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Why do I have to normalise my dataset to do a PERMANOVA?

What is the difference between Euclidean distance and Bray-Curtis similarity? Which is the most suitable for CPUE (abundance) data?

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In general, permutation-based approaches are not as closely tied to distributional assumptions. In the case of the ill-named permanova, or analysis of variance using distance matrices, at least sensu adonis {vegan}, it is the distance matrices that you need to check for compliance with linearity assumptions. This may be a good reference to check.

A rather philosophical question of the difference between a distance and a similarity has a surprising number of bizarre answers if you google it. But it is rather simple: BC is 1-Sorensen index, which gives double weight to double presences in an effort to increase information content of species presence vs. absence (because absences are so ambivalent in ecology: maybe it was not there or maybe you could not catch it in your UE, imo less to do with 'unimodal distribution to environmental gradient' then with the fact that our sampling effort usually sucks). Because it is weighted, it is usually non-Euclidean.

Species matrices such as CPUE are zero-heavy, skewed data, not really special in any other way. Decision on how to treat them is more of an a priori assumption of how valuable your zero data are (hence, whether you should down-weight them), and the general paradigm in that respect in your sub-field at the moment.

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