data talking to theory, theory talking to data: how can we make the connections? stevan j. arnold...
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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
variance- covariance matrices … Evolution• Jones et al. 2003, 2004, 2007 Stability and evolution of the G-
matrix … 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
• 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 1983correlated characters
• Original goal: Understand the selection gradient,
• 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,
• New goal: Estimate β (and γ) using data from natural populations
zW /ln
sP 1
The selection gradient as the direction of steepest uphill slope on the adaptive landscape
1z
2z
Arnold 1983morphology, 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 ( )wf
A path diagram view of the relationships between morphology, performance and fitness,
showing partitioned selection gradients
Arnold 1983
Arnold & Wade 1984natural 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 plotof Howard’s data, showing that most of the selection body size is due to sexual
selection
Phillips & Arnold 1989visualizing multivariate selection
• Original goal: How can one visualize the selection implied by a set of β- and γ-coefficients?
• 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 1999comparison 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, 2004,2007stability 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 2007paradox 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
z
Wθ
z
p(z)
Lande 1976
Hohenlohe & Arnold 2008MIPoD
• Original goal: Combine data on: inheritance (G-matrix), 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
50
60
70
80
90
100
110
120 130 140 150 160 170 180
body vertebrae
tail
ve
rte
bra
e
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 formtransform 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)
Summary
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)
Wait for it, wait for it …
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.)