eng International Academy of Ecology and Environmental Sciences Computational Ecology and Software 2220-721X 2015-12-1 5 4 328 339 6 article H.O. Minoarivelo 1 2 G. Diedericks 1 2 C. Hui 1 2 Centre for Invasion Biology, Department of Mathematical Sciences, Stellenbosch University, Matieland 7602, South Africa Centre for Invasion Biology, Department of Botany and Zoology, Stellenbosch University, Matieland 7602, South Africa Mathematical and Physical Biosciences, African Institute for Mathematical Sciences, Muizenberg 7945, South Africa Phylogenetic systematics seeks to describe and reconstruct the evolutionary relationships among and between organisms making use of molecular data. This field has become immensely popular in recent years, with the associated computational demands growing in leaps and bounds. Here, we review the progress made in statistical phylogenetics, compare the various methods and highlight the recent trends and pitfalls. Furthermore, we delve into the mathematical models associated with these methods to understand the underlying assumptions, while tracking the improvements made. Lastly, we look at the impact and use of phylogenetics in ecology. http://www.iaees.org/publications/journals/ces/articles/2015-5(4)/phylogenetic-analyses-and-modelling.pdf Markov process Bayesian inference substitution matrix likelihood-based approach parsimony