phylogenetic comparative trait and community analyses

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. 5

ch. 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 c

ch. 1Based 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

siz

e

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

siz

e

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

0

50

100

150

0 10 20 30

Character 1

Ch

ara

cte

r 2

Independent Contrasts

B C DA

E

5

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

E

5

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 = 6.32

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

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 =6.9

10 + 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=17.4

5 + 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

Co

ntr

as

t 2

Note: these should be fit through the origin

Independent Contrasts

0

50

100

150

0 10 20 30

Character 1

Ch

ara

cte

r 2

0

10

20

-4 -2 0 2

Contrast 1

Co

ntr

as

t 2

B C DA

E

5

15

10

10

55

G

F

E FG

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