Orthology is the relationship of two or more genes as a result of speciation. All other uses of the term are wrong, including those based on conserved function or conserved gene position after rearrangement. Each of these factors, along with patterns of sequence similarity, is material to the determination of whether genes are orthologous, but is not an alternative definition.

This is far beyond a semantic issue. The muddled use of this term has resulted in a great deal of illogical nonsense being published. Frankly, I'm bewildered that more of that is not eliminated by peer review. (None of this is a criticism of this article, except perhaps that it presents these alternative definitions without the negative critique that they merit.)