Transcript comparative_method

How to control for phylogenetic
non-independence in comparative
analyses: an update on the
comparative method
Tom Wenseleers
Laboratorium voor Entomologie
KULeuven
[email protected]
Lecture can be downloaded from
bio.kuleuven.be/ento/wenseleers/twpub.htm#courses
EvoGen workgroup, June 2006
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
Testes size
Example
E
F
D
C
B
A
Degree of sperm competition
Plain correlation doesn’t mean much –
if species D, E and F are closely
related they could have evolved
larger testes sizes only once
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 reconstruction
“concentrated changes” (Maddison 1990)
1. Independent contrasts
Felsenstein 1985, 1988
6
2
6
2
9
5
Trait 2 Contrast
5
1
Trait 1: (6-5=1)
Trait 2: (2-1=1)
contrast: (1,1)
Felsenstein 1985
Trait 1 Contrast
1. Independent contrasts
6
2
6
2
9
5
Trait 2 Contrast
5
1
Trait 1: (9-6=3)
Trait 1: (5-2=3)
contrast: (3,3)
Trait 1 Contrast
1. Independent contrasts
6
2
5.5
1.5
6
2
Average
of
descendents
9
5
7.5
3.5
Trait 2 Contrast
5
1
Trait 1: 7.5-5.5=2
Trait 1: 3.5-1.5=2
contrast: (2,2)
Trait 1 Contrast
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.
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
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 a=evolutionary constraint
acting on phenotypes (equivalent to raw
correlation when a=0)
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
Software – continuous variables
Mesquite +
PDAP/PDTREE
package
analyses
platform
pros
independent contrasts
PC/Mac
very versatile
user interface
actively developed
cons
http://mesquiteproject.org/mesquite/mesquite.html
http://www.mesquiteproject.org/pdap_mesquite/
COMPARE
CAIC
- independent contrasts
- PGLS with alpha
- phylogenetic mixed
model (PMM)
- phylogenetic
autocorrelation
web
independent contrasts
Mac
most recent
up-to-date methods
no longer
developed,
buggy
http://www.indiana.edu/~martinsl/compare/
user interface,
data import
http://www.bio.ic.ac.uk/evolve/software/caic/
CONTRAST
package of
PHYLIP
independent contrasts
PC/Mac
user inferface
http://evolution.genetics.washington.edu/phylip/phylip.html
Software – binary variables
Mesquite +
PDAP/PDTREE
package
analyses
platform
pros
- independent contrasts
(with binary coding)
- Pagel’s 1994 correlation test
- pairwise comparisons
(Maddison 2000)
PC/Mac
very versatile
user interface
actively developed
data export to
DISCRETE
cons
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
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 – categorical variables
Mesquite +
PDAP/PDTREE
package
analyses
platform
pros
- independent contrasts
(with dummy coding)
PC/Mac
very versatile
user interface
actively developed
data export to
MULTISTATE
cons
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
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/
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.
% of males workers‘ sons
Comparative test
100
10
ANTS
BEES
WASPS
workers more related
to queen's sons
t-test,
p=0.0000000001
1
0
n=90 species
-0.15 -0.10 -0.05 0.00
0.05
0.10
0.15
relatedness difference between
workers' and queen's sons
Wenseleers & Ratnieks 2006 Am. Nat.
Sphecid wasps
sweat bees
bumblebees
st.
bees
bees
honeybees
Polistini
Polistinae
wasps
Epiponini
Vespinae
ants
n=90 species
red: worker policing predicted
Wenseleers & Ratnieks 2006 Am. Nat.
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
Using independent contrasts
1.2
NC4
C11
Contrast in Log 10(WPM+1)
1.0
C3
C8
0.8
C10
0.6
C7
0.4
C2
C1
0.2
C9
NC3
0.0
NC1
-0.2
after controlling
for phylogenetic
non-independence:
p=0.0002
-0.4
-0.6
0.0
0.1
0.2
0.3
0.4
0.5
Contrast in rdiff
0.6
0.7
Example 2: allometric scaling laws
West et al. Science 1999 (Volume 284:1677-1679)
“The fourth dimension of Life: Fractal geometry and allometric scaling
of organisms”
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
Vascular and respiratory
system have a fractal
geometry
• 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