In this paper we describe a new heuristic strategy designed to find optimal
(parsimonious) trees for data sets with large numbers of taxa and characte
rs. This new strategy uses an iterative searching process of branch swappin
g with equally weighted characters, followed by swapping with reweighted ch
aracters. This process increases the efficiency of the search because, afte
r each round of swapping with reweighted characters, the subsequent swappin
g with equal weights will start from a different group (island) of trees th
at are only slightly, if at all, less optimal. In contrast, conventional he
uristic searching with constant equal weighting can become trapped on islan
ds of suboptimal trees. We test the new strategy against a conventional str
ategy and a modified conventional strategy and show that, within a given ti
me, the new strategy finds trees that are markedly more parsimonious. We al
so compare our new strategy with a recent, independently developed strategy
known as the Parsimony Ratchet.