= Solution
Conditional predictions for observed birds and years add their fitted <random intercepts> to the fixed part of the <Gaussian linear mixed model>:
$$
\boxed{\widehat Y_{11,2012}=2.274+0.123(3)+0.383420+0.023624=3.050044},
$$
$$
\boxed{\widehat Y_{12,2014}=2.274+0.123(7)-0.426676-0.056633=2.651691}.
$$
These are predicted <expected values>, so they need not be <integers>. The first is likely more reliable: age three is within the displayed age range, whereas age seven requires <extrapolation> beyond ages one to six. A quantitative comparison would need the <prediction intervals>, including uncertainty in both fixed coefficients and <random effects>; the displayed coefficients alone do not supply them.
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