The document discusses assessing the adequacy of phylogenetic trait models by comparing observed trait data to simulated trait data generated under the fitted model. It proposes building a "unit tree" by rescaling branch lengths based on the expected covariance structure implied by the model, so that contrasts on this tree should be independent and normally distributed if the model is adequate. A variety of test statistics can then be computed on the contrasts of the observed data and compared to the distribution of those statistics on simulated contrasts to evaluate the model.
26. When model is not Brownian motion
Contrasts no longer expected to be ~ Gaussian
Rescale branch lengths of phylogeny
27. When model is not Brownian motion
Contrasts no longer expected to be ~ Gaussian
Rescale branch lengths of phylogeny
28. For models that predict tip states to
be multivariate Gaussian
ln L = -0.5[n ln(2Ο) + ln|Ξ£| + (Y - ΞΌX)βΞ£-1(Y - ΞΌX)]
29. For models that predict tip states to
be multivariate Gaussian
ln L = -0.5[n ln(2Ο) + ln|Ξ£| + (Y - ΞΌX)βΞ£-1(Y - ΞΌX)]
Y is the observed tip states for the n species
ΞΌ is the mean of observed data
X is a column vector of 1
Ξ£ is the expected variance-covariance matrix
for the tip states under the model
30. For models that predict tip states to
be multivariate Gaussian
ln L = -0.5[n ln(2Ο) + ln|Ξ£| + (Y - ΞΌX)βΞ£-1(Y - ΞΌX)]
Y is the observed tip states for the n species
ΞΌ is the mean of observed data
X is a column vector of 1
Ξ£ is the expected variance-covariance matrix
for the tip states under the model
31. For models that predict tip states to
be multivariate Gaussian
ln L = -0.5[n ln(2Ο) + ln|Ξ£| + (Y - ΞΌX)βΞ£-1(Y - ΞΌX)]
Y is the observed tip states for the n species
ΞΌ is the mean of observed data
X is a column vector of 1
Ξ£ is the expected variance-covariance matrix
for the tip states under the model
32. For models that predict tip states to
be multivariate Gaussian
ln L = -0.5[n ln(2Ο) + ln|Ξ£| + (Y - ΞΌX)βΞ£-1(Y - ΞΌX)]
Y is the observed tip states for the n species
ΞΌ is the mean of observed data
X is a column vector of 1
Ξ£ is the expected variance-covariance matrix
for the tip states under the model
33. The Ξ£ matrix
If we fit a Ornstein-Uhlenbeck model
Ξ£ij = Ο2/2Ξ±(1-e-2Ξ±T)e-Ξ±Cij
34. The Ξ£ matrix
If we fit a Ornstein-Uhlenbeck model
Ξ£ij = Ο2/2Ξ±(1-e-2Ξ±T)e-Ξ±Cij
Ο2 rate of diο¬usion
Ξ± pull towards optimum
T tree height
Cij shared branch length
between tips i and j
35. The Ξ£ matrix
If we fit a Ornstein-Uhlenbeck model
Ξ£ij = Ο2/2Ξ±(1-e-2Ξ±T)e-Ξ±Cij
Ο2 rate of diο¬usion
Ξ± pull towards optimum
T tree height
Cij shared branch length
between tips i and j
36. The Ξ£ matrix
If we fit a Ornstein-Uhlenbeck model
Ξ£ij = Ο2/2Ξ±(1-e-2Ξ±T)e-Ξ±Cij
Ο2 rate of diο¬usion
Ξ± pull towards optimum
T tree height
Cij shared branch length
between tips i and j
37. The Ξ£ matrix
If we fit a Ornstein-Uhlenbeck model
Ξ£ij = Ο2/2Ξ±(1-e-2Ξ±T)e-Ξ±Cij
Ο2 rate of diο¬usion
Ξ± pull towards optimum
T tree height
Cij shared branch length
between tips i and j
38. Building a unit tree
Rescale branch lengths by the amount of co(variance)
we expect to accumulate under the model
A
B
C
viβ = Ξ£AB - Ξ£AC
vi
40. 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)
41. 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
42. Can compute test statistics on
unit tree contrasts to assess adequacy
67. Analysis of 337 comparative datasets
ξ’ree important plant functional traits
72 datasets (20-2,200 spp.) for specific leaf area
226 datasets (20-22,817 spp.) for seed mass
39 datasets (20-936 spp.) for leaf nitrogen
Wright et al. 2004
Kleyer et al. 2008
Kew SID 2014
69. For each dataset
Fit three simple models of trait evolution
(Brownian Motion, Ornstein-Uhlenbeck, Early Burst)
Compared model fit using AIC
Assessed the adequacy of the best-supported model
70. Model comparison using AIC
Datasets (1-337)
AICw
Brownian motion Ornstein-Uhlenbeck Early Burst
92. Pay attention to parameter estimates
Look carefully at the data
Plot the test statistics
Keep the question in mind
93. Pay attention to parameter estimates
Look carefully at the data
Plot the test statistics
Keep the question in mind
94. Pay attention to parameter estimates
Look carefully at the data
Plot the test statistics
Keep the question in mind
95. Pay attention to parameter estimates
Look carefully at the data
Plot the test statistics
Keep the question in mind
96. Advice and encouragement
Josef Uyeda
Daniel Caetano
Paul Joyce
Graham Slater
Amy Zanne
Roxana Hickey
Anahi Espindola
Simon Uribe-Convers
Funding
NSF
NSERC
NESCent
University of Idaho
NESCent Tempo & mode working group