Ecological Archives E093-057-A2

Benedikt R. Schmidt, Walter Hödl, and Michael Schaub. 2012. From metamorphosis to maturity in complex life cycles: equal performance of different juvenile life history pathways. Ecology 93:657–667.

Appendix B. Tables showing model selection results for intermediate steps of the mark-recapture analysis.

TABLE B1. Results of model selection analysis for the relationship between body condition at and date of metamorphosis and body condition at maturity. Linear regression models of body condition (score of first principal component axis of size and body mass) at maturity (PCmat) of spadefoot toads as functions of body condition (score of the first principal component axis of size and body mass; PCmeta) and date at metamorphosis. Males and females were analysed separately. Given are the coefficient of determination (R²), the number of estimated parameters, the difference of the Akaike information criterion of the current and the best model (ΔAIC) and the Akaike weight (AIC weight).

Regression model Model
R²
No.
parameters
ΔAIC AIC
weight
Males
Intercept only 0.000 2 20.73 0.00
Body condition 0.027 3 14.94 0.00
Body condition + body condition² 0.022 4 16.91 0.00
Date 0.000 3 22.41 0.00
Date + date² 0.083 4 0.00 1.00
Body condition + date 0.028 4 15.36 0.00
Body condition + date + body condition × date 0.049 5 10.61 0.00
Females
Intercept only 0.000 2 9.61 0.01
Body condition 0.010 3 8.49 0.01
Body condition + body condition² 0.009 4 9.77 0.00
Date 0.004 3 9.69 0.00
Date + date² 0.016 4 8.25 0.01
Body condition + date 0.055 4 0.00 0.69
Body condition + date + body condition × date 0.051 5 1.81 0.28

Parameter count includes intercept and σ².


TABLE B2. Modelling recapture probabilities of spadefoot toads in relation to sex and time effects. In all models the age of full reproduction was fixed to 6 years, and the probability to reproduce for the first time was age, time and sex-specific (αa[6] × t × ex). Moreover survival was always time-, sex-, and age (2 age classes) dependent (φa2 × sex × t). In the model notification we omit these model parts and only show the recapture part. We also show the fit of the most general model, which considered for each capture cohort of the metamorphs and of the adults time- and sex-dependent survival and recapture probabilities. Subscript t refers to a time effect, subscript sex to a sex-effect, and subscript c to a cohort effect. Given are the for overdispersion corrected deviance (Qdeviance), the number of estimated parameters, the difference of the small sample size and overdispersion adjusted Akaike information criterion of the current and the best model (ΔQAICc) and the Akaike weight (QAICc weight). The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
pt × sex 157.8 76 8.20 0.01
pt + sex 163.9 70 1.85 0.28
pt 164.1 69 0.00 0.71
psex 183.6 65 11.17 0.00
p. 185.2 64 10.72 0.00
φc × t × sex, pc × t × sex 127.2 122 74.74 0.00

TABLE B3. Modelling age of full reproduction (i.e. the age at which as yet inexperienced breeders start to reproduce is 1) of spadefoot toads. In all models survival was kept at its most complex structure (φa2 × t × sex) and recapture probabilities at their most parsimonious structure (pt). The structures for the ages of full reproduction were generally sex-, age- and time-dependent, but with different ages of full reproduction. All combination of the sex-specific age of full reproduction were considered. The figure in parentheses is the age at which full reproduction is reached (i.a. α [1]: age of full reproduction = 1 year). The superscript m refers to males, the superscript f to females. The table entries are the ΔQAICc values and in parentheses the QAIC weights. The overdispersion coefficient was ĉ = 1.385.

  αf[1] αf[2] αf[3] αf[4] αf[5] αf[6]
αm[1] 387.45
(0.00)
228.33
(0.00)
196.55
(0.00)
198.06
(0.00)
223.62
(0.00)
225.67
(0.00)
αm[2] 274.36
(0.00)
67.16
(0.00)
5.78
(0.04)
0.00
(0.75)
3.32
(0.14)
7.44
(0.02)
αm[3] 275.79
(0.00)
76.79
(0.00)
14.09
(0.00)
7.60
(0.02)
10.11
(0.00)
12.17
(0.00)
αm[4] 277.78
(0.00)
80.58
(0.00)
17.33
(0.00)
9.48
(0.01)
13.89
(0.00)
15.95
(0.00)
αm[5] 279.82
(0.00)
85.97
(0.00)
16.85
(0.00)
9.03
(0.01)
10.99
(0.00)
17.20
(0.00)
αm[6] 277.78
(0.00)
92.15
(0.00)
23.03
(0.00)
11.10
(0.00)
15.13
(0.00)
17.20
(0.00)

TABLE B4. Testing for time-dependence of the age-specific probabilities of first time breeding (α) in spadefoot toads. In all models survival (φa2 × t × sex) and recapture probabilities (pt) were kept at their most parsimonious structures. Because only one α is estimated in males, the parameter could only be time-dependent or constant. In the females, 3 different α were estimated for each cohort, and consequently different combinations of time (t) and age (a) combinations are possible. See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
αm[2]t, αf[4]a*t 179.9 53 10.66 0.00
αm[2]t, αf[4]a+t 187.4 46 3.77 0.13
αm[2]t, αf[4]a 193.9 41 0.00 0.85
αm[2], αf[4]a*t 199.5 49 22.04 0.00
αm[2], αf[4]a+t 201.6 42 9.80 0.01
αm[2], αf[4]a 211.7 37 9.70 0.01

TABLE B5. Modelling the general shape of first-year juvenile and adult (i.e. after first-year) survival of spadefoot toads. In all models the recapture probability (pt) and the age-specific probabilities of first time breeding (αm[2]t, αf[4]a) were kept at their most parsimonious structures. Note that the model notation φa2 × t × sex refers to the same model as notation φ1y: t ×sex; ad: t × sex. See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
φ1y: t × sex; ad: t + sex 201.76 34 0.00 0.49
φ1y: t; ad: t + sex 213.14 29 1.21 0.26
φ1y: t + sex; ad: t + sex 213.10 30 3.21 0.10
φ1y: .; ad: t + sex 225.41 25 5.37 0.03
φ1y = ad: t + sex 228.05 24 5.99 0.02
φ1y: t × sex; ad: t × sex 193.85 41 6.37 0.02
φ1y: t + sex; ad: sex 230.91 23 6.82 0.02
φ1y: t × sex; ad: sex 221.25 28 7.30 0.01
φ1y: sex; ad: t + sex 225.39 26 7.38 0.01
φ1y: t + sex; ad: t 220.28 29 8.36 0.01
φ1y: t; ad: t × sex 206.13 36 8.44 0.01
φ1y: t + sex; ad: t × sex 204.57 37 8.92 0.01
φ1y: t; ad: sex 233.13 23 9.04 0.01
φ1y: t × sex; ad: t 214.23 33 10.44 0.00
φ1y: t + sex; ad: . 236.83 22 10.72 0.00
φ1y = ad: t × sex 219.40 31 11.53 0.00
φ1y: .; ad: t × sex 219.42 31 11.56 0.00
φ1y: sex; ad: t × sex 218.72 32 12.89 0.00
φ1y: t × sex; ad: . 231.59 27 15.60 0.00
φ1y: sex; ad: t 236.95 25 16.92 0.00
φ1y = ad: t 248.89 23 24.80 0.00
φ1y: .; ad: t 249.14 24 27.08 0.00
φ1y: t; ad: . 253.96 22 27.85 0.00
φ1y: .; ad: sex 265.59 19 33.42 0.00
φ1y = ad: sex 269.30 18 35.10 0.00
φ1y: sex; ad: sex 265.26 20 35.11 0.00
φ1y: sex; ad: . 272.81 19 40.63 0.00
φ1y = ad: . 287.80 17 51.59 0.00
φ1y: .; ad: . 287.07 18 52.87 0.00

TABLE B6. A posteriori modelling of survival of spadefoot toads directed to test whether there were age-dependent effects. In these models the juvenile first-year survival probability of the females of cohort 1989 is separately estimated from all other survival probabilities (indicated by subscript f89). We tested whether the survival probabilities were age-, sex-, and time dependent. Moreover we tested whether the age of full reproduction in male for the cohorts 1990 to 1993 is the same and only that of cohort 1989 is different (indicated by αm[2]89, 90-93, αf[4]a). In all models the recapture probability (pt) was always kept at its best structure. For comparison we included the best model from the a priori modelling (φ1y: t × sex, ad: t + sex, f89, αm[2]t, αf[4]a). See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
φ1y = ad: t + sex, f89, αm[2]89, 90-93, αf[4]a 219.28 22 0.00 0.70
φ1y = ad: t + sex, f89, αm[2]t, αf[4]a 215.73 25 2.52 0.20
φ1y = ad: t × sex, f89, αm[2] 89, 90-93, αf[4]a 210.14 29 5.05 0.06
φ1y: t × sex, ad: t + sex, f89, αm[2]t, αf[4]a 201.76 34 6.83 0.02
φ1y = ad: t × sex, f89, αm[2]t, αf[4]a 206.49 32 7.49 0.02
φ1y = ad: t, f89, αm[2]89, 90-93, αf[4]a 235.98 21 14.68 0.00
φ1y = ad: t, f89, αm[2]t, αf[4]a 232.45 24 17.22 0.00
φ1y = ad: sex, f89, αm[2]89, 90-93, αf[4]a 267.99 16 36.59 0.00
φ1y = ad: sex, f89, αm[2]t, αf[4]a 265.26 19 39.92 0.00
φ1y = ad: ., f89, αm[2]89, 90-93, αf[4]a 283.82 15 50.40 0.00
φ1y = ad: ., f89, αm[2]t, αf[4]a 281.09 18 53.72 0.00

TABLE B7. Modelling the probabilities of first reproduction at an age of 1 year as function of individual covariates at metamorphosis in male spadefoot toads (αm). These covariates were the scores of the first principal component axes of body mass and size (reflecting body condition, PCmeta) and date at metamorphosis. While modelling α, the other parts of the model were kept at their best structure (φ1y = ad: t + sex, f89, αm[2]89, 90-93, αf[4]a, pt). See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
Cohorts 90 to 93
αm[1] (.) 3530.59 21 4.59 0.06
αm[1] (PCmeta) 3530.39 22 6.42 0.03
αm[1] (PCmeta + PCmeta²) 3530.06 23 8.10 0.01
αm[1] (date) 3527.94 22 3.97 0.09
αm[1] (date + date²) 3521.94 23 0.00 0.64
αm[1] (PCmeta + date) 3526.21 23 4.26 0.08
αm[1] (PCmeta × date) 3523.72 24 3.80 0.10

TABLE B8. Modelling age-specific probabilities of first reproduction in female spadefoot toads (αf) as function of individual covariates at metamorphosis. These covariates were the scores of the first principal component axes of body mass and size (reflecting body condition, PCmeta) and date at metamorphosis.. While modelling a, the other parts of the model were kept at their best structure (φ1y = ad: t + sex, f89, αm[2]89, 90-93, αf[4]a, pt). See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
First-time reproducer at age 1y
αf[4] (.) 3530.59 21 0.00 0.25
αf[4] (PCmeta) 3528.80 22 0.23 0.22
αf[4] (PCmeta + PCmeta²) 3527.43 23 0.89 0.16
αf[4] (date) 3530.04 22 1.47 0.12
αf[4] (date + date²) 3529.77 23 1.21 0.14
αf[4] (PCmeta+date) 3528.63 23 2.09 0.09
αf[4] (PCmeta × date) 3528.59 24 4.07 0.03
First-time reproducer at age 2y
αf[4] (.) 3530.59 21 1.24 0.14
αf[4] (PCmeta) 3527.39 22 0.06 0.26
αf[4] (PCmeta + PCmeta²) 3527.39 23 2.08 0.09
αf[4] (date) 3529.77 22 2.44 0.08
αf[4] (date + date²) 3528.25 23 2.94 0.06
αf[4] (PCmeta + date) 3527.34 23 2.03 0.10
αf[4] (PCmeta × date) 3523.28 24 0.00 0.27
First-time reproducer at age 3y
αf[4] (.) 3530.59 21 0.00 0.36
αf[4] (PCmeta) 3529.92 22 1.35 0.18
αf[4] (PCmeta + PCmeta²) 3529.36 23 2.81 0.09
αf[4] (date) 3530.59 22 2.02 0.13
αf[4] (date + date²) 3530.58 23 2.00 0.13
αf[4] (PCmeta + date) 3529.91 23 3.37 0.07
αf[4] (PCmeta × date) 3529.46 24 4.94 0.03

TABLE B9. Modelling age-specific probabilities of first reproduction (αf) in female spadefoot toads as a function of individual covariates at metamorphosis. These covariates were the scores of the first principal component axes of body mass and size (reflecting body condition, PCmeta) and date at metamorphosis. While modelling a, the other parts of the model were kept at their best structure (φ1y = ad: t + sex, f89, αm[2]89, 90-93, αf[4]a, pt). See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385. Table B8 shows an analysis done separately for ages 1 through 4.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
Additive over all ages
αf[1, 2, 3] (.) 3530.59 21 3.04 0.08
αf[1, 2, 3] (PCmeta) 3525.52 22 0.00 0.37
αf[1, 2, 3] (PCmeta + PCmeta²) 3525.52 23 2.02 0.13
αf[1, 2, 3] (date) 3529.68 22 4.16 0.05
αf[1, 2, 3] (date + date²) 3527.79 23 4.30 0.04
αf[1, 2, 3] (PCmeta + date) 3525.45 23 1.96 0.14
αf[1, 2, 3] (PCmeta × date) 3522.80 24 1.33 0.19

TABLE B10. Modelling the effects of body condition (PCmeta) and date of metamorphosis (date) on first-year juvenile survival probabilities of male and female spadefoot toads. In all models the recapture probability (pt) and the age-specific probabilities of first time breeding (αm[2]t, αf[4]a) were kept at their most parsimonious structures. See Table B2 for the significance of the column headings. The overdispersion coefficient was ĉ = 1.385.

Model QDeviance No.
parameters
ΔQAICc QAICc
weight
Males
φ1y: t 3530.59 21 1.97 0.10
φ1y: t + PCmeta 3528.67 22 2.08 0.09
φ1y: t + PCmeta + PCmeta² 3528.53 23 3.96 0.04
φ1y: t + date 3527.74 22 1.15 0.15
φ1y: t + date + date² 3525.68 23 1.11 0.15
φ1y: t + PCmeta + date 3524.57 23 0.00 0.26
φ1y: t + PCmeta × date 3523.00 24 0.45 0.21
Females
φ1y: t 3530.59 21 0.00 0.35
φ1y: t + PCmeta 3530.27 22 1.71 0.15
φ1y: t + PCmeta + PCmeta² 3529.89 23 3.35 0.07
φ1y: t + date 3529.47 22 0.90 0.23
φ1y: t + date + date² 3529.18 23 2.64 0.09
φ1y: t + PCmeta + date 3529.47 23 2.29 0.08
φ1y: t + PCmeta × date 3529.42 24 4.90 0.03

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