  Cosmic ray (CR) knees (spectral steepenings) encode information on CR
accelerator populations. We seek population features that imprint onto knee
observables in a manner that is robust enough to be discernible even in the
presence of significant systematics in CR data. In particular, we explore how
diversity among population members could imprint on the knee phenomenology,
under the assumption that a knee is due to a fixed-rigidity cutoff in the
source spectra. We use a simple theoretical model for a population of CR
accelerators. Each population member accelerates CR to a power-law spectrum, up
to a cutoff rigidity. We allow for variance among members, in cutoff rigidity
and power-law slope. We find that: (a) the slope step of the spectrum is $\sim
0.5$, decreasing weakly with increasing spread in either property; (b)
composition always breaks first; (c) the difference between the break energies
in composition and flux increases with increasing diversity; (d) composition
and flux break together only if population diversity is minimal. These trends
are robust under our assumptions; deviations from them would indicate more
complex physics than encoded in our simple model. Comparing these trends with
observed CR knees, we conclude that: (i) the primary knee at $\sim
4\times10^{15}$ eV is consistent with a constant-rigidity cutoff according to
KASCADE-Grande data processed with post-LHC hadronic models, but not according
to other datasets; (ii) the second knee at $\sim 5 \times 10^{17}$ eV requires
more complexity than our model; (iii) the spectral feature identified by Auger
at $\sim 10^{19}$ eV is consistent with a constant-rigidity source cutoff only
if there is a substantial spread in both cutoff rigidity and slope.
Interestingly, a significant spread in slope would also result in spectral
curvature before the break, which would in turn be contributing to the ankle
feature.
