Reading the methods
In the methods, it is stated that haplotype blocks were inferred with the software Haploview:
Genotype information for ESR1 and ESR2 and regions
approximately 10 000 base pairs up- and downstream of
these genes were downloaded from HAPMAP in May
2005 [33]. Genotype data for the population of individuals of European ancestry were visualized using Haploview
[34]. We initially selected tag-SNPs defining all haplotypes with frequency > 5% from the block-by-block tags
displayed in the HAPLOVIEW "Haplotypes" window.
However, sometimes these tag-SNPs were exchanged to
other SNPs on the same haplotype due to difficulties in
designing genotyping assays. In addition, in regions not
covered by common haplotypes we aimed to select one
common SNP (allele frequency > 5%) every 5 000 base
pair. No non-synonymous SNPs full-filling these criteria
were detected in the ESR genes.
Haploview documentation writes:
Blocks
Haploview generates blocks whenever a file is opened, but these blocks can be edited and redefined in a number of ways. In the Analysis menu, you can clear all the blocks in order to start over, define blocks based on one of several automated methods or customize the parameters of those algorithms. Additionally, the blocks can be edited by hand.
Confidence Intervals [DEFAULT]
The default algorithm is taken from Gabriel et al, Science, 2002. 95% confidence bounds on D prime are generated and each comparison is called "strong LD", "inconclusive" or "strong recombination". A block is created if 95% of informative (i.e. non-inconclusive) comparisons are "strong LD". This method by default ignores markers with MAF < 0.05. The MAF cutoff and the confidence bound cutoffs can be edited by choosing "Customize Block Definitions" (Analysis menu). This definition allows for many overlapping blocks to be valid. The default behavior is to sort the list of all possible blocks and start with the largest and keep adding blocks as long as they don't overlap with an already declared block.
So, assuming that they used default parameters, you can reconstruct their methodology from the default method documentation and their description:
- Take that default haplotype block output.
- Where that default output didn't describe a block, select a common SNP every ~5Kbp in the unblocked region.
Answering your questions
In figure 1, the SNPs displayed are all tag SNPs. They are not the only SNPs in the block, but rather the tag SNPs used to represent the block. I am not clear on why multiple SNPs are used in some cases and single SNPs in others, unless they just try to have 1 SNP every ~5Kbp in general. I don't think that's what they did, judging from the figures.
In Figure 2, presumably the blocks are the output of the Gabriel et al. 2002 algorithm using D'.
The single SNPs that are not part of any block are presumably derived from the "every 5Kbp" procedure for regions not labeled with haplotype blocks.