Computing Optimal Tree-Child Networks for Sets of Binary Phylogenetic Trees: the algorithm from this paper.
Treeduce: A preprocessing algorithm for Hybridization Number on any number of binary or nonbinary trees. See the paper.
NonbinaryCycleKiller: A practical algorithm for constructing a phylogenetic network from two large (possibly multifurcating) trees. See the paper.
ILPEACE: Reconciling a binary gene tree with a binary undated species tree, see the paper.
MPNet: Computing the Maximum Parsimony score of a phylogenetic NETwork, see the paper.
MAF: Maximum Agreement Forests for nonbinary trees, see the paper.
CycleKiller: A practical algorithm for constructing a phylogenetic network from two large bifurcating trees. The number of reticulations is very close to the minimum, see the paper.
Cass: Integrated into Dendroscope. Combines any set of phylogenetic trees into a phylogenetic network representing all clusters of all input trees. CASS uses significanly fewer reticulations than other methods. Paper. User Guide.
LEV1ATHAN: A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks. Combines any set of phylogenetic trees into a level-1 phylogenetic network (a galled tree) that is consistent with a large number of the triplet topologies of the input trees. Paper. Download.
SIMPLISTIC: Constructs level-k phylogenetic networks from triplets. This program always returns a phylogenetic network consistent with all input triplets. Partly based on the SL-k and MINPITS algorithms in this paper. Download.
MARLON: Constructs a level-1 phylogenetic network with a minimum number of reticulations consistent with a dense set of triplets, if such a network exists. Paper. Download.
LEVEL2: Constructs a level-2 phylogenetic network consistent with a dense set of triplets, if such a network exists. Paper. Download.
Cass, Simplistic and various other phylogenetic network methods can be found in the user-friendly software package Dendroscope.