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Suppose I have a distance matrix created by applying the weighted unifrac measure. For instance, using a phyloseq object:

weighted_unifrac = UniFrac(
  physeq=ps,
  weighted=T,
  normalized=T,
  parallel=T,
  fast=T
)

weighted_unifrac is now a distance matrix. Then I perform PERMANOVA using adonis, and showing the default method parameter:

permanova = adonis(
  formula=weighted_unifrac ~ CaseString, 
  data=sample_data,
  permutations=999,
  method='bray'
  )

What is method doing here? I think of Bray-Curtis as a way to generate the distance matrix itself. How does method="bray" or my choice of another method value affect my PERMANOVA analysis?

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In adonis you can provide either a dissimilarity matrix or a community data matrix. If the left hand side of your formula is a community data matrix, adonis will use the vegdist function to calculate a dissimilarity matrix using the method you've specified (Bray-Curtis by default). If the left hand side of your formula is a dissimilarity matrix then this step is skipped, and method is ignored.

Short answer: "method" doesn't do anything when you pass in a distance matrix

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