Emergence of allometric scaling in genealogical trees

We investigate the emergence of power-law scalings in genealogical trees. Especially, we study the topological properties of genealogical trees both in the neutral evolution and the selective evolution. In all instances, we observe that the topologies of these trees are well described by a power-law scaling C-k similar to A(k)(n), where A(k) is the number of nodes which are direct or indirect descendants of node k and C-k = Sigma(j) A(j) where the sum is taken over all nodes that contribute to A(k). This relation is well known in transportation networks as well as in metabolic networks, and it is referred to as allometric scaling. Furthermore, we observe a slight dependence of the scaling exponent eta on the intensity of selection.