Models for Phylogenetic comparative methods and how to diagnose misspecified assumptions Most commonly used models continuous traits Brownian motion BM neutral drift Ornstein Uhlenbeck OU selection toward optimum value What are their assumptions What to do with uncertain branch lengths How do we know we use appropriate branch lengths Brownian motion BM dYt N 0 dt 2 Neutral drift change in y during short time dt is not influenced by the past or by the current state yt BM variance increases with time From Butler King Am Nat 2004 164 683 695 Ornstein Uhlenbeck OU process dYt Yt dt dBt optimum value selection strength dBt neutral drift variation from a BM Selection toward change in y is influenced by the current state yt trend to decrease if yt and to increase if yt Ornstein Uhlenbeck OU process Stable process variance does not increase 2 2 After a long time mean and variance Yt N 2 2 OU stable variance ancestral state forgotten From Butler King Am Nat 2004 164 683 695 OU covariance matrix If the ancestral state at the root is a model parameter 2 2 tij d ij ij V 1 e 2 tij e dij i j OU covariance matrix If the root state NOT a model parameter assume the root has N 2 2 2 d ij ij V e 2 dij i j OU variance matrix is equivalent to BM on same topology but transformed branches ONLY if ultrametric tree Time OU process small large BM variance branch length The paper discussed researchers decisions about branch lengths especially in terms of transformations OU ACDC Do researchers use ultrametric trees for these analyses Not always but I think that we should prefer ultrametric trees Unless Why review the package of the BM assumption What do we really assume BM an assumption package In a nutshell This includes Y N 2V with Vij tij How can we diagnose any problem with these hypotheses Normality usual checks for the normality of contrasts plot Constant variance if ultrametric tree not usually checked But methods to tests if different parts of the tree have different rates Ex variance smaller in one clade compared to another Correct correlations 1 Check independence variance homogeneity of contrasts 2 Or use branch transformation to use the most appropriate correlation structure The three main phylogenetically based statistical methods described in the reading IC GLS and Monte Carlo simulations rely on correct information about tree topology and branch lengths If we are unsure of the correctness of these basic assumptions what is the best way to analyze our data Purpose of branch length transformation meet the BM assumptions Correct branch lengths correct correlation specification 1 Check independence variance homogeneity of contrasts Plot contrasts or absolute values against contrast s SD v i v j contrast s node height There should be no relationship and homogeneous variance from Garland et al 1992 Syst Biol 41 18 32 2 Transform branches to get most appropriate correlations Power transformation p 1 for no change branch length b bp for some p 0 or log b corresponds to p 0 Grafen s rho 1 for no change node height h h for some 0 Pagel s lambda 1 for no change node height h h for some 0 for all internal nodes Keep original tip heights OU like alpha or d e d 1 or 0 for no change but Acceleration Deceleration ACDC g 1 node height h g 1 g 1 for no change 1 g h 1 g 1 for some g 0 2 Transform branches to get most appropriate correlations From Garland et al 1992 Syst Biol 41 18 32 p 0 25 Original tree 0 5 p 0 75 2 p 2 From Diaz Uriarte Garland 1998 Syst Biol 47 654 672 Which transformation change both correlations and variances correlations only Original tree 0 75 0 50 Criteria for choosing the best transformation and its parameter No correlation between absolute contrasts and their SD s No correlation between absolute contrasts and their node heights Largest K value where K measures adequacy of the correlation matrix to the data Blomberg et al 2003 MSE 0 MSE 0 K observed expected MSE tree MSE tree Caution with significance testing Test of 0 iid permute species values reassign to tips Test of 1 BM permute contrasts values reassign them to branches at random Branch lengths transformation It is not clear for me when I should use OU or ACDC branch length transformations If most of the comparative analyses assume a Brownian motion model how do I decide to use OU or ACDC branch length transformations I don t know anything about the rules or circumstances involved in using transformed data I intuitively feel if you alter the data you aren t representing the true data signal The authors mention that OU and ACDC transformations work for well behaved evolutionary models But how do you approach transformations if your evolutionary model is poorly behaved The OU or ACDC transformations feel somewhat circular Now I m thinking of them as tests rather than as a means for inferring the actual timing of cladogenesis If I m trying to examine correlation between a trait and its underlying phylogeny why use ideas about the evolution of the trait to transform the phylogeny Is this a way to test if there were something like stabilizing selection on a given trait In what kinds of subsequent analyses could I use these transformed branch lengths How different are these kinds of transformations for instance ACDC from those that we employ for creating chronometric trees nprs penalized likelihood Quantification and test of phylogenetic signal The article proposes two alternative methods to detect phylogenetic signal randomization and branch length transformation If both methods give consistent results when is it more appropriate to choose one method over another for detecting signal in a data set 3 expresses the idea that a test for phylogenetic signal can be viewed as 1 A test for hierarchical tree structure if BM is assumed Or 2 A test for BM if tree topology branch lengths are known The latter case is less intuitive does this test say more about the evolutionary process than the first case On p 734 the authors recommend a number of tests and steps for a comparative analysis What does this say about the usefulness or validity of comparative studies before this paper or before Felsenstein s oft quoted 1985 paper Lack of phylogenetic signal from character displacement Character displacement results in closely related species being more dissimilar for certain traits when in sympatry than in allopatry Could the low levels of phylogenetic signal exhibited by behavioral traits be the result of such a character displacement The
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