tom wenseleers laboratorium voor entomologie kuleuven [email protected]

How to control for phylogenetic non-independence in comparative

analyses: an update on the comparative method

Tom WenseleersLaboratorium voor Entomologie

[email protected]

Lecture can be downloaded from bio.kuleuven.be/ento/wenseleers/twpub.htm#courses

EvoGen workgroup, June 2006

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?

Example

Degree of sperm competition

Test

es s

ize

AB

CD

E F

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

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

1. Independent contrasts

Trait 1 Contrast

Trai

t 2 C

ontra

st

51

62

62

95

Trait 1: (6-5=1)Trait 2: (2-1=1)contrast: (1,1)

Felsenstein 1985

Felsenstein 1985, 1988

Trait 1 Contrast

Trai

t 2 C

ontra

st

51

62

62

95

Trait 1: (9-6=3)Trait 1: (5-2=3)contrast: (3,3)


Trait 1 Contrast

Trai

t 2 C

ontra

st

51

62

62

95

5.51.5

7.53.5

Averageof

descendents

Trait 1: 7.5-5.5=2Trait 1: 3.5-1.5=2contrast: (2,2)


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

Remarksassumption 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

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 motionallowing estimation of =evolutionary

constraint acting on phenotypes (equivalent to raw correlation when )

implemented in “Compare” program

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

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

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

analyses platform pros cons

Mesquite + PDAP/PDTREE package

independent contrasts PC/Mac very versatileuser interfaceactively developed

http://mesquiteproject.org/mesquite/mesquite.htmlhttp://www.mesquiteproject.org/pdap_mesquite/

COMPARE - independent contrasts- PGLS with alpha- phylogenetic mixed model (PMM)- phylogenetic autocorrelation

web most recent up-to-date methods

no longer developed, buggy

CAIC independent contrasts Mac user interface, data import

http://www.bio.ic.ac.uk/evolve/software/caic/

CONTRAST package of PHYLIP

independent contrasts PC/Mac user inferface

Software – continuous variables

http://www.indiana.edu/~martinsl/compare/

http://evolution.genetics.washington.edu/phylip/phylip.html



- independent contrasts (with binary coding)- Pagel’s 1994 correlation test- pairwise comparisons (Maddison 2000)

PC/Mac very versatileuser interfaceactively developed data export to DISCRETE


COMPARE - independent contrasts, PGLS, PMM, autocorrelation (with binary coding)

web most recent, up-to-date methods



MacClade - Maddison’s concentrated changes test

Mac

http://macclade.org/macclade.html

DISCRETE Pagel’s 1994 correlation test PC user interface, data import

http://www.rubic.rdg.ac.uk/meade/Mark/

Software – binary variables



- independent contrasts (with dummy coding)

PC/Mac very versatileuser interfaceactively developeddata export to MULTISTATE


COMPARE - independent contrasts, PGLS, PMM, autocorrelation (with dummy coding)

web most recent, up-to-date methods



MULTISTATE Pagel’s 1994 correlation test PC user interface, data import

http://www.rubic.rdg.ac.uk/meade/Mark/

Software – categorical variables

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.

Wenseleers & Ratnieks 2006 Am. Nat.

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

% o

f mal

es w

orke

rs‘s

ons

relatedness difference betweenworkers' and queen's sons

0

1

10

100

workers more related to queen's sons

ANTSBEESWASPS

-0.15 -0.10 -0.05 0.00 0.05 0.10 0.15

% o

f mal

es w

orke

rs‘s

ons

relatedness difference betweenworkers' and queen's sons

0

1

10

100

workers more related to queen's sons

ANTSBEESWASPS

Comparative test

n=90 species

t-test, p=0.0000000001

Microstigmus comesAugochlorella striataLasioglossum malachurumLasioglossum laevissimumLasioglossum zephyrumBombus terrestrisBombus hypnorumBombus melanopygusTetragona clavipesTrigona carbonariaTrigona clypearisTrigona hockingsiTrigona mellipesPlebeia droryanaPlebeia remotaPlebeia saiquiSchwarziana quadripunctataMelipona beecheiiMelipona favosaMelipona marginataMelipona quadrifasciataMelipona scutellarisMelipona subnitidaParatrigona subnudaScaptotrigona posticaAustroplebeia australisAustroplebeia symeiApis dorsataApis floreaApis ceranaApis melliferaPolistes chinensisPolistes gallicusPolistes dorsalisPolistes bellicosusPolistes fuscatus variatusPolistes metricusPolybioides tabidusBrachygastra mellificaParachartergus colobopterusVespa ducalisVespa mandariniaVespa crabro flavofasciataVespa crabro gribodiDolichovespula maculataDolichovespula mediaDolichovespula arenariaDolichovespula saxonica LPDolichovespula saxonica HPDolichovespula norwegicaDolichovespula sylvestrisVespula rufaVespula squamosaVespula germanicaVespula maculifronsVespula vulgarisDinoponera quadricepsDorylus molestusIridomyrmex purpureusRhytidoponera chalybaeaRhytidoponera confusaColobopsis nipponicusCamponotus ocreatusLasius nigerFormica fuscaFormica rufaFormica truncorumFormica exsectaFormica sanguineaPolyergus rufescensNothomyrmecia macropsCrematogaster smithiHarpagoxenus sublaevisLeptothorax acervorumLeptothorax allardyceiEpimyrma ravouxiLeptothorax nylanderiLeptothorax unifasciatusProtomognathus americanusAphaenogaster carolinensisMyrmica punctiventrisMyrmica tahoensisMyrmica ruginodisPogonomyrmex rugosusCyphomyrmex costatusCyphomyrmex longiscapusSericomyrmex amabilisTrachymyrmex cf zetekiTrachymyrmex cometzi sp1Acromyrmex echinatiorAcromyrmex octospinosus

Sphecid waspssweat bees

bumblebees

st. bees

honeybees

Polistini

Epiponini

Polistinae

wasps

Vespinae

ants

n=90 species

red: worker policing predicted

Wenseleers & Ratnieks 2006 Am. Nat.

bees

Using independent contrasts

C1

C9

NC4

NC1

C2

C11

C3

C8

C10

C7

NC3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

Contrast in rdiff

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Con

trast

in L

og10

(WPM

+1)

after controllingfor phylogeneticnon-independence:p=0.0002

Example 2: allometric scaling laws

West et al. West et al. ScienceScience 1999 (Volume 284:1677-1679) 1999 (Volume 284:1677-1679)““The fourth dimension of Life: Fractal geometry and allometric scaling The fourth dimension of Life: Fractal geometry and allometric scaling of organisms”of organisms”

Vascular and Vascular and respiratoryrespiratorysystem have a fractalsystem have a fractalgeometrygeometry

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

• 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 = 0.49Large mammal b = 0.96

Lovegrove, Am. Nat. 2000

tom wenseleers laboratorium voor entomologie kuleuven [email protected]

Documents