the phylogenetic tree are equally likely to change, that the rate of evolution is slow, and that the chance of losing or gaining a characteristic is the same. In reality, assumptions are often violated, leading to several issues: Variation in rates of evolution. Fitch's method assumes that changes between all character states are equally likely to occur; thus, any change incurs the same cost for a given tree. This assumption is often unrealistic and can limit the accuracy of such methods. For example, transitions tend to occur more often than transversions in the evolution of nucleic acids. This assumption can be relaxed by assigning differential costs to specific character state changes, resulting in a weighted parsimony algorithm. Rapid evolution. The upshot of the "minimum evolution" heuristic underlying such methods is that such methods assume that changes are rare, and thus are inappropriate in cases where change is the norm rather than the exception. Variation in time among lineages. Parsimony methods implicitly assume that the same amount of evolutionary time has passed along every branch of the tree. Thus, they do not account for variation in branch lengths in the tree, which are often used to quantify the passage of evolutionary or chronological time. This limitation makes the technique liable to infer that one change occurred on a very short branch rather than multiple changes occurring on a very long branch, for example. In addition, it is possible that some branches of the tree could be experiencing higher selection and change rates than others, perhaps due to changing environmental factors. Some periods of time may represent more rapid evolution than others, when this happens parsimony becomes inaccurate. This shortcoming is addressed by model-based methods (both maximum likelihood and Bayesian methods) that infer the stochastic process of evolution as it unfolds along each branch of a tree. Statistical justification. Without a statistical model underlying the method, its estimates do not have well-defined uncertainties. Convergent evolution. When considering a single character state, parsimony will automatically assume that two organisms that share that characteristic will be more closely related than those who do not. For example, just because dogs and apes have fur does not mean that they are more closely related than apes are to humans. Maximum likelihood Maximum likelihood (ML) methods of ancestral state reconstruction treat the character states at internal nodes of the tree as parameters, and attempt to find the