We want to determine if there are statistical differences in the structure of the microbial communities of a lake. For this, samples were taken, monthly, for 10 years, from two depths and considering two fractions (particle associated and free-living). In this way, we have a Species-Sites table where in the columns we have the OTUs and in the rows, for each date, the depth-fraction combinations. Normaly we perform the statistical analysis using the function adonis of package Vegan (Permanova). However, we would like to know if it is correct to assume that each one of the dates as repetitions? Is there any other test e.g. mixed model or LASSO that can determine significance in the differences between depths or fractions considering the time series? Any suggestion on how to perform this analysis will be appreciated.
If you want to know what happens month by month, then you can use month as a factor, but it is usual to pool data for years and assess seasonal or yearly changes
One idea is check before which factor influence the pool data and after analyse only the factor influence more your data.
Yes, you have a repeated measures issue. Using monthly samples as replicates adds variability from the annual cycle, and vice versa. You could try the method described in Clarke KR, Somerfield PJ, Airoldi L, Warwick RM (2006) Exploring interactions by second-stage community analyses. J. Exp. Mar. Biol. Ecol. 338:179-192. You need replicated time-series, so probably use the samples from each time-series within each year as replicates, so one factor is depth and the other is year.
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