= Solution
The initial <Poisson regression> contains altitude, temperature, and their <interaction term>, with a <logarithmic link function>. Its interaction <Wald test> has $p=0.521927$, suggesting removal of that term while initially preserving both main effects. The resulting additive model has a negligible temperature effect ($p=0.874$), suggesting a second simplification to altitude alone. The nested <analysis of deviance for nested generalized linear models> gives the same provisional decisions: deviance increases are $83.326-82.916=0.410$ and $83.351-83.326=0.025$, each for one removed coefficient, with approximate $\chi^2_1$ upper-tail probabilities $0.522$ and $0.874$. The <Akaike information criterion> also decreases at each step.
For independent island counts the final proposed model is
$$
Y_i\sim\operatorname{Poisson}(\mu_i),\qquad
\log\mu_i=\beta_0+\beta_aa_i,
$$
with fitted relation
$$
\boxed{\widehat\mu(a)=\exp(3.24926+0.01898a).}
$$
This is an exponential mean relation on the count scale, not a linear relation between count and altitude. One additional metre multiplies the fitted expected count by $e^{0.01898}\approx1.01916$. The null model's insignificance of individual main effects in the interaction fit does not require discarding every predictor: correlated design columns can make those conditional tests imprecise. These reductions concern relative mean complexity under the working <Poisson regression>; the large residual deviance in all three models warns that their variance or mean assumptions still need investigation.
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