the nearly neutral theory was put forward in 1973 as an extension of the neutral theory ( ohta 1973 ) . simply put , the nearly neutral theory posits that there exists a significant class of alleles that are sufficiently weakly selected such that the evolutionary dynamics are governed by both drift and selection . at the beginning , there are now various data from amino acid substitutions to genomic structural variations relating to the nearly neutral theory . in the following , i present progress in the applicability of the theory ; near - neutrality is widely observed at the protein level , and divergence pattern of gene expression is mostly consistent with near - neutrality . another interesting development on near - neutrality is found in the concept of robustness of gene regulatory networks . the nearly neutral theory has become more significant in understanding morphological evolution because gene regulation is thought to be the basis of organismal development , and nearly neutral mutations would increase under robust systems as compared with sensitive systems . figure 1 shows the comparison of the selection , the neutral and the nearly neutral theories on how new mutations are classified . an important prediction of the nearly neutral theory is the negative correlation between the evolutionary rate and the effective population size of species . this is because , in the nearly neutral class , slightly deleterious mutations are much more abundant than slightly advantageous ones ( ohta 1992 ) . also , if selection coefficients are dependent upon conditions determined by genetic backgrounds and environments , even slightly advantageous mutant substitutions may become rapid in small populations as compared with large populations ( ohta 1972 ) . diagram to show how new mutations are classified under the selection , the neutral , and the nearly neutral theories . the diagram of the nearly neutral theory is made by folding that of the neutral theory . therefore , the selected class includes both advantageous and deleterious mutations and the nearly neutral class , both slightly advantageous and slightly deleterious one . comparison of the pattern of synonymous and nonsynonymous substitutions at the protein - coding regions gives opportunities for verifying the population size effect . note that mammalian lineages are characterized as follows : organisms with long generation time tend to have small population size and vice versa . so population size tends to be large for rodents , middle for artiodactyls , and small for primates . i analyzed the 49 gene sequences of three orders , primates , artiodactyls , and rodents ( ohta 1995 ) . the results are in accord with the prediction , that is , the rodent branch is much longer than the primate branch for the synonymous tree , but the difference of the two lineages is not so large for nonsynonymous tree . this is because of the population size effect of nearly neutral amino acid substitutions in comparison with synonymous changes . genome data show similar pattern , for example , the ratio of nonsynonymous to synonymous divergence is higher in human  chimpanzee comparison than in mouse  rat comparison ( the chimpanzee sequencing and analysis consortium 2005 ) . a second key prediction of the nearly neutral theory is abundance of low - frequency polymorphisms as compared with strict neutrality . data on dna polymorphisms reveal prevalence of nearly neutral amino acid substitutions . for example , hughes et al . ( 2003 ) have analyzed human snp data and found that amino acid changing snps show reduced diversity as compared with synonymous snps in agreement with the nearly neutral prediction . the mcdonald  kreitman ( m - k ) test ( mcdonald and kreitman 1991 ) , that compares the relative numbers of synonymous and nonsynonymous substitutions within a population and those between closely related species , is popular for detecting selection . several reports have been published on data analyses by using an extended m - k test . for example , smith and eyre - walker ( 2002 ) analyzed data of drosophila simulans and d. yakuba and emphasized that 45% of amino acid substitutions have been fixed by positive selection . 2007 ) have performed a solid analysis of x chromosome data of drosophila melanogaster and d. simulans , that is , polymorphisms in 91 genes in an african population of the former and the divergence between the two species . the result is interesting : about 70% of amino acid changing polymorphisms are slightly deleterious , but about 95% of fixed differences are positively selected . they also estimated that about 50% of amino acid changes are nearly neutral , if the near - neutrality is defined as |nes| < 1 . they conclude that weak selection of which substantial fraction is nearly neutral is efficient for adaptive evolution of proteins . functional approach on amino acid substitutions is becoming to have impact on near - neutrality . ( 2010 ) examined functional effects of single amino acid substitutions in isopropylmalate dehydrogenase ( imdh ) of escherichia coli . they have found that the transition from e. coli imdh to pseudomonas aeruginosa imdh can not be explained without assuming slightly deleterious amino acid substitutions followed by compensatory substitutions . this nearly neutral process is thought to be caused by cryptic epistasis among amino acids within the protein molecule . by using genome - wide polymorphism data of closely related species of yeast , elyashiv et al . ( 2010 ) have performed detailed statistical analyses to estimate the effect of purifying selection . the yeast species used are characterized by having several completely isolated subpopulations with varying sizes . they have found negative correlation between heterozygosity and the ratio of nonsynonymous to synonymous polymorphisms on these subpopulations , whereas this ratio is larger for the within - population polymorphisms than on fixed differences among subpopulations . these results have verified the prevalence of weak purifying selection supporting the nearly neutral theory . they have further found that the shifts in intensity of selection across populations can be explained by the change of a single parameter , that is , population size . the best - studied case of gene regulation is the interaction of transcription factors and enhancers in the upstream of the transcription start site . gene regulation is thought to be in a well - balanced state , and any mutations that disturb the balance are deleterious . ludwig et al . ( 2000 ) have found that the enhancer regions are in constant turnover , that is , nucleotide substitutions at the enhancer region of the gene , even skipped , are occurring within the allowed latitude of stabilizing selection on this gene expression . in other words , the turnover is nearly neutral . by measuring the level of mrna in various organs of human and chimpanzee , khaitovich et al . ( 2006 ) have clarified the relationship between diversity of mrna levels among human individuals and the divergence of mrna levels between human and chimpanzee . they have found that the results for various organs have been mostly consistent with the nearly neutral prediction . the authors interpret that this rapid divergence reflects positive selection on gene expression for testis . by using quantitative genetics approach , bedford and hartl ( 2009 ) examined the observed variance of mrna levels among seven drosophila species . based on this observation , they estimated the intensity of stabilizing selection on expression levels and have found that the selection is weak , may be regarded as mostly nearly neutral . however , they emphasize that divergence among the species is mostly attributed to positive selection , and therefore , weak selection is effective . in this section , let us consider why such a large fraction of mutations both at the protein level and at the level of gene regulation are subject to weak selection . although robustness of biological systems has been recognized since waddington , molecular methods to tackle this subject have become available only recently . our knowledge on this is now rapidly expanding and should be incorporated into discussions of evolution . particularly , the concept seems to provide an important clue to the long - standing issue on how molecular changes and morphological evolution are linked . also it is important to recognize that robustness increases the width of near - neutrality ( ohta 2002 ) . wagner ( 2005 ) argues that pathways of gene expression are complex , and numerous networks are entangled and that the system becomes robust to any perturbations . another type of robustness is found by the morphological anomaly induced by mutations of the hsp90 ( rutherford and lindquist 1998 ) . hsp90 is a molecular chaperone and helps to stabilize signal transduction systems , and its defects cause phenotypic anomalies . participation of micrornas to the stability of various genetic systems is also suggested ( hornstein and shomron 2006 ) . let us survey various types of robustness , that is , mutational ( genetic ) , environmental , and stochastic ones . for the analysis , data on large - scale synthetic lethal or sick screens of yeast and other model organisms are useful . by examining such data , lehner ( 2010 ) in other words , when genetic perturbation by a mutation has minor effect but have large effects in combination with defects of other genes ( i.e. , synthetic lethal or sick and therefore robust ) , the gene shows resilience to environmental stress ( environmental robustness ) and/or stochastic change ( stochastic robustness ) . this negative interaction is equivalent to robustness , and mutations will have initially small ( or nearly neutral ) effects . lehner ( 2010 ) argues that , under variable environment , resilience to many environmental conditions is advantageous and selected for , and genetic robustness has evolved as a by - product of evolution of environmental robustness yeast data also provide some important characteristics of quantitative genetic interactions relating to robustness . ( 2010 ) surveyed quantitative mapping of genetic interactions of yeast data on colony size of mutant strains . by using the multiplicative model , they classified the interaction types into the following three , positive , neutral , and negative interactions . positive interaction means that the fitness effect of the double mutants is less than that expected from the two single mutations . negative interaction means that effect of the double mutants is more than that expected from the two single mutations . ( 2010 ) have focused on proteins involved in chromatin biology , such as chromosome segregation , transcription , and chromatin modeling / remodeling . note that proteins form complex set consisting of functional modules , each of which is made of several clusters . their significant finding is that , within each cluster , genetic interactions are mostly positive , whereas , among the clusters , they are mostly negative . remember that the three clusters are involved in chromatin modeling / remodeling , and proteins in each cluster often physically associate . it has often been emphasized that genetic interactions are rapidly changing in evolution as compared with proteins ( roguev et al . 2008 ) . in the chromatin modeling / remodeling system above , beltrao et al . ( 2010 ) have further noticed that positive interactions are more conserved than negative interactions . by assuming that interactive effects parallel with fitness values , negative interactions result in more robust and more nearly neutral systems than positive interactions . above findings based on genome - wide data proteins are more conserved than genetic interaction systems as mentioned before . however , note that the previous example of slightly deleterious plus compensatory amino acid substitutions in evolution of idmh ( lunzer et al . 2010 ) may be regarded as a robust system of amino acids that makes the protein . the meaning of epigenetics is broad and various processes involved in  the inheritance of variation above and beyond changes in the dna sequence , let us define epigenetics as more than one phenotypes under the same genotype that are heritable for some generations . epigenetics is intimately related to robustness as both lie between genotypes and phenotypes , and their incorporation into evolutionary problems is a most urgent task . among various processes involved in epigenetics , it is thought that dna methylation is linked to chromatin structure and to participate in gene regulation . it has been known for some time that the spectrum of genome methylation is very broad , that is , it is different among species and among loci within a genome and that its function is related to gene regulation . following suzuki and bird ( 2008 ) , however , this global methylation pattern is limited to vertebrates , and mosaic patterns are observed in yeast and fruitfly . in plants , global pattern is seen , but the methylation system of transposons is different from that of animals . it has been known for some time that dna methylation works to silence gene expression . in the following , i present summary of suzuki and bird ( 2008 ) . dna methylation pattern is different according to cell types and therefore may contribute to development . comparison of such methylation maps provides basic data for considering the meaning of within - species ( among individuals ) and between - species differences of methylation patterns . also active research is going on how dna methylation map is different among various human tissues . next , i discuss an interesting idea on how dna methylation may contribute to evolution of complex systems . variation of dna methylation at regulatory regions among individuals of the same genotype increases variation of gene expression and hence variability of phenotypes . feinberg and irizarry ( 2010 ) consider that the increase of variability is important for coping with environmental stresses and examined variation of methylation patterns in human and mouse tissues . they have identified the locations of variable regions of dna methylation among individuals in mouse liver and termed them variably methylated regions ( vmrs ) . they have extended the analysis to mouse brain , human liver , and human brain and found that vmrs are often associated with genes for development and morphogenesis . it has also been noted that the variation in methylation is likely to be caused by gain or loss of cpg in regions involved in gene regulation . based on these findings , they argue that , if variable methylation at a regulatory region of a gene is advantageous under variable environments , its genetic basis , that is , loss or gain of cpg dinucleotides , is selected for , and provides plasticity in the developmental program . note that variation of gene expression is intimately related to robustness because it is reciprocal of stochastic robustness ( kaneko 2007 ) , and the latter is linked to genetic and environmental robustness ( lehner 2010 ) . both epigenetics and robustness are involved in processes that lie between genotype and phenotype , and their effects on weak selection must be significant . although robustness of biological systems has been recognized since waddington , molecular methods to tackle this subject have become available only recently . our knowledge on this is now rapidly expanding and should be incorporated into discussions of evolution . particularly , the concept seems to provide an important clue to the long - standing issue on how molecular changes and morphological evolution are linked . also it is important to recognize that robustness increases the width of near - neutrality ( ohta 2002 ) . wagner ( 2005 ) argues that pathways of gene expression are complex , and numerous networks are entangled and that the system becomes robust to any perturbations . another type of robustness is found by the morphological anomaly induced by mutations of the hsp90 ( rutherford and lindquist 1998 ) . hsp90 is a molecular chaperone and helps to stabilize signal transduction systems , and its defects cause phenotypic anomalies . participation of micrornas to the stability of various genetic systems is also suggested ( hornstein and shomron 2006 ) . so there are various mechanisms to increase robustness . following lehner ( 2010 ) , let us survey various types of robustness , that is , mutational ( genetic ) , environmental , and stochastic ones . for the analysis , data on large - scale synthetic lethal or sick screens of yeast and other model organisms are useful . by examining such data , lehner ( 2010 ) has found that genetic robustness is often correlated with stochastic robustness and/or environmental robustness . in other words , when genetic perturbation by a mutation has minor effect but have large effects in combination with defects of other genes ( i.e. , synthetic lethal or sick and therefore robust ) , the gene shows resilience to environmental stress ( environmental robustness ) and/or stochastic change ( stochastic robustness ) . this negative interaction is equivalent to robustness , and mutations will have initially small ( or nearly neutral ) effects . lehner ( 2010 ) argues that , under variable environment , resilience to many environmental conditions is advantageous and selected for , and genetic robustness has evolved as a by - product of evolution of environmental robustness yeast data also provide some important characteristics of quantitative genetic interactions relating to robustness . ( 2010 ) surveyed quantitative mapping of genetic interactions of yeast data on colony size of mutant strains . by using the multiplicative model , they classified the interaction types into the following three , positive , neutral , and negative interactions . positive interaction means that the fitness effect of the double mutants is less than that expected from the two single mutations . negative interaction means that effect of the double mutants is more than that expected from the two single mutations . ( 2010 ) have focused on proteins involved in chromatin biology , such as chromosome segregation , transcription , and chromatin modeling / remodeling . note that proteins form complex set consisting of functional modules , each of which is made of several clusters . their significant finding is that , within each cluster , genetic interactions are mostly positive , whereas , among the clusters , they are mostly negative . remember that the three clusters are involved in chromatin modeling / remodeling , and proteins in each cluster often physically associate . it has often been emphasized that genetic interactions are rapidly changing in evolution as compared with proteins ( roguev et al . 2008 ) . in the chromatin modeling / remodeling system above , beltrao et al . ( 2010 ) have further noticed that positive interactions are more conserved than negative interactions . by assuming that interactive effects parallel with fitness values , negative interactions result in more robust and more nearly neutral systems than positive interactions . above findings based on genome - wide data however , note that the previous example of slightly deleterious plus compensatory amino acid substitutions in evolution of idmh ( lunzer et al . 2010 ) may be regarded as a robust system of amino acids that makes the protein . the meaning of epigenetics is broad and various processes involved in  the inheritance of variation above and beyond changes in the dna sequence  are included ( bonasio et al . 2010 ) . here , let us define epigenetics as more than one phenotypes under the same genotype that are heritable for some generations . epigenetics is intimately related to robustness as both lie between genotypes and phenotypes , and their incorporation into evolutionary problems is a most urgent task . among various processes involved in epigenetics , it is thought that dna methylation is linked to chromatin structure and to participate in gene regulation . it has been known for some time that the spectrum of genome methylation is very broad , that is , it is different among species and among loci within a genome and that its function is related to gene regulation . following suzuki and bird ( 2008 ) , however , this global methylation pattern is limited to vertebrates , and mosaic patterns are observed in yeast and fruitfly . in plants , global pattern is seen , but the methylation system of transposons is different from that of animals . it has been known for some time that dna methylation works to silence gene expression . in the following , i present summary of suzuki and bird ( 2008 ) . dna methylation pattern is different according to cell types and therefore may contribute to development . comparison of such methylation maps provides basic data for considering the meaning of within - species ( among individuals ) and between - species differences of methylation patterns . also active research is going on how dna methylation map is different among various human tissues . next , i discuss an interesting idea on how dna methylation may contribute to evolution of complex systems . variation of dna methylation at regulatory regions among individuals of the same genotype increases variation of gene expression and hence variability of phenotypes . feinberg and irizarry ( 2010 ) consider that the increase of variability is important for coping with environmental stresses and examined variation of methylation patterns in human and mouse tissues . they have identified the locations of variable regions of dna methylation among individuals in mouse liver and termed them variably methylated regions ( vmrs ) . they have extended the analysis to mouse brain , human liver , and human brain and found that vmrs are often associated with genes for development and morphogenesis . it has also been noted that the variation in methylation is likely to be caused by gain or loss of cpg in regions involved in gene regulation . based on these findings , they argue that , if variable methylation at a regulatory region of a gene is advantageous under variable environments , its genetic basis , that is , loss or gain of cpg dinucleotides , is selected for , and provides plasticity in the developmental program . note that variation of gene expression is intimately related to robustness because it is reciprocal of stochastic robustness ( kaneko 2007 ) , and the latter is linked to genetic and environmental robustness ( lehner 2010 ) . both epigenetics and robustness are involved in processes that lie between genotype and phenotype , and their effects on weak selection must be significant . let us now consider the problem of drift and selection , that is , the nearly neutral zone of figure 1 in relation to robustness and epigenetics . natural selection works on phenotypes , but its effects are transmitted by underlying genotypes , and the two are linked by epigenetics and robustness of organismal development . , it is important to notice that epigenetic processes provide variable phenotypes that may be useful in changing environments because regulatory systems would readily respond to environmental stresses . a scenario to show the meaning of near - neutrality in relation to epigenetics and robustness that connect phenotypes with genotypes . in relation to robustness , the human genome has extraactivity as shown by the encode project consortium ( 2007 ) , that is , transcriptional activity is more widespread in human genome than expected from protein - coding regions . such activities are thought to be mainly nearly neutral , that is , they occur and may survive in allowed latitude under weak selection , drift , and robustness . actual patterns on gene expression divergence analyzed by bedford and hartl ( 2009 ) and by khaitovich et al . ( 2006 ) , mentioned previously , may fit to the present scenario . from the above scenario , it may be said that near - neutrality prevails at the genotype level but that natural selection may predominate at the phenotype level . important points of this scenario are environmental contacts to gene expression and availability of enough room for modifying gene networks . note also that , under the scenario , some proposals on epigenetic effects in evolution and variation ( jablonka and lamb 2002 ; west - eberhard 2003 ; slatkin 2009 ) may become more understandable . as to  chance and necessity  by jacques monod , he might have considered natural selection at the phenotype level because molecular bases of epigenetics and robustness were not known 40 years ago . here , i would like to emphasize again that this scenario may have significant implications for understanding evolution of enormously complicated systems at various levels in biological world .
the nearly neutral theory emphasizes the interaction of drift and weak selection in evolution . with progress of genome biology 
 , the applicability of the nearly neutral theory has expanded . 
 the genome - wide analyses of synonymous and nonsynonymous substitutions at protein - coding regions show prevalence of very weak selection . 
 many patterns of evolution of gene regulation are also in agreement with the nearly neutral prediction . our consideration on near - neutrality expands in relation to the progress on molecular understanding of robustness and epigenetics . 
 both are bridges to link genotypes with phenotypes and important for understanding how weak selection and drift interact in the evolution of complex systems .