Gene Expression Evolution Figure 3. Time development of gene expression divergence. Each point shows the gene expression divergence averaged over 100 repetitions of the simulation. (A) L = 0.0. (B) L = 1.0. Other model parameters are: M = 300,000 and N = 20,000. Initial distribution (t = 0) of the simulations follows Zipf’s law. doi:10.1371/journal.pone.0007943.g003 in about additional 2.3 million generations (Figure 4) [22]. Here we assume that divergence of human-chimpanzee, human- orangutan, and human-macaque takes approximately some 6, 13, and 23 million years, respectively [60], and that average generations in human, chimpanzee, orangutan, and macaque are 28, 22, 20, and 11.4 years, respectively [61,62]. In addition, an upper limit can be clearly seen in the time- course of gene expression divergence based on a subset of genes which has the largest evolutionary rate (25% of genes that has the largest human variation among 2,926 genes measured). From a human-chimpanzee comparison to human-orangutan compari- son, the divergence increases about 0.44, but from human- orangutan to human-macaque, the divergence increases only about 0.06 [22]. Therefore, at present, the refined model appears to be more consistent with observations than previous models. Moreover, our model supports the suggestion by Whitehead and Crawford (2006) [30] that the inconsistency of results from several previous studies is caused by the loss of linearity between gene expression divergence and generation over the long-run. There- fore our model might be used for predicting appropriate time scales for distinguishing the effects of random drift and natural selection in the primate lineage. The estimate of standard deviation sk under the neutral model can be obtained from the expression divergence data of primates [22] as follows. Monte Carlo simulations indicate that the number of generations needed for gene expression divergence to reach a given value, say 0.3 (human-orangutan), decreases rapidly and that the evolutionary rate of the previous model (L = 0.0) is generally larger than that of the refined model (L = 1.0). The relationship between sk and the number of generations is well fitted to 2T = 4.79 sk22.02 (L = 1.0) and 2T = 1.67 sk21.99 (L = 0). From this formula, the standard deviation sk of the primate lineage was estimated from the observations of Khaitovich et al. (2004) [22] as about 2.1561023 under the neutral model (Figure 4). Figure 4. Time development of gene expression divergence of primate brains. (A) The number of generations required for gene expression divergence to be 0.3. Each point is the mean value averaged over 100 repetitions. The red line is L = 1 and the blue line is L = 0. (B) Time development of gene expression divergence. Red points are the gene expression divergence between humans and other primates reported by Khaitovich et al [22]. Black points are the result of the simulation averaged over 10 repetitions, and error bars represent standard deviation. In the both panels, model parameters are: L = 1.0, M = 300,000, and N = 20,000. Initial distribution (t = 0) of the simulations followed Zipf’s law. doi:10.1371/journal.pone.0007943.g004 PLoS ONE | www.plosone.org 5 November 2009 | Volume 4 | Issue 11 | e7943