Lander-Waterman theory explanation

[netpumber]

Hi.

Could someone post any reference or describe the logic of the that theory (even with images). I read the text on wikipedia but couldn't understand much because i'm now beginning with NGS.

Is this a method to estimate the quality of your library and the size of its fragments ? When do we use calculators for that ?

Thank you.

[dariober]

Is this a method to estimate the quality of your library and the size of its fragments ? When do we use calculators for that ?

Assuming reads map randomly to the reference genome, you can plan your experiments and answer questions like: How much coverage do I expect if I sequence so many reads? How many genomic positions can I expect to be covered by at least n reads (useful for SNP detection)?

Say your genome is of size G, you sequence N reads of length L, this R code answers the two questions above (given all the assumptions required):

L<- 100
G<- 3*1e9
N<- 100*1e6

## Expected coverage
C<- (L*N)/G

## % genome covered with depth...
depth<- 0:10
exp_cov<- dpois(depth, lambda= C) * 100
ggdepth<- qplot(x= depth, y= exp_cov, xlab= 'Depth', ylab= '% genome', main= 'Amount of genome\ncovered at depth n') + geom_line()
ggCum<- qplot(x= rev(depth), y= cumsum(rev(exp_cov)), xlab= 'Depth', ylab= '% genome', main= 'Amount of genome \ncovered at least with depth n') + geom_line()

This is just a use case example...

[dpryan]

Just to make explicit something in dariobers great reply, the general theory is that if reads are uniformly drawn from the genome, then coverage should follow a Poisson distribution.

It should be noted that in reality this isn't the case, and I don't think anyone actually uses this equation for these purposes anymore. In fact, it's vastly more reliable to just generate fake reads and then map them, since it turns out that not all regions are very mappable and there's also often a bias in what's even sequenced.

Having said that, the original context of the equations was more useful for assembly, since the equations can answer how many gaps one should expect given a certain number of reads (clones originally, but this was all pre-NGS). Again, though, I think people would be more likely to use k-mer frequency histograms for this sort of thing these days.

[netpumber]

Thank you very much guys.