Phylogenetic methods based on optimality criteria are highly desirable for their logic properties, but time-consuming when compared to other methods of tree construction. Traditionally, researchers have been limited to exploring tree space by using multiple replicates of Wagner addition followed by typical hill climbing algorithms such as SPR or/and TBR branch swapping but these methods have been shown to be insuficient for “large” data sets (or even for small data sets with a complex tree space). Here, I review different algorithms and search strategies used for phylogenetic analysis with the aim of clarifying certain aspects of this important part of the phylogenetic inference exercise. The techniques discussed here apply to both major families of methods based on optimality criteria—parsimony and maximum likelihood—and allow the thorough analysis of complex data sets with hundreds to thousands of terminal taxa. A new technique, called pre-processed searches is proposed for reusing phylogenetic results obtained in previous analyses, to increase the applicability of the previously proposed jumpstarting phylogenetics method. This article is aimed to serve as an educational and algorithmic reference to biologists interested in phylogenetic analysis.
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