How to control for phylogenetic non-independence in comparative analyses: an update on the comparative method

1. How to control for phylogenetic non-independence in comparative analyses: an update on the comparative method Tom WenseleersLaboratorium voor EntomologieKULeuven tom.wenseleers@bio.kuleuven.be Lecture can be downloaded from bio.kuleuven.be/ento/wenseleers/twpub.htm#courses EvoGen workgroup, June 2006

2. How to test evolutionary theories? • e.g. more sperm competition should select for larger testes experimental evolution: often not practical interspecific comparison: test whether traits correlate across species • problem: related species may share the same traits due to shared ancestry = phylogenetic non-independence • result is that species cannot be taken as independent data points

3. Example F E D Testes size C B A Degree of sperm competition

4. Plain correlation doesn’t mean much – if species D, E and F are closely related they could have evolved larger testes sizes only once

5. Methods to correct for phylogenetic non-independence 1. independent contrasts (Felsenstein 1985, 1988) 2. extensions of independent contrasts: phylogenetic generalized least squares methods(PGLS, Grafen 1989; Martins and Hansen 1997)phylogenetic mixed model(PMM, Housworth et al. 2004) 3. phylogenetic autocorrelation (Cheverud et al. 1985) 4. ancestral state reconstruction“concentrated changes” (Maddison 1990)

6. 1. Independent contrasts Felsenstein 1985, 1988 Trait 1: (6-5=1) Trait 2: (2-1=1)contrast: (1,1) 5 1 6 2 6 2 9 5 Trait 2 Contrast Trait 1 Contrast Felsenstein 1985

7. 1. Independent contrasts Trait 1: (9-6=3) Trait 1: (5-2=3) contrast: (3,3) 5 1 6 2 6 2 9 5 Trait 2 Contrast Trait 1 Contrast

8. 1. Independent contrasts Trait 1: 7.5-5.5=2 Trait 1: 3.5-1.5=2 contrast: (2,2) 5 1 6 2 6 2 9 5 Average of descendents 5.5 1.5 7.5 3.5 Trait 2 Contrast Trait 1 Contrast

9. Note: Independent contrastsweigh trait values by the length of the branch leading to it. The previous example assumed all branches were of equal length.

10. Remarks • assumption of independent contrasts: evolution by Brownian motion (drift or fluctuating directional selection) • phylogeny: from DNA sequences, morphology,… • branch lengths: ideally divergence times,if unknown use arbitrary lengths, e.g. set all to 1, sometimes need transforming • traits: often Log transformed (to model proportionate changes across a phylogeny), binary variables can be coded as 0/1 • there should be no correlation between the contrasts and branch lengths (standard deviations), otherwise trait or branch lengths may need transforming

11. 2a. Phylogenetic generalized least squares (PGLS) in the simplest case equivalent to independent contrast analysis (Grafen 1989; Martins & Hansen 1997) but various extensions, e.g. allowing for stabilizing selection rather than evolution via Brownian motion allowing estimation of a=evolutionary constraint acting on phenotypes (equivalent to raw correlation when a=0) implemented in “Compare” program

12. 2b. Phylogenetic mixed model (PMM) partitions the phenotypic variance in a data set into phylogenetically heritable and ahistorical components (Housworth et al. 2004) a high phylogenetic heritability, or resemblance among relatives, is indicative of constraints on phenotypic evolution a lack of constraint suggests that phenotypes are free to change in response to other factors that are not strictly inherited, such as environmental variation usually gives a result intermediate between an IC analysis and raw correlation

13. 3. Phylogenetic autocorrelation • partitions variation in each trait into “phylogenetic” or “specific” effects • we “correct” for phylogeny by estimating the “specific” effects and conducting further statistical analyses on these (Cheverud et al. 1985) • approach similar to spatial autocorrelation where neighbouring points can be correlated • all methods discussed so far perform quite well – see Martins et al. 2002 article, and better than nonphylogenetic methods

14. 4. Ancestral state reconstruction “concentrated changes test” for binary characters (Maddison 1990) determines whether changes in a first character are significantly concentrated on those branches on which the second character has a specified state ancestral states of nodes reconstructed using maximum parsimony disadvantage: does not take into accunt uncertainty in reconstruction of ancestral states

15. Software – continuous variables http://www.indiana.edu/~martinsl/compare/ http://evolution.genetics.washington.edu/phylip/phylip.html

16. Software – binary variables

17. Software – categorical variables

18. Example 1: social insects workers can lay eggs other workers frequently remove other workers’ eggs (“worker policing”) Theory: worker policing should occur when workers are on average morerelated to the queen’s sons than to other workers’ sons (Ratnieks 1988). Worker policing should reduce the % of adult males that are workers’ sons.

19. Comparative test t-test, p=0.0000000001 n=90 species Wenseleers & Ratnieks 2006 Am. Nat.

20. Sphecid wasps Microstigmus comes sweat bees Augochlorella striata Lasioglossum malachurum Lasioglossum laevissimum Lasioglossum zephyrum bumblebees Bombus terrestris Bombus hypnorum Bombus melanopygus Tetragona clavipes Trigona carbonaria Trigona clypearis Trigona hockingsi Trigona mellipes Plebeia droryana Plebeia remota st. bees Plebeia saiqui Schwarziana quadripunctata Melipona beecheii Melipona favosa Melipona marginata bees Melipona quadrifasciata Melipona scutellaris Melipona subnitida Paratrigona subnuda Scaptotrigona postica Austroplebeia australis Austroplebeia symei Apis dorsata Apis florea honeybees Apis cerana Apis mellifera Polistes chinensis Polistini Polistes gallicus Polistes dorsalis Polistinae Polistes bellicosus Polistes fuscatus variatus Polistes metricus Polybioides tabidus Brachygastra mellifica wasps Epiponini Parachartergus colobopterus Vespa ducalis Vespa mandarinia Vespa crabro flavofasciata Vespa crabro gribodi Dolichovespula maculata Dolichovespula media Vespinae Dolichovespula arenaria Dolichovespula saxonica LP Dolichovespula saxonica HP Dolichovespula norwegica Dolichovespula sylvestris Vespula rufa Vespula squamosa Vespula germanica Vespula maculifrons Vespula vulgaris Dinoponera quadriceps Dorylus molestus Iridomyrmex purpureus Rhytidoponera chalybaea ants Rhytidoponera confusa Colobopsis nipponicus Camponotus ocreatus Lasius niger Formica fusca Formica rufa Formica truncorum Formica exsecta Formica sanguinea Polyergus rufescens Nothomyrmecia macrops Crematogaster smithi n=90 species Harpagoxenus sublaevis Leptothorax acervorum Leptothorax allardycei Epimyrma ravouxi Leptothorax nylanderi Leptothorax unifasciatus Protomognathus americanus Aphaenogaster carolinensis Myrmica punctiventris red: worker policing predicted Myrmica tahoensis Myrmica ruginodis Pogonomyrmex rugosus Cyphomyrmex costatus Cyphomyrmex longiscapus Sericomyrmex amabilis Wenseleers & Ratnieks 2006 Am. Nat. Trachymyrmex cf zeteki Trachymyrmex cometzi sp1 Acromyrmex echinatior Acromyrmex octospinosus

21. Using independent contrasts after controllingfor phylogeneticnon-independence: p=0.0002

22. Example 2: allometric scaling laws

23. West et al. Science 1999 (Volume 284:1677-1679) “The fourth dimension of Life: Fractal geometry and allometric scaling of organisms” ALLOMETRIC SCALING LAWSe.g. metabolic rate vs body size theory normally predicts a scaling exponent of 2/3, but of 3/4 if fractal geometry is taken into account Vascular and respiratorysystem have a fractalgeometry

24. Performed phylogenetically independent analysis to remove phylogeny from analysis • Result 1: Scaling exponent b varies among animals from different geographic zones • Result 2: Scaling exponent b varies between large and small mammals: Small mammal b = 0.49 Large mammal b = 0.96 Lovegrove, Am. Nat. 2000