Two processes can influence the evolution of protein interaction networks: addition and elimination of interactions between proteins, and gene duplications increasing the number of proteins and interactions. The rates of these processes can be estimated from available Saccharomyces cerevisiae genome data and are sufficiently high to affect network structure on short time-scales. For instance, more than 100 interactions may be added to the yeast network every million years, a fraction of which adds previously unconnected proteins to the network. Highly connected proteins show a greater rate of interaction turnover than proteins with few interactions. From these observations one can explain (without natural selection on global network structure) the evolutionary sustenance of the most prominent network feature, the distribution of the frequency P(d) of proteins with d neighbours, which is broad-tailed and consistent with a power law, that is: P(d) proportional, variant d (-gamma).