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Pennell-Evolution-2014-talk

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Talk on assessing the adequacy of phylogenetic trait models. Presented at Evolution 2014.
Transcript:
  • The adequacy of phylogenetic trait models Matthew Pennell @mwpennell
  • In collaboration with Rich FitzJohn Will Cornwell Luke Harmon
  • R2=0.67; p=0.002 R2=0.67; p=0.002 R2=0.67; p=0.002 R2=0.67; p=0.002 Anscombe 1973
  • Is the model appropriate? If not, what are we missing?
  • Is the model appropriate? And if not, what are we missing?
  • For simple regression models Cooksdistance Observation
  • For simple regression models Residuals Fitted values
  • Statistical tests of model adequacy compliment visual intuition
  • For phylogenetic trait models Plotting the relevant data is challenging No general methods for assessing model adequacy
  • Especially for complex models 1 2 3
  • For phylogenetic trait models Plotting the relevant data is challenging No general methods for assessing model adequacy
  • Our approach
  • Establishing scope Quantitative traits Univariate trait models Tip states assume to ~ multivariate Gaussian
  • Fit a model to comparative data Use fitted parameters to simulate data Compare observed to simulated data The general idea
  • The general idea Fit a model to comparative data Use fitted parameters to simulate data Compare observed to simulated data
  • The general idea Fit a model to comparative data Use fitted parameters to simulate data Compare observed to simulated data
  • Old statistical idea Pr(D|) Pr(|D) Parametric bootstrapping Posterior predictive simulation
  • If we re-ran evolution, how likely are we to see a dataset like ours?
  • Simulated data similar to observed Model likely adequate Simulated data very dierent from observed Model likely inadequate
  • Comparing observed to simulated data No two datasets are exactly alike Use test statistics to summarize data in meaningful ways
  • No two datasets are exactly alike Use test statistics to summarize data in meaningful ways Comparing observed to simulated data
  • Species are not independent data points Calculate test-statistics on contrasts Comparing observed to simulated data
  • Species are not independent data points Calculate test statistics on contrasts Comparing observed to simulated data
  • Independent contrasts A B C Ci Cj n-1contrasts for n tips Under BM model C ~ Gaussian(0, )
  • When model is not Brownian motion Contrasts no longer expected to be ~ Gaussian Rescale branch lengths of phylogeny
  • When model is not Brownian motion Contrasts no longer expected to be ~ Gaussian Rescale branch lengths of phylogeny
  • For models that predict tip states to be multivariate Gaussian ln L = -0.5[n ln(2) + ln|| + (Y - X)-1(Y - X)]
  • For models that predict tip states to be multivariate Gaussian ln L = -0.5[n ln(2) + ln|| + (Y - X)-1(Y - X)] Y is the observed tip states for the n species is the mean of observed data X is a column vector of 1 is the expected variance-covariance matrix for the tip states under the model
  • For models that predict tip states to be multivariate Gaussian ln L = -0.5[n ln(2) + ln|| + (Y - X)-1(Y - X)] Y is the observed tip states for the n species is the mean of observed data X is a column vector of 1 is the expected variance-covariance matrix for the tip states under the model
  • For models that predict tip states to be multivariate Gaussian ln L = -0.5[n ln(2) + ln|| + (Y - X)-1(Y - X)] Y is the observed tip states for the n species is the mean of observed data X is a column vector of 1 is the expected variance-covariance matrix for the tip states under the model
  • For models that predict tip states to be multivariate Gaussian ln L = -0.5[n ln(2) + ln|| + (Y - X)-1(Y - X)] Y is the observed tip states for the n species is the mean of observed data X is a column vector of 1 is the expected variance-covariance matrix for the tip states under the model
  • The matrix If we fit a Ornstein-Uhlenbeck model ij = 2/2(1-e-2T)e-Cij
  • The matrix If we fit a Ornstein-Uhlenbeck model ij = 2/2(1-e-2T)e-Cij 2 rate of diusion pull towards optimum T tree height Cij shared branch length between tips i and j
  • The matrix If we fit a Ornstein-Uhlenbeck model ij = 2/2(1-e-2T)e-Cij 2 rate of diusion pull towards optimum T tree height Cij shared branch length between tips i and j
  • The matrix If we fit a Ornstein-Uhlenbeck model ij = 2/2(1-e-2T)e-Cij 2 rate of diusion pull towards optimum T tree height Cij shared branch length between tips i and j
  • The matrix If we fit a Ornstein-Uhlenbeck model ij = 2/2(1-e-2T)e-Cij 2 rate of diusion pull towards optimum T tree height Cij shared branch length between tips i and j
  • Building a unit tree Rescale branch lengths by the amount of co(variance) we expect to accumulate under the model A B C vi = AB - AC vi
  • Unit tree example Ornstein-Uhlenbeck model 2 = 0.5 | = 1 A B C A B C
  • The nice thing about unit trees Transformation applies to most* models of continuous trait evolution If model is adequate, contrasts on unit tree will be I.I.D. ~ Gaussian(0, 1)
  • Also applies to PGLS-style models Create unit tree from parameter estimates Compute contrasts on the residuals If model is adequate contrasts of residuals will be Gaussian(0,1) - same test statistics apply
  • Can compute test statistics on unit tree contrasts to assess adequacy
  • Var(contrasts) |Contrasts| Ancestral state Node height Contrasts2 Density Density Contrasts X CumulativePr } |Contrasts| |Contrasts|
  • Var(contrasts) |Contrasts| Ancestral state Node height Contrasts2 Density Density Contrasts X CumulativePr } |Contrasts| |Contrasts|
  • Var(contrasts) |Contrasts| Ancestral state
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