From archival ground-based images of the Leo I dwarf spheroidal galaxy we have identified and characterized the pulsation properties of 164 candidate RR Lyrae variables and 55 candidate Anomalous and/or short-period Cepheids . We have also identified nineteen candidate long-period variable stars and thirteen other candidate variables whose physical nature is unclear , but due to the limitations of our observational material we are unable to estimate reliable periods for them . On the basis of its RR Lyrae star population Leo I is confirmed to be an Oosterhoff-intermediate type galaxy , like several other dwarf spheroidals . From the RR Lyrae stars we have derived a range of possible distance moduli for Leo I : 22.06 \pm 0.08 \lower 2.58 pt \hbox { $ \sim$ } \kern - 9.2 pt \raise 1.72 pt \hbox { $ < $ } % \mu _ { 0 } \lower 2.58 pt \hbox { $ \sim$ } \kern - 9.2 pt \raise 1.72 pt \hbox { $ < $ } 22.25 % \pm 0.07 mag depending on the metallicity assumed for the old population ( [ Fe/H ] from –1.43 to –2.15 ) . This is in agreement with previous independent estimates . We show that in their pulsation properties , the RR Lyrae stars—representing the oldest stellar population in the galaxy—are not significantly different from those of five other nearby , isolated dwarf spheroidal galaxies . A similar result is obtained when comparing them to RR Lyrae stars in recently discovered ultra-faint dwarf galaxies . We are able to compare the period distributions and period-amplitude relations for a statistically significant sample of ab–type RR Lyrae stars in dwarf galaxies ( \sim 1300 stars ) with those in the Galactic halo field ( \sim 14,000 stars ) and globular clusters ( \sim 1000 stars ) . Field RRLs show a significant change in their period distribution when moving from the inner ( d _ { G } \lower 2.58 pt \hbox { $ \sim$ } \kern - 9.2 pt \raise 1.72 pt \hbox { $ < $ } 14 kpc ) to the outer ( d _ { G } \lower 2.58 pt \hbox { $ \sim$ } \kern - 9.5 pt \raise 1.72 pt \hbox { $ > $ } 14 kpc ) halo regions . This suggests that the halo formed from ( at least ) two dissimilar progenitors or types of progenitor . Considered together , the RR Lyrae stars in classical dwarf spheroidal and ultra-faint dwarf galaxies—as observed today—do not appear to follow the well defined pulsation properties shown by those in either the inner or the outer Galactic halo , nor do they have the same properties as RR Lyraes in globular clusters . In particular , the samples of fundamental-mode RR Lyrae stars in dwarf galaxies seem to lack H igh A mplitudes and S hort P eriods ( “ HASP ” : A _ { V } \geq 1.0 mag and P \lower 2.58 pt \hbox { $ \sim$ } \kern - 9.2 pt \raise 1.72 pt \hbox { $ < $ } 0.48 d ) when compared with those observed in the Galactic halo field and globular clusters . The observed properties of RR Lyrae stars do not support the idea that currently existing classical dwarf spheroidal and ultra-faint dwarf galaxies are surviving representative examples of the original building blocks of the Galactic halo .