. 2009 Oct 26;106(44):18638–18643. doi: 10.1073/pnas.0905497106

Table 1.

Classical fitness landscapes with the exponential form and the corresponding fitness and substitution trajectories obtained from Eqs. 1 and 2

	NFD Φ_x(y)	Expected fitness increment^*r(x)	Fitness trajectory F(t)	Expected fixation probability^*q(x)	Substitution trajectory S(t)
HOC	$\frac{1}{a} e^{- \frac{y}{a}}, y \geq 0$	$4 a^{2} e^{- \frac{x}{a}}$	$a \ln (e^{\frac{x_{0}}{a}} + 4 a t)$	$2 a e^{- \frac{x}{a}}$	$\frac{1}{2 a} \ln (e^{\frac{x_{0}}{a}} + 4 a t) - \frac{x_{0}}{2 a^{2}}$
NEPI	$\frac{1}{a} e^{- \frac{y - x}{a}}, y \geq x$	$\frac{4 a^{2}}{x}$	$\sqrt{x_{0}^{2} + 8 a^{2} t}$	$\frac{2 a}{x}$	$\frac{1}{2 a} (\sqrt{x_{0}^{2} + 8 a^{2} t} - x_{0})$
STH	$\frac{1}{a x} e^{- \frac{y - x}{a x}}, y \geq x$	$\frac{4 a^{2} (1 + a)}{{(1 + 2 a)}^{2}} x$	$x_{0} \exp (\frac{4 a^{2} (a + 1)}{{(2 a + 1)}^{2}} t)$	$\frac{2 a}{1 + 2 a}$	$\frac{2 a}{2 a + 1} t$

*Expressions for the r − and q-functions are derived in the limit x ≫ 1 (HOC, NEPI) and under the approximation N ≫ 1 (HOC, NEPI, STH). These approximations are highly accurate, especially for large x (see Fig. 1). See SI Appendix for details.