Table 1. Frequently used notation.

Symbol	Meaning
n	Number of (scaled) phenotypic dimensions
λ	Variance in mutant phenotypes along each dimension
$m_{max}$	Maximum growth rate
$f\left(m\prime |m\right)$	Distribution of growth rates among mutants from a genotype with growth rate m (eq. 1)
U	Per genome mutation probability
$N_0$	Initial number of wild-type individuals
$m_0$	Wild-type growth rate
$p_0$	Probability a wild-type individual has descendants that rescue the population
P	Probability of rescue (eq. 2)
$p\left(m,\text{Λ}\left(m\right)\right)$	Probability a genotype with growth rate m, itself fated for extinction, has descendants that rescue the population (eq. 3)
$p_{est}\left(m\right)$	Probability a genotype with growth rate m establishes, i.e., rescues the population (eq. 4)
$\text{Λ}\left(m\right)$	Probability that an individual with growth rate m produces a mutant that has descendants that rescue the population
${\text{Λ}}_i\left(m\right)$	Probability that an individual with growth rate m produces a mutant that has descendants with $i-1$ additional mutations that rescue the population
${\text{Λ}}_2^i\left(m\right)$	Probability that an individual with growth rate m produces sufficiently subcritical $\left(i=”-”\right)$, critical $\left(i=0\right)$, or supercritical $\left(i=”+”\right)$ first-step mutants that eventually lead to two-step rescue (eq. 8)
ψ	$2\left(1-\sqrt{1-m/m_{max}}\right)$
${\psi }_0$	$2\left(1-\sqrt{1-m_0/m_{max}}\right)$
${\rho }_{max}$	$m_{max}/\lambda$
α	${\rho }_{max}{\psi }_0^2/4$