ON THE BIFURCATION OF RADIALLY SYMMETRICAL STEADY-STATE SOLUTIONS ARISING IN POPULATION-GENETICS

This paper considers a semilinear elliptic equation which arises in a selection-migration model in population genetics, involving two alleles A1 and A2 such that A1 is at an advantage over A2 in certain subregions and at a disadvantage in others. The system is studied on all of R(n) and is assumed to possess radial symmetry. Existence and asymptotic properties of solutions of the corresponding ordinary differential equation are investigated and, by using shooting method type arguments, results are obtained on the bifurcation of solutions from the trivial solutions corresponding to the cases where A1 or A2 is extinct. The nature of the results obtained varies according to whether A1 or A2 has an overall advantage.