1. EVOLUTION ALONG SELECTIVE LINES OF LEAST RESISTANCE* Stevan J. Arnold Oregon State University *ppt available on Arnold’s website

2. Overview A visualization of the selection surface tell us more than directional selection gradients can. Selection surfaces and inheritance matrices have major axes (leading eigenvectors). Peak movement along these axes could account for adaptive radiation. We can test for different varieties of peak movement using MIPoD, a software package. A test case using MIPoD: the evolution of vertebral numbers in garter snakes. Conclusions

3. Directional selection gradients and what they tell us 1.Suppose you have data on the fitness ( w ) of each individual in a sample and measurements of values for two traits ( z 1 and z 2 ). 2.You can fit a planar selection surface to the data, which has two regression slopes, β 1 and β 2 : 3.The two slopes are called directional selection gradients. They measure the force of directional selection and can be used to predict the change in the trait means from one generation to the next: e.g., Lande & Arnold 1983

4. Stabilizing selection gradients and what they tell us 1.You can fit a curved (quadratic) selection surface to the data using a slightly more complicated model: 2. γ 11 and γ 22 measure the force of stabilizing (disruptive) selection and are called stabilizing selection gradients. 3. γ 12 measures the force of correlational selection and is called a correlational selection gradient. 4.The two kinds of selection gradients can be used to predict how much the inheritance matrix, G, is changed by selection (within a generation): Lande & Arnold 1983

5. Average value of trait 1 Value of trait 1 Value of trait 2 Average value of trait 2 (a) (b) (c) (d) Individual selection surfaces Adaptive landscapes Selection surfaces and adaptive landscapes have a major axis, ω max Arnold et al. 2008 ω max

6. The G-matrix also has a major axis, g max Arnold et al. 2008 g max

7. Average value of trait 1 Average value of trait 2 Peak movement along ω max could account for correlated evolution: how can we test for it? Arnold et al. 2008

8. MIPoD: Microevolutionary Inference from Patterns of Divergence P. A. Hohenlohe & S. J. Arnold American Naturalist March 2008 Software available online

9. MIPoD: what you can get Input: phylogeny trait values selection surface (≥1) G-matrix (≥1) N e Output: Test for adaptive, correlated evolution Tests for diversifying and stabilizing selection Tests for evolution along genetic lines of least resistance Tests for evolution along selective lines of least resistance neutral process model

10. A test case using MIPoD The evolution of vertebral numbers in garter snakes: a little background body tail

11. Phylogeny of garter snake species based on four mitochondrial genes; vertebral counts on museum specimens de Queiroz et al. 2002 bodytail vertebral counts 190K generations 4.5 Mya ≈ 900,000 generations ago

12. Observe correlated evolution of body and tail vertebral numbers in garter snakes Hohenlohe & Arnold 2008

13. Correlated evolution: described with a 95% confidence ellipse with a major axis, d max d max Hohenlohe & Arnold 2008

14. An adaptive landscape vision of the radiation: a population close to its adaptive peak ω max

15. An adaptive landscape vision of the radiation: peak movement principally along a selective line of least resistance ω max Arnold et al. 2001

16. Vertebral numbers may be an adaptation to vegetation density Jayne 1988, Kelley et al. 1994

17. MIPoD Input: phylogeny of garter snake species mean numbers of body and tail vertebrae selection surfaces (2) G-matrices (3) N e estimates Output: uses a neutral model to assess the importance and kind of selection Hohenlohe & Arnold 2008

18. Arnold 1988 +1σ+2σ -1σ-2σ 0 +1σ +2σ -1σ -2σ 0 body vertebrae tail vertebrae selective line of least resistance ω max Field growth rate as a function of vertebral numbers

19. +1σ+2σ -1σ 0 -2σ +1σ +2σ -1σ -2σ 0 body vertebrae tail vertebrae ω max selective line of least resistance Arnold & Bennett 1988 Crawling speed as a function of vertebral numbers

20. 165175 65 75 85 95 155 body vertebrae tail vertebrae Humboldt T. elegans Lassen T. elegans Similar G-matrices in three poplations, two species Dohm & Garland 1993, Phillips & Arnold 1999 T. sirtalis

21. 165175 65 75 85 95 155 body vertebrae tail vertebrae Humboldt T. elegans Lassen T. elegans Schluter’s conjecture: population differentiation occurs along a genetic line of least resistance, g max Similar G-matrices in three poplations, two species Dohm & Garland 1993, Phillips & Arnold 1999 g max T. sirtalis

22. Estimates of N e for two species from microsatellite data: average N e ≈ 500 Manier & Arnold 2005 T. elegans T. sirtalis

23. Neutral model for a single trait: specifies the distribution of the trait means as replicate lineages diverge Trait means normally distributed with variance proportional to elapsed time, t, and genetic variance, G, and inversely proportional to N e Lande 1976 mean body vertebrae Probability t=200 t=1,000 t=5,000 t=20,000 generations h 2 = 0.4 N e = 1000

24. Neutral model for two traits: as replicate populations diverge, the cloud of trait means is bivariate normal Size: proportional to elapsed time and the size of the average G-matrix, inversely proportional to N e Shape: same as the average G-matrix Orientation: same as the average G-matrix, d max = g max Lande 1979 t=200 t=1,000 t=5,000 generations body vertebrae tail vertebrae

25. Neutral model: equation format One trait, replicate lineages Multiple traits, replicate lineages Multiple traits, lineages on a phylogeny D(t) = G(t/N e ) A(t) = G(T/N e )

26. Neutral model: specifies a trait distribution at time t Trait means are normally distributed with mean μ and variance-covariance A Using that probability, we can write a likelihood expression Using that expression, we can test hypotheses with likelihood ratio tests

27. Neutral model: specifies a trait distribution at time t Trait means are normally distributed with mean μ and variance-covariance GT/N e Using that probability, we can write a likelihood expression Using that expression, we can test hypotheses with likelihood ratio tests

28. Hypothesis testing in the MIPoD maximum likelihood framework bold = parameters estimated by maximum likelihood (95% confidence interval)

29. Size: we observe too little divergence Implication: some force (e.g., stabilizing selection) has constrained divergence P < 0.0001 body vertebrae tail vertebrae Hohenlohe & Arnold 2008

30. Shape:divergence is more elliptical than we expect Implication: the restraining force acts more strongly along PCII than along PCI P = 0.0122 body vertebrae tail vertebrae Hohenlohe & Arnold 2008

31. Orientation: the main axis of divergence is tilted down more than we expect Implication: the main axis of divergence is not a genetic line of least resistance P = 0.0001 body vertebrae tail vertebrae d max g max Hohenlohe & Arnold 2008

32. Divergence occurs along a selective line of least resistance Implication: adaptive peaks predominantly move along a selective line of least resistance Yes, P = 0.2638 No, P = 0.0003 tail vertebrae body vertebrae  max (growth)  max (speed) d max Hohenlohe & Arnold 2008

33. Arnold 1988 +1σ+2σ -1σ-2σ 0 +1σ +2σ -1σ -2σ 0 body vertebrae tail vertebrae Field growth rate as a function of vertebral numbers ω max coincides with d max

34. An adaptive landscape vision of the radiation: peaks move along a selective line of least resistance in the garter snake case Hohenlohe & Arnold 2008

35. General conclusions Using estimates of the selection surface, the G-matrix, N e, and a phylogeny enables us to visualize the adaptive landscape and to assess the role that it plays in adaptive radiation. Need empirical tests for homogeneity of selection surfaces. Need a ML hypothesis testing framework that explicitly incorporates a model of peak movement.

36. Acknowledgements Lynne Houck (Oregon State Univ.) Russell Lande (Imperial College) Albert Bennett (UC, Irvine) Charles Peterson (Idaho State Univ.) Patrick Phillips (Univ. Oregon) Katherine Kelly (Ohio Univ.) Jean Gladstone (Univ. Chicago) John Avise (UC, Irvine) Michael Alfaro (UCLA) Michael Pfrender (Univ. Notre Dame) Mollie Manier (Syracuse Univ.) Anne Bronikowski (Iowa State Univ.) Brittany Barker (Univ. New Mexico) Adam Jones (Texas A&M Univ.) Reinhard Bürger (Univ. Vienna) Suzanne Estes (Portland State Univ.) Paul Hohenlohe (Oregon State Univ.) Beverly Ajie (UC, Davis) Josef Uyeda (Oregon State Univ.)

37. References* Lande & Arnold 1983 Evolution 37: 1210-1226. Arnold et al. 2008 Evolution 62: 2451-2461. Hohenlohe & Arnold 2008 Am Nat 171: 366-385. de Queiroz et al. 2002 Mol Phylo Evol 22:315-329. Estes & Arnold 2007 Am Nat 169: 227-244. Arnold et al. 2001 Genetica 112-113:9-32. Jayne 1988 Kelley et al. 1994 Func Ecol 11:189-198. Arnold 1988 in Proc. 2 nd Internat Conf Quant Genetics Arnold & Bennett 1988 Biol J Linn Soc 34:175-190. Phillips & Arnold 1999 Evolution 43:1209-1222. Dohm & Garland 1993 Copeia 1993: 987-1002. Manier et al. 2007 J Evol Biol 20:1705-1719. Lande 1976 Evolution 30:314-334. Lande 1979 Evolution 33: 402-416. Arnold & Phillips 1999 Evolution 43: 1223- __________________________________________________ * Many are available as pdfs on Arnold’s website