Wave model in the context of "Dialect continuum"

In historical linguistics, the tree model (also Stammbaum, genetic, or cladistic model) is a model of the evolution of languages analogous to the concept of a family tree, particularly a phylogenetic tree in the biological evolution of species. As with species, each language is assumed to have evolved from a single parent or "mother" language, with languages that share a common ancestor belonging to the same language family.

Popularized by the German linguist August Schleicher in 1853, the tree model has been a common method of describing genetic relationships between languages since the first attempts to do so. It is central to the field of comparative linguistics, which involves using evidence from known languages and observed rules of language feature evolution to identify and describe the hypothetical proto-languages ancestral to each language family, such as Proto-Indo-European and the Indo-European languages. However, this is largely a theoretical, qualitative pursuit, and linguists have always emphasized the inherent limitations of the tree model due to the large role played by horizontal transmission in language evolution, ranging from loanwords to creole languages that have multiple mother languages. The wave model was developed in 1872 by Schleicher's student Johannes Schmidt as an alternative to the tree model that incorporates horizontal transmission.

An isogloss, also called a heterogloss, is the geographic boundary of a certain linguistic feature, such as the pronunciation of a vowel, the meaning of a word, or the use of some morphological or syntactic feature. Isoglosses are a subject of study in dialectology, in which they demarcate the differences between regional dialects of a language; in areal linguistics, in which they represent the extent of borrowing of features between languages in contact with one another; and in the wave model of historical linguistics, in which they indicate the similarities and differences between members of a language family.

Major dialects are typically demarcated by bundles of isoglosses, such as the Benrath line that distinguishes High German from the other West Germanic languages and the La Spezia–Rimini Line that divides the Northern Italian languages and Romance languages west of Italy from Central Italian dialects and Romance languages east of Italy. However, an individual isogloss may or may not have any coterminus with a language border. For example, the front-rounding of /y/ cuts across France and Germany, while the /y/ is absent from Italian and Spanish words that are cognates with the /y/-containing French words.

Johannes Friedrich Heinrich Schmidt (29 July 1843 – 4 July 1901) was a German linguist. He developed the Wellentheorie ('wave theory') of language development.

Hapa (/ˈhɑːpə/) is a Hawaiian word for someone of multiracial ancestry. In Hawaii, the word refers to any person of mixed ethnic heritage, regardless of the specific mixture. The term is used for any multiracial person of partial East Asian, Southeast Asian, or Pacific Islander mixture in California. In what can be characterized as trans-cultural diffusion or the wave model, this latter usage has also spread to Massachusetts, Ohio, and Oregon. Both uses are concurrent.