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Abstract: Despite its intrinsic difficulty, ancestral character state reconstruction is an essential tool for testing evolutionary hypothesis. Two major classes of approaches to this question can be distinguished: parsimony- or likelihood-based approaches. We focus here on the second class of methods, more specifically on approaches based on continuous-time Markov modeling of character evolution. Among them, we consider the most-likely-ancestor reconstruction, the posterior-probability reconstruction, the likelihood-ratio method, and the Bayesian approach. We discuss and compare the above-mentioned methods over several phylogenetic trees, adding the maximum-parsimony method performance in the comparison. Under the assumption that the character evolves according a continuous-time Markov process, we compute and compare the expectations of success of each method for a broad range of model parameter values. Moreover, we show how the knowledge of the evolution model parameters allows to compute upper bounds of reconstruction performances, which are provided as references. The results of all these reconstruction methods are quite close one to another, and the expectations of success are not so far from their theoretical upper bounds. But the performance ranking heavily depends on the topology of the studied tree, on the ancestral node that is to be inferred and on the parameter values. Consequently, we propose a protocol providing for each parameter value the best method in terms of expectation of success, with regard to the phylogenetic tree and the ancestral node to infer. [Copyright &y& Elsevier]