How to control for phylogenetic non-independence in comparative
analyses: an update on the comparative method
Tom WenseleersLaboratorium voor Entomologie
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)
1. Independent contrasts
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)
1. Independent contrasts
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
analyses platform pros cons
Mesquite + PDAP/PDTREE package
- independent contrasts (with binary coding)- Pagel’s 1994 correlation test- pairwise comparisons (Maddison 2000)
PC/Mac very versatileuser interfaceactively developed data export to DISCRETE
http://mesquiteproject.org/mesquite/mesquite.htmlhttp://www.mesquiteproject.org/pdap_mesquite/
COMPARE - independent contrasts, PGLS, PMM, autocorrelation (with binary coding)
web most 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 test PC user interface, data import
http://www.rubic.rdg.ac.uk/meade/Mark/
Software – binary variables
analyses platform pros cons
Mesquite + PDAP/PDTREE package
- independent contrasts (with dummy coding)
PC/Mac very versatileuser interfaceactively developeddata export to MULTISTATE
http://mesquiteproject.org/mesquite/mesquite.htmlhttp://www.mesquiteproject.org/pdap_mesquite/
COMPARE - independent contrasts, PGLS, PMM, autocorrelation (with dummy coding)
web most recent, up-to-date methods
no longer developed, buggy
http://www.indiana.edu/~martinsl/compare/
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