parameter values that maximize the probability of the data (the observed character states) given the hypothesis (a model of evolution and a phylogeny relating the observed sequences or taxa). In other words, this method assumes that the ancestral states are those which are statistically most likely, given the observed phenotypes. Some of the earliest ML approaches to ancestral reconstruction were developed in the context of genetic sequence evolution; similar models were also developed for the analogous case of discrete character evolution. The use of a model of evolution accounts for the fact that not all events are equally likely to happen. For example, a transition, which is a type of point mutation from one purine to another, or from one pyrimidine to another is much more likely to happen than a transversion, which is the chance of a purine being switched to a pyrimidine, or vice versa. These differences are not captured by maximum parsimony. However, just because some events are more likely than others does not mean that they always happen. We know that throughout evolutionary history there have been times when there was a large gap between what was most likely to happen, and what actually occurred. When this is the case, maximum parsimony may actually be more accurate because it is more willing to make large, unlikely leaps than maximum likelihood is. Maximum likelihood has been shown to be quite reliable in reconstructing character states, but it does not do as good of a job at giving accurate estimations of the stability of proteins. Maximum likelihood always overestimates the stability of proteins, which makes sense since it assumes that the proteins that were made and used were the most stable and optimal. The merits of maximum likelihood have been subject to debate, with some having concluded that maximum likelihood test represents a good medium between accuracy and speed. However, other studies have complained that maximum likelihood takes too much time and computational power to be useful in some scenarios. These approaches employ the same probabilistic framework as used to infer the phylogenetic tree. In brief, the evolution of a genetic sequence is modelled by a time-reversible continuous time Markov process. In the simplest of these, all characters undergo independent state transitions (such as nucleotide substitutions) at a constant rate over time. This basic model is frequently extended to allow different rates on each branch of the tree.