Stars in the Milky Way drift relative to one another with a characteristic speed of a few tens of kilometres per second. Depending on the effective spreading speed of life, interstellar panspermia can fall within three possible regimes. (1) If interstellar panspermia takes place at speeds much greater than the characteristic speed of stars in the galaxy, then the drifting of stars is expected to be negligible in the clustering of related life-bearing extrasolar systems. This can happen if an intelligent species spreads life at high speeds.
(3) If interstellar panspermia occurs at speeds much less than the characteristic speed of stars in the galaxy, life can still spread to extrasolar systems within a continuous region of space until such a region of space becomes so large that the rotation of the Milky Ways starts to shear and break it apart.
Interesting, the position-space correlations of life-bearing extrasolar systems (i.e. the way in which life-bearing extrasolar systems are spatially distributed) can potentially indicate whether primitive life can spread naturally to other extrasolar systems (i.e. via lithopanspermia), or whether primitive life will have to wait for intelligent life to spread it to other extrasolar systems.
Interstellar panspermia is expected to be more effective if stars are closer to one another. In dense stellar systems such as globular clusters, all potentially habitable extrasolar systems can be life-bearing due to effective interstellar panspermia. As a result, it is possible that globular clusters are saturated with life-bearing extrasolar systems, while other places with lower stellar densities have a much lower abundance of life-bearing extrasolar systems.
Lin & Loeb (2015), "Statistical Signatures of Panspermia in Exoplanet Surveys", arXiv:1507.05614 [astro-ph.EP]