Ecological Unpredictability

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Phylogenetic comparative methods Comparative
studies (nuisance) Evolutionary studies
(objective) Community ecology (lack of
alternatives)
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Current growth of phylogenetic comparative
methods New statistical methods Availability of
phylogenies Culture
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One of many possible types of problems
or as a special case
This model structure can be used for a variety of
types of problems
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Assumptions y takes continuous values x can be
a random variable or a set of known values
(continuous or not) y is linearly related to
x ? are random variables with expectation 0 and
finite (co)variances that are known
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Statistical methods (P)IC GLS Phylogenetic
independent contrasts Generalized Least
Squares (these are methods, not models) Other
methods for other statistical models ML, REML,
EGLS, GLM, GLMM, GEE, Bayesian methods
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• are random variables with expectation 0 and
  finite (co)variances that are known
• Phylogeny provides a hypothesis for these
  covariances

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What does this represent? How is it
constructed? Is it known for certain?
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Assume that this represents time and is known
without error
Translate into the pattern of covariances in ?
among species
V
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Hypothetical trait for a single species under
Brownian motion evolution
Trait value
possible course of evolution
Time
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another possible course of evolution
Trait value
Time
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another possible course of evolution
Trait value
Time
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Brownian motion evolution gives the hypothetical
variance of a trait
Trait value
Variance
Time
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Brownian motion evolution
Trait value
Variance
Time
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Brownian motion evolution of a hypothetical trait
during speciation
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Variance between species Time
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Total variance Total time
Variance between species Time
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Total variance Total time
Covariance Shared time
Variance between species Time
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Brownian motion
Covariance matrix giving phylogenetic covariances
among species
diagonal elements give the total variance for
species i off-diagonal elements give covariances
between species i and species j
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I am confused by the authors use of "branch
lengths" on page 3023. I'm not sure if "different
types of branch lengths" mean different
phylogenetic analyses or something else I'm not
aware of. Digression - non-Brownian models of
evolution
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Ornstein-Uhlenbeck evolution
Stabilizing selection with strength given by d
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Variance between species lt Time
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Total variance ltlt Total time
Variance between species lt Time
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Ornstein-Uhlenbeck evolution
Time
Variance
Stabilizing selection means information is lost
through time Phylogenetic correlations between
species decrease
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Phylogenetic Signal (Blomberg, Garland, and
Ives 2003)
OU process
? measures the strength of signal
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• Assumptions
• y takes continuous values
• x can be a random variable or a set of known
  numbers
• y is linearly related to x
• are random variables with expectation 0 and
  finite (co)variances that are known
• If d must be estimated, cannot be analyzed using
  PIC or GLS

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If we are dealing with a recent, rapid radiation,
(supported clade but with short branches) will
the lack of branch length data render any PIC not
very informative biologically, because we would
expect non-significant probabilities, based
solely on the branch lengths alone? page 3022,
second paragraph.
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Phylogenetic Signal (Blomberg, Garland, and
Ives 2003)
OU process
? measures the strength of signal
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Statistical methods (P)IC GLS Phylogenetic
independent contrasts Generalized Least
Squares (these are methods, not models) Other
methods for other statistical models ML, REML,
EGLS, GLM, GLMM, GEE, Bayesian methods
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PIC
?1
y1
?4
y4
?2
y2
?3
y3
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?1
y1
?4
y4
?2
y2
?3
y3
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PIC
Regression through the origin
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PIC
You could also use different branch lengths for x
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Branch lengths of y
Branch lengths of x
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PIC
You could also use different branch lengths for x
When could this be justified?
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When could this be justified?
Never (?)
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Statistical methods (P)IC GLS Phylogenetic
independent contrasts Generalized Least
Squares (these are methods, not models) Other
methods for other statistical models ML, REML,
EGLS, GLM, GLMM, GEE, Bayesian methods
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Elements of V are given by shared branch lengths
under the assumption of Brownian motion
evolution
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Generalized Least Squares, GLS
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Ordinary least squares
V I
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Related to ordinary least squares
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Values of
are linear combinations of yi
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If IC and GLS can yield identical results and the
authors refer to IC as "a special case of GLS
models" (p. 3032), in what situation(s) would GLS
be a more appropriate method? In other words, why
not just use IC?
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Divergence time for desert and montane ringtail
populations assumed to be 10,000 years
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Predicting values for ancestral and new species
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Is the prediction of the estimate of y for
species I more or less precise than what you
would expect from a standard regression analysis?
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When dealing with multiple, incongruent gene
trees, we can perform multiple PIC's on each
tree, and find a correlation or not. How do we
know which is the "right" answer? 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?
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• I'm unclear how data can be statistically
  significant when transformed, but not significant
  otherwise. This seems like cheating/lying.
• The paper discussed researchers' decisions about
  branch lengths, especially in terms of
  transformations (OU, ACDC). Do researchers use
  ultrametric trees for these analyses?