If the normal distribution assumption is violated, and you are unable to find a transformation that works (see the Checking assumptions and data transformations tutorial), then you can try a non-parametric test.
A tutorial on non-parametric tests is under development, but will not be deployed until 2023. Consult chapter 13 in the Whitlock & Schluter text, and this website for some R examples.
In general, you might find that the “Kruskal-Wallis” rank sum test is a good non-parametric alternative to ANOVA. This can be implemented using the