I have some problems with this paper. I describe the terms I use here....Terms
1st. No DNA services use small segments (IBS) in deciding if 2 DNA samples are a match. They require at least 1 IBD segment. The small segments that are the subject of this paper and this discussion are clearly IBS. IBS segments are only used to predict a particular relationship between matches such as being 4th cousins. I believe that these predictions play no role in Wikitree DNA rules/guidelines.
In his FTDNA example, the matches between him and his father to his Distant Cousin is based on the 8.25 cM (IBD) segment and not the other IBS segments.
2nd. Even in a perfect world, it is possible for a child to report a longer segment than the parent, or report a segment that is not reported for a parent. This would require a more detailed explanation but an explanation as to how this happens in an imperfect world would be a good start.
Segments are reported for small segments when a comparison of at least 500 consecutive SNP's that are valid. For example, a child will report a segment 1cM segment because the 500 SNP's compared with the distant cousin are valid. The same comparisons are performed on the parent and distant cousin, but 1 of the parent SNP's is a no-call which puts the parent below the 500 SNP threshold.
The segment is reported for the child and not the parent.
There maybe a more predictable reason, especially if you use Gedmatch for the comparisons. I believe that FTDNA has used 3 different chips to produce its results, I am not sure if the SNP chipset was the same, but I know that 23andme had 4 chipsets and allowed their V2 chipset to upgrade to V3.
I am sure similar results will be more noticeable when you compare a child and parent to Distant cousins when they are not using the same chipset. This is one reason I upload my 3 DNA tests to gedmatch.
Here are the #SNP's for my father's 3 kits.
Number of regular SNPs = 680,968
Heterozygosity index = 0.148916 (fraction of total SNPs that are heterozygous)
No-calls = 10593 = 1.5317520797153 percent.
Number of regular SNPs = 943,313
Heterozygosity index = 0.206257 (fraction of total SNPs that are heterozygous)
No-calls = 4552 = 0.47338705735658 percent.
Number of regular SNPs = 686, 078
Heterozygosity index = 0.277065 (fraction of total SNPs that are heterozygous)
No-calls = 24,323 = 3.4238409011249 percent.
FTDNA is clearly a problem for gathering statistics.