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Can anyone help Jeremy specify an asymmetrical “distance” matrix for a partial redundancy analysis?

Trying something new for me: using the blog to get help with a technical issue.

Briefly, I did an microcosm metacommunity experiment in which inter-patch dispersal was experimentally controlled. So I know the rates at which species dispersed from any given patch (microcosm) to any other patch. Some of those rates were zero–not all pairs of patches were connected by dispersal. And dispersal was asymmetrical–the rate of dispersal from patch A to B wasn’t the same as the rate from B to A.

I’d like to code up up the dispersal rates in the form of a “distance” matrix. But the problem is, it wouldn’t be a metric distance matrix since it’d be asymmetrical. It’d just play the same role as a metric distance matrix in the analysis I have in mind. That analysis being a partial redundancy analysis, partitioning the variance in species abundances attributable to environmental variation from that attributable to “space” (here, dispersal). Basically, I want to do the same analysis as in Cottenie 2005 EcoLetts (and many subsequent papers by various authors), the difference being that the “distance” between any two of my patches isn’t determined by their geographic coordinates (since they don’t have any), it’s determined by the experimentally-imposed dispersal rates.

But I can’t figure out how to code up my asymmetrical “distance” matrix  in a form that works with the rda function in the vegan package in R. Note that I’m pretty sure partial redundancy analysis can be done with a non-metric distance matrix (right?), so I think my question here is just a matter of how to get R to do what I want it to do. But I’ve never done any sort of ordination besides PCA, and I only started reading up on redundancy analysis yesterday, and so maybe the problem is that I’m trying to do the impossible. Googling and searching Stack Overflow hasn’t helped, hence my resort to this post.

There’s a beer at the ESA* in it for you if you can help me out, whether in the comments or via email ( Thanks!

*Or equivalent reward