Lecture 9

Question 1

character

Answer 1

heritable trait, assumed here to vary between but not within lineages

Question 2

character evolution

Answer 2

1) reconstruct history: seq of ancestral states and inferred changes on branches
or
2) use a model to infer parameters that describe underlying processes of change
-questions about general trends

Question 3

step matrix for parsimony

Answer 3

-costs (relative weights) associated with state changes in parsimony inference of ancestral states

Question 4

Fitch parsimony

Answer 4

default, all costs equal

Question 5

other step matrices (pars)

Answer 5

• asymmetric-> yield equally parsimonious reconstructions that differ in direction of change
• linearly ordered states: abcd

Question 6

parsimony algorithm for estimating ancestral states at node

Answer 6

1) down pass: tips to root, collects info from descendants of node
2) up pass: root to tips, collects info from rest of tree

each traversal visits every internal node-> computes conditional length for each character state

Question 7

What kind of matrix does likelihood inference of ancestral states have?

Answer 7

• matrix of transition rates (Q)

- assume tree has branch lengths measured in expected # of changes

Question 8

transition probability equation

Answer 8

P(t) = e^Qt

P is prob matrix for all combos of ancestor-descendant states for branch of length (t)

Question 9

Likelihood inference of ancestral states process

Answer 9

• down pass calculating conditional likelihoods(CL) for each state at every node
• CL at a node incorporate CLs of immediate descendants (recursion)
• total likelihood at root is sum of CL of states
• find rates (a & b) that maximize TL at root node
• after finding optimal rates-> estimate the fractional likelihoods at internal nodes

Question 10

Likelihood/ancestral states to estimate ML at each node

Answer 10

For each state at each node:

1) fix node to that state
2) recalculate fractional likelihood for that state at root

Question 11

Likelihood ratio test for directional bias in evolution

Answer 11

• estimate likelihood for null hypothesis (a=b) w/1 free parameter
• next estimate L with 2 free parameters (a and b can differ)-> going to be higher
• look at twice the difference in log-likelihood (likelihood ratio)-> will be chi-squared with 1 degree of freedom

Question 12

Brownian motion

Answer 12

• most common null model of evolution for continuous characters
• start at t=0, value = 0; at each step move up or down by amount randomly drawn from normal distribution

Question 13

variance parameter in Brownian motion

Answer 13

rate of random walk

Question 14

squared change parsimony (general)

Answer 14

• used to estimate continuous ancestral states
• find states at internal nodes that minimize the sums of squared ancestor-descendant differences, weighted by branch length

Question 15

squared change parsimony algorithm

Answer 15

1) recursively traverse the tree (down pass)assign states to internal nodes that minimize sum of weighted squared differences of descendant node values
2) up pass: root to tips, adjust internal node values based on parent nodes

Question 16

generalized least-squares to identify if trait values are correlated with phylogenetic divergence

Answer 16

• uses phylogenetic regression model
• each spp’ value treated as random walk from root
• estimate y-intercept(ancestral value at root) and slope (correlation of trait values with divergence), given variance-covariance structure of the tree (e)
• can ask if slope is significant using likelihood ratio tests

Question 17

phylogenetic regression model

Answer 17

y =Xß + e

• y is species’ trait values
• X is spp’ distances from the root
• ß is regression parameters (slope/intercept)
• e is error (residuals)-> the phylogeny

Question 18

How do you determine if the evolution of a character of interest is actually predicted by assumed branch lengths, or if they can be transformed to improve the fit?

Answer 18

likelihood ratio test with kappa parameter that scales branch lengths exponentially
-k=1 means branch lengths are unchanged; gradualism
-k=0: all lengths equal to 1-> indicates character evolution is independent of branch length; punctuated
k>1: on longer branches, more change occurs than expected

Question 19

gradualism

Answer 19

character change predicted by “true” branch lengths; k=1

Question 20

punctuated evolution

Answer 20

character change predicted by equal branch lengths; associated with lineage divergence