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We deal with the study of the evolution of the allelic frequencies, at asingle locus, for a population distributed continuously over a bounded habitat.We consider evolution which occurs under the joint action of selection andarbitrary migration, that is independent of genotype, in absence of mutationand random drift. The focus is on a conjecture, that was raised up inliterature of population genetics, about the possible uniqueness of polymorphicequilibria, which are known as clines, under particular circumstances. We studythe number of these equilibria, making use of topological tools, and we give anegative answer to that question by means of two examples. Indeed, we providenumerical evidence of multiplicity of positive solutions for two differentNeumann problems satisfying the requests of the conjecture.

A negative answer to a conjecture arising in the study of selection-migration models in population genetics