Lecture 8

Question 1

What are some examples of discrete characters?

Answer 1

spike numbers of HIV virions, number of legs in arthropods, fur patterns in rodents

Question 2

What are some examples of continuous characters?

Answer 2

height, surface to weight ratio, shape of dinosaur jaws

Question 3

If we only look at the correlation between traits, why could this analysis be biased?

Answer 3

because of relatedness of individuals.

Question 4

When comparing discrete characters how can we account for relatedness?

Answer 4

First of all we need a tree which shows the evolutionary history of the traits, and we consider each edge independent. We formulate the null hypothesis as “changes are equally likely on every branch/ there is no correlation between behaviours”

Question 5

Why can neglecting the phylogenic background lead to false conclusions on correlation between characters?

Answer 5

Due to non-independence of species data points as a result of shared ancestry.

Question 6

What do methods for finding correlations on discrete need to address?

Answer 6

1- mapping trait evolution onto a tree
2- assessing correlation between traits
3- account for branch lengths such changes are more likely to happen on longer branches

Question 7

One commonly used model to describe evolution of continuous traits on a phylogeny is —-.

Answer 7

Brownian motion model

Question 8

In brownian motion, the process starts in —, if not, we can apply an —.

Answer 8

0, offset

Question 9

In Brownian motion time is —- surely discrete/ continuous?

Answer 9

almost, continuos

Question 10

Is Brownian motion memoryless or does it have memory?

Answer 10

It is memoryless, as each increment is independent of the other.

Question 11

In brownian motion, increments are —- distributed with mean —-, and a variance that is —-proportional to —-

Answer 11

normally, 0, linearly proportional to the time difference being considered.

Question 12

In discrete character models we have the — to visit any state, in continuous we have —– on state space.

Answer 12

probability, probability density

Question 13

Discrete models are memory —- due to —-, continuous are memory —- due to —-.

Answer 13

less, Markov chain model, less, Brownian motion

Question 14

In discrete models transition probabilities scale with —-, in continuous models variance scales with —-.

Answer 14

time, branch length

Question 15

How does a linear regression model look like?

Answer 15

y = Bxi+b+e, where e is a normally distributed variance

Question 16

With what method do we fit linear regression?

Answer 16

least squares

Question 17

R^2 shows ——–, if it’s a perfect fit its close to —-, no dependency is close to —-.

Answer 17

goodness of the fit, 1, 0

Question 18

Why linear regression cant be used to compare two characters evolved on a phylogeny.

Answer 18

Since when two characters evolve on a tree, they share common evolutionary history(not independent realisation). also , the variance added by brownian motion isn’t equally distributed. both of which violates the assumption of the models.

Question 19

What is the method for overcoming the interdependencies of the evolutionary trait?

Answer 19

the contrast method.

Question 20

In the contrast method, instead of looking at characters we look at —-?

Answer 20

their contrasts

Question 21

To perform linear regression we need to calculate the values of —- and their —–.

Answer 21

contrasts and variance

Question 22

The value for contrast at cherries can be calculated by —-.

Answer 22

decreasing the trait values at the tips from each other

Question 23

variance is proportional to ——.

Answer 23

branch lengths between two external nodes

Question 24

All contrasts need to have the same —-, so we need to —- them.

Answer 24

variance, normalise

Question 25

All contrasts will finally have the variance of N(0, sigma^2)

Question 26

After calculating the contrasts at cherries, what do we need to find?

Answer 26

trait value at internal nodes

Question 27

Is it possible to find a correlation between continuous and discrete traits?

Answer 27

yes

Question 28

If individuals evolved in a phylogeny, can we directly compare correlation between characters with regression?How can we solve the then?

Answer 28

No, since the individuals are related and have a common evolutionary history our analysis is incorrect. we need to using some method such as independent contrasts to account for the shared evolutionary trajectory.

Question 29

In a fisher's exact test, how would you calculate which values for one of the cells in the contingency table would lead to rejection of null hypothesis, given that row and column sums remain the same?

Answer 29

we take small values of x and add them until we reach value of 0.05, and we find the range of x. wether if its two tailed or not depends on what we defined as extreme

Question 30

Is brownian motion a good model for all continuous? Is there a situation where this isn't the case and the assumptions of the model would be violated?

Answer 30

The assumptions of this model are : -starts from 0, variance is assumed to increase linearly, memory-lessness in situations where there is directional selection or evolutionary constraints, these assumptions are violated

Question 31

Is it a good strategy to first determine the species tree and then look at character evolution, or would the co-estimation of the characters and the phylogeny make more sense?

Answer 31

co-estimation, because if we were to break up the analysis information, it would only be in one direction ( the character wouldnt affect the tree), and it could in fact affect the phylogeny.

Question 32

Contrasts need to be ---- and ----.

Answer 32

independent, identically distributed