Background
The concepts of Identity By Descent (IBD) vs Identity By State (IBS) are central in population genetics, yet I fail to fully wrap my head around the definitions.
You can find examples where my understanding of IBD vs IBS is quite poor in @DermotHarnett's answer here or in the comments with @PaulStaab here. @PaulStaab suggests that different authors have used different definitions of IBD and IBS.
What is unclear to me
From what I remember from Hartl and Clark (I don't have the book with me to quote), IBD depends on an arbitrary time threshold in the past beyond which if coalescent events occurred, then we still call the two alleles IBS (Identical by state) and not IBD. The idea that the concept of IBD depends on an arbitrary threshold bothers me though!
I suppose that two alleles can be IBD without being IBS in the case where a mutation or recombination event in the middle of the sequence of interest prior (looking backward in time; more recent) to their coalescence. I suppose two alleles can be IBS can not be IBD only if we use an arbitrary threshold that is older than their coalescent time or if convergent/parallel evolution happened.
Questions
- Does IBD depends on an arbitrary threshold?
- Are there several definitions of IBD and IBS in use?
- Does IBD implies IBS?
- Does IBS implies IBD?
- Can you please make a short review of these definitions to clear things up?
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