I have a phylogeny and two categorical traits (one binary, one multi-state) mapped to its tips. My claim is that there is a correlation in their phylogenetic distribution, i.e. that they evolved in concert, or dependently.
How can I test that formally?
I have tested for phylogenetic signal using Fritz' D (Fritz & Purvis 2010,Article Selectivity in Mammalian Extinction Risk and Threat Types: a...
)of which there is plenty. But I am stumped on how to show that there is a correlation in presence/absence of one trait and the state of another. I can visualise that in a traitgram/phylomorphospace plot in phytools, but that doesn't give me a number that says "these are not independent".
In principle, phylogenetic independent contrasts (Felsenstein 1985) could be used to test for correlation, right? But PIC is for continuous characters, not categorical ones.
I have found phylogenetic logistic regression (Ives & Garland 2010, https://academic.oup.com/sysbio/article/59/1/9/1723322), but this is only for binary traits. I have read the "Analysis of Phylogenetics and Evolution in R" (Paradis 2012) and "Modern Phylogenetic Comparative Methods and Their Application in Evolutionary Biology" (Garamszegi (Ed.) 2014) books and googled myself to perplexion. I hope someone more knowledgeable can help me!
Many thanks in advance.
Hi Malte,
the formal way to test this would be by doing a model comparison. Let's say that your multi-state character has 3 states (your binary state has 2). This means that there are 6 possible combinations in total: 00, 01, 02, 10, 11, 12 (here I put the binary state first, then the multistate). You might consider each of these a state, and so there can be transitions between these. For example, 00 => 01 is a transition where the multistate character goes from 0 to 1 while the binary state stays the same.
The trick is to now specify a 6 x 6 transition rate matrix whose parameters you define for two (or more) competing hypotheses. For example, in a correlated model where your multistate character cannot have state 0 when the binary character is in state 1, you would set the rates into and/or out of state 10 to rate 0.0. Whereas the rate might be free to be whatever if the characters and states are uncorrelated.
Whatever the right values are is really going to depend on your biological insight: you now have 6 x 6 (minus the diagonal) = 30 different transitions in your rate matrix to play around with and to set up scenarios for.
Once you have set up your competing hypotheses, you will then compute their respective likelihood, and pick the best fitting model. You might do this with AIC, or you might get fancier and use BIC. You might even use multiple phylogenies if you're unsure about those.
For these kinds of analyses I use BayesTraits. I recommend you check it out and go through the manual. Best of luck!
Rutger
Rutger is quite right. You have an 18-parameter model with dependence, and an 8-parameter model without dependence. You can compute the lnL_18 (for the dependence model) and lnL_8 (for the independence model), and use a likelihood ratio test with likelihood ratio chi-square = 2(lnL_18 - lnL_8) with 10 degrees of freedom (for the null hypothesis that the dependence model and the independence model fit the data equally well).
Hello, everyone. You can try to use the threshold model of felsenstein, which in turn was improved and implemented in R by Liam Revell. It basically consists in the estimation of liabilities of a given state to change to another. So, the discrete states become continuous values because the liabilities are estimated during MCMC run. Cheers.
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