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A quasispecies on a moving oasis. (English) Zbl 1071.92026
Summary: A population evolving in an inhomogeneous environment will adapt differently to different areas. We study the conditions under which such a population can maintain adaptations to a particular region when that region is not stationary, but can move. In particular, we consider a haploid population living near a moving favorable patch (“oasis”) in the middle of a large “desert.” At one genetic locus, individuals may have one of a few gene sequences that convey an advantage while in the oasis at the cost of a disadvantage in the desert. The distribution of genetic states in the population, possibly localized in genome space around the oasis-adapted genotypes, is known as a quasispecies.
We find that the ratio of oasis-adapted individuals to desert-adapted ones exhibits sharp transitions at particular oasis velocities. We calculate an extinction velocity, and a switching velocity above which the dominance switches from the oasis-adapted genotype to the desert-adapted one. This switching velocity is analogous to the quasispecies mutational error threshold. Above this velocity, the population cannot maintain adaptations to the properties of the oasis.

MSC:
92D15 Problems related to evolution
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D40 Ecology
35B20 Perturbations in context of PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
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