The Neanderthal extinction approximately 30kaBP has been a contentious issue in archaeology, where the role of the deteriorating climate and/or the arrival of modern humans (from 40kaBP) could have played a part. By reconstructing the evolutionary and demographic model alongside a palaeo-climatic chronology, this can allow the changing demography over time to be observed, in order to view how the Neanderthals responded to their environment. Such changes in the demography can then be linked to either a significant change in the deterioration of the climate or the arrival of modern humans. This could then allow for the initial trigger behind the Neanderthal extinction to be identified. One way to reconstruct the evolutionary/demographic model is through the use of a Bayesian based software programme known as BEAST (Bayesian Evolutionary Analysis of Sampling Trees). An evolutionary/demographic model has been reconstructed for North American bison (Bison cf. priscus) whereby their decline in population growth was associated with the climate instead of overhunting by modern humans.The long term goal of this study is to reconstruct the Neanderthal evolutionary/demographic model in order to answer the question of the factors behind the Neanderthal extinction. However, as the Neanderthal genetic data is currently limited, the aim of this study is to identify the more practical issues behind the construction of an evolutionary model and then apply this to the Neanderthal dataset. This shall be done by analyses of a bison genetic dataset in BEAST. The results outline the practical issues affecting the potential reconstruction of the Neanderthal evolutionary/demographic model.