Possible mathematical definitions of the biological term “breed”

Abstract

For scientific discussions it is necessary to clearly define the terms used. Otherwise, scientific statements are open to interpretation and remain unclear which hampers scientific progress. A clear specification of scientific terms can be reached using tools such as mathematical definitions. So far, the biological term breed lacks a mathematical definition. Based on common biological literature, four mathematical definitions of the term breed for gonochoric species are proposed in this paper. These definitions were tested on the dog breed whippet. It was discussed if bully whippets and their offspring can be considered to be part of the whippet dog breed. Although all mathematical definitions proposed are consistent with common word-based definitions, the results of the bully whippet test differ. According to two definitions bully whippets may be considered part of the whippet breed. However, according to the other definitions bully whippets are not part of the whippet breed. Under certain conditions the introduced mathematical structure may also be used to define other biological terms like variety or species.