Seasonal Survival Estimation for a Long-Distance Migratory Bird and the Influence of Winter

Rockwell et al.

Seasonal survival estimation for a long-distance migratory bird and the influence of winter precipitation

Sarah M. Rockwell*, Joseph M. Wunderle, Jr.,T. Scott Sillett, Carol I. Bocetti,David N. Ewert, Dave Currie, Jennifer D. White, and Peter P. Marra

*corresponding author:

Online Resource 1. Full version of Table 3: first model subset of monthly survival (φ) and recapture (p) probabilities for male Kirtland’s warblers in Michigan from 2006-2011, including demographic and time parameters. Includes number of estimable parameters (K), QAICc values, differences between current QAICc and QAICc value for the best model (ΔQAICc), QAICc weights (wi), and model likelihoods. Variables in parentheses give parameterization for ф and p: time (t) refers to monthly variation, year to annual variation, age to second-year (a first-time breeder; SY) vs. after second-year (returning adult; ASY), and ‘season’ refers to the summer vs. overwinter+migration seasons. A dot model (.) represents constant probability.Goodness of fit test for the global, full group x time model (фage*t, page*t) indicated a minor lack of fit to the data (χ241 = 31.4, p = 0.07), so a ĉ adjustment was used (ĉ = 1.40).

Model / QAICc / Delta QAICc / wi / Model Likelihood / K
{Phi(season)p(t)} / 1377.41 / 0.00 / 0.203 / 1.000 / 13
{Phi(age)p(t)} / 1378.08 / 0.67 / 0.145 / 0.716 / 13
{Phi(year)p(t)} / 1378.34 / 0.93 / 0.127 / 0.629 / 15
{Phi(age+season)p(t)} / 1378.59 / 1.18 / 0.112 / 0.554 / 14
{Phi(age+year)p(t)} / 1378.70 / 1.29 / 0.106 / 0.525 / 16
{Phi(season+year)p(t)} / 1378.77 / 1.36 / 0.103 / 0.507 / 16
{Phi(season+age+year)p(t)} / 1379.02 / 1.61 / 0.090 / 0.446 / 17
{Phi(age*year)p(t)} / 1380.69 / 3.28 / 0.039 / 0.194 / 20
{Phi(age*season)p(t)} / 1381.31 / 3.90 / 0.029 / 0.142 / 15
{Phi(.)p(t)} / 1381.77 / 4.37 / 0.023 / 0.113 / 12
{Phi(season*year) p(t)} / 1382.26 / 4.86 / 0.018 / 0.088 / 18
{Phi(age*season*year)p(t)} / 1386.18 / 8.77 / 0.003 / 0.013 / 25
{Phi(t)p(t)} / 1387.07 / 9.66 / 0.002 / 0.008 / 21
{Phi(t*age)p(t)} / 1396.64 / 19.23 / 0 / 0 / 31
{Phi(t)p(season*year)} / 1420.51 / 43.10 / 0 / 0 / 18
{Phi(.)p(season*year)} / 1426.53 / 49.12 / 0 / 0 / 9
{Phi(age)p(season*year)} / 1427.68 / 50.27 / 0 / 0 / 10
{Phi(year)p(season*year)} / 1427.95 / 50.54 / 0 / 0 / 12
{Phi(age*year)p(season*year)} / 1428.03 / 50.62 / 0 / 0 / 16
{Phi(season)p(season*year)} / 1428.24 / 50.83 / 0 / 0 / 10
{Phi(age+season)p(season+year)} / 1429.10 / 51.69 / 0 / 0 / 9
{Phi(age+season)p(season*year)} / 1429.34 / 51.93 / 0 / 0 / 11
{Phi(t*age)p(season*year)} / 1430.04 / 52.63 / 0 / 0 / 28
{Phi(age*season)p(season*year)} / 1430.84 / 53.43 / 0 / 0 / 12
{Phi(age+season)p(season+year)} / 1431.13 / 53.72 / 0 / 0 / 10
{Phi(year)p(year)} / 1433.28 / 55.87 / 0 / 0 / 9
{Phi(season*year)p(season*year)} / 1433.51 / 56.10 / 0 / 0 / 15
{Phi(season)p(year)} / 1433.91 / 56.50 / 0 / 0 / 7
{Phi(age*season)p(year)} / 1436.59 / 59.18 / 0 / 0 / 9
{Phi(age)p(year)} / 1437.98 / 60.57 / 0 / 0 / 7
{Phi(age*season*year)p(season*year)} / 1439.90 / 62.49 / 0 / 0 / 23
{Phi(t)p(season)} / 1441.22 / 63.82 / 0 / 0 / 13
{Phi(t*age)p(.)} / 1441.73 / 64.32 / 0 / 0 / 17
{Phi(t)p(.)} / 1442.82 / 65.41 / 0 / 0 / 12
{Phi(.)p(.)} / 1449.10 / 72.59 / 0 / 0 / 2
{Phi(.)p(season)} / 1450.03 / 72.62 / 0 / 0 / 3
{Phi(year)p(season)} / 1450.44 / 73.03 / 0 / 0 / 7
{Phi(year)p(.)} / 1450.81 / 73.40 / 0 / 0 / 6
{Phi(age)p(season)} / 1450.92 / 73.51 / 0 / 0 / 4
{Phi(age)p(.)} / 1450.93 / 73.52 / 0 / 0 / 3
{Phi(season)p(season)} / 1451.93 / 74.52 / 0 / 0 / 4
{Phi(season)p(.)} / 1451.97 / 74.56 / 0 / 0 / 3
{Phi(age*year)p(season)} / 1452.02 / 74.62 / 0 / 0 / 12
{Phi(t*age)p(season)} / 1452.32 / 74.91 / 0 / 0 / 24
{Phi(age*year)p(.)} / 1452.56 / 75.16 / 0 / 0 / 11
{Phi(age+season)p(season)} / 1452.77 / 75.36 / 0 / 0 / 5
{Phi(age+season)p(.)} / 1452.92 / 75.51 / 0 / 0 / 4
{Phi(age*season)p(season)} / 1454.22 / 76.82 / 0 / 0 / 6
{Phi(age*season)p(.)} / 1454.51 / 77.10 / 0 / 0 / 5
{Phi(season*year)p(season)} / 1455.34 / 77.93 / 0 / 0 / 10
{Phi(season*year)p(.)} / 1456.08 / 78.67 / 0 / 0 / 9
{Phi(age*season*year)p(season)} / 1458.06 / 80.65 / 0 / 0 / 17
{Phi(age*season*year)p(.)} / 1459.18 / 81.77 / 0 / 0 / 16

Online Resource 2. Full version of Table 3: second model subset of monthly survival (φ) and recapture (p) probabilities for male Kirtland’s warblers in Michigan from 2006-2011, including climate variables and all other annual covariates. Includes number of estimable parameters (K), QAICc values, differences between current QAICc and QAICc value for the best model (ΔQAICc), QAICc weights (wi), and model likelihoods. Variables in parentheses give parameterization for ф and p. See Table 2 in text for variable definitions.Goodness of fit test for the global, full group x time model (фage*t, page*t) indicated a minor lack of fit to the data (χ241 = 31.4, p = 0.07), so a ĉ adjustment was used (ĉ = 1.40).

Model / QAICc / Delta QAICc / wi / Model Likelihood / K
{Phi(March rain)p(t)} / 1374.67 / 0.00 / 0.243 / 1.000 / 13
{Phi(latewinterrain)p(t)} / 1376.19 / 1.51 / 0.114 / 0.469 / 13
{Phi(ENSO n-1)p(t)} / 1376.23 / 1.56 / 0.111 / 0.458 / 13
{Phi(summer rain)p(t)} / 1376.75 / 2.08 / 0.086 / 0.354 / 13
{Phi(hurricane)p(t)} / 1377.61 / 2.94 / 0.056 / 0.230 / 13
{Phi(Maymintemp)p(t)} / 1377.94 / 3.27 / 0.047 / 0.195 / 13
{Phi(wintermaxtemp)p(t)} / 1378.13 / 3.46 / 0.043 / 0.178 / 13
{Phi(May freeze)p(t)} / 1378.19 / 3.51 / 0.042 / 0.173 / 13
{Phi(year)p(t)} / 1378.34 / 3.66 / 0.039 / 0.160 / 15
{Phi(winter90degdays)p(t)} / 1378.34 / 3.67 / 0.039 / 0.160 / 13
{Phi(linear)p(t)} / 1378.82 / 4.15 / 0.030 / 0.125 / 13
{Phi(popsize)p(t)} / 1378.87 / 4.20 / 0.030 / 0.122 / 13
{Phi(May rain)p(t)} / 1378.94 / 4.26 / 0.029 / 0.119 / 13
{Phi(winter rain)p(t)} / 1378.97 / 4.30 / 0.028 / 0.116 / 13
{Phi(winter NAO)p(t)} / 1379.00 / 4.33 / 0.028 / 0.115 / 13
{Phi(ENSO)p(t)} / 1379.01 / 4.33 / 0.028 / 0.115 / 13
{Phi(.)p(t)} / 1381.77 / 7.10 / 0.007 / 0.029 / 12
{Phi(t)p(t)} / 1387.07 / 12.40 / 0.000 / 0.002 / 21

Online Resource 3. Full version of Table 3: final model set of monthly survival (φ) and recapture (p) probabilities for male Kirtland’s warblers in Michigan from 2006-2011. Includes number of estimable parameters (K), QAICc values, differences between current QAICc and QAICc value for the best model (ΔQAICc), QAICc weights (wi), and model likelihoods. Variables in parentheses give parameterization for ф and p.Goodness of fit test for the global, full group x time model (фage*t, page*t) indicated a minor lack of fit to the data (χ241 = 31.4, p = 0.07), so a ĉ adjustment was used (ĉ = 1.40).

Model / QAICc / Delta QAICc / wi / Model Likelihood / K
{Phi(Marchrain)p(t)} / 1374.67 / 0.00 / 0.129 / 1.00 / 13
{Phi(Marchrain+season)p(t)} / 1375.36 / 0.69 / 0.091 / 0.71 / 14
{Phi(Marchrain+age)p(t)} / 1375.91 / 1.23 / 0.069 / 0.54 / 14
{Phi(lwrain)p(t)} / 1376.19 / 1.51 / 0.060 / 0.47 / 13
{Phi(ENSOn-1)p(t)} / 1376.23 / 1.56 / 0.059 / 0.46 / 13
{Phi(lwr+season)p(t)} / 1376.54 / 1.87 / 0.051 / 0.39 / 14
{Phi(ENSOn-1+season)p(t)} / 1376.55 / 1.88 / 0.050 / 0.39 / 14
{Phi(Marchrain+age+season)p(t)} / 1376.72 / 2.04 / 0.046 / 0.36 / 15
{Phi(ENSOn-1+age)p(t)} / 1376.74 / 2.06 / 0.046 / 0.36 / 14
{Phi(Marchrain*season)p(t)} / 1376.76 / 2.09 / 0.045 / 0.35 / 15
{Phi(lwr+age)p(t)} / 1376.77 / 2.10 / 0.045 / 0.35 / 14
{Phi(ENSOn-1+age+season)p(t)} / 1377.22 / 2.55 / 0.036 / 0.28 / 15
{Phi(lwr+age+season)p(t)} / 1377.29 / 2.62 / 0.035 / 0.27 / 15
{Phi(season)p(t)} / 1377.41 / 2.74 / 0.033 / 0.25 / 13
{Phi(MarchRain*age)p(t)} / 1377.58 / 2.91 / 0.030 / 0.23 / 15
{Phi(age)p(t)} / 1378.08 / 3.41 / 0.023 / 0.18 / 13
{Phi(ENSOn-1*age)p(t)} / 1378.14 / 3.46 / 0.023 / 0.18 / 15
{Phi(lwr*age)p(t)} / 1378.18 / 3.51 / 0.022 / 0.17 / 15
{Phi(year)p(t)} / 1378.34 / 3.66 / 0.021 / 0.16 / 15
{Phi(lwr*season)p(t)} / 1378.40 / 3.73 / 0.020 / 0.16 / 15
{Phi(ENSOn-1*season)p(t)} / 1378.41 / 3.74 / 0.020 / 0.15 / 15
{Phi(age+season)p(t)} / 1378.59 / 3.92 / 0.018 / 0.14 / 14
{Phi(ENSOn-1*age*season)p(t)} / 1380.25 / 5.58 / 0.008 / 0.06 / 18
{Phi(age*season) p(t)} / 1380.30 / 5.62 / 0.008 / 0.06 / 15
{Phi(Marchrain*age*season)p(t)} / 1380.68 / 6.01 / 0.006 / 0.05 / 19
{Phi(.)p(t)} / 1381.77 / 7.10 / 0.004 / 0.03 / 12
{Phi(lwr*age*season)p(t)} / 1383.90 / 9.22 / 0.001 / 0.01 / 19
{Phi(t)p(t)} / 1387.07 / 12.40 / 0.000 / 0.00 / 21
{Phi(t)p(.)} / 1442.82 / 68.15 / 0.000 / 0.00 / 12
{Phi(.)p(.)} / 1450.00 / 75.33 / 0.000 / 0.00 / 2

Online Resource 4. Full version of Table 6: Models of monthly winter survival (φ) and recapture (p) probabilities for Kirtland’s warblers in the Bahamas from 2003-2010. Includes number of estimable parameters (K), AICc values, differences between current AICc and AICc value for the best model (ΔAICc), AICc weights (wi), and model likelihoods. Subscripts give parameterization for ф and p: age = two age classes (AHY or HY), sex = male or female, year = annual variation, t = monthly variation, and season = overwinter (Oct – Mar) vs.summer+migration (Apr – Sept). The global, full group x time model (фsex*age*t, psex*age*t) fit the data well (χ2162= 137.6, p = 0.92).

Model / AICc / Delta AICc / wi / Model Likelihood / K
{Phi(age*season)p(sex+season)} / 1859.39 / 0.00 / 0.38 / 1.00 / 7
{Phi(age*season)p(sex*season)} / 1860.43 / 1.03 / 0.23 / 0.60 / 8
{Phi(age+season)p(sex+season)} / 1861.12 / 1.73 / 0.16 / 0.42 / 6
{Phi(sex+age+season)p(sex+season)} / 1861.15 / 1.75 / 0.16 / 0.42 / 7
{Phi(sex*age*season)p(sex*season)} / 1864.49 / 5.09 / 0.03 / 0.08 / 12
{Phi(age*season)p(season*year)} / 1867.66 / 8.27 / 0.01 / 0.02 / 21
{Phi(sex*age*season)p(season*year)} / 1867.68 / 8.29 / 0.01 / 0.02 / 25
{Phi(age+season+year)p(sex+season)} / 1868.30 / 8.91 / 0.00 / 0.01 / 13
{Phi(sex*age*season)p(season) - fixed} / 1869.41 / 10.02 / 0.00 / 0.01 / 10
{Phi(age*season)p(season) - fixed} / 1869.56 / 10.17 / 0.00 / 0.01 / 6
{Phi(sex+age)p(sex+season)} / 1869.66 / 10.26 / 0.00 / 0.01 / 6
{Phi(age)p(sex+season)} / 1869.72 / 10.32 / 0.00 / 0.01 / 5
{Phi(sex*season)p(sex*season)} / 1870.16 / 10.76 / 0.00 / 0.00 / 8
{Phi(sex+age+season)p(season)} / 1870.25 / 10.85 / 0.00 / 0.00 / 6
{Phi(sex+season)p(sex+season)} / 1870.56 / 11.16 / 0.00 / 0.00 / 6
{Phi(age)p(sex*season)} / 1870.57 / 11.18 / 0.00 / 0.00 / 6
{Phi(sex*age)p(season*year)} / 1872.59 / 13.20 / 0.00 / 0.00 / 21
{Phi(sex*age)p(sex*season)} / 1872.63 / 13.23 / 0.00 / 0.00 / 8
{Phi(age)p(season*year)} / 1873.00 / 13.61 / 0.00 / 0.00 / 19
{Phi(sex+age+year)p(sex+season)} / 1873.33 / 13.94 / 0.00 / 0.00 / 12
{Phi(age+year)p(sex+season)} / 1873.59 / 14.20 / 0.00 / 0.00 / 11
{Phi(sex+age+season+year)p(sex+season+year)} / 1873.90 / 14.51 / 0.00 / 0.00 / 21
{Phi(sex*season)p(season*year)} / 1874.03 / 14.63 / 0.00 / 0.00 / 21
{Phi(season)p(sex+season)} / 1874.42 / 15.03 / 0.00 / 0.00 / 5
{Phi(sex+age+season+year)p(sex+season)} / 1875.03 / 15.64 / 0.00 / 0.00 / 15
{Phi(sex+season+year)p(sex+season)} / 1875.38 / 15.98 / 0.00 / 0.00 / 12
{Phi(season)p(sex*season)} / 1875.57 / 16.17 / 0.00 / 0.00 / 6
{Phi(sex)p(sex+season)} / 1876.71 / 17.32 / 0.00 / 0.00 / 5
{Phi(sex*season)p(season)} / 1876.74 / 17.34 / 0.00 / 0.00 / 6
{Phi(sex)p(sex*season)} / 1877.70 / 18.31 / 0.00 / 0.00 / 6
{Phi(sex*age)p(season)} / 1878.17 / 18.77 / 0.00 / 0.00 / 6
{Phi(season+year)p(sex+season)} / 1878.79 / 19.40 / 0.00 / 0.00 / 11
{Phi(sex)p(season*year)} / 1879.85 / 20.45 / 0.00 / 0.00 / 19
{Phi(sex+year)p(sex+season)} / 1880.00 / 20.60 / 0.00 / 0.00 / 11
{Phi(age*season)p(sex)} / 1881.15 / 21.75 / 0.00 / 0.00 / 6
{phi(.)p(sex*season)} / 1881.28 / 21.89 / 0.00 / 0.00 / 5
{Phi(age*season)p(t)} / 1881.89 / 22.49 / 0.00 / 0.00 / 54
{Phi(age*season)p(sex*season*year)} / 1882.16 / 22.77 / 0.00 / 0.00 / 38
{Phi(season*year)p(sex*season)} / 1883.20 / 23.80 / 0.00 / 0.00 / 21
{Phi(sex*age*season)p(t)} / 1883.28 / 23.89 / 0.00 / 0.00 / 58
{Phi(sex*age)p(t)} / 1883.58 / 24.19 / 0.00 / 0.00 / 54
{Phi(year)p(sex+season)} / 1883.89 / 24.50 / 0.00 / 0.00 / 10
{Phi(sex)p(season)} / 1884.86 / 25.47 / 0.00 / 0.00 / 4
{Phi(sex+age+season)p(sex)} / 1885.14 / 25.74 / 0.00 / 0.00 / 6
{Phi(sex*age*season)p(sex)} / 1885.22 / 25.82 / 0.00 / 0.00 / 10
{Phi(sex*age*season)p(sex*season*year)} / 1887.83 / 28.44 / 0.00 / 0.00 / 42
{Phi(sex*season)p(t)} / 1888.00 / 28.60 / 0.00 / 0.00 / 54
{Phi(age)p(sex*season*year)} / 1888.78 / 29.39 / 0.00 / 0.00 / 36
{Phi(year)p(sex*season)} / 1889.02 / 29.62 / 0.00 / 0.00 / 13
{phi(.)p(season*year)} / 1889.18 / 29.79 / 0.00 / 0.00 / 18
{Phi(season)p(season*year)} / 1889.20 / 29.81 / 0.00 / 0.00 / 19
{Phi(age*season)p(.)} / 1890.63 / 31.24 / 0.00 / 0.00 / 5
{Phi(sex*age*season)p(.)} / 1890.65 / 31.26 / 0.00 / 0.00 / 9
{Phi(season)p(season)} / 1891.64 / 32.25 / 0.00 / 0.00 / 4
{Phi(sex*year)p(season*year)} / 1891.80 / 32.41 / 0.00 / 0.00 / 32
{Phi(sex*age)p(sex*season*year)} / 1892.39 / 33.00 / 0.00 / 0.00 / 38
{Phi(age*season*year)p(sex*season)} / 1892.67 / 33.27 / 0.00 / 0.00 / 38
{Phi(season*year)p(season*year)} / 1893.00 / 33.60 / 0.00 / 0.00 / 31
{Phi(sex*season)p(sex*season*year)} / 1893.01 / 33.62 / 0.00 / 0.00 / 38
{Phi(sex*year)p(sex*season)} / 1893.06 / 33.67 / 0.00 / 0.00 / 22
{Phi(season*year)p(season)} / 1895.92 / 36.52 / 0.00 / 0.00 / 19
{Phi(year)p(season*year)} / 1896.73 / 37.34 / 0.00 / 0.00 / 24
{Phi(age*season)p(sex*year)} / 1896.91 / 37.52 / 0.00 / 0.00 / 22
{Phi(age*season)p(year)} / 1897.38 / 37.98 / 0.00 / 0.00 / 13
{Phi(sex*age*season)p(year)} / 1897.55 / 38.16 / 0.00 / 0.00 / 17
{Phi(sex*season*year)p(season*year)} / 1897.61 / 38.22 / 0.00 / 0.00 / 46
{Phi(season*year)p(sex*season*year)} / 1897.64 / 38.25 / 0.00 / 0.00 / 46
{Phi(season)p(sex*season*year)} / 1897.93 / 38.54 / 0.00 / 0.00 / 36
{Phi(sex)p(sex*season*year)} / 1898.64 / 39.25 / 0.00 / 0.00 / 36
{Phi(sex*season*year)p(sex*season)} / 1899.01 / 39.61 / 0.00 / 0.00 / 38
{Phi(sex*year)p(season)} / 1899.37 / 39.98 / 0.00 / 0.00 / 20
{Phi(.) p(t)} / 1899.41 / 40.02 / 0.00 / 0.00 / 51
{Phi(sex*season)p(.)} / 1899.45 / 40.06 / 0.00 / 0.00 / 5
{Phi(age*season*year)p(season)} / 1899.75 / 40.36 / 0.00 / 0.00 / 36
{Phi(year)p(season)} / 1900.34 / 40.95 / 0.00 / 0.00 / 11
{phi(.)p(sex*season*year)} / 1900.43 / 41.04 / 0.00 / 0.00 / 35
{Phi(sex*age*season)p(sex*year)} / 1902.50 / 43.11 / 0.00 / 0.00 / 26
{Phi(age)p(sex)} / 1904.33 / 44.93 / 0.00 / 0.00 / 4
{Phi(sex*season*year)p(season)} / 1904.76 / 45.37 / 0.00 / 0.00 / 36
{Phi(year)p(sex*season*year)} / 1906.99 / 47.60 / 0.00 / 0.00 / 40
{Phi(age*season*year)p(sex*season*year)} / 1907.19 / 47.79 / 0.00 / 0.00 / 61
{Phi(sex*year)p(sex*season*year)} / 1908.40 / 49.01 / 0.00 / 0.00 / 47
{Phi(sex*age)p(.)} / 1911.47 / 52.08 / 0.00 / 0.00 / 5
{Phi(age)p(.)} / 1911.88 / 52.49 / 0.00 / 0.00 / 3
{Phi(age*season*year)p(sex)} / 1914.13 / 54.73 / 0.00 / 0.00 / 36
{Phi(sex*season*year)p(sex*season*year)} / 1915.39 / 55.99 / 0.00 / 0.00 / 61
{Phi(season)p(.)} / 1915.39 / 56.00 / 0.00 / 0.00 / 3
{Phi(sex)p(.)} / 1917.54 / 58.15 / 0.00 / 0.00 / 3
{Phi(season*year)p(t)} / 1920.15 / 60.76 / 0.00 / 0.00 / 65
{Phi(t) p(season*year)} / 1921.24 / 61.84 / 0.00 / 0.00 / 54
{Phi(age*season*year)p(.)} / 1922.23 / 62.84 / 0.00 / 0.00 / 35
{Phi(age*season*year)p(sex*year)} / 1922.99 / 63.59 / 0.00 / 0.00 / 47
{Phi(age*season*year)p(year)} / 1925.12 / 65.72 / 0.00 / 0.00 / 40
{Phi(.)p(.)} / 1926.15 / 66.75 / 0.00 / 0.00 / 2
{Phi(age*season*year)p(t)} / 1927.00 / 67.60 / 0.00 / 0.00 / 81
{Phi(year)p(year)} / 1938.51 / 79.11 / 0.00 / 0.00 / 17
{Phi(t) p(sex*season)} / 1940.14 / 80.75 / 0.00 / 0.00 / 54
{Phi(t) p(season)} / 1946.67 / 87.28 / 0.00 / 0.00 / 52
{Phi(sex*age*season*year)p(season*year)} / 1956.00 / 96.60 / 0.00 / 0.00 / 78
{Phi(sex*age*season*year)p(sex*season)} / 1960.82 / 101.43 / 0.00 / 0.00 / 72
{Phi(age*season)p(sex*t)} / 1963.21 / 103.82 / 0.00 / 0.00 / 104
{Phi(sex*age*season*year)p(season)} / 1964.12 / 104.73 / 0.00 / 0.00 / 70
{Phi(t) p(sex*season*year)} / 1967.64 / 108.25 / 0.00 / 0.00 / 80
{Phi(sex*age*season)p(sex*t)} / 1969.82 / 110.43 / 0.00 / 0.00 / 108
{Phi(t) p(.)} / 1976.08 / 116.69 / 0.00 / 0.00 / 51
{Phi(sex*age*season*year)p(sex*season*year)} / 1978.25 / 118.86 / 0.00 / 0.00 / 92
{Phi(t) p(t)} / 1989.06 / 129.67 / 0.00 / 0.00 / 99
{Phi(age*season*year)p(sex*t)} / 2019.06 / 159.67 / 0.00 / 0.00 / 129
{Phi(sex*t) p(season)} / 2036.53 / 177.14 / 0.00 / 0.00 / 102
{Phi(sex*age*t) p(sex*t)} / 2847.96 / 988.57 / 0.00 / 0.00 / 295