  In the case of neutral populations of fixed sizes in equilibrium whose
genealogies are described by the Kingman $N$-coalescent back from time $t$
consider the associated processes of total tree length as $t$ increases. We
show that the (c\`adl\`ag) process to which the sequence of compensated tree
length processes converges as $N$ tends to infinity is a process of infinite
quadratic variation; therefore this process cannot be a semimartingale. This
answers a question posed in Pfaffelhuber et al. (2011).
