  We analyse absorption line-strength indices for ~3000 red-sequence galaxies
in 94 nearby clusters, to investigate systematic variations of their stellar
content with location in the host cluster. The data are drawn from the NOAO
Fundamental Plane Survey. Our adopted method is a generalization of that
introduced by Nelan et al. to determine the global age-mass and
metallicity-mass relations from the same survey. We find strong evidence for a
change in galaxy properties, at fixed mass, over a range from the cluster
centre to the virial radius, R_200. For example, red-sequence galaxies further
out in the clusters have weaker Mgb5177 (at ~8 sigma significance) and stronger
Hbeta and Hgamma absorption (~3 sigma, ~4 sigma) than galaxies of the same
velocity dispersion in the cluster cores. The Fe5270 and Fe5335 indices show
only very weak trends with radius. Using a total of twelve indices, the pattern
of cluster-centric gradients is considered in light of their different
dependences on stellar age and chemical composition. The measured gradients for
all twelve indices can be reproduced by a model in which red-sequence galaxies
at ~1 R_200 have on average younger ages (by 15+/-4%) and lower alpha-element
abundance ratios (by 10+/-2%), than galaxies of the same velocity dispersion
but located near the cluster centre. For the total metallicity, Z/H, no
significant gradient is found (2+/-3% larger at R_200 than in the core). The
cluster-centric age and alpha/Fe gradients are in the sense expected if
galaxies in the cluster core were accreted at an earlier epoch than those at
larger radii, and if this earlier accretion contributed to an earlier cessation
of star formation. The size of the observed age trend is comparable to
predictions from semi-analytic models of hierarchical galaxy formation.
