Parameters - Ne and u

[Vanina Castroagudin]

Dear  all,

I am working with Migrate. v4 and Microsatelite data.

Considering that theta = 4 Ne u  

                                     u = m/M

How or with which software can I calculate Ne (Population size), m, M or u  (  expected mutation rate )to be able to obtained the remaining parameter value? which is the value in the Migrate output M or m?  Should I create an ecuation sistem including Thete = 4Ne and the other parameters?

Sorry if my question is confussing... I am a bit cobnfused.

Vanina

[Peter Beerli]

Dear Vanina,

Theta = 4 Ne mu  with Ne the effective population size , and mu = the mutation rate per locus and generation [for msat]

M = m/mu   with m = the immigration rate and mu the mutation rate.

you will see this as Theta_1 or Theta_2

and M_1->2 or M_2->1 

the latter are sometimes written ad M_12 = m_12 / mu 

if you prefer 4Ne m for the immigration you can simply multiple Theta with M

Theta * M = 4 Ne mu * m/mu = 4 Ne m

more precisely:

Theta_1 * M_21 = 4 Ne_1 * m_21  , the m and M are all _immigration_ rates; therefore you will need always to multiply with the receiving population Theta.

Just use your calculator or write a small python or R script, mu needs to come from some other source (literature?). 

Peter

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[Renan Portela]

Greetings Professor Beerli, I would like to understand the meaning of the Theta parameter separately from 4 Ne mu, how can I name this parameter and what it tells me about populations. (it is possible to say that theta corresponds to the expected number of mutations between any two sequences up to the moment in which both coalesce in the past)

I know that Theta = 4 Ne mu with Ne the effective population size , and mu = the mutation rate per locus and generation [for msat]

sorry if it's a basic question, but it's important for me to know this

[Peter Beerli]

The coalescent is the relationship tree of a sample in a model population (originally the Cannings’ population model — this model is a close relative to the Wright-Fisher (WF) population model). In its original form, we would talk about the rate of coalescence of two random samples, which is a function of the population size in such a model; if the WF model has 100 individuals in it, that the population size is 100, this is independent of the sample size.

Natural populations do not exactly behave like a WF population, so we use the term effective population size Ne as a placeholder for the number of individuals in the population if this population would be ideal (like a WF).

We use genetic data to estimate Ne because there is a relationship between Ne and the number of mutations in the population. The mutation rate mu and the population size Ne can be used to think about how many mutations are in the population (Ne*mu). If a population has a Ne=1000 and mu=0.001 or it has a Ne=5000 and mu=0.0002, both lead to the same value. Since we do not know the mutation rate, we usually use a compound and call it Theta. I call this construct the mutation-scaled effective population size; the coalescent literature from England called this the population-scaled mutation rate. You can think of it as a relative number of how many mutations we expect in the population. For example, a population with a Theta of 0.01 has, on average, 10x more mutations than one that has a Theta=0.001. This could either mean the mutation rate is 10x different and the population size is the same, or the population size is 10x different and the mutation rate is the same [I usually would subscribe to the latter]

hope this helps

Peter

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