A SNP is a location on the genome where a single base is replaced by another one. In other words, a SNP is the result of a point mutation. This is illustrated in the figure below at the right where pieces of DNA sequence are given for four individuals. All four individuals are identical except for a single position, where the bases A and G both occur. The only genetic variation between these four individuals, considering this piece of DNA, can be described by considering the variation in this SNP. As it only involves a single nucleotide, the number of alleles is only 2 at maximum. In theory it could happen that the same nucleotide has mutated twice, resulting in three varieties, so three alleles, but in practice this is never the case. In an increasing number of species very many SNP (>>>100,000) have been detected. Commercial companies have designed so-called SNP chips that are used for genotyping animals for a selection of SNP (varying in size from 10,000 to >700,000 SNP), that are spread nicely across the genome.
And when you want to read the complete DNA sequence of an animal, when you want to identify all nucleotides at all chromosomes you can choose for Whole Genome Sequencing. Costs are still decreasing, so this methods is applied moreover more often when e.g. the genetic variation in a population has to be established very accurately.
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