 Solution

The regression diagnostics raise concerns about the mean and variance assumptions. The residual-versus-fitted smoother is curved rather than horizontal, and the scale-location plot suggests changing residual spread, contrary to homoscedasticity. Diagonal bands are expected when an integer-valued response is fitted by a continuous model, since each fixed response value gives $r=y-\hat{y}$. They are not, by themselves, proof of a failed mean model. The residual Q-Q plot is broadly linear but has tail departures and unusual observations, so exact normality is questionable.

The Cook's distance plot identifies observations worth checking for recording errors and influence on the age estimate. A rough $4/n\simeq 0.023$ screening threshold flags several points, but it is not an automatic deletion rule. Repeat the fit with and without influential observations as a sensitivity analysis and report material changes.

The bird random intercept Q-Q plot has a pronounced upper-tail departure; the year plot is closer to a line, although eleven groups give little power to assess normality. These plotted effects are estimated, shrunken conditional mode of Gaussian random effects, not independent observed draws from the latent normal distribution, so their appearance requires care.

The analysis is therefore provisional. Check a nonlinear age effect, the changing residual variance, dependence beyond the fitted random intercepts, and a response model appropriate for counts. If clutch size is known, a binomial distribution model for hatched eggs out of available eggs may be more meaningful. A bootstrap from the existing Gaussian model cannot validate the assumptions questioned by these plots. Distinguishing within-bird ageing from between-bird differences would also strengthen interpretation.