Transcript Measuring Evolution - Oregon State University

Data talking to theory, theory
talking to data: how can we make
the connections?
Stevan J. Arnold
Oregon State University
Corvallis, OR
Conclusions
• The most cited scientific articles are methods,
reviews, and conceptual pieces
• A worthy goal in methods papers is to connect
the best data to the most powerful theory
• The most useful theory is formulated in terms of
measureable parameters
• Obstacles to making the data-theory connection
can lie with the data, the theory or because the
solution resides in a different field
• Sometimes a good solution is worth waiting for
The papers
• Lande & Arnold 1983 The measurement of selection on correlated
characters. Evolution
• Arnold 1983 Morphology, performance, and fitness. American
Zoologist
• Arnold & Wade 1984 On the measurement of natural and sexual
selection … Evolution
• Phillips & Arnold 1989 Visualizing multivariate selection.
Evolution
• Phillips & Arnold 1999 Hierarchial comparison of genetic variancecovariance matrices … Evolution
• Jones et al. 2003, 2004, 2007 Stability and evolution of the Gmatrix … Evolution
• Estes & Arnold 2007 Resolving the paradox of stasis … American
Naturalist
• Hohenlohe & Arnold 2008 MIPoD: a hypothesis testing framework
for microevolutionary inference … American Naturalist
Citations
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Lande & Arnold 1983 ……………..1454
Arnold 1983 …………………………413
Arnold & Wade 1984………………..560
Phillips & Arnold 1989 ……………..165
Phillips & Arnold 1999 …………......123
Jones et al. 2003, 2004, 2007 ………76
Estes & Arnold 2007………………….24
Hohenlohe & Arnold 2008 …………....2
Format
• Original goal: What we were looking for in
the first place
• Obstacle: Why we couldn’t get there
• Epiphany: How we got past the block
• New goal: What we could do once we got
past the block
Lande & Arnold 1983
correlated characters
• Original goal: Understand the selection
gradient,    ln W / z
• Obstacle: β impossible to estimate because it
is the first derivative of an adaptive landscape
• Epiphany: β is also a vector of partial
regressions of fitness on traits,   P 1s
• New goal: Estimate β (and γ) using data from
natural populations
The selection gradient as the direction of steepest
uphill slope on the adaptive landscape
z2
z1
Arnold 1983
morphology, performance, & fitness
• Original goal: What is the relationship between
performance studies and selection?
• Obstacle: Performance measures are distantly
related to fitness
• Epiphany: Recognize two parts to fitness and
selection (β), one easy to measure, the other
difficult
• New goal: Estimate selection gradients
corresponding to these two parts (    f  w )
A path diagram view of the relationships
between morphology, performance and fitness,
showing partitioned selection gradients
Arnold 1983
Arnold & Wade 1984
natural vs. sexual selection
• Original goal: Find a way to measure sexual
selection using Howard’s (1979) data
• Obstacle: Howard used multiple measures of
reproductive success
• Epiphany: Use a multiplicative model of fitness
to analyze multiple episodes of selection
• New goal: Measure the force of natural vs.
sexual selection
Howard’s 1979 data table
Arnold & Wade’s 1984 parameterization of Howard’s data
Howard’s 1979 plot showing selection of body size
Arnold & Wade’s 1984 analysis and plot
of Howard’s data, showing that most of
the selection body size is due to sexual
selection
Phillips & Arnold 1989
visualizing multivariate selection
• Original goal: How can one visualize the
selection implied by a set of β- and γcoefficients?
• Obstacle: Univariate and even bivariate
diagrams can be misleading, so what is the
solution?
• Epiphany: Canonical analysis is a long-standing
solution to this standard problem
• New goal: Adapt canonical analysis to the
interpretation of selection surfaces
The canonical solution is a rotation of axes
Arnold et al. 2008
Phillips & Arnold 1999
comparison of G-matrices
• Original goal: How can one test for the
equality and proportionality of G-matrices
• Obstacle: Sampling covariances (family
structure) complicates test statistics
• Epiphany: Use Flury’s (1988) hierarchial
approach; use bootstrapping to account
for family structure
• New goal: Implement a hierarchy of tests
that compares eigenvectors and values
The G-matrix can be portrayed as an ellipse
Arnold et al. 2008
The Flury hierarchy of matrix comparisons
Arnold et al. 2008
Jones et al. 2003, 2004,2007
stability and evolution of G
• Original goal: What governs the stability
and evolution of the G-matrix?
• Obstacle: No theory accounts
simultaneously for selection and finite
population size
• Epiphany: Use simulations
• New goal: Define the conditions under
which the G-matrix is least and most
stable
Alignment of mutation and
selection stabilizes the G-matrix
Arnold et al. 2008
Estes & Arnold 2007
paradox of stasis
• Original goal: Use Gingerich’s (2001) data to
test stochastic models of evolutionary process
• Obstacle: Data in the form of rate as a function
of elapsed time; models make predictions about
divergence as a function of time
• Epiphany: Recast the data so they’re in the
same form as the models
• New goal: Test representatives of all available
classes of stochastic models using the data
Gingerich’s 2001 plot, showing decreasing rates
as a function of elapsed time
Estes and Arnold 2007 plot of Gingerich’s data in a format for
testing stochastic models of evolutionary process
DISPLACED OPTIMUM MODEL
θ
W
z
p(z)
z
Lande 1976
Hohenlohe & Arnold 2008
MIPoD
• Original goal: Combine data on: inheritance (Gmatrix), effective population size (Ne), selection,
divergence and phylogeny to make inferences
about processes producing adaptive radiations
• Obstacle: What theory?
• Epiphany: Use neutral theory; use maximum
likelihood to combine the data
• New goal: Implement a hierarchy of tests that
compares the G-matrix with the divergence
matrix (comparison of eigenvectors and values)
An adaptive landscape vision of the radiation:
peak movement along a selective line of least
resistance
110
tail vertebrae
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120
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body vertebrae
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Summary
Paper
Goal
Obstace
Epiphany
Lande & Arnold 1983
conceptual
data to theory connection not apparent
algebraic revelation
Arnold 1983
data to theory connection
wrong fitness currency
use multiplicative ftiness model
Arnold & Wade 1984
data to theory connection
wrong fitness currency
use multiplicative ftiness model
Phillips & Arnold
1989
conceptual
available solution not applied
apply solution (canonical analysis)
Phillips & Arnold
1999
statistical
available solution not applied
apply solution (Flury hierarchy)
Jones et al. 2003-7
theoretical
no theory / limited data
simulate
Estes & Arnold 2007
data to theory connection
data in wrong form
transform data so they mesh with
theory
Hohenlohe & Arnold
2008
data to theory connection
data to theory connection not apparent
use neutral theory (+ Flury
hierarchy & ML)
Wait for it, wait for it …
Paper
Goal
Obstacle
Epiphany
Lande & Arnold 1983
conceptual
4 years
algebraic revelation
Arnold 1983
data to theory connection
weeks
use multiplicative ftiness model
Arnold & Wade 1984
data to theory connection
weeks
use multiplicative ftiness model
Phillips & Arnold 1989
conceptual
months
apply solution (canonical analysis)
Phillips & Arnold 1999
statistical
10 years
apply solution (Flury hierarchy + bootsrapping)
Jones et al. 2003-7
theoretical
1 year
simulate
Estes & Arnold 2007
data to theory connection
weeks
transform data so they mesh with theory
Hohenlohe & Arnold 2008
data to theory connection
10 years
use neutral theory (+ Flury hierarchy & ML)
Conclusions
• The most cited scientific articles are methods,
reviews, and conceptual pieces
• A worthy goal in methods papers is to connect
the best data to the most powerful theory
• The most useful theory is formulated in terms of
measureable parameters
• Obstacles to making the data-theory connection
can lie with the data, the theory, or because the
solution resides in a different field or needs to be
invented
• Sometimes a good solution is worth waiting for
Acknowledgments
Russell Lande (Imperial College)
Michael J. Wade (Indiana Univ)
Patrick C. Phillips (Univ. Oregon)
Adam G. Jones (Texas A&M
Univ.)
Reinhard Bürger (Univ. Vienna)
Suzanne Estes (Portland State
Univ.)
Paul A. Hohenlohe (Oregon State
Univ.)