Do I need a nested random effect if I do not care about decomposing variance within clusters? Consider I have a linear mixed effect model fitted via the R package lme4 with a nested random effect structure as:
model<-lmer(y~x+(1|A/B/C))

If I look at the variances of A, A:B, A:B:C do they tell me how much variance is left in say C when controlling already for the random intercepts in A and B?
If I do not care about this partition, does:
model2<-lmer(y~x+(1|C))

Always gives me aprox. the same total variance of the random effects?
so that the sum of my variances A, A:B, A:B:C in model as given say by the summary()call to the model always is aprox. the same as the variance of C alone in model2 ?
If this is true and I do not care about the variance partitioning of the nested structure can I just stick to model2 then?
I know that the random structure of a model should be based on the study design but when using empirical data it is often not known beforehand and just suspected , e.g. if the taxonomic level has an effect say phylum/genus/family/species.
Here, I would just stick to species as the only random effect then, if I do not care if my variance is in phylum, genus, family or species as using a model with only species would absorb those variances?
If I am however interested in checking how much variance is left in species when controlling for phylum/genus/family I would do phylum/genus/family/species?
Is this correct or how can I interpret the variance partitioning in a nested random effect?
Or should I rather do a likelihood ratio test (AIC, BIC criteria) comparing all possible random effect structures from fully nested to single category each to decide which random effect structure to use?

The variances of A, A:B, A:B:C you see in summary(), plus the variance of the residuals, add up to the variance of y. The variance of the residuals can be found in the summary() output of lme4 in the line Residual.
Thus, if you take the two models:
M1: y ~ x + (1 | A/B/C)

and
M2: y ~ x + (1 | C)

you should indeed get roughly the same sum of variances of residuals and random effects since both consider the same y. However, more complex models will usually create less residual variance (with the possibility of overfitting). So M1, being more complex, i.e. having more parameters (more random effects), will probably have less residual variance, so the sum of the variances of the random effects of M1 will be larger than those of M2.
If you want to know which model is better, you need to apply model selection techniques, e.g. information criteria like AIC or BIC as you have mentioned, or others like cross-validation.
