Houston, we have a problem! I seem to be plunged into technical depths trying to make sense of the findings.
Thanks Devon, for you explanations, but something further seem to have gone wrong here!
I think I have a problem with the difference between Identical by Descent (IBD) and Identical by State (IBS). The suggestion seems to be that they somehow already filter for this (by not including strings that don't usually get mixed during the (mitosis/meiosis?? (long time since I studied DNA) process). However, I think that maybe I have a number of unusual preserved blocks.
Of my 7 suggested third cousins, and one suggested 4th cousin, I have six where most of (up to 2/3 of) the match comes from a single very extended block. Is that at all normal??
2 matches who seem to be related, share these very extended blocks in the same place on the same chromosome, the very extended blocks in common with another 4 are each on different chromosomes.
When I look at the comparison with my second cousin, we have several extended blocks in common, but none as long as the ones with these "matches", although in two cases (that are related to each other), I do share about half of the very extended block with my cousin. I also have many other shared areas (looked at on the 1cM view of the chromosomes).
If these very extended shared blocks are not normal, is there some statistical method I could use to weed out false positives? - e.g. all those where more than half the shared data comes from one block?
Sorry, this has got so technical but I really don't know whether it is better to ignore pretty much all these potential matches or to follow up some of the ones that at least seem to be in the right place at the right time, even though not very close connections.