Newly emerging data from genome sequencing projects suggest that gene duplication, often accompanied by genetic map changes, is a common and ongoing feature of all genomes. This raises the possibility that differential expansion/contraction of various genomic sequences may be just as important a mechanism of phenotypic evolution as changes at the nucleotide level. However, the population-genetic mechanisms responsible for the success vs. failure of newly arisen gene duplicates are poorly understood. We examine the influence of various aspects of gene structure, mutation rates, degree of linkage, and population size (N) on the joint fate of a newly arisen duplicate gene and its ancestral locus. Unless there is active selection against duplicate genes, the probability of permanent establishment of such genes is usually no less than 1/(4N) (half of the neutral expectation), and it can be orders of magnitude greater if neofunctionalizing mutations are common. The probability of a map change (reassignment of a key function of an ancestral locus to a new chromosomal location) induced by a newly arisen duplicate is also generally >1/(4N) for unlinked duplicates, suggesting that recurrent gene duplication and alternative silencing may be a common mechanism for generating microchromosomal rearrangements responsible for postreproductive isolating barriers among species. Relative to subfunctionalization, neofunctionalization is expected to become a progressively more important mechanism of duplicate-gene preservation in populations with increasing size. However, even in large populations, the probability of neofunctionalization scales only with the square of the selective advantage. Tight linkage also influences the probability of duplicate-gene preservation, increasing the probability of subfunctionalization but decreasing the probability of neofunctionalization.