Lecture 9 Flashcards
In phylogenetic trees tips of the trees are —-.
individuals
Generation — in time, inference — in time.
Forward, backward
In macroevolution, what its evolution?
makeup of species changes through time.
What does a phylogeny display?
It displays species relationships.
What is phylodynamics?
The speciation and extinction process.
What is the basic reproductive number?
The average number of secondary infections caused by a single infected individual at the start of an epidemic.
What does population dynamics model?
It models the birth and death of individuals (not literally death)
The birth and death process gives rise to a —–
phylogenetic tree.
What is the main aim of phylodnamics?
Understanding and quantifying the population dynamics based on a phylogenetic tree
Draw a the linear birth-death process.
Rate of birth of new individuals perinidiviual in I: B, rate of death per individual in I : s
The probability of giving birth to another individual in a very small time step is —.
B*delta_t
The probability of dying in a very small time step is?
s*delta_T
How is the waiting time to the first event, birth/death distributed?
Exponentially distributed with parameter B+S
What does a phylodynamic do?
it adds a sampling process of individual to the population dynamics. Sampling is equivalent to sequencing the individual and adding it to the phylogenetic tree
What parameters does the simplest phylodynamic model include?
Birth rate, Death rate, Process duration T, Extant tip sampling probability, Extinct tip sampling probability.
if I place extant sampling probability as 1 ,and extinct as 0, what does that mean?
In means we only sequence everything from today and nothing from the past.
How do we get to phylogenetic trees from population tree?
the subtree of the complete population tree connecting the sampled individuals, and ignoring the parent-children labels is the phylogenetic tree.
What does the lineages through time plot shows?
It shows the number of lineages throughout time.
Look at slide 23, what does the blue, solid black line and dashed black like show?
blue line shows the average number of lineages in the phylogenetic tree. Solid black shows the average of surviving population trajectories. Dashed black shows the exponential growth curve which Is linear with slope B-s
In slide 23, what is the early solid black part called? what is the slope? What is the late blue part called? what is the slope?
push of the past B+S, pull of the present B
Why do we observe a push of the past?
since only individuals with a quick replication early on will produce surviving populations.
Why do we observe pull of the present?
because the very recent lineages didnt have time to go extinct.
How can we estimate birth and death rates?
By using LLT plots, we can fit a regression line to the early branching events and estimate the slop : B-S, and for late branches the slope is B
What is the issue when estimating birth and death rates from linear time plots?
It’s not clear how we can incorporate the regression and how to chose the time interval for the two regression lines, so it isn’t statistically coherent.
Write down the expressions of phylogenetic and phylodynamic likelihood.
slide 26
Phylogenetic likelihood is :…., phylogdynamic likelihood is:…
Probability of sequence alignment given the tree and model parameters.
probability of the tree given the bird-death model parameters. So we want to maximise the bith-death parameters
What is the first set for finding the maximum likelihood estimation of phylodynamic likelihood.
We first need to find the probability of a single individual after time t leaving 0 or 1 offspring.
What does leaving 0 offspring mean?
It mean eventually they all died, it could have had an offspring but they both died.
derive the differentiation equation for p(0|t)
slide 28,29
What is the solution of the differential equation for p(0|t)
slide 29
derive the differentiation equation for p(1|t)
slide 31
what is the solution of the differential equation for p(1|t)?
slide 31
When looking at probability density of the tree, do we go forward or backwards in time?
W flip time and we go backwards in time. so initially we have time 0 and when going back in time, time increases.
What is the probability density of a tree with age X0?
slide 33
derive the differential equation for probability density of a branch
side 34
What is the initial condition when finding the probability density of a branch
p(x1,x1)=1
p(x0,x1) =?
p(1|x0)/p(1|x1)
what is the probability density of a tree?
slide 35
How does the approximate number of steps required to calculate the phylodynamic likelihood depend on the number of leaves in a phylogenetic tree??
check from video
What kind of population dynamic process could decrease in a slope in the LTT plot reflect?
truth and death rates
Assume a birth death process where each individual at present is sampled with probability p. How is the derivation of p(0|t,p), the probability of sampling no individual at present different compared to the derivation of p(0|t)
p(0|t) = probability of having no individual remaining at time t. p(0|t=0) = 0
p(0|t=0,p) = 1-p –> look at boundary conditions
