 |
0.90 ± 0.006 |
0.97 ± 0.003 |
|
2006 |
1778 |
0.57 ± 0.03 |
0.93 ± 0.03 |
0.90 ± 0.03 |
0.86 ± 0.02 |
0.88 ± 0.010 |
0.96 ± 0.007 |
|
2007 |
1838 |
0.46 ± 0.03 |
0.85 ± 0.03 |
0.87 ± 0.04 |
0.84 ± 0.02 |
0.87 ± 0.011 |
0.96 ± 0.008 |
|
2008 |
1904 |
0.29 ± 0.03 |
0.84 ± 0.04 |
0.93 ± 0.03 |
0.85 ± 0.02 |
|
0.87 ± 0.012 |
0.95 ± 0.010 |
|
The standard errors associated with the age-specific survival estimates represent the RMSE estimates reported by program MARK, which give the unconditional sampling standard errors. Results are adjusted for overdispersion (ĉ = 1.16, see Methods).
Table B4. Estimates (and 95% confidence intervals) of resighting probabilities during capture occasions (p) and intervals (R and R') and recovery probability (r) of the full model: S0(t) S1(t) S2(t) S≥3(t) F012(Nlin) F≥3(Nlin) p1(t) p2(t) p≥3(t) r(.) R(t) R'(t).
|
Resighting probability during capture occasions (p) |
|
Resighting probability during interval |
||||
Year |
|
Age 1 |
Age 2 |
Age ≥ 3 |
|
of survivors (R) |
of non-survivors (R') |
1988 |
|
n.a. |
n.a. |
n.a. |
|
0.71 (0.56-0.83) |
0.78 (0.64-0.88) |
1989 |
|
0.00 (0.00-1.00) |
n.a. |
n.a. |
|
0.45 (0.35-0.55) |
0.67 (0.54-0.77) |
1990 |
|
0.02 (0.00-0.15) |
0.13 (0.06-0.28) |
n.a. |
|
0.36 (0.29-0.45) |
0.49 (0.39-0.60) |
1991 |
|
0.00 (0.00-0.00) |
0.07 (0.02-0.20) |
0.38 (0.23-0.55) |
|
0.40 (0.33-0.46) |
0.64 (0.51-0.75) |
1992 |
|
0.00 (0.00-0.00) |
0.06 (0.02-0.19) |
0.38 (0.27-0.51) |
|
0.40 (0.35-0.46) |
0.55 (0.46-0.64) |
1993 |
|
0.04 (0.01-0.09) |
0.04 (0.01-0.13) |
0.40 (0.31-0.50) |
|
0.38 (0.34-0.43) |
0.57 (0.47-0.66) |
1994 |
|
0.05 (0.02-0.10) |
0.09 (0.05-0.16) |
0.48 (0.40-0.57) |
|
0.48 (0.44-0.52) |
0.70 (0.58-0.80) |
1995 |
|
0.01 (0.00-0.05) |
0.12 (0.07-0.19) |
0.48 (0.41-0.54) |
|
0.36 (0.32-0.40) |
0.43 (0.21-0.68) |
1996 |
|
0.00 (0.00-0.00) |
0.13 (0.08-0.19) |
0.50 (0.45-0.56) |
|
0.63 (0.59-0.66) |
0.57 (0.46-0.68) |
1997 |
|
0.06 (0.03-0.12) |
0.00 (0.00-0.00) |
0.61 (0.56-0.66) |
|
0.63 (0.59-0.67) |
0.70 (0.59-0.79) |
1998 |
|
0.14 (0.08-0.22) |
0.28 (0.20-0.39) |
0.62 (0.57-0.67) |
|
0.61 (0.57-0.64) |
0.65 (0.54-0.74) |
1999 |
|
0.11 (0.06-0.18) |
0.13 (0.07-0.23) |
0.55 (0.50-0.60) |
|
0.58 (0.54-0.61) |
0.62 (0.52-0.71) |
2000 |
|
0.02 (0.01-0.05) |
0.04 (0.01-0.11) |
0.40 (0.35-0.45) |
|
0.52 (0.48-0.55) |
0.70 (0.57-0.80) |
2001 |
|
0.06 (0.03-0.13) |
0.22 (0.16-0.30) |
0.44 (0.39-0.49) |
|
0.47 (0.43-0.50) |
0.66 (0.55-0.76) |
2002 |
|
0.07 (0.04-0.12) |
0.17 (0.10-0.27) |
0.43 (0.39-0.48) |
|
0.46 (0.43-0.49) |
0.64 (0.54-0.74) |
2003 |
|
0.08 (0.03-0.16) |
0.31 (0.23-0.40) |
0.45 (0.40-0.50) |
|
0.54 (0.50-0.57) |
0.67 (0.57-0.76) |
2004 |
|
0.08 (0.05-0.14) |
0.29 (0.20-0.41) |
0.45 (0.40-0.49) |
|
0.52 (0.49-0.55) |
0.56 (0.48-0.63) |
2005 |
|
0.06 (0.03-0.11) |
0.14 (0.09-0.22) |
0.39 (0.35-0.44) |
|
0.51 (0.48-0.54) |
0.65 (0.57-0.72) |
2006 |
|
0.04 (0.02-0.08) |
0.20 (0.13-0.28) |
0.57 (0.53-0.62) |
|
0.51 (0.48-0.54) |
0.58 (0.51-0.65) |
2007 |
|
0.17 (0.12-0.23) |
0.20 (0.14-0.28) |
0.61 (0.57-0.66) |
|
0.61 (0.58-0.63) |
0.68 (0.62-0.74) |
2008 |
|
0.07 (0.04-0.12) |
0.28 (0.21-0.37) |
0.55 (0.51-0.60) |
|
0.56 (0.53-0.59) |
0.61 (0.56-0.66) |
2009 |
|
0.12 (0.07-0.20) |
0.28 (0.21-0.37) |
0.64 (0.60-0.69) |
|
0.56 (0.52-0.60) |
0.88 (0.51-0.98) |
Recovery probability (r) was estimated at 0.03 (0.03–0.04). Confidence intervals are adjusted for overdispersion (ĉ = 1.16, see Methods).