  We show that generalized multiquadric radial basis functions (RBFs) on
$\mathbb{R}^d$ have a mean dimension that is $1+O(1/d)$ as $d\to\infty$ with an
explicit bound for the implied constant, under moment conditions on their
inputs. Under weaker moment conditions the mean dimension still approaches $1$.
As a consequence, these RBFs become essentially additive as their dimension
increases. Gaussian RBFs by contrast can attain any mean dimension between 1
and d. We also find that a test integrand due to Keister that has been
influential in quasi-Monte Carlo theory has a mean dimension that oscillates
between approximately 1 and approximately 2 as the nominal dimension $d$
increases.
