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.)