  We consider an evolving network of a fixed number of nodes. The allocation of
edges is a dynamical stochastic process inspired by biological reproduction
dynamics, namely by deleting and duplicating existing nodes and their edges.
The properties of the degree distribution in the stationary state is analysed
by use of the Fokker-Planck equation. For a broad range of parameters
exponential degree distributions are observed. The mechanism responsible for
this behaviour is illuminated by use of a simple mean field equation and
reproduced by the Fokker-Planck equation treating the degree-degree
correlations approximately. In the limit of zero mutations the degree
distribution becomes a power law.
