ei is the relative error in the i-th cell, and d0 is a constant given by the hypothesis. Using those symbols, the hypothesis of the Pearson chi-square test can be described as H0: d = 0. When there is a discrepancy between the reference and observed distribution, the distribution of Pearson’s chi-square statistics can be approximated by a non-central chi-square distribution with mean nzd, where v is the degree of freedom and d is the non-centrality parameter calculated by d~d=n, where n is the sample size. We used the EST based gene expression profiles of livers of human, mouse, chicken, and X. laevis, since liver tissue is composed primarily of a homogeneous population of differentiated cells, and the EST frequency data can provide the estimate of the absolute mRNA abundance. (For other tissues primarily composed of a mixture of different kind of cells, we do not have enough parameters necessary for the goodness-of-fit test, such as the numbers and proportions of different kinds of cells and the degree of discrepancy of gene expression profiles among those types of cells.) Common logarithms of EST counts were binned into five bins (0–0.5, 0.5–1.0, 1.0–1.5, 1.5–2.0, and more than 2.0), because the gene expression profiles based on ESTs are very sparse sequences of discrete values of EST counts and the number of genes. The reference distribution of tag frequencies was obtained from the Monte Carlo simulation with the model parameters L = 1.0, M = 300,000, and N = 20,000 as follows. The hypothetical gene expression profiles were generated by the Monte Carlo simulation (sk = 0.01, 100,000 generations), and we randomly chose 10,000 tags, and binned the result as described above. This trial was References 1. King MC, Wilson AC (1975) Evolution at two levels in humans and chimpanzees. Science 188: 107–116. 2. Ferea TL, Botstein D, Brown PO, Rosenzweig RF (1999) Systematic changes in gene expression patterns following adaptive evolution in yeast. Proc Natl Acad Sci USA 96: 9721–9726. 3. Brem RB, Yvert G, Clinton R, Kruglyak L (2002) Genetic dissection of transcriptional regulation in budding yeast. Science 296: 752–755. 4. Cavalieri D, Townsend JP, Hartl DL (2000) Manifold anomalies in gene expression in a vineyard isolate of Saccharomyces cerevisiae revealed by DNA microarray analysis. Proc Natl Acad Sci USA 97: 12369–12374. 5. Townsend JP, Cavalieri D, Hartl DL (2003) Population genetic variation in genome-wide gene expression. Mol Biol Evol 20: 955–963. 6. Jin W, Riley RM, Wolfinger RD, White KP, Passador-Gurgel G, et al. (2001) The contributions of sex, genotype and age to transcriptional variance in Drosophila melanogaster. Nat Genet 29: 389–395. 7. Rifkin SA, Kim J, White KP (2003) Evolution of gene expression in the Drosophila melanogaster subgroup. Nat Genet 33: 138–144. 8. Gibson G, Riley-Berger R, Harshman L, Kopp A, Vacha S, et al. (2004) Extensive sex-specific nonadditivity of gene expression in Drosophila melanogaster. Genetics 167: 1791–1799. 9. Nuzhdin SV, Wayne ML, Harmon KL, McIntyre LM (2004) Common pattern of evolution of gene expression level and protein sequence in Drosophila. Mol Biol Evol 21: 1308–1317. 10. Wayne ML, Pan YJ, Nuzhdin SV, McIntyre LM (2004) Additivity and trans- acting effects on gene expression in male Drosophila simulans. Genetics 168: 1413–1420. 11. Pritchard CC, Hsu L, Delrow J, Nelson PS (2001) Project normal: defining normal variance in mouse gene expression. Proc Natl Acad Sci USA 98: 13266–13271. 12. Schadt EE, Monks SA, Drake TA, Lusis AJ, Che N, et al. (2003) Genetics of gene expression surveyed in maize, mouse and man. Nature 422: 297–302. 13. Cheung VG, Conlin LK, Weber TM, Arcaro M, Jen K-Y, et al. (2003) Natural variation in human gene expression assessed in lymphoblastoid cells. Nat Genet 33: 422–425. 14. Monks SA, Leonardson A, Zhu H, Cundiff P, Pietrusiak P, et al. (2004) Genetic inheritance of gene expression in human cell lines. Am J Hum Genet 75: 1094–1105. 15. Sharma A, Sharma VK, Horn-Saban S, Lancet D, Ramachandran S, et al. (2005) Assessing natural variations in gene expression in humans by comparing with monozygotic twins using microarrays. Physiol Genomics 21: 117–123. 16. Tan Q, Christensen K, Christiansen L, Frederiksen H, Bathum L, et al. (2005) Genetic dissection of gene expression observed in whole blood samples of elderly Danish twins. Hum Genet 117: 267–274. Gene Expression Evolution repeated 100 times and the averaged hypothetical tag frequency were used as the reference distribution of the goodness-of-fit test. The relative error of each bin was estimated by the CV (standard deviation/mean) calculated from EST profile data of human liver (dbEST library IDs: 6989, 252, 12555). The CV of each bin was 0.037, 0.35, 0.11, 0.63, and 0.056, respectively. Supporting Information Figure S1 Time development of hypothetical mRNA abun- dance generated by Monte Carlo simulations of the previous model (L = 0.0). Other model parameters were: M = 20,000, N = 300,000. The line shows y = 0.1/x. Found at: doi:10.1371/journal.pone.0007943.s001 (0.37 MB PDF) Figure S2 Time development of hypothetical mRNA abun- dance generated by Monte Carlo simulations of the refined neutral model (L = 1.0) Other model parameters were: M = 20,000, N = 300,000. The line shows y = 0.1/x. Found at: doi:10.1371/journal.pone.0007943.s002 (0.39 MB PDF) Author Contributions Conceived and designed the experiments: OO. Performed the experi- ments: OO. Analyzed the data: OO KO. Contributed reagents/materials/ analysis tools: OO. Wrote the paper: OO. 17. Oleksiak MF, Churchill GA, Crawford DL (2002) Variation in gene expression within and among natural populations. Nat Genet 32: 261–266. 18. Oleksiak MF, Roach JL, Crawford DL (2005) Natural variation in cardiac metabolism and gene expression in Fundulus heteroclitus. Nat Genet 37: 67–72. 19. Enard W, Khaitovich P, Klose J, Zollner S, Heissig F, et al. (2002) Intra- and interspecific variation in primate gene expression patterns. Science 296: 340–343. 20. Hsieh W-P, Chu T-M, Wolfinger RD, Gibson G (2003) Mixed-model reanalysis of primate data suggests tissue and species biases in oligonucleotide-based gene expression profiles. Genetics 165: 747–757. 21. Yanai I, Graur D, Ophir R (2004) Incongruent expression profiles between human and mouse orthologous genes suggest widespread neutral evolution of transcription control. OMICS 8: 15–24. 22. Khaitovich P, Weiss G, Lachmann M, Hellmann I, Enard W, et al. (2004) A neutral model of transcriptome evolution. PLoS Biol 2: E132. 23. Lemos B, Meiklejohn CD, Caceres M, Hartl DL (2005) Rates of divergence in gene expression profiles of primates, mice, and flies: stabilizing selection and variability among functional categories. Evolution Int J Org Evolution 59: 126–137. 24. Whitehead A, Crawford DL (2005) Variation in tissue-specific gene expression among natural populations. Genome Biol 6: R13. 25. Whitehead A, Crawford DL (2006) Neutral and adaptive variation in gene expression. Proc Natl Acad Sci USA 103: 5425–5430. 26. Khaitovich P, Pa¨a¨bo S, Weiss G (2005) Toward a neutral evolutionary model of gene expression. Genetics 170: 929–939. 27. Lande R (1976) Natural selection and random genetic drift in phenotypic evolution. Evolution 30: 314–334. 28. Lande R (1977) Statistical tests for natural selection on quantitative characters. Evolution 31: 442–444. 29. Turelli M, Gillespie JH, Lande R (1988) Rate tests for selection on quantitative characters during macroevolution and microevolution. Evolution 42: 1085–1089. 30. Whitehead A, Crawford DL (2006) Variation within and among species in gene expression: raw material for evolution. Mol Ecol 15: 1197–1211. 31. Zipf GK (1949) Human Behavior and the Principle of Least Effort. Cambridge, MA: Addison-Wesley. 32. Luscombe NM, Qian J, Zhang Z, Johnson T, Gerstein M (2002) The dominance of the population by a selected few: power-law behaviour applies to a wide variety of genomic properties. Genome Biol 3: RESEARCH0040. 33. Furusawa C, Kaneko K (2003) Zipf’s law in gene expression. Phys Rev Lett 90: 088102. 34. Kuznetsov VA (2003) Family of skewed distributions associated with the gene expression and protein evolution. Signal Processing 83: 889–910. PLoS ONE | www.plosone.org 10 November 2009 | Volume 4 | Issue 11 | e7943