How does Γ_⊕ Relate to <i>η</i> _⊕?

Abstract η ⊕ is the expected number of rocky habitable zone planets per star. Γ ⊕ , the slope of the planet population in log space at Earth’s parameter values, is a quantity that is often used as a proxy for η ⊕ . I discuss their relationship, focusing on how Γ ⊕ is an approximation to η ⊕ that may have large errors. I provide an explicit example showing that Γ ⊕ may underestimate η ⊕ by a factor of 2 in common cases.