In particular, one frequently reconstructs the evolution along a phylogenetic tree of ancestral characters of diverse nature, for example: molecular ( Grass Phylogeny Working Group II 2012 Werner et al. However, phylogeny is not an end in itself it is generally the support for more complete studies. A first step is often phylogenetic reconstruction, which is central to understanding the origin, evolution and classification of species, protein families, and pathogens such as HIV, as well as for reconstructing the evolution of communities and ecosystems. Reconstruction of the past is central to evolutionary biology ( Maddison 1994 Felsenstein 2004 Liberles 2007). For certain tree shapes (typically speciation trees) the uncertainty of simultaneous estimation is reduced when more tips are present however, for other tree shapes it does not (e.g., coalescent trees used in population genetics).ДЄncestral states, evolutionary patterns and processes, information theory, phylogeny, transition rates, Yule and coalescent trees This inherent вЂњDarwinian uncertainty principleвЂќ concerning the simultaneous estimation of вЂњpatternsвЂќ and вЂњprocessesвЂќ governs ancestral reconstructions in biology. This is because the global rates of state changes along the branches that are optimal for the two estimation tasks have opposite trends, leading to a fundamental trade-off in accuracy. In this framework, we use mathematics and simulations to demonstrate that although each goal can be achieved with high accuracy individually, it is generally impossible to accurately estimate both the root state and the rates of state changes along the tree branches, from the observed data at the tips of the tree. We deal here with discrete characters, which are вЂњunique,вЂќ as opposed to sequence characters (nucleotides or amino-acids), where we assume the same model for all the characters (or for large classes of characters with site-dependent models) and thus benefit from multiple information sources. The goal is 2-fold: to reconstruct the character state at the tree root (e.g., the region of origin of some species) and to understand the process of state changes along the tree (e.g., species flow between countries). It is the key to understanding morphology changes among species, inferring ancestral biochemical properties of life, or recovering migration routes in phylogeography. Reconstructing ancestral characters and traits along a phylogenetic tree is central to evolutionary biology.

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