Lecture 7

Question 1

How do we search the tree space for the maximum likelihood tree?

Answer 1

We need to propose different unrooted trees : NNI, SPR, TBR moves
We also need to propose different branch length: multiply each branch length by some factor
We can use hill climbing strategies by taking small step sizes in the tree space to find the optimum tree

Question 2

How does the NNI move work? draw

Answer 2

Each branch in the tree connect to different subtrees or nearest neighbours. interchanging a subtree on one side of the branch with another on on the other side is an NNI. Such rearrangement is possible for each internal branch

Question 3

How does SPR work? draw

Answer 3

it works by branch swapping by subtree pruning and regrafting. for instance a subtree is pruned and then reattached to a different location on the tree. steps are repeated until the optimal alignment is reached.

Question 4

How does TBR work? draw

Answer 4

IT works by branch swapping by tree bisection and reconnection. Tree is broken into two subtrees by cutting an internal branch. two branches one from each subtree are then chosen and rejoined to form a new tree.

Question 5

Which evolutionary models can we use for testing?

Answer 5

likelihood ratio test and AIC

Question 6

How can we assess confidence of the inferred parameters (phylogeny and the substitution rates)

Answer 6

likelihood ratios and bootstrapping

Question 7

Does bootstrapping require ML?

Answer 7

no

Question 8

How do we formulate our null hypothesis in model testing?

Answer 8

We ask if we can reject model H0 in favour of model H1

Question 9

How do we formulate the likelihood ratio?

Answer 9

We assume data evolved under a model H0, and a model H1 whithin which H0 is nested. under mild conditions: refer to slide 18

Question 10

How does the likelihood ratio test work?

Answer 10

we consider two models: H1 which is the general model and H0 being the null model. we then find the 2*(log l (parameter 1)-logl(parameter0)
if this value lies in the end of the a alpha tail of the chi distribution, we can reject the null model

Question 11

if the null model is the tree model, we would falsely reject it in what proportion of the tests?

Answer 11

alpha proportion of the test

Question 12

if the null model was the false model, we expect the null model to have —- likelihood than there true model, and we could —- the null model only in a very — proportion of the tests

Answer 12

much lower, accept, low

Question 13

What specific fit are we assessing here?

Answer 13

we assess the fit of H0 relative to H1. even tho H1 may be a very bad model, we may reject H0 In favour of H1, since H0 is even worse

Question 14

When comparing nested models, the simple model is obtained by —- the parameters of the general model.

Answer 14

restricting

Question 15

Could the simple model have free parameters here?

Answer 15

yes, the simple model may include free parameters.

Question 16

What is the type I and type II errors?

Answer 16

Type 1: when the simple model is tree but we reject it. Type 2: when the simple model is false but we accept it.

Question 17

Accuracy =

Answer 17

1- type I error

Question 18

Type I error is the —–, and is controlled by setting —-.

Answer 18

significance, alpha

Question 19

Power =

Answer 19

1- type II error

Question 20

How do we generally asses the power?

Answer 20

by simulating under the general model and assessing the number of times that H0 is accepted.

Question 21

if null model is false and is rejected in all experiments the power is estimated to be what?

Answer 21

1

Question 22

The power — with an increasing difference of the tree modern and the null model.

Answer 22

increases

Question 23

AIC is for what type of models?

Answer 23

non-nested

Question 24

AIC = ?

Answer 24

-2logLi(theta)+2pi, pi is the number of parakeets and Li is the likelihood function of the model I

Question 25

How AIC used? what is the rationale behind it?

Answer 25

-Its used to calculate the AIC for each model - then the model with the lowest AIC is chosen rationale : AIC basically picks the model with the smallest expected pullback-leibler distance to the true model

Question 26

Models having AIC within 1-2 of the minimum:

Answer 26

substation support, should receive consideration in inference

Question 27

Models having AIC within 4-7 of the minimum:

Answer 27

considerably less support

Question 28

Models having AIC>10 above the minimum:

Answer 28

essentially no support

Question 29

Slide 21**

Question 30

How many branches can a rooted tree with 12 species have?

Answer 30

21

Question 31

if we want to test JC against GTR, can we do a likelihood ratio test?

Answer 31

yes if we perform the test on the same tree with fixed branch lengths. no if we perform it on different trees, since each tree is a different parameter therefore the models wont be nested anymore and so we need to use AIC

Question 32

How do we determine the confidence interval in a fixed tree given the evolutionary parameters ?

Answer 32

we determine the value of the log likelihood function in parameter estimate l(Theta;x), we then subtract l(Theta;x) - 0.5 chi-squared. and determine the actual values of the estimate for which the equation above is tree. see slide 51.

Question 33

Calculating the confidence interval for complex objects such as tree topologies isn't possible using the previous method. so what can we do? what is the limitation of this

Answer 33

We can do more experiments, and ignore the smallest and largest 2.5% of the outcomes and consider the minimum and maximum, however for many question we cant repeat experiments, for instance we cant repeat plant speciation.

Question 34

So then what else can we do to find the CI?

Answer 34

we can mimic more experiments by bootstrapping, ie creating artificially new datasets.

Question 35

How does bootstrapping work?

Answer 35

we do testes by relying on random sampling with replacement. if we have enough data initially we. should receive the same results as what we do with the replacement.

Question 36

How do we use bootrapping for phylogenies based on an alignment sequences with length m?

Answer 36

we sample m sites at random with replacement and infer a phylogeny based on the new data and repeated he procedure many times

Question 37

Explain each step of maximum likelihood inference.

Answer 37

1- infer a maximum likelihood tree : - employ flesentein's pruning algorithm for each tree and branch lengths - choose the tree with branch lengths which maximise the likelihood - do this for each substation model and calculates its AIC 2- determine the model and tree with the highest support using AIC 3- determine the confidence interval for the substitution model parameters based on the likelihood ratios 4- determine the confidence in maximum likelihood tree using bootstrap

Question 38

bootstrap is used to determine the confidence in ---, and likelihood ratio is used to determine the confidence interval for the ----.

Answer 38

maximum likelihood tree, substitution model

Question 39

Is there a way to test how to best root a maximum likelihood tree without employing any extra information?

Answer 39

yes. only unrooted form has a meaning in a likelihood contest

Question 40

Can you use the bootrstrapping ideas for assessing confidence in UPGMA?

Answer 40

yes. if we have a very large sequecne alignment since we expect to see some variation. we can usually use it for different phylogeny methods.

Question 41

What is required to infer a direction of transmission from a phylogeny?

Answer 41

by including more sequences , and getting a more detailed tree. if one sequence is contained in one we could tell the direction of transmission. and its a bit difficult to say 100% which one was better.