Title: How to control for phylogenetic non-independence in comparative analyses: an update on the comparative method
1How 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
2How 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
3Example
F
E
D
Testes size
C
B
A
Degree of sperm competition
4Plain correlation doesnt mean much if species
D, E and F are closely related they could have
evolved larger testes sizes only once
5Methods 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)
61. 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
71. 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
81. 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
9Note Independent contrastsweigh trait values
by the length of the branch leading to it. The
previous example assumed all branches were of
equal length.
10Remarks
- 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
112a. 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
122b. 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
133. 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
144. 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
15Software 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
16Software 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/
17Software 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/
18Example 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.
19Comparative test
t-test, p0.0000000001
n90 species
Wenseleers Ratnieks 2006 Am. Nat.
20Sphecid 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
21Using independent contrasts
after controllingfor phylogeneticnon-independenc
e p0.0002
22Example 2 allometric scaling laws
23West 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