In the standard cosmological model, any single galaxy is expected to have formed from a few or many successive mergers of dark matter haloes, in which gas cools and forms stars at the centres of the haloes, becoming the optically visible objects historically identified as galaxies during the twentieth century. Modelling the mathematical graph of the mergers of these dark matter haloes, and in turn, the corresponding star formation, was initially treated either by analysing purely gravitational N-body simulations or by using numerical realisations of statistical ("semi-analytical") formulae. In a 1992 observational cosmology conference in Milan, Roukema, Quinn and Peterson showed the first merger history trees of dark matter haloes extracted from cosmological N-body simulations. These merger history trees were combined with formulae for star formation rates and evolutionary population synthesis, yielding synthetic luminosity functions of galaxies (statistics of how many galaxies are intrinsically bright or faint) at different cosmological epochs. Given the complex dynamics of dark matter halo mergers, a fundamental problem in modelling merger history tree is to define when a halo at one time step is a descendant of a halo at the previous time step. Roukema's group chose to define this relation by requiring the halo at the later time step to contain strictly more than 50 percent of the particles in the halo at the earlier time step; this guaranteed that between two time steps, any halo could have at most a single descendant. This galaxy formation modelling method yields rapidly calculated models of galaxy populations with synthetic spectra and corresponding statistical properties comparable with observations. Independently, Lacey and Cole showed at the same 1992 conference how they used the Press–Schechter formalism combined with dynamical friction to statistically generate Monte Carlo realisations of dark matter halo merger history trees and the corresponding formation of the stellar cores (galaxies) of the haloes. Kauffmann, White and Guiderdoni extended this approach in 1993 to include semi-analytical formulae for gas cooling, star formation, gas reheating from supernovae, and for the hypothesised conversion of disc galaxies into elliptical galaxies. Both the Kauffmann group and Okamoto and Nagashima later took up the N-body simulation derived merger history tree approach. Examples Some of the galaxies that are in the process of merging or are believed to have formed by merging are: Antennae Galaxies Mice Galaxies Centaurus A NGC 7318 Gallery See also Andromeda–Milky Way collision Bulge (astronomy) Galaxy formation and evolution Interacting