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. 2016 Dec 13;7:13849. doi: 10.1038/ncomms13849

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Copyright © 2016, The Author(s)

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We use a graphical method similar to the one developed by van Baalen and Sabelis⁴³ to determine which ESS virulence will be greater. (a) Comparison between the ESS virulence with and without vertical transmission in the absence of sex-specific strategies. Without vertical transmission (α=0) the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function (β′(δ)) crosses the abscissa in δ=0. With vertical transmission (α>0), the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function (β′(δ)) crosses the abscissa in . Notice that the tangent of the horizontal transmission function at the ESS is higher or equal with vertical transmission, that is . This implies that the ESS virulence is greater or equal without vertical transmission, that is . (b) Comparison between the ESS virulence when the virulence can differ in males and females. With male-specific virulence () the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function crosses the abscissa in δ_m=0. With female-specific virulence () the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function crosses the abscissa in . Notice that the tangent of the horizontal transmission function at the ESS is higher or equal with female-specific virulence, that is . This implies that the ESS virulence is greater or equal in males, .

Inline graphic — We use a graphical method similar to the one developed by van Baalen and Sabelis⁴³ to determine which ESS virulence will be greater. (a) Comparison between the ESS virulence with and without vertical transmission in the absence of sex-specific strategies. Without vertical transmission (α=0) the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function (β′(δ)) crosses the abscissa in δ=0. With vertical transmission (α>0), the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function (β′(δ)) crosses the abscissa in . Notice that the tangent of the horizontal transmission function at the ESS is higher or equal with vertical transmission, that is . This implies that the ESS virulence is greater or equal without vertical transmission, that is . (b) Comparison between the ESS virulence when the virulence can differ in males and females. With male-specific virulence () the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function crosses the abscissa in δ_m=0. With female-specific virulence () the ESS exploitation strategy () is the point where the tangent of the horizontal transmission function crosses the abscissa in . Notice that the tangent of the horizontal transmission function at the ESS is higher or equal with female-specific virulence, that is . This implies that the ESS virulence is greater or equal in males, .