Table 1.
Summary of the posterior distributions of relevant parameters for the three competing models
Parameters | H1. No IH | H2. Fixed IH | H3. Variable IH | ||||||
---|---|---|---|---|---|---|---|---|---|
Mean | 2.5% LCI | 97.5% LCI | Mean | 2.5% LCI | 97.5% LCI | Mean | 2.5% LCI | 97.5% LCI | |
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0.62 | 0.55 | 0.67 | 0.66 | 0.59 | 0.72 | 0.65 | 0.58 | 0.71 |
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0.50 | 0.42 | 0.57 | 0.54 | 0.45 | 0.62 | 0.52 | 0.43 | 0.60 |
ψEE | 0.67 | 0.62 | 0.72 | 0.67 | 0.61 | 0.73 | 0.67 | 0.60 | 0.72 |
ψSE | 0.67 | 0.61 | 0.72 | 0.76 | 0.70 | 0.81 | 0.74 | 0.68 | 0.79 |
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−0.06 | −0.10 | −0.03 | −0.06 | −0.10 | −0.01 | −0.06 | −0.10 | −0.02 |
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−0.08 | −0.12 | −0.04 | −0.10 | −0.15 | −0.06 | −0.09 | −0.14 | −0.05 |
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0.12 | 0.09 | 0.18 | 0.14 | 0.10 | 0.19 | 0.13 | 0.09 | 0.19 |
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– | – | – | 0.15 | 0.13 | 0.18 | 0.13 | 0.10 | 0.16 |
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– | – | – | – | – | – | 0.18 | 0.13 | 0.23 |
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– | – | – | – | – | – | 0.11 | 0.01 | 0.20 |
The acronym “IH” stands for “individual heterogeneity”. The mean, and the lower (2.5%) and upper (97.5%) limits of a 95% credible interval (LCI), of the posterior distribution are shown. Symbols with a star (e.g., ) correspond to parameters which value has been transformed back to the more interpretable scale of a probability of reproduction (i.e., in the interval [0,1]). The parameters displayed in this table are as follows: (i)
, mean reproductive rate, corresponding to a theoretical value (logit−1(μ)) averaging across states (k), ages, years, and individuals; (ii) rates of reproduction, specific to the reproductive state k at t − 1 and averaged across ages, years, and individuals: first-time breeders (ψFE), experienced breeders (ψEE), and skip breeders (ψSE), (iii) first-order
and second-order
age-effect parameters; we note that both posterior means of
and
are negative, but the quadratic trend is still parabolic concave (Fig. 2) because age values were standardized (see Methods); (iv) standard deviation of the normal distribution of random year effects
, of random “baseline” individual effects
, and of random individual effects expressed during iceberg years
; and (v) the correlation between the two types of individual effects (ρα,β).