  A near-infrared imaging study of the evolved stellar populations in the dwarf
spheroidal galaxy Leo I is presented. Based on JHK observations obtained with
the WFCAM wide-field array at the UKIRT telescope, we build a near-infrared
photometric catalogue of red giant branch (RGB) and asymptotic giant branch
(AGB) stars in Leo I over a 13.5 arcmin square area. The V-K colours of RGB
stars, obtained by combining the new data with existing optical observations,
allow us to derive a distribution of global metallicity [M/H] with average
[M/H] = -1.51 (uncorrected) or [M/H] = -1.24 +/- 0.05 (int) +/- 0.15 (syst)
after correction for the mean age of Leo I stars. This is consistent with the
results from spectroscopy once stellar ages are taken into account. Using a
near-infrared two-colour diagram, we discriminate between carbon- and
oxygen-rich AGB stars and obtain a clean separation from Milky Way foreground
stars. We reveal a concentration of C-type AGB stars relative to the red giant
stars in the inner region of the galaxy, which implies a radial gradient in the
intermediate-age (1-3 Gyr) stellar populations. The numbers and luminosities of
the observed carbon- and oxygen-rich AGB stars are compared with those
predicted by evolutionary models including the thermally-pulsing AGB phase, to
provide new constraints to the models for low-metallicity stars. We find an
excess in the predicted number of C stars fainter than the RGB tip, associated
to a paucity of brighter ones. The number of O-rich AGB stars is roughly
consistent with the models, yet their predicted luminosity function is extended
to brighter luminosity. It appears likely that the adopted evolutionary models
overestimate the C star lifetime and underestimate their K-band luminosity.
