Dynamics of the bit-string model of age structured populations

The dynamics of age structured populations in the framework of the bit-string model developed by T.J.P. Penna and collaborators is analyzed in terms of the spectral properties of a time-evolution generator. This is a functional of inclusive properties of the current state of the population which is closely related to the well-known Leslie operators. The analysis of the generator allows for the identification of propagation modes associated with invariant subspaces of the propagator matrix, to which in general different gain factors are associated. Restrictions on the reproductive age span translate into the number, structure and relative dominance of the propagation modes. The time evolution of semelparous populations is found to be associated in general with oscillatory steady regimes through the appearance of a dominant family of propagation modes with identical gain factors, in complete analogy with the semelparous regime of the Leslie model. Explicit results are given and discussed for the case in which one deleterious trait is lethal.