I suppose z-scoring the data would give them all the same variance (1). Transformations like log and sqrt aren't used to change the variance of a dataset (as far as I know), they're used to change the skewness.

However, I am not sure transformation is ideal. It would be better to just use other methods that don't assume homogeneity of variance. These include non-parametric linear regression (with bootstrapping) and linear mixed effects models.

Thank you, Stephen! Yes, it seems transformation is not the ideal one.

I wonder, what is the contribution of homogenity test to our interpretation of the result of post-hoc test? For example variance is not homogeneous but for one of the species post-hoc says treatment is significantly (p

Good question; others here might be able to give better feedback about how safe it is or isn't to try to interpret results in the face of non-homogeneity (I don't have a strong sense about this), but as for trying to make the variance homogeneous, I always hesitant to do something like this. The difference in variance is a feature of your data, and potentially a meaningful one; by trying to normalize variance you'll be throwing it away. I think it would be preferable to use a test that doesn't require homogeneity of variance. If you have repeated measures (it sounds like you do) then you could do this with a linear mixed-effect model, and (if I recall correctly) these don't have as strong assumptions about stuff like that as ANOVA does. If not, you could still do a non-parametric regression.

Thank you Stephen, I will try the ones you suggested.