Is the contribution of Mathematical Models to Biology limited to supply correct predictions?

Abstract: Two simple mathematical models of Population Genetics are introduced to master students in Biology. The first model shows that, in asexual populations, frequency independent selection alone cannot explain the maintenance of polymorphisms. In the second we see that, with the introduction of sexual reproduction, natural selection may allow a stable polymorphism, at least in large populations. A necessary and sufficient condition for it, in the case of two alleles on one locus, is heterozygote advantage. The result is applied to the case of sickle-cell anemia, where a polymorphism is apparently maintained without heterozygote advantage. This example underlines how the contribution of a mathematical model to Biology is not only in supplying correct quantitative predictions, but also in forcing to reconsider the assumptions, hence the entire view of a situation, when the predictions do not fit reality