In historical linguistics, a linkage is a group of related languages that is formed when a proto-language breaks up into a network of dialects that gradually differentiates into separate languages. This term was introduced by Malcolm Ross in his study of the Western Oceanic languages (Ross 1988); it is contrasted with a family, which arises when the proto-language speech community separates into groups that are isolated from each other, rather than forming a network.
Linkages are formed when languages emerged historically from the diversification of an earlier dialect continuum: it may be that its members diverged while sharing subsequent innovations, or that such dialects came into contact and converged. In any dialect continuum, innovations are shared between neighbouring dialects in intersecting patterns; the patterns of intersecting innovations continue to be evident as the dialect continuum turns into a linkage.
According to the comparative method, a group of languages that exclusively shares a set of innovations constitutes a "(genealogical) subgroup"; thus, a linkage is usually characterised by the presence of intersecting subgroups. The tree model does not allow for the existence of intersecting subgroups and so is ill-suited to represent linkages: they are better approached using the wave model.
The cladistic approach underlying the tree model requires that the common ancestor of each subgroup be discontiguous from other related languages and cannot share any innovation with them after their "separation". Such an assumption is absent from Ross and François's approach to linkages: their genealogical subgroups also consist of languages descended from a common ancestor (as defined by a set of exclusively shared innovations), but that common ancestor does not have to be discretely separated from its neighbours. For example, a chain of dialects {A B C D E F} may undergo a number of linguistic innovations, some affecting {BCD}, others {CDE}, others {DEF}. Insofar as each of these sets of dialects were mutually intelligible at the time of the innovations, each can be seen as forming a language. Among them, Proto-BCD will be the language ancestral to the subgroup BCD, Proto-CDE the language ancestral to CDE, etc. As for the language descended from dialect D, it will belong simultaneously to three "intersecting subgroups" (BCD, CDE and DEF). In both the tree and the linkage approaches, genealogical subgroups are strictly defined by their shared inheritance from a common ancestor. Simply, although trees entail that all proto-languages must be discretely separated, the linkage model refuses to make that assumption.