  Using mass-radius-composition models, small planets ($\mathrm{R}\lesssim 2
\mathrm{R_\oplus}$) are typically classified into three types: iron-rich,
nominally Earth-like, and those with solid/liquid water and/or atmosphere.
These classes are generally expected to be variations within a compositional
continuum. Recently, however, Luque & Pall\'e observed that potentially
Earth-like planets around M dwarfs are separated from a lower-density
population by a density gap. Meanwhile, the results of Adibekyan et al. hint
that iron-rich planets around FGK stars are also a distinct population. It
therefore remains unclear whether small planets represent a continuum or
multiple distinct populations. Differentiating the nature of these populations
will help constrain potential formation mechanisms. We present the RhoPop
software for identifying small-planet populations. RhoPop employs mixture
models in a hierarchical framework and a nested sampler for parameter and
evidence estimates. Using RhoPop, we confirm the two populations of Luque &
Pall\'e with $>4\sigma$ significance. The intrinsic scatter in the Earth-like
subpopulation is roughly half that expected based on stellar abundance
variations in local FGK stars, perhaps implying M dwarfs have a smaller spread
in the major rock-building elements (Fe, Mg, Si) than FGK stars. We apply
RhoPop to the Adibekyan et al. sample and find no evidence of more than one
population. We estimate the sample size required to resolve a population of
planets with Mercury-like compositions from those with Earth-like compositions
for various mass-radius precisions. Only 16 planets are needed when
$\sigma_{M_p} = 5\%$ and $\sigma_{R_p} = 1\%$. At $\sigma_{M_p} = 10\%$ and
$\sigma_{R_p} = 2.5\%$, however, over 154 planets are needed, an order of
magnitude increase.
