lecture 3

Question 1

cladograms, phylograms, and chronograms have

Answer 1

branch lengths that contain useful information.

Question 2

phylogenetic methods

Answer 2

• goal: need to estimate phylogeny.
• approach:
  1. collect data (evidence)
  2. align data (homology)
  3. find the “best” tree (phylogenetic analysis)

Question 3

types of data

Answer 3

morphology and molecular.

Question 4

phylogenetic methods

Answer 4

distance-based methods, maximum parsimony, maximum likelihood, and Bayesian inference.

Question 5

distance based methods steps

Answer 5

• step 1: convert data to a measure of genetic distance between each pair of sequences.
• step 2: calculate a tree using the table of genetic disorders.

Question 6

distance based methods process

Answer 6

1. sequence alignment
2. distances between sequences -> distance tables
3. calculate unrooted tree

Question 7

distanced based methods pros

Answer 7

ultra-fast and can handle large number of species.

Question 8

distance based methods cons

Answer 8

replaces sequences with distances, has problems when distances are tied, and no model of evolution.

Question 9

maximum parsimony

Answer 9

find the tree that explains the observed data with a minimal number of changes. choosing the tree with the least steps or minimal number of substitutions.

Question 10

maximum parsimony steps

Answer 10

• step 1: propose a tree and compute parsimony score (least number of changes for a given tree).
• step 2: repeat step 1 until the tree with the minimum number of changes is found.
• changes: informative vs uninformative

Question 11

maximum parsimony pros

Answer 11

simple to understand.

Question 12

maximum parsimony cons

Answer 12

easily trapped on local max, no branch lengths, too many equally parsimonious trees, statistically inconsistent (fails to find the correct tree; more data only increases support for incorrect result).

Question 13

bootstrap

Answer 13

calculating support for relationships. how strong is the signal in the data?

• statistical procedure: random re-sampling of the data, with replacement.
• pseudoreplicates

Question 14

maximum likelihood

Answer 14

what is the probability of observing a set of data given a hypothesis? the equation of the conditional probability is: likelihood = probability (data | hypothesis) or P(data | tree).

• calculate the likelihood for each hypothesis. look for the hypothesis with the highest likelihood.
• propose new topology, branch lengths, model parameters -> calculate scores; repeat.

Question 15

substitutions model (max. likelihood)

Answer 15

model the rates of changes among base pairs.

• 1 rate: all changes equal
• 2 rates: transitions vs. transversions
• 6 rates: unique rates - general time - reversible model

Question 16

maximum likelihood pros

Answer 16

statistically consistent (guaranteed accuracy with sufficient data).

Question 17

maximum likelihood cons

Answer 17

slow, “hill climbing,” which makes it easy to be trapped on a local max.

Question 18

hill climbing

Answer 18

maximum parsimony and maximum likelihood objective is to find the ““maximum” solution.
- propose new: topology (ML and MP), branch lengths (ML only), model parameters (ML only) -> calculate score; repeat.

Question 19

is there really an optimal tree?

Answer 19

can’t enumerate all possible trees for 10+ species.

Question 20

Bayesian phylogenetics

Answer 20

instead of trying to find the “maximum” solution, we summarize the entire distribution using simulation called Markov Chain Monte Carlo (MCMC).

Question 21

MP and ML vs Bayesian

Answer 21

• provides a single “point estimation” vs provides a probability distribution
• requires bootstrapping vs probabilities are provided
• can get trapped on local max vs can escape local max
• no uncertainty in estimates vs estimate uncertainty for each parameter.

Question 22

Baye’s theorem

Answer 22

Pr(tree | data) = (Pr(data | tree) * Pr(tree)) / Pr(data)

posterior probability = likelihood * prior probability

Question 23

marginal likelihood

Answer 23

summation over all trees and, for each tree, integration over all possible combinations of branch length and substitution model parameter values.

Question 24

prior distribution

Answer 24

probability assumed before observing data.

Question 25

likelihood

Answer 25

L = P(data | tree), same as one used in ML.

Question 26

posterior distribution

Answer 26

combination of the prior and likelihood.

Question 27

how do you put a prior on a phylogenetic tree?

Answer 27

give all trees equal prior probability.

Question 28

Start at a random location and follow these two MCMC rules:

Answer 28

1. if the proposed step takes you uphill, you automatically take the step.
2. if the proposed step takes you downhill, you take the step at “random.”
   - approximates the posterior distribution.

Question 29

1. convergence - how long to run the MCMC analysis?

Answer 29

• are you sampling from the “global peak”?

- have you collected enough samples to summarize?

Question 30

2. burn in - how many of the initial samples are useless?

Answer 30

• you being at a random spot, when did you reach the “goal”?

Question 31

tree space

Answer 31

each dot is a tree visited during the MCMC. the number of times a tree is visited is proportional to the probability of the tree.

Question 32

phylogenetic methods:

Answer 32

• distance: convert data to distance values and calculate the tree.
• maximum parsimony: the tree that explains the data with the least amount of evolutionary change.
• maximum likelihood: the tree with the highest probability of generating the observed data.
• bayesian - a probability distribution of trees based on prior knowledge and current data.