Hi Luke,

Thank you so much for your reply!  I never thought about the possibility to 
model the trend as a fixed effect.  After you mentioned it, I think it makes 
sense to me.  

Indeed, after inspecting my data merely by eyes, I think I do find a trend that 
species with longer branches to have longer DNA deletions (the trait that I 
mentioned that always increases).  It's just amazing how I didn't find this 
pattern in the dataset that I've stared at for months.  

Anyway, thank you for your suggestion, and I'll incorporate branch length into 
the model.

Best,
Yanzhu

> -----原始邮件-----
&gt; 发件人: "Luke Matthews" <lmatt...@rand.org>
&gt; 发送时间: 2022-10-18 22:18:22 (星期二)
&gt; 收件人: "r-sig-phylo@r-project.org" <r-sig-phylo@r-project.org>
&gt; 抄送: 
&gt; 主题: [R-sig-phylo] reply to alternative error structures in PGLS
&gt; 
&gt; Hi Yanzhu,
&gt; 
&gt; You raise and excellent question. I think the Brownian model would not be 
statistically correct if implemented naively to a dataset that shows a strong 
trend over time (increase but never decrease). There are a couple ways the 
overall model, however, might be adjusted to accommodate this. If change 
happens at speciation points, then entering a fixed effect variable for the 
number of nodes root-to-tip would, in theory, account for the trend as a fixed 
effect. Then the phylogenetic error term is OK that it is modeling Brownian 
motion, because it is modeling the residual after the trend was already netted 
out by the fixed effect.
&gt; 
&gt; Depending on your biological system, the molecular branch length, or the 
time branch length (with fossils) might be appropriate fixed effects to model a 
trend like this.
&gt; 
&gt; There are also a variety of methods out there to model variation in the 
rates of a trait change down various branches of a tree. Those might be 
relevant to your question, but others on this list serve know much more about 
them than I do.
&gt; 
&gt; My best
&gt; Luke
&gt; 
&gt; -----Original Message-----
&gt; From: R-sig-phylo <r-sig-phylo-boun...@r-project.org> On Behalf Of 
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&gt; Sent: Tuesday, October 18, 2022 6:00 AM
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&gt; Subject: [EXT] R-sig-phylo Digest, Vol 177, Issue 2
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&gt;    1. Alternative error structures in PGLS (jiyan...@ioz.ac.cn)
&gt; 
&gt; ----------------------------------------------------------------------
&gt; 
&gt; Message: 1
&gt; Date: Tue, 18 Oct 2022 09:49:19 +0800 (GMT+08:00)
&gt; From: jiyan...@ioz.ac.cn
&gt; To: r-sig-phylo@r-project.org
&gt; Subject: [R-sig-phylo] Alternative error structures in PGLS
&gt; Message-ID: &lt;3bdf3a4c.4b8c.183e8c7eb1d.coremail.jiyan...@ioz.ac.cn&gt;
&gt; Content-Type: text/plain; charset="utf-8"
&gt; 
&gt; Dear all,
&gt; 
&gt;  
&gt; 
&gt; I have a question related to the residual structure of PGLS models.  If I 
understand correctly, PGLS models implemented in R assume a Brownian motion (or 
lambda model) of the correlation structure of the residuals when using 
corBrownian or corPagel functions.  However, I am just wondering if anyone has 
any idea if these models  could still be applied for PGLS tests where the 
dependent variable does not follow Brownian motion but instead, for example, 
can only increase instead of decrease through time?  If the residuals of OLS 
exhibit phylogenetic signals, would it be sufficient to justify the use of 
Brownian motion to correct for phylogeny? 
&gt; 
&gt;  
&gt; 
&gt; Many thanks!
&gt; 
&gt;  
&gt; 
&gt; Yanzhu
&gt; 
&gt; 
&gt; 
&gt; 
&gt; Yanzhu Ji
&gt; 
&gt; Postdoctoral researcher
&gt; 
&gt; Key Laboratory of Zoological Systematics and Evolution | Institute of 
Zoology | Chinese Academy of Sciences
&gt;    [[alternative HTML version deleted]]
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