My reply to Andrea the other day bounced from the list and Andrea only copied some of it in his reply so I'm reposting the whole thing in case anyone is interested. (thanks Dennis Slice for helping me with the bounce).

Hi Andrea, Using a Brownian motion model, ancestor reconstructions are essentially means of the tip taxa weighted by the branch lengths connecting them to the nodes. Branch length is arguably more important for the outcome than tree topology. In your example, B and C are likely to have much stronger influence on the reconstruction than A because of this. Consider a scenario in which A, B, and C form a trichotomy and you are trying to reconstruct their ancestral trait value. If they are all extant species they will contribute equally because their branch lengths will be the same, the ancestral estimate would therefore be the simple average of the three. But if B and C are extinct, their branch lengths will be shorter and they will contribute proportionally more to the reconstruction. If B and C lie very close in time to the node, A will have very little impact on the reconstruction. Consider another scenario with relationships ((A,B), C) and you are reconstructing the ancestor of (A,B). If all three taxa are extant, A and B will have the strongest influence because the total branch length between C and the node of interest is longer. However, if C lived only a short time after the base node and if the node (A,B) is deep (closer to the base of the tree than to its tips) then C will have a stronger influence on the ancestral reconstruction of node (A,B) than do the tip taxa A & B. I think part of your question involves the morphology of B and C being poorly estimated (as they might be if you are using mean values of quantitative traits for the tips of A, B, and C). These estimates are also important. If B & C are badly estimated, they will bias the ancestor reconstruction. If they are connected to the nodes by long branches relative to well estimated taxa, the effect will be minimal, but if they are connected by short branches their bias will overwhelm the contribution of better estimated but more distant taxa. With best wishes, David P. David Polly Robert R. Shrock Professor Department of Earth and Atmospheric Sciences Adjunct Professor, Biology and Anthropology Indiana University 1001 E. 10th Street Bloomington, IN 47405-1405 pdpo...@indiana.edu<mailto:pdpo...@indiana.edu> +1 (812) 855-7994 http://pages.iu.edu/~pdpolly/ P. David Polly Robert R. Shrock Professor Department of Earth and Atmospheric Sciences Adjunct Professor, Biology and Anthropology Indiana University 1001 E. 10th Street Bloomington, IN 47405-1405 pdpo...@indiana.edu<mailto:pdpo...@indiana.edu> +1 (812) 855-7994 http://pages.iu.edu/~pdpolly/ On 30 Jul 2018, at 10:57 AM, Polly, P. David <pdpo...@indiana.edu<mailto:pdpo...@indiana.edu>> wrote: Hi Andrea, Using a Brownian motion model, ancestor reconstructions are essentially means of the tip taxa weighted by the branch lengths connecting them to the nodes. Branch length is arguably more important for the outcome than tree topology. In your example, B and C are likely to have much stronger influence on the reconstruction than A because of this. Consider a scenario in which A, B, and C form a trichotomy and you are trying to reconstruct their ancestral trait value. If they are all extant species they will contribute equally because their branch lengths will be the same, the ancestral estimate would therefore be the simple average of the three. But if B and C are extinct, their branch lengths will be shorter and they will contribute proportionally more to the reconstruction. If B and C lie very close in time to the node, A will have very little impact on the reconstruction. Consider another scenario with relationships (A,B), C) and you are reconstructing the ancestor of (A,B). If all three taxa are extant, A and B will have the strongest influence because the total branch length between C and the node of interest is longer. However, if C lived only a short time after the base node and if the node (A,B) is deep (closer to the base of the tree than to its tips) then C will have a stronger influence on the ancestral reconstruction of node (A,B) than do the tip taxa A & B. I think part of your question involves the morphology of B and C being poorly estimated (as they might be if you are using mean values of quantitative traits for the tips of A, B, and C). These estimates are also important. If B & C are badly estimated, they will bias the ancestor reconstruction. If they are connected to the nodes by long branches relative to well estimated taxa, the effect will be minimal, but if they are connected by short branches their bias will overwhelm the contribution of better estimated but more distant taxa. With best wishes, David P. David Polly Robert R. Shrock Professor Department of Earth and Atmospheric Sciences Adjunct Professor, Biology and Anthropology Indiana University 1001 E. 10th Street Bloomington, IN 47405-1405 pdpo...@indiana.edu<mailto:pdpo...@indiana.edu> +1 (812) 855-7994 http://pages.iu.edu/~pdpolly/ On 30 Jul 2018, at 10:33 AM, andrea cardini <alcard...@gmail.com<mailto:alcard...@gmail.com>> wrote: Dear All, a curiosity about ancestral shape reconstruction using comparative methods, which I know very little about. Say I want to reconstruct the shapes of the ancestors of A, B and C. A is a modern lineage for which I have many modern representatives. B and C are extinct clades represented by just a few fossils. I have an independent DNA phylogeny (ancient DNA for the fossils) and I use it for predicting shapes in the nodes of the ABC radiation. Regardless of the likely huge confidence intervals around those predictions, how much will ancestral shapes be influenced by the 'dominance' of A (in terms of species/populations used for the inference) over B and C and how much will instead that depend on the tree topology (specific relationships, branch lengths etc.)? Put it another way: could I (theoretically) bias the reconstruction simply because I inevitably undersample B and C? I suspect there could be a variety of cases ranging from negligible (A representatives are all very recent - and morphological evolution has not accelerated - and well separated by long evolutionary times from B and C) to much less negligible in which reconstructed shapes are strongly biased by 'taxonomic sampling'. I am sure it's already all in the literature but it's not stuff I am working on and just have a 'quick curiosity' I'd like some feedback on from more experienced people. Many thanks in advance for comments and thoughts. Cheers Andrea -- Dr. Andrea Cardini Researcher, Dipartimento di Scienze Chimiche e Geologiche, Università di Modena e Reggio Emilia, Via Campi, 103 - 41125 Modena - Italy tel. 0039 059 2058472 Adjunct Associate Professor, School of Anatomy, Physiology and Human Biology, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia E-mail address: alcard...@gmail.com<mailto:alcard...@gmail.com>, andrea.card...@unimore.it<mailto:andrea.card...@unimore.it> WEBPAGE: https://sites.google.com/site/alcardini/home/main FREE Yellow BOOK on Geometric Morphometrics: http://www.italian-journal-of-mammalogy.it/public/journals/3/issue_241_complete_100.pdf ESTIMATE YOUR GLOBAL FOOTPRINT: http://www.footprintnetwork.org/en/index.php/GFN/page/calculators/ -- MORPHMET may be accessed via its webpage at http://www.morphometrics.org<http://www.morphometrics.org/> --- You received this message because you are subscribed to the Google Groups "MORPHMET" group. 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