  Consider a population of fixed size that evolves over time. At each time, the
genealogical structure of the population can be described by a coalescent tree
whose branches are traced back to the most recent common ancestor of the
population. As time goes forward, the genealogy of the population evolves,
leading to what is known as an evolving coalescent. We will study the evolving
coalescent for populations whose genealogy can be described by the
Bolthausen-Sznitman coalescent. We obtain the limiting behavior of the
evolution of the time back to the most recent common ancestor and the total
length of the branches in the tree. By similar methods, we also obtain a new
result concerning the number of blocks in the Bolthausen-Sznitman coalescent.
