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    $\begingroup$ The sites in your sample can be thought of as random draw from a larger, normally distributed population of all sites you could have chosen. This is why it makes sense to model site as random and year as fixed. There may be a cyclic effect of the seasons throughout the year, but the effect of time is still fixed. So the answer is neither, you have only one random effect. $\endgroup$ Commented Jul 19, 2024 at 13:43
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    $\begingroup$ @FransRodenburg, I totally agree, but I'd point out that that whether effects are fixed or random, and whether they're crossed or nested, are two separate questions. $\endgroup$ Commented Jul 19, 2024 at 15:59