Invasion properties of locally beneficial alleles. In a, the maximum recombination rate between loci \documentclass[12pt]{minimal}
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\begin{document}$$\mathsf{A }$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$\mathsf{B }$$\end{document}, below which invasion of \documentclass[12pt]{minimal}
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\begin{document}$$\mathsf A _1$$\end{document} can occur, is displayed as a function of \documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}. The parameters \documentclass[12pt]{minimal}
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\begin{document}$$\alpha _1=-\alpha _2=0.1$$\end{document}, \documentclass[12pt]{minimal}
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\begin{document}$$\beta _1=-2\beta _2=2$$\end{document}, and \documentclass[12pt]{minimal}
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\begin{document}$$m=1$$\end{document} are fixed. Therefore, \documentclass[12pt]{minimal}
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\begin{document}$$\phi ^\mathsf{A }=\tfrac{1}{2}$$\end{document} and \documentclass[12pt]{minimal}
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\begin{document}$$\phi _\mathrm{inv}=0.55$$\end{document}. In b, the minimum selective advantage \documentclass[12pt]{minimal}
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\begin{document}$$\alpha _1$$\end{document} required for invasion of \documentclass[12pt]{minimal}
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\begin{document}$$\mathsf A _1$$\end{document} is shown as a function of \documentclass[12pt]{minimal}
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\begin{document}$$\rho $$\end{document} for different values of \documentclass[12pt]{minimal}
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\begin{document}$$\phi $$\end{document}. The parameters \documentclass[12pt]{minimal}
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\begin{document}$$\alpha _2=-0.1$$\end{document}, \documentclass[12pt]{minimal}
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\begin{document}$$\beta _1=-2\beta _2=2$$\end{document}, and \documentclass[12pt]{minimal}
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\begin{document}$$m=1$$\end{document} are fixed
