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What would be an appropriate method for meta-analyzing a set of five ecological dissimilarity matrices to generate an overall 'pooled' effect size? I have five ecological monitoring datasets that each recorded community structure through time at "control" sites and "treatment" sites (some have shared sites, others do not, but the treatment levels are the same). Each dataset was collected using different methods, but using the same treatment levels (control, treatment). I am interested in meta-analyzing community structure change before and after a drought across the different monitoring datasets and the two treatment levels. I've thoroughly analyzed the within-group changes using Bray-Curtis dissimilarity nMDS plots and PERMANOVAs. Now I'd like to generate on overall 'pooled' effect that describes the synthetic change across the different communities. What is an appropriate method to do this?

The figure below shows the B-C distance between the before-drought centroid and the after-drought centroid for the two treatment levels, and for each community dataset (using vegan::betadisper in R) . The error bars are simply the pooled standard deviation between the two time periods (before vs. after). Would it be appropriate to calculate a pooled effect size using the mean across the different datasets, weighted by the number of 'sites' for each community (communities with more 'sites' have higher weight in the pooled effect)?

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I'm not 100% sure you can do this using distance matrices. I'd advocate for the use of model-based methods (e.g., gllvm, HMSC or mvabund), which can take multivariate abundance data following a probability distribution, that allow you to calculate test statistics. From these you can then compare between different datasets.

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