public static int geneDistance(Gene g0, Gene g1) would be part of a separate utility class like Collections and Arrays in Java whereas public int geneDistance(Gene other) will be part of the Gene class. Considering you have other operations like "trimmed versions of two genes, finding matches between genes, finding matches between animals (which contain collections of genes), etc" I would create a separate static utility class for them as these operations aren't semantically meaningful to what a Gene is.
If the the semantics of "gene distance" can be wrapped up into your equals(Object o) method then you could consume it there or else include it in your static utility.
