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_at_bio.kuleuven.b
e
Lecture can be downloaded from bio.kuleuven.be/en
to/wenseleers/twpub.htmcourses
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 doesnt 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 reconstructionconcentrated
  changes (Maddison 1990)

6
1. Independent contrasts
Felsenstein 1985, 1988
Trait 1 (6-51) Trait 2 (2-11)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 (9-63) Trait 1 (5-23) contrast (3,3)
5 1
6 2
6 2
9 5
Trait 2 Contrast
Trait 1 Contrast
8
1. Independent contrasts
Trait 1 7.5-5.52 Trait 1 3.5-1.52 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 aevolutionary
  constraint acting on phenotypes (equivalent to
  raw correlation when a0)
• 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
analyses platform pros pros cons
Mesquite PDAP/PDTREE package independent contrasts PC/Mac very versatile user interface actively developed very versatile user interface actively developed
http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//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 no longer developed, buggy
CAIC independent contrasts Mac user interface, data import user interface, data import
http//www.bio.ic.ac.uk/evolve/software/caic/ http//www.bio.ic.ac.uk/evolve/software/caic/ http//www.bio.ic.ac.uk/evolve/software/caic/ http//www.bio.ic.ac.uk/evolve/software/caic/ http//www.bio.ic.ac.uk/evolve/software/caic/ http//www.bio.ic.ac.uk/evolve/software/caic/
CONTRAST package of PHYLIP independent contrasts PC/Mac user inferface user inferface
http//www.indiana.edu/martinsl/compare/
http//evolution.genetics.washington.edu/phylip/ph
ylip.html
16
Software binary variables
analyses platform pros pros cons
Mesquite PDAP/PDTREE package - independent contrasts (with binary coding) Pagels 1994 correlation test pairwise comparisons (Maddison 2000) PC/Mac very versatile user interface actively developed data export to DISCRETE very versatile user interface actively developed data export to DISCRETE
http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//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 no longer developed, buggy
http//www.indiana.edu/martinsl/compare/ http//www.indiana.edu/martinsl/compare/ http//www.indiana.edu/martinsl/compare/ http//www.indiana.edu/martinsl/compare/
MacClade Maddisons concentrated changes test Mac
http//macclade.org/macclade.html http//macclade.org/macclade.html http//macclade.org/macclade.html http//macclade.org/macclade.html
DISCRETE Pagels 1994 correlation test PC user interface, data import user interface, data import
http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/
17
Software categorical variables
analyses platform pros pros cons
Mesquite PDAP/PDTREE package - independent contrasts (with dummy coding) PC/Mac very versatile user interface actively developed data export to MULTISTATE very versatile user interface actively developed data export to MULTISTATE
http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//www.mesquiteproject.org/pdap_mesquite/ http//mesquiteproject.org/mesquite/mesquite.html http//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 no longer developed, buggy
http//www.indiana.edu/martinsl/compare/ http//www.indiana.edu/martinsl/compare/ http//www.indiana.edu/martinsl/compare/ http//www.indiana.edu/martinsl/compare/
MULTISTATE Pagels 1994 correlation test PC user interface, data import user interface, data import
http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/ http//www.rubic.rdg.ac.uk/meade/Mark/
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 queens 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, p0.0000000001
n90 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
Epiponini
wasps
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
n90 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-independenc
e p0.0002
22
Example 2 allometric scaling laws
23
West et al. Science 1999 (Volume
2841677-1679) 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