Phylogenetic comparative trait
and community analyses
Questions
• Discussions:
– Robbie: posting paper and questions for this week
– Vania & Samoa: will be picking a paper to post for
week after spring break
• Reschedule Monday’s class?
– 9:30-10:45 Wed in Benton 240
• Any questions?
Ferns
Gymnosperms
Angiosperms
Part 1: Evolutionary trees
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What is systematics?
What are phylogenies?
Why are phylogenies useful?
Background information
What is systematics?
• Systematics is the study of the diversity of
organisms and the relationships among these
organisms
Ways to examine relationships
• Evolutionary systematics: Based on similarity as
determined by expert (Mayr, Simpson)
• Phenetics: Based on overall similarity (Rolf,
Sokal, Sneath)
• Cladistics: Based on shared derived characters
(synapomorphies; Hennig)
Ways to examine relationships
• Cladistics: Based on synapomorphies
– Maximum Parsimony: Form the shortest possible
tree (based on minimum steps)
– Maximum Likelihood: Based on probability of
change in character state and then calculate
likelihood that a tree would lead to data (useful for
molecular data)
– Bayesian Inference: Based on the likelihood that the
data would lead to the tree based on prior
probabilities assigned using Bayes Theorem
Part 1: Evolutionary trees
•
•
•
•
What is systematics?
What are phylogenies?
Why are phylogenies useful?
Background information
What are phylogenies?
• Phylogenies are our hypotheses of
evolutionary relationships among groups
(taxa or taxon for singular)
• Graphically represented by trees
• When based on shared derived characters =
c
cladogram a b
node 1
ch. 3
ch. 2
node 2
ch. 1
Part 1: Evolutionary trees
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•
•
•
What is systematics?
What are phylogenies?
Why are phylogenies useful?
Background information
Why are phylogenies useful?
• Useful for studying
– Evolutionary relationships
– Evolution of characters: Correlated (PICs vs. sister pairs),
Signal, Partition variation, Ancestral state, Simulations
– Types (Brownian vs. OU) and rates of evolution
(Homogenous vs. heterogeneous)
– Group ages (fossils, biogeography)
– Diversity/Diversification: Speciation vs. Extinction?
– Biogeographic history
– Community phylogenetics
– Phyloclimatic modeling and conservation
• Assist in
– Identification
– Classification
Part 1: Evolutionary trees
•
•
•
•
What is systematics?
What are phylogenies?
Why are phylogenies useful?
Background information
Background information
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•
•
Trees
Characters
Groups
Other
Trees
• Tips: Living taxa
• Nodes: Common ancestor
• Branches: Can represent time since
divergence
• Root: Common ancestor to all species in study
a
b
c
tips
node 1
branch
root
node 2
Trees
• Sister group: Closest relative to a taxon
– c and d are sister
– b = sister to c,d
– a = sister to b,c,d
a
b
c
d
Trees
• Our goal is to make bifurcating trees
• But a polytomy is when we are unable to
resolve which are the sister taxa (hard vs. soft)
a
b
c
d
Trees
• Phylogenetic trees can be rotated around their
nodes and not change the relationships
d
a
b
c
d
b
c
a
Trees
• Toplogy: shape
• Branch lengths: differentiation (e.g., 1 =
punctuated, speciational) or time =
ultrametric
Characters
• Characters: Attribute (e.g., morphological,
genetic)
– Eye color
– Production of flowers
– Position 33 in gene X
• Character state: Value of that character
– Blue, green, hazel, brown
– Yes, No
– A, T, G, C
Picking Characters
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•
•
•
Variable
Heritable
Comparable (homologous)
Independent
Characters
• Homology: A character is homologous in > 2
taxa if found or derived from their common
ancestor
1
1
1 or 1’
homologous
Homology
• Homology is determined by:
– Similar position or structures
– Similar during development
– Similar genetically
– Evolutionary character series (transformational
homology) from ancestor to descendents
Characters
• Homoplasy: A character is homoplasious in > 2
taxa if the common ancestor did not have this
character
1
1
0
analogous
Homoplasy
• Due to
– Convergent evolution: Similar character states in
unrelated taxa
– Reversals: A derived character state returns to the
ancestral state
Characters
• Apomorphy: Derived character
• Pleisiomorphy: Ancestral character
a
b
c
ch. 2
ch. 1
Characters
• Synapomorphy: Shared derived character
• Autapomorphy: Uniquely derived character
• Symplesiomorphy: Shared ancestral character
1,4,5
a
1,2,3,4
b
ch. 4
ch. 5
ch. 4
1,2,3,6
c
ch. 6
node 1
ch. 3
ch. 2
node 2
ch. 1
chs. 2, 3 = Synapomorphies
chs. 5, 6 = Autapomorphies
ch. 1 = Symplesiomorphy
ch. 4 = False synapomorphy
Monophyletic groups
• Monophyletic groups: Contain the common
ancestor and all of its descendents
• What are the monophyletic groups?
–c,d
–b,c,d
–a,b,c,d
a
b
c
d
Other groups (not recognized)
• Paraphyletic groups: Contain the common
ancestor and some of its descendents
a
b
c
d
ch. 1
Based on
sympleisiomorphic
character
Other groups (not recognized)
• Polyphyletic groups: Descendants with 2 or
more ancestral sources
a
Based on false
synapomorphy
b
c
d
ch. 4
e
Getting trees
• From the literature, Phylomatic, Genbank,
collect data yourself (may need name
scrubbing tools: Phylomatic, TaxonScrubber)
– Methods for assembly: Supertree, Supermatrix,
Megatree, Zip them together
– Getting the topology vs. getting branch lengths?
– Discord among trees based on different
characters? Gene trees vs. species trees
Storing trees
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Newick: ((b:1, c:1), a:1):1;
Nexus (output of Paup)
Pagel
Distance matrix
a
b
c
a
b
c
a
0
3
3
b
3
0
2
c
3
2
0
Part 2: Hypothesis Testing Using
Evolutionary Trees
Part 2: Hypothesis testing
http://treetapper.org/, http://cran.r-project.org/web/views/Phylogenetics.html
• What sort of hypotheses can we test?
– Phylogeography
– Evolutionary dating
– Phylogenetic community structure
– Coevolution/Cospeciation
– Mapping characters
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Types of characters
Correlated Change
Dependent Change
Phylogenetic Signal
When do we need to use
phylogenies?
• Is it always necessary in ecological questions?
– Yes, taxa are not independent points so we must
“correct for” phylogeny
– Sometimes, it is interesting to “incorporate”
phylogenetic hypotheses to see how they
influence our analyses
– No, evolutionary questions can be asked by
incorporating phylogenies but each species
represents a separate successful event and should
be analyzed with that in mind
Part 2: Hypothesis testing
• What sort of hypotheses can we test?
– Phylogenetic community structure
– Mapping characters
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•
•
•
Types of characters
Correlated Change
Dependent Change
Phylogenetic Signal
Phylogenetic Community Structure
• Webb (2000) tested the alternate hypotheses
that co-occurring species are (1) more or (2)
less closely related than a random assembly of
species
• He examined the phylogenetic structure in 28
plots in 150 ha of Bornean forest
Phylogenetic Community Structure
• He found species were more closely related
than a random distribution
Phylogenetic Community Structure
• Recent development of metrics:
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NRI, NTI, PSV, PSC
Do you use abundance or presence/absence?
What regional pool do you compare to?
What null models should you use?
Part 2: Hypothesis testing
• What sort of hypotheses can we test?
– Phylogenetic community structure
– Mapping characters
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•
•
•
Types of characters
Correlated Change
Dependent Change
Phylogenetic Signal
Mapping Characters
• Once we have a known phylogeny, we can
map on characters of interest to test
hypotheses
• The phylogeny must be built on characters
independent of those of interest
Types of Characters
• If we have a character that appears in a
number of taxa, we may
– Test the alternate hypotheses that it is (1)
analogous or (2) homologous
– Test hypotheses as to which state is ancestral and
derived
• We can map the character onto the phylogeny
to test these hypotheses
Homologous vs. Analogous
Characters
Part 2: Hypothesis testing
• What sort of hypotheses can we test?
– Phylogenetic community structure
– Mapping characters
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•
•
•
Types of characters
Correlated Change
Dependent Change
Phylogenetic Signal
Correlated Change
• Comparative biologists often try to test
hypotheses about the relationships between two
or more characters by taking measurements
across many species
Branch size
– Seed size and seedling size
– Body mass and surface area
– Fruit size and branch size
Fruit size
Correlated Change
• We might want to ask whether the
correlation between traits is due to
repeated coordinated evolutionary
divergences
• We might expect closely related species to
resemble one another
Correlated Change
Branch size
• If our phylogeny looked something like this
• Then all of the change is really the result of
one evolutionary event
Fruit size
Correlated Change
• To incorporate phylogeny into comparative
analyses, looking for correlated change, we
can use
– Sister pairs analyses
– Felsenstein’s Independent Contrasts
– Grafen’s Phylogenetic regression (ML and Bayesian
approaches too)
– Pagel’s Discrete and Multistate (Change in
character state)
Sign test: 32 of 45 are negative (p < 0.01)
Strychnos
3
2
1
Hamelia
0
Miconia
-1
trees &
lianas
shrubs
Correlated Change
• To incorporate phylogeny into comparative
analyses, looking for correlated change, we
can use
– Sister pairs analyses
– Felsenstein’s Independent Contrasts (Brownian)
– Grafen’s Phylogenetic regression (Other models)
• ML and Bayesian approaches too
– Pagel’s Discrete and Multistate (Change in
character state)
Independent Contrasts
Character 2
A
B
C
D
Character 1 Character 2
20
10
10
40
2
100
4
120
150
100
50
0
0
10
20
Character 1
30
Independent Contrasts
Ch 1
Ch 2
20
10
10
40
2
100
4
120
A
B
C
D
5
10
5
E
5
10
Red = Branch Lengths
F
15
G
X = Character Values, V = Branch Length Values
Independent Contrasts
• Contrasts values: Ck = Xi – Xj
Vi + Vj
• Ancestral Values: Xk = Vj Xi + Vi Xj
Vi + Vj
• Branch Length: V’k = Vk + Vi Vj
Correction
Vi + Vj
X = Character Values, V = Branch Length Values
Independent Contrasts
Ch 1
Ch 2
20
10
10
40
2
100
4
120
A
B
C
D
5
10
5
E
5
10
Red = Branch Lengths
F
15
G
X = Character Values, V = Branch Length Values
Independent Contrasts
CE1 = 4 - 2 = 2 = 0.63
5 + 5 10
CE2 = 120 - 100 = 20 = 6.32
5+5
10
XE1 = 5 * 4 + 5 * 2 = 10 + 20 = 3
5+5
10
XE2 =5 * 120 + 5 * 100 =600 + 500=110
5+5
10
Ch 1
Ch 2
V’E = 10 + 5 * 5 = 10 + 25 = 12.5
5+5
10
2
100
4
120
C
D
5
X = Character Values, V = Branch Length Values
5
E
10
Independent Contrasts
CF1 = 3 - 10 = -7 = -1.5
10 + 12.5 22.5
CF2 = 110 - 40 = 70 = 14.8
10 + 12.5 22.5
XF1=10 * 3 +12.5 * 10=30 +125 =6.9
10 + 12.5
22.5
XF2=10*110+12.5 *40=1100 +500=71.1
10 + 12.5
22.5
Ch 1
Ch 2
V’F =15 + 10 * 12.5 =15 + 125 =20.6
10 + 12.5
22.5
10
40
3
110
B
10
E
12.5
X = Character Values, V = Branch Length Values
F
15
Independent Contrasts
CG1 = 6.9 - 20 = -13.1 = -2.6
5 + 20.6 25.6
CG2 = 71.1 - 10 = 61.1 = 12.1
5 + 20.6 25.6
XG1=5*6.9+20.6*20=34.5+411=17.4
5 + 20.6
25.6
XG2=5*71.1+20.6 *10=355.5 +206=22
5 + 20.6
25.6
Ch 1
Ch 2
20
10
6.9
71.1
A
5
F
X = Character Values, V = Branch Length Values
20.6
G
Independent Contrasts
Contrast 2
12.1
14.8
6.3
Contrast 2
Contrast 1
E
-2.6
F
-1.5
G
0.6
20
10
0
-4
-2
0
Contrast 1
Note: these should be fit through the origin
2
Independent Contrasts
Ch 1
Ch 2
20
10
Character 2
A
10
40
2
100
4
120
B
C
D
5
150
100
50
0
10
0
10
20
30
E
5
10
Contrast 2
Character 1
20
F
10
G
F
E
15
0
G
-4
-2
0
Contrast 1
2
5
Part 2: Hypothesis testing
• What sort of hypotheses can we test?
– Phylogenetic community structure
– Mapping characters
•
•
•
•
Types of characters
Correlated Change
Dependent Change
Phylogenetic Signal
Dependent Change
• We find that two characters show correlated
change
• We might hypothesize that change in one
character is dependent on the state of a
second character
• This can be tested easily on discrete
characters
– Seed size and disperser size
Dependent Change
Part 2: Hypothesis testing
• What sort of hypotheses can we test?
– Phylogenetic community structure
– Mapping characters
•
•
•
•
Types of characters
Correlated Change
Dependent Change
Phylogenetic Signal
Phylogenetic Signal
• We may want to test the alternate hypotheses
that (1) the evolutionary history or (2) the
recent ecological pressures most strongly
influence species’ characters
• We can examine the amount of “phylogenetic
signal” (whether two closely related species
are more similar than two random species) for
a character
Phylogenetic Signal
Y
Strong correlation
with phylogeny
Weak correlation
with phylogeny
Phylogenetic Signal
• Ackerly: Based on PICs (randomizing across
the tree)
• Pagel’s lambda
• Blomberg’s K: K<1 (overdispersed), K=1
(Brownian random), K>1 (clustered)
• Mantel tests: distance based
Partitioning variation
• Previously done with Taxonomic Hierarchical
ANOVA (e.g., the Family, Genus, Species
levels)
– This assumes that Families are equivalent units
• But instead the % variation in a trait can be
calculated for each node and compared across
the tree