Lecture 8 Flashcards
What are some examples of discrete characters?
spike numbers of HIV virions, number of legs in arthropods, fur patterns in rodents
What are some examples of continuous characters?
height, surface to weight ratio, shape of dinosaur jaws
If we only look at the correlation between traits, why could this analysis be biased?
because of relatedness of individuals.
When comparing discrete characters how can we account for relatedness?
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”
Why can neglecting the phylogenic background lead to false conclusions on correlation between characters?
Due to non-independence of species data points as a result of shared ancestry.
What do methods for finding correlations on discrete need to address?
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
One commonly used model to describe evolution of continuous traits on a phylogeny is —-.
Brownian motion model
In brownian motion, the process starts in —, if not, we can apply an —.
0, offset
In Brownian motion time is —- surely discrete/ continuous?
almost, continuos
Is Brownian motion memoryless or does it have memory?
It is memoryless, as each increment is independent of the other.
In brownian motion, increments are —- distributed with mean —-, and a variance that is —-proportional to —-
normally, 0, linearly proportional to the time difference being considered.
In discrete character models we have the — to visit any state, in continuous we have —– on state space.
probability, probability density
Discrete models are memory —- due to —-, continuous are memory —- due to —-.
less, Markov chain model, less, Brownian motion
In discrete models transition probabilities scale with —-, in continuous models variance scales with —-.
time, branch length
How does a linear regression model look like?
y = Bxi+b+e, where e is a normally distributed variance
With what method do we fit linear regression?
least squares
R^2 shows ——–, if it’s a perfect fit its close to —-, no dependency is close to —-.
goodness of the fit, 1, 0
Why linear regression cant be used to compare two characters evolved on a phylogeny.
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.
What is the method for overcoming the interdependencies of the evolutionary trait?
the contrast method.
In the contrast method, instead of looking at characters we look at —-?
their contrasts
To perform linear regression we need to calculate the values of —- and their —–.
contrasts and variance
The value for contrast at cherries can be calculated by —-.
decreasing the trait values at the tips from each other
variance is proportional to ——.
branch lengths between two external nodes
All contrasts need to have the same —-, so we need to —- them.
variance, normalise
All contrasts will finally have the variance of N(0, sigma^2)
After calculating the contrasts at cherries, what do we need to find?
trait value at internal nodes
Is it possible to find a correlation between continuous and discrete traits?
yes
If individuals evolved in a phylogeny, can we directly compare correlation between characters with regression?How can we solve the then?
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.
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?
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
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?
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
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?
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.
Contrasts need to be —- and —-.
independent, identically distributed
