  We show that the rapid evolution in the fraction of blue, star-forming
galaxies seen in clusters as a function of redshift (the Butcher-Oemler effect)
can be explained very simply if structure formation in the universe proceeeds
hierarchically. We show that a rich cluster observed at high redshift has had a
significantly different evolutionary history to a cluster of the same richness
observed today. High redshift clusters take longer to assemble and thus under-
go more merging at small lookback times. We have investigated two models of
star formation in cluster galaxies: 1) a model in which star formation is
induced by galaxy-galaxy mergers and interactions and 2) a model in which star
formation is regulated by the infall of galaxies onto larger systems such as
groups and clusters. Both models produce trends consistent with the Butcher-
Oemler effect. Our models of cluster formation and evolution allow us to make
predictions about trends in the observed properties of clusters with redshift.
We find that there should be a correlation between the mass of the cluster or
group and the strength of the observed Butcher-Oemler effect, with more massive
systems exhibiting more evolution than less massive systems. We also predict
that both the blue galaxy fraction and the incidence of interacting galaxies in
rich clusters should rise continuously with redshift. Finally, we have explored
the influence of cosmological parameters on our predictions for cluster
evolution. We find that models in which structure formation occurs at very
early epochs, such as low $\Omega$ models, predict rather little recent star
formation and merging activity in clusters at redshifts of around 0.4.
