phylogenetic comparative trait and community analyses
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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?
FernsGymnosperms
Angiosperms
Part 1: Evolutionary trees
• 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
= cladograma
node 1
b c
node 2
ch. 3ch. 2
ch. 1
Part 1: Evolutionary trees
• 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
• 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
node 1
b c
node 2
branch
root
tips
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 db c
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 db c
Trees
• Phylogenetic trees can be rotated around their nodes and not change the relationships
a b cd b c ad
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
• Variable• Heritable• Comparable (homologous)• Independent
Characters
• Homology: A character is homologous in > 2 taxa if found or derived from their common ancestor
1 or 1’
1 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
0
1 1
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
chs. 2, 3 = Synapomorphieschs. 5, 6 = Autapomorphiesch. 1 = Symplesiomorphych. 4 = False synapomorphy
a
node 1
b c
node 2
ch. 3ch. 2
ch. 1
ch. 6ch. 4ch. 5ch. 4
1,4,5 1,2,3,4 1,2,3,6
Monophyletic groups
• Monophyletic groups: Contain the common ancestor and all of its descendents
• What are the monophyletic groups?
a db c
–c,d–b,c,d–a,b,c,d
Other groups (not recognized)
• Paraphyletic groups: Contain the common ancestor and some of its descendents
a db cch. 1
Based on sympleisiomorphic character
Other groups (not recognized)
• Polyphyletic groups: Descendants with 2 or more ancestral sources
a db c
Based on false synapomorphy
e
ch. 4
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
• Newick: ((b:1, c:1), a:1):1;• Nexus (output of Paup)• Pagel• Distance matrix
a b ca b c
a 0 3 3b 3 0 2c 3 2 0
Part 2: Hypothesis Testing Using Evolutionary Trees
Part 2: Hypothesis testing
• What sort of hypotheses can we test?– Phylogeography– Evolutionary dating– Phylogenetic community structure– Coevolution/Cospeciation– Mapping characters
• Types of characters• Correlated Change• Dependent Change• Phylogenetic Signal
http://treetapper.org/, http://cran.r-project.org/web/views/Phylogenetics.html
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
• 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:• 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
• 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
• 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– Seed size and seedling size– Body mass and surface area– Fruit size and branch size
Fruit size
Bra
nch
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
• If our phylogeny looked something like this• Then all of the change is really the result of
one evolutionary event
Bra
nch
size
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)
-1
0
1
2
3
trees &lianas
shrubs
Sign test: 32 of 45 are negative (p < 0.01)
Strychnos
Hamelia
Miconia
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 ContrastsCharacter 1 Character 2
A 20 10B 10 40C 2 100D 4 120
050
100150
0 10 20 30
Character 1
Cha
ract
er 2
Independent Contrasts
B C DA
E5
15
10
10
55
G
F
Ch 1 20 10 2 4Ch 2 10 40 100 120
Red = Branch Lengths
X = Character Values, V = Branch Length Values
• 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
Independent Contrasts
X = Character Values, V = Branch Length Values
Independent Contrasts
B C DA
E5
15
10
10
55
G
F
Red = Branch Lengths
X = Character Values, V = Branch Length Values
Ch 1 20 10 2 4Ch 2 10 40 100 120
Independent ContrastsCE1 = 4 - 2 = 2 = 0.63 5 + 5 10
CE2 = 120 - 100 = 20 = 6.325 + 5 10
XE1 = 5 * 4 + 5 * 2 = 10 + 20 = 35 + 5 10
XE2 =5 * 120 + 5 * 100 =600 + 500=110 5 + 5 10
V’E = 10 + 5 * 5 = 10 + 25 = 12.5 5 + 5 10
C D
E
10
55
Ch 1 2 4Ch 2 100 120
X = Character Values, V = Branch Length Values
Independent ContrastsCF1 = 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 =6.910 + 12.5 22.5
XF2=10*110+12.5 *40=1100 +500=71.1 10 + 12.5 22.5
V’F =15 + 10 * 12.5 =15 + 125 =20.6 10 + 12.5 22.5
B
E
15
10
12.5
F
Ch 1 10 3Ch 2 40 110
X = Character Values, V = Branch Length Values
Independent ContrastsCG1 = 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=17.45 + 20.6 25.6
XG2=5*71.1+20.6 *10=355.5 +206=22 5 + 20.6 25.6
A
5
20.6
G
F
Ch 1 20 6.9Ch 2 10 71.1
X = Character Values, V = Branch Length Values
Independent ContrastsContrast 1 Contrast 2
E -2.6 12.1F -1.5 14.8G 0.6 6.3
0
10
20
-4 -2 0 2
Contrast 1
Con
trast
2
Note: these should be fit through the origin
Independent Contrasts
050
100150
0 10 20 30
Character 1
Cha
ract
er 2
0
10
20
-4 -2 0 2
Contrast 1
Con
trast
2
B C DA
E5
15
10
10
55
G
F
E F G
Ch 1 20 10 2 4Ch 2 10 40 100 120
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