Types of Trees and Networks
An output of a quantitative historical linguistic analysis is normally a tree or a network diagram. This allows summary visualisation of the output data but is not the complete result. A tree is a connected acyclic graph, consisting of a set of vertices (also known as "nodes") and a set of edges ("branches") each of which connects a pair of vertices. An internal node represents a linguistic ancestor in a phylogenic tree or network. Each language is represented by a path, the paths showing the different states as it evolves. There is only one path between every pair of vertices. Unrooted trees plot the relationship between the input data without assumptions regarding their descent. A rooted tree explicitly identifies a common ancestor, often by specifying a direction of evolution or by including an "outgroup" that is known to be only distantly related to the set of languages being classified. Most trees are binary, that is a parent has two children. A tree can always be produced even though it is not always appropriate. A different sort of tree is that only based on language similarities / differences. In this case the internal nodes of the graph do not represent ancestors but are introduced to represent the conflict between the different splits ("bipartitions") in the data analysis. The "phenetic distance" is the sum of the weights (often represented as lengths) along the path between languages. Sometimes an additional assumption is made that these internal nodes do represent ancestors.
When languages converge, usually with word adoption ("borrowing"), a network model is more appropriate. There will be additional edges to reflect the dual parentage of a language. These edges will be bidirectional if both languages borrow from one another. A tree is thus a simple network, however there are many other types of network. A phylogentic network is one where the taxa are represented by nodes and their evolutionary relationships are represented by branches. Another type is that based on splits, and is a combinatorial generalisation of the split tree. A given set of splits can have more than one representation thus internal nodes may not be ancestors and are only an "implicit" representation of evolutionary history as distinct from the "explicit" representation of phylogenetic networks. In a splits network the phrenetic distance is that of the shortest path between two languages. A further type is the reticular network which shows incompatibilities (due to for example to contact) as reticulations and its internal nodes do represent ancestors. A network may also be constructed by adding contact edges to a tree. The last main type is the consensus network formed from trees. These trees may be as a result of bootstrap analysis or samples from a posterior distribution.
Read more about this topic: Quantitative Comparative Linguistics
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