This is excellent

Anyway, doing great this morning

There’s not one more cruel, sadistic sports town anywhere. These teams excel at tempting you into hope. They drag you into deep water and drown you

It’s the green light on the dock across the bay?

They don’t deserve it is what I’m saying

Thanks Jesper!

We hope you find this paper and the phylopairs package useful. Please have a read and get in touch if questions arise.

Finally, a major impediment to the comp analysis of LP traits has been a lack of ready-made tools for empiricists to deploy. To help on this front, I created the R package 'phylopairs', a tool entirely devoted to working with LP traits. Phylopairs encodes our method plus previous approaches

The paper goes into much more detail on our approach and a few other methods that have been used in the past. We also provide the first test of the performance of any of the methods that have been used in comparative analyses of LP traits, some of which turn out to be potentially problematic

A major breakthrough for us was stumbling across Isserlis' theorem, which allows us to write the expected covariance among lineage-pairs in terms of the expected covariance among the component lineages (which we know if we have a tree).

From this basic assumption, we can derive metrics for the expected covariance among PAIRS of lineages. In effect, we convert a standard phylogenetic covariance matrix into a lineage-pair covariance matrix -- and we can use this to account for non-independence in comp. studies of lineage-pair traits

Our basis for these expectations is the idea that C and D are similar in some trait(s) due to shared evolutionary history, and this affects the value of the LP traits measured for AC and AD. That is, we assume phylogenetic signal in some underlying character that affects the LP trait we care about

Our answer is that, yes, as a NULL expect'n, AC and AD should be more similar to each other in an LP trait than either is to AB. E.g., if A has strong postzygotic RI w/ species C, then it prob. does so w/ D also. If A competes strongly for food w/ C, it prob does so w/ D as well (as a null expect'n)

We start by considering the following tree. Six lineage-pairs can be derived from this tree, three of which are AB, AC, and AD. We ask: of those three pairs, would we expect any two to be more similar to each other than either is to the third in some continuous lineage-pair trait?