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

2. 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 How to test evolutionary theories?

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

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. 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) Methods to correct for phylogenetic non-independence

6. 1. Independent contrasts Trait 1 Contrast Trait 2 Contrast 5151 6262 6262 9595 Trait 1: (6-5=1) Trait 2: (2-1=1) contrast: (1,1) Felsenstein 1985 Felsenstein 1985, 1988

7. Trait 1 Contrast Trait 2 Contrast 5151 6262 6262 9595 Trait 1: (9-6=3) Trait 1: (5-2=3) contrast: (3,3) 1. Independent contrasts

8. Trait 1 Contrast Trait 2 Contrast 5151 6262 6262 9595 5.5 1.5 7.5 3.5 Average of descendents Trait 1: 7.5-5.5=2 Trait 1: 3.5-1.5=2 contrast: (2,2) 1. Independent contrasts

9. Note: Independent contrasts weigh 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  =evolutionary constraint acting on phenotypes (equivalent to raw correlation when  ) 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. analysesplatformproscons Mesquite + PDAP/PDTREE package independent contrastsPC/Macvery versatile user interface actively developed http://mesquiteproject.org/mesquite/mesquite.html http://www.mesquiteproject.org/pdap_mesquite/ COMPARE - independent contrasts - PGLS with alpha - phylogenetic mixed model (PMM) - phylogenetic autocorrelation webmost recent up-to-date methods no longer developed, buggy CAIC independent contrastsMacuser interface, data import http://www.bio.ic.ac.uk/evolve/software/caic/ CONTRAST package of PHYLIP independent contrastsPC/Macuser inferface Software – continuous variables http://www.indiana.edu/~martinsl/compare/ http://evolution.genetics.washington.edu/phylip/phylip.html

16. analysesplatformproscons Mesquite + PDAP/PDTREE package - independent contrasts (with binary coding) - Pagel’s 1994 correlation test - pairwise comparisons (Maddison 2000) PC/Macvery versatile user interface actively developed data export to DISCRETE http://mesquiteproject.org/mesquite/mesquite.html http://www.mesquiteproject.org/pdap_mesquite/ COMPARE - independent contrasts, PGLS, PMM, autocorrelation (with binary coding) webmost recent, up-to-date methods no longer developed, buggy http://www.indiana.edu/~martinsl/compare/ MacClade - Maddison’s concentrated changes test Mac http://macclade.org/macclade.html DISCRETE Pagel’s 1994 correlation testPCuser interface, data import http://www.rubic.rdg.ac.uk/meade/Mark/ Software – binary variables

17. analysesplatformproscons Mesquite + PDAP/PDTREE package - independent contrasts (with dummy coding) PC/Macvery versatile user interface actively developed data export to MULTISTATE http://mesquiteproject.org/mesquite/mesquite.html http://www.mesquiteproject.org/pdap_mesquite/ COMPARE - independent contrasts, PGLS, PMM, autocorrelation (with dummy coding) webmost recent, up-to-date methods no longer developed, buggy http://www.indiana.edu/~martinsl/compare/ MULTISTATE Pagel’s 1994 correlation testPCuser interface, data import http://www.rubic.rdg.ac.uk/meade/Mark/ 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 more related 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. Wenseleers & Ratnieks 2006 Am. Nat. Comparative test n=90 species t-test, p=0.0000000001

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

21. Using independent contrasts after controlling for phylogenetic non-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” Vascular and respiratory system have a fractal geometry ALLOMETRIC SCALING LAWS e.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

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