Reconstructing phylogenies from intraspecific data (such as human mitochond
rial DNA variation) is often a challenging task because of large sample siz
es and small genetic distances between individuals. The resulting multitude
of plausible trees is best expressed by a network which displays alternati
ve potential evolutionary paths in the form of cycles. We present a method
("median joining" [MJ]) for constructing networks from recombination-free p
opulation data that combines features of Kruskal's algorithm for finding mi
nimum spanning trees by favoring short connections, and Farris's maximum-pa
rsimony (MP) heuristic algorithm, which sequentially adds new vertices call
ed "median vectors", except that our MJ method does not resolve ties. The M
J method is hence closely related to the earlier approach of Foulds, Hendy,
and Penny for estimating MP trees but can be adjusted to the level of homo
plasy by setting a parameter epsilon. Unlike our earlier reduced median (RM
) network method, MJ is applicable to multistate characters (e.g., amino ac
id sequences). An additional feature is the speed of the implemented algori
thm: a sample of 800 worldwide mtDNA hypervariable segment I sequences requ
ires less than 3 h on a Pentium 120 PC. The MJ method is demonstrated on a
Tibetan mitochondrial DNA RFLP data set.