  The species scale $\Lambda_s\leq M_{pl}$ serves as a UV cutoff in the
gravitational sector of an EFT and can depend on the moduli of the theory as
the spectrum of the theory varies. We argue that the dependence of the species
scale $\Lambda_s (\phi)$ on massless (or light) modes $\phi^i$ satisfies
$M_{pl}^{d-2} |\Lambda_s'/\Lambda_s|^2< \mathcal{O}(1)$. This bound is true at
all points in moduli space including also its interior. The argument is based
on the idea that the short distance contribution of massless modes to
gravitational terms in the EFT cannot dramatically affect the black hole
entropy. Based on string theory arguments we expect the $\mathcal{O}(1)$
constant in this bound to be equal to ${1\over {d-2}}$ as we approach the
boundary of the moduli space. However, we find that the slope of the species
scale can approach its asymptotic value from above as we go from interior
points to the boundaries, thereby implying that the constant in the bound must
be larger than ${1\over {d-2}}$. The bound on the variation of the species
scale also implies that the mass of towers of light modes cannot go to zero
faster than exponential in field distance in accordance with the Distance
Conjecture.
