Medianjoining

Median-joining is a method for constructing phylogenetic networks from a set of haplotypes, widely used in population genetics to visualize relationships among closely related sequences. It is designed to accommodate uncertainties in evolutionary history, allowing for reticulations that reflect ambiguous or unsampled ancestral variants. The resulting median-joining network represents plausible connections among observed sequences while highlighting alternative links that may exist under parsimony.

The algorithm combines elements of minimum- and median- networks. Starting from observed haplotypes and a distance matrix (typically the number of mutational differences), a minimum-joining network is built to connect sequences with a minimal total edge length. For every triple of nodes, a median vector is defined as a sequence that minimizes the sum of distances to the three nodes. If this median is not already present, it is added as a hypothetical node and connected to the triple. This process may be repeated to insert several median vectors, with the aim of shortening the overall network length and increasing fit to the observed data. The final network often contains reticulations, represented as boxes or complex junctions, indicating alternative pathways among haplotypes.

Median-joining networks are especially popular for analyzing intra-species variation, such as mitochondrial DNA or Y-chromosome data, where evolutionary histories may be reticulate due to recombination, homoplasy, or sampling gaps. The method was introduced by Bandelt, Forster, and Röhl in 1999 as a practical tool for constructing parsimonious networks. It is implemented in multiple software packages, including the NETWORK program and various population genetics tools, enabling researchers to explore relationships without enforcing a strictly bifurcating tree. Limitations include potential over-interpretation of reticulations and dependence on distance measures and data quality.