I am studying differences in microbiome composition across 11 different populations and attempting to identify correlations between microbiome community beta diversity and population-level covariates. I have measurements for ~20 population-level traits but was only able to sample 11 populations with 10 individuals sampled randomly from each population, resulting in a total sample size of ~110 individuals stratified across 11 populations.

I know the number of population-level replicates is regrettably low, but I am wondering how to best leverage my dataset to maximize statistical power while still controlling for population membership of each individual sampled.

My initial thought was that I would have to somehow aggregate the data from each population (e.g. merge the microbiome community data from all individuals within each population) and then run a constrained correspondence analysis comparing the aggregated microbiome community data against the population-level explanatory variables.

However, looking at the documentation for vegan::cca, it appears that I can add "+ Condition(Population)" to the end of the cca formula to control for population. Alternatively, it looks like I could run anova.cca() and include "strata = Population" to control for group membership.

After reading the package documentation, I am still unsure what the underlying distinction is between using "+ Condition(Population)" in the cca model or using "strata = Population" in the anova.cca() command. Can anyone explain this to me? Also, are either of these methods appropriate when population membership is completely confounded with the explanatory variables of interest? E.g. average fiber intake differs between all populations, but we have no information on differences in individual fiber intake within populations.


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