We consider an asexually reproducing population on a finite trait space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this population can be modeled as a measure-valued Markov process. Multiple variations of this system have been studied in the  limit of large populations and rare mutations, where the regime is chosen such that mutations are separated. We consider the deterministic system, resulting from the large population limit, and  let the mutation probability tend to zero. This corresponds to a much higher frequency of mutations, where multiple subcritical traits are present at the same time. The limiting process is a deterministic adaptive walk that jumps between different equilibria of coexisting traits . The graph structure on the trait space, determined by the possibilities to mutate, plays an important role in defining the adaptive walk . In a variation of the above model, where the radius in which mutants can be spread is limited, we study the possibility of crossing valleys in the fitness landscape and derive different kinds of limiting walks.
We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this population can be modelled as a measure-valued Markov process. Multiple variations of this system have been studied in the simultaneous limit of large populations and rare mutations, where the regime is chosen such that mutations are separated. We consider the deterministic system, resulting from the large population limit, and then let the mutation probability tend to zero. This corresponds to a much higher frequency of mutations, where multiple microscopic types are present at the same time. The limiting process resembles an adaptive walk or flight and jumps between different equilibria of coexisting types . The graph structure on the type space, determined by the possibilities to mutate, plays an important role in defining this jump process . In a variation of the above model, where the radius in which mutants can be spread is limited, we study the possibility of crossing valleys in the fitness landscape and derive different kinds of limiting walks.
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trait
type
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modeled
modelled
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simultaneous
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then
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subcritical traits
microscopic types
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is a deterministic adaptive walk that
resembles an adaptive walk or flight and
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traits
types
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trait
type
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the adaptive walk
this jump process