In the large population limit, logarithmic selective sweep curves converge uniformly to tents for strong selection and in Skorokhod M1 to houses for moderate selection in the Moran model.
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Stochastic individual-based branching models lead to free-boundary Hamilton-Jacobi equations with state constraints in logarithmic large-population small-mutation limits, incorporating extinction effects.
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Logarithmic scaling of selective sweep curves: from tents to houses
In the large population limit, logarithmic selective sweep curves converge uniformly to tents for strong selection and in Skorokhod M1 to houses for moderate selection in the Moran model.
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From stochastic individual-based models to free-boundary Hamilton-Jacobi equations
Stochastic individual-based branching models lead to free-boundary Hamilton-Jacobi equations with state constraints in logarithmic large-population small-mutation limits, incorporating extinction effects.