On the number of markers and the number of individuals

This thread passed through the Stacks mailing list, and it covered some things I hadn't really considered all that thoroughly before. I'm posting it here so that I can remember to consider it some more.

The original question posted by a user named Anpn:

Hi,

Sorry, this question is way off topic. Since, the question is about linkage
mapping, it might be of interest to some.

Does anybody have suggestions for finding the right number of markers for a
particular number of individuals?

If i have 300 RAD markers on a genome that is say 200 CentiMorgan long in
total, how many (minimum and maximum) F2 individuals should i use to get each
chromosome in one linkage group?

My understanding is that one needs more markers as the number of individuals
increases(number of recombination events increases), or is this not the
case?

Thanks,
Anpn

And the response from Julian Catchen (the developer of Stacks), with a piece from a colleague of his named Angel:

Hi Anpn,

Ideally you want to have one or more markers on either end of a recombination
event. So, as the number of individuals in your cross increases you will get
more recombination events and hence will need more markers. However, using RAD
the number of recombination events should easily be the limiting factor, not the
number of markers.

Given one recombination event per chromosome per progeny you could roughly
estimate the number of markers you need. And since you are have an F2 cross, you
have another set of recombination events in the second generation. So, one
progeny, one recombination = two markers. One progeny, two generations and
therefore two recombinations = three markers.

 From my linkage mapping colleague, Angel:

> You don't "need" more markers per se when you increase the number of
> individuals, but if you have a limited number of markers, past a certain
> number of individuals you won't get any more resolution and therefore the
> extra effort is wasted. If you get 1-2 recombination events per individual
> per chromosome and you have a couple hundred markers, with a couple hundred
> individuals you could potentially have a recombination event between any
> given pair of markers and then be able to order every single marker in every
> LG. In that case, additional individuals would have additional recombinations
> but those additional recombinations will only show up as additional distance
> between markers. SO if you have 10 markers in a LG, you'll be able to order
> them 1-10, but after that the order is established.

> If you have a limited number of progeny (almost always the case) but a large
> number of markers, you'll still be able to link and order the markers, but in
> that case you won't be able to resolve all the markers because of the lack of
> recombination events. So in the same case of before, if you have 100 markers,
> you could have them in the same order as before but now with 10 markers at
> any given point.

> In this case, additional progeny could supply additional recombination events
> that would further resolve those groups of markers, so if you get 10 more
> recombinations you could now have 20 groups of 5 markers each. Given enough
> recombinations you could ideally resolve all 100 markers in that LG, the
> assumption is always that the recombination events and the markers are
> distributed equally along the genome, and that's seldom the case. After a
> certain number of progeny you start getting diminishing returns and most
> recombinations would occur around the same places and you probably wouldn't
> be able to resolve the ends of the LG.

> When there are recombination hot spots or just places with more
> recombination, having more markers will increase the chances than one marker
> will expand the gap and link things together. With more individuals you'll
> also be able to increase the LOD and be sure that things are really linked
> together.


Best,

julian