Phylogenetic analysis and intraspecific variation: performance of parsimony,likelihood, and distance methods

Intraspecific variation is abundant in all types of systematic characters but is rarely addressed in simulation studies of phylogenetic method performance. We compared the accuracy of 15 phylogenetic methods using simulations to (1) determine the most accurate method(s) for analyzing polymorphic data (under simplified conditions) and (2) test if generalizations about the performance of phylogenetic methods based on previous simulations of fixed (nonpolymorphic) characters are robust to a very different evolutionary model that explicitly includes intraspecific variation. Simulated data sets consisted of allele frequencies that evolved by genetic drift. The phylogenetic methods included eight parsimony coding methods, continuous maximum likelihood, and three distance methods (UPGMA, neighbor joining, and Fitch-Margoliash) applied to two genetic distance measures (Nei's and the modified Cavalli-Sforza and Edwards chord distance). Two sets of simulations were performed. The first examined the effects of different branch lengths, sample sizes (individuals sampled per species), numbers of characters, and numbers of alleles per locus in the eight-taxon case. The second examined more extensively the effects of branch length in the four-taxon, two-allele case. Overall, the most accurate methods were likelihood, the additive distance methods (neighbor joining and Fitch-Margoliash), and the frequency parsimony method. Despite the use of a very different evolutionary model in the present article, many of the results are similar to those from simulations of fixed characters. Similarities include the presence of the "Felsenstein zone," where methods often fail, which suggests that long-branch attraction may occur among closely related species through genetic drift. Differences between the results of fixed and polymorphic data simulations include the following: (1) UPGMA is as accurate or more accurate than nonfrequency parsimony methods across nearly all combinations of branch lengths, and (2) likelihood and the additive distance methods are not positively misled under any combination of branch lengths tested (even when the assumptions of the methods are violated and few characters are sampled). We found that sample size is an important determinant of accuracy and affects the relative success of methods (i.e., distance and likelihood methods outperform parsimony at small sample sizes). Attempts to generalize about the behavior of phylogenetic methods should consider the extreme examples offered by fixed-mutation models of DNA sequence data and genetic-drift models of allele frequencies.     

Generalized character process models: estimating the genetic basis of traits that cannot be observed and that change with age or environmental conditions

The genetic analysis of characters that change as a function of some independent and continuous variable has received increasing attention in the biological and statistical literature. Previous work in this area has focused on the analysis of normally distributed characters that are directly observed. We propose a framework for the development and specification of models for a quantitative genetic analysis of function-valued characters that are not directly observed, such as genetic variation in age-specific mortality rates or complex threshold characters. We employ a hybrid Markov chain Monte Carlo algorithm involving a Monte Carlo EM algorithm coupled with a Markov chain approximation to the likelihood, which is quite robust and provides accurate estimates of the parameters in our models. The methods are investigated using simulated data and are applied to a large data set measuring mortality rates in the fruit fly, Drosophila melanogaster.     

Deleterious mutations and the genetic variance of male fitness components in Mimulus guttatus

Deleterious mutations are relevant to a broad range of questions in genetics and evolutionary biology. I present an application of the "biometric method" for estimating mutational parameters for male fitness characters of the yellow monkeyflower, Mimulus guttatus. The biometric method rests on two critical assumptions. The first is that experimental inbreeding changes genotype frequencies without changing allele frequencies; i.e., there is no genetic purging during the experiment. I satisfy this condition by employing a breeding design in which the parents are randomly extracted, fully homozygous inbred lines. The second is that all genetic variation is attributable to deleterious mutations maintained in mutation-selection balance. I explicitly test this hypothesis using likelihood ratios. Of the three deleterious mutation models tested, the first two are rejected for all characters. The failure of these models is due to an excess of additive genetic variation relative to the expectation under mutation-selection balance. The third model is not rejected for either of two log-transformed male fitness traits. However, this model imposes only "weak conditions" and is not sufficiently detailed to provide estimates for mutational parameters. The implication is that, if biometric methods are going to yield useful parameter estimates, they will need to consider mutational models more complicated than those typically employed in experimental studies.     

GENETIC COMPONENTS OF VARIATION IN ENERGY STORAGE IN DROSOPHILA MELANOGASTER

One approach to examining the underlying genetic structure of the variation in a continuous phenotype is to measure a set of possibly mechanistically related traits and determine the quantitative genetic aspects of their transmission. In this study the quantities of stored triacylglycerol and glycogen were measured along with the activities of 10 enzymes in related metabolic pathways in a set of 1,157 half-sib families of Drosophila melanogaster. The families were structured with each male being mated to 10 females and two offspring were scored from each female. Parents and offspring were scored for the phenotypes, and the components of variance (additive, dominance, and environmental) were estimated in three ways, including analysis of variance on offspring alone, parent-offspring regression, and maximum likelihood methods. While there were differences among the estimates made by the three methods, a consistent result was that substantial additive genetic variation was detected for all the traits. Consistent with models for the quantitative genetics of enzyme kinetics, the genetic variances of global properties were largely additive. Previous studies with extracted chromosome lines had indicated several significant genetic correlations among these characters, and much of the correlation was attributable to additive effects. The results imply that there is substantial opportunity for natural or artificial selection to act on quantities of stored lipid and carbohydrate, and that the response to selection is likely to be in part mediated by changes in the kinetics of the enzymes targeted in this study.     

Evolutionary mode, tempo, and phylogenetic association of continuous morphological traits in the aquatic moss genus Amblystegium

Evolutionary significance of morphological characters that have traditionally been used for species delineation in the aquatic moss genus Amblystegium was tested by partitioning the environmentally and genetically induced morphological variation and focusing on morphological evolution using comparative methods. Cultivation experiments under controlled condition showed that most of the morphological variation in nature resulted from plasticity. Information regarding genetically fixed morphological variation and genetic similarity derived from polymorphic inter-simple sequence repeat markers was combined into an explicit model of morphological evolution. Maximum likelihood estimates of the model parameters indicated that evolution of most characters tended to accelerate in the most recent taxa and was often independent from the phylogeny. Constraining the different characters to be independent from each other most often produced a less likely result than when the characters were free to evolve in a correlated fashion. Thus, the morphological characters that have traditionally been used to circumscribe different Amblystegium species lack the independence, diagnostic value for specific lineages, and stability that would be required for distinguishing different species.     

GENOTYPE-ENVIRONMENT INTERACTION AND THE EVOLUTION OF PHENOTYPIC PLASTICITY

Studies of spatial variation in the environment have primarily focused on how genetic variation can be maintained. Many one-locus genetic models have addressed this issue, but, for several reasons, these models are not directly applicable to quantitative (polygenic) traits. One reason is that for continuously varying characters, the evolution of the mean phenotype expressed in different environments (the norm of reaction) is also of interest. Our quantitative genetic models describe the evolution of phenotypic response to the environment, also known as phenotypic plasticity (Gause, 1947), and illustrate how the norm of reaction (Schmalhausen, 1949) can be shaped by selection. These models utilize the statistical relationship which exists between genotype-environment interaction and genetic correlation to describe evolution of the mean phenotype under soft and hard selection in coarse-grained environments. Just as genetic correlations among characters within a single environment can constrain the response to simultaneous selection, so can a genetic correlation between states of a character which are expressed in two environments. Unless the genetic correlation across environments is ± 1, polygenic variation is exhausted, or there is a cost to plasticity, panmictic populations under a bivariate fitness function will eventually attain the optimum mean phenotype for a given character in each environment. However, very high positive or negative correlations can substantially slow the rate of evolution and may produce temporary maladaptation in one environment before the optimum joint phenotype is finally attained. Evolutionary trajectories under hard and soft selection can differ: in hard selection, the environments with the highest initial mean fitness contribute most individuals to the mating pool. In both hard and soft selection, evolution toward the optimum in a rare environment is much slower than it is in a common one. A subdivided population model reveals that migration restriction can facilitate local adaptation. However, unless there is no migration or one of the special cases discussed for panmictic populations holds, no geographical variation in the norm of reaction will be maintained at equilibrium. Implications of these results for the interpretation of spatial patterns of phenotypic variation in natural populations are discussed.     

Selection on floral characters in natural Spanish populations of Silene latifolia

In insect-pollinated plants, floral characters are expected to play an important role in paternal and maternal reproductive success. Bateman's principle states that male reproductive success increases with more mating opportunities, while female reproductive success is limited by the amount of resources available to produce progeny, thus there should be greater selection on male floral characters than on female. In the case of the dioecious plant Silene latifolia, floral characters are likely to be influenced by its association within its native European range with moths of the genus Hadena, which serve as both pollinators and seed predators. The present study addresses relationships between male and female reproductive success, spatial location and floral characters (corolla, calyx and claw) over a 2-year period in two Spanish populations of S. latifolia in the presence of Hadena moths. A maximum likelihood paternity analysis using genetic variation at six allozyme markers showed heterogeneity in male reproductive success. There was much less variation in female reproductive success. When this analysis was extended to include interplant distance as a causal factor underlying variation in male success, we found that successful pollination tended to be limited to nearby females, in accordance with exponential decay of pollen dispersal with increasing distance. When the paternity analysis included floral characters as a causal factor underlying variation in male success, our data showed little evidence for directional selection, but there was stabilizing selection in one of the two years for calyx diameter. Selection on female characters varied widely between sites and years, in most of the site/year combinations there was little selection on female floral characters; however, in one site/year there was evidence for selection on all three floral characters. We conclude that pollinators visit flowers that are close together, and that while floral characters are important for the attraction of pollinators, larger flowers do not necessarily attract more pollinators at all sites and that variation among sites and years makes difficult any conclusions about the long-term importance of the predictions suggested by Bateman's principle.     

QUANTITATIVE VARIATION OF PROGENY FROM CHASMOGAMOUS AND CLEISTOGAMOUS FLOWERS IN THE GRASS DANTHONIA SPICATA

Progeny from chasmogamous (CH) and cleistogamous (CL) flowers of the grass Danthonia spicata were raised in their native habitat and in the greenhouse in order to determine how genetic variation was distributed among families and between CH and CL progeny within families. Twelve quantitative characters were measured on clones from individuals known to have arisen from either CH or CL flowers on a particular plant. Significant genetic variation existed for all characters measured. Most genetic variation was between families and two morphologically similar groups of families were identified. Relatively little genetic variation was found within families (approximately 5% of the total phenotypic variance). In field-raised plants, variance component analysis suggested that CL progeny were genetically more similar to each other than were CH progeny from the same plant. Levene's test of the average deviation of CH and CL progenies from their group means was nonsignificant but suggested there was a trend (0.05 < P < 0.10) for CH progeny to be more variable than CL progeny in the field but less variable in the greenhouse. The amount and distribution of genetic variation in the study population indicates that selective differentials would be larger among families than within families.     

Quantitative Trait Loci Differentiating the Outbreeding Mimulus Guttatus from the Inbreeding M. Platycalyx

Theoretical predictions about the evolution of selfing depend on the genetic architecture of loci controlling selfing (monogenic vs. polygenic determination, large vs. small effect of alleles, dominance vs. recessiveness), and studies of such architecture are lacking. We inferred the genetic basis of mating system differences between the outbreeding Mimulus guttatus and the inbreeding M. platycalyx by quantitative trait locus (QTL) mapping using random amplified polymorphic DNA and isozyme markers. One to three QTL were detected for each of five mating system characters, and each QTL explained 7.6-28.6% of the phenotypic variance. Taken together, QTL accounted for up to 38% of the variation in mating system characters, and a large proportion of variation was unaccounted for. Inferred QTL often affected more than one trait, contributing to the genetic correlation between those traits. These results are consistent with the hypothesis that quantitative variation in plant mating system characters is primarily controlled by loci with small effect.     

FITNESS VARIATION DUE TO SEXUAL ANTAGONISM AND LINKAGE DISEQUILIBRIUM

Extensive fitness variation for sexually antagonistic characters has been detected in nature. However, current population genetic theory suggests that sexual antagonism is unlikely to play a major role in the maintenance of variation. We present a two‐locus model of sexual antagonism that is capable of explaining greater fitness variance at equilibrium than previous single‐locus models. The second genetic locus provides additional fitness variance in two complementary ways. First, linked loci can maintain gene variants that are lost in single‐locus models of evolution, expanding the opportunity for polymorphism. Second, linkage disequilibrium results between any two sexually antagonistic genes, producing an excess of high‐ and low‐fitness haplotypes. Our results uncover a unique contribution of conflicting selection pressures to the maintenance of variation, which simpler models that neglect genetic architecture overlook.     

A genetic analysis of early development in pink (Oncorhynchus gorbuscha) and chum salmon (Oncorhynchus keta) at three different temperatures

A factorial mating design was employed in which five males were mated to each of five females in each of two stocks for both pink and chum salmon. The resulting embryos and alevins were incubated at constant water temperatures of 4, 8, and 16 degrees C for pink salmon and 3, 8, and 15 degrees C for chum salmon. Variation among families in alevin and fry survival rates, hatching, button-up time, length, and weight was the least at 8 degrees C. Heritability of traits directly correlated with fitness, such as survival rates and button-up time, was low at all temperatures (h2 less than or equal to 0.25). Maternal effects could account for a substantial portion of the variation in alevin and fry size characters. Nonadditive genetic variance accounted for more of the variation in fry size characters than in those of alevins. Negative genetic correlations were observed between embryo survival and subsequent alevin size and between hatching time and subsequent alevin and fry size. Genotype-temperature interactions could underlie a substantial amount of phenotypic variation in the developmental characters examined for both species.     

GENETIC BASIS OF ACTIVITY METABOLISM. I. INHERITANCE OF SPEED,STAMINA, AND ANTIPREDATOR DISPLAYS IN THE GARTER SNAKE THAMNOPHIS SIRTALIS

Recent conceptual advances in physiological ecology emphasize the potential selective importance of whole-animal performance. Empirical studies of locomotor performance in reptiles have revealed surprising amounts of individual variation in speed and stamina. The present study is the first in a series examining the genetic basis of variation in locomotor performance, activity metabolism, and associated behaviors in garter snakes. Maximal sprint crawling speed, treadmill endurance, and antipredator displays (Arnold and Bennett, 1984; exhibited as snakes reached exhaustion on the treadmill) were measured for approximately six offspring (presumed to be full siblings) from each of 46 wild-caught gravid garter snakes (Thamnophis sirtalis). Each character was measured on two days; all were individually repeatable. Correlations of these characters with body mass, snout–vent length, age at testing, litter size, dam mass, and dam snout–vent length were removed by computing residuals from multiple-regression equations. These residuals were used in subsequent genetic analyses. Approximate coefficients of variation of residuals were 17% for speed, 48% for endurance, and 31% for antipredator displays. Broad-sense heritabilities were significant for all characters: speed h² = 0.58; stamina h² = 0.70; antipredator display h² = 0.42. All three residual characters showed positive and statistically significant phenotypic correlations (r = 0.19–0.36). Genetic correlations (estimated and tested by restricted maximum likelihood) among residuals were positive and highly significant between speed and endurance (0.58), but nonsignificant between speed and antipredator display (0.43), and between endurance and antipredator display (0.26). All environmental correlations were nonsignificant. These data suggest that, contrary to expectations based on previous physiological studies, there may be no necessary evolutionary trade-off between speed and stamina in these animals. This tentative conclusion will have important implications for future theoretical studies of the evolution of locomotor performance and associated antipredator behaviors.     

THE QUANTITATIVE GENETICS OF SEXUAL DIMORPHISM IN SILENE LATIFOLIA (CARYOPHYLLACEAE). I. GENETIC VARIATION

It is widely recognized that there are basic conflicts between the resource needs of a plant for paternal versus maternal functions. In dioecious species, these divergent demands, and the selection pressures they impose, can lead to the evolution of sexual dimorphism. The present study was conducted to assess the potential for the evolution of sexual dimorphism in Silene latifolia by evaluating the genetic variation and genetic correlation between characters and between the sexes for a range of growth and reproductive characters. Sexual dimorphism is largely restricted to reproductive characters, particularly flower number and flower size. A canonical correlation analysis revealed considerable intercorrelation between growth characters, such as germination date, height, and leaf size, and reproductive characters; plants that grow fast early on also flower earlier, and plants that produce big leaves also produce big flowers. There was genetic variation for several sexually dimorphic characters; much of the focus in this analysis was on flower size, particularly calyx diameter. Finally, genetic correlations within and between the sexes were found that limit the rate of evolutionary divergence between the sexes. The genetic results suggest that S. latifolia has been subject to divergent selection on the two sexes for a long period of time, bringing about a gradual fixation of sex-limited gene effects, so that the remaining genetic effects are expressed in both sexes. Genetic correlations between the sexes that arise from this residual variation impose limits on further evolutionary change.     

QUANTITATIVE GENETICS OF MORPHOLOGICAL DIFFERENTIATION IN PEROMYSCUS. I. TESTS OF THE HOMOGENEITY OF GENETIC COVARIANCE STRUCTURE AMONG SPECIES AND SUBSPECIES

Phenotypic and additive genetic covariance matrices were estimated for 15 morphometric characters in three species and subspecies of Peromyscus. Univariate and multivariate ANOVAs indicate these groups are highly diverged in all characters, P. leucopus having the largest body size, P. maniculatus bairdii the smallest, and P. maniculatus nebrascensis being intermediate. Comparing the structure of P and G within each taxon revealed significant similarities in all three cases. This proportionality was strong enough to justify using P in the place of G to analyze evolutionary processes using quantitative genetic models when G can not be estimated, as in fossil material. However, the similarity between genetic and phenotypic covariance structures is sufficiently low that estimates of the genetic parameters should be used when possible. The additive genetic covariance matrices were compared to examine the assumption that they remain constant during evolution, an assumption which underlies many applications of quantitative-genetic models. While matrix permutation tests indicated statistically significant proportionality between the genetic covariance structures of the two P. maniculatus subspecies, there is no evidence of significant genetic structural similarity between species. This result suggests that the assumption of constant genetic covariance structure may be valid only within species. (It does not, however, necessarily imply a causal relationship between speciation and heterogeneity of genetic covariance structures.) The low matrix correlation for the two P. maniculatus subspecies' genetic covariance matrices indicates G may not be functionally constant, even within species. The lack of similarity observed here may be due partly to sampling variation.     

Chemical and genetic variability of selected Turkish oregano (Origanum onites L.) clones

Turkish oregano (Origanum onites L.) is a major aromatic plant that belongs to Labiatae family. In this work fourteen Turkish oregano clones have been characterized chemically and genetically. Essential oil obtained by hydro-distillation was characterized by gas chromatography. Genetic variation was determined by use of random amplified polymorphic DNA (RAPD) markers. Variation of essential oils in the selected clones was subjected to cluster analysis, and two chemotypes, carvacrol and thymol, were identified. Carvacrol was found to be the main component in all clones except clone-661, the main component of which was thymol. The oregano clones were divided into three main groups by clustering on the basis of RAPD markers. Genetic similarity values among the oregano clones ranged between 0.49 and 0.73 which was indicative of a low level of genetic variation. Clones originating from locations close to each other had similar RAPD markers. Correlation analysis of the genetic distance matrix and the Euclidian distance matrix revealed no significant correlation between them. The results also indicated that there is no relationship between genetic structure of the selected clones and essential oil composition.     

母体遗传效应对绒山羊生产性状遗传参数估计的影响

利用非求导约束最大似然法(DF-REML), 比较了内蒙古白绒山羊在两种不同动物模型下估计遗传参数的差异, 两种模型的区别在于是否考虑母体遗传效应。对两种模型的差异用似然比进行检验。结果表明, 母体遗传效应对于体重和绒厚影响极显著(P<0.01), 对于抓绒量、毛长、绒长度以及绒细度影响不显著(P>0.05)。     

GENETIC CONSTRAINTS ON MACROEVOLUTION: THE EVOLUTION OF HOST AFFILIATION IN THE LEAF BEETLE GENUS OPHRAELLA

We hypothesize that the evolution of an ecologically important character, the host associations of specialized phytophagous insects, has been influenced by limitations on genetic variation. Using as a historical framework a phylogenetic reconstruction of the history of host associations in the beetle genus Ophraella (Chrysomelidae), we have employed quantitative-genetic methods to screen four species for genetic variation in larval survival, oviposition (in one species only), and feeding responses to their congeners' host plants, in the Asteraceae. We here report results of studies of one species and evaluate the results from all four. Analysis of half-sib/full-sib families and of progenies of wild females of O. notulata, a specialist on Iva (Ambrosiinae), provided evidence of genetic variation in larval consumption of five of six test plants and in adult consumption of four of six. Larval mortality was complete on five plants; only on Ambrosia, a close relative of the natural host, was there appreciable, and genetically variable, survival. Oviposition on Ambrosia showed marginally significant evidence of genetic variation; a more distantly related plant elicited no oviposition at all. In compiling results from four Ophraella species, reported in this and two other papers, we found no evidence of genetic variation in 18 of 39 tests of feeding responses and 14 of 16 tests of larval survival on congeners' hosts. This result is consistent with the hypothesis that absence or paucity of genetic variation may constrain or at least bias the evolution of host associations. The lower incidence of genetic variation in survival than in feeding behavior may imply, according to recent models, that avoidance is a more common evolutionary response to novel plants than adaptation. The usually great disparity between mean performance on congeners' hosts and the species' natural hosts, and an almost complete lack of evidence for negative genetic correlations, argue against the likelihood that speciation has occurred by sympatric host shift. The presence versus apparent absence of genetic variation in consumption was correlated with the propinquity of relationship between the beetle species tested and the species that normally feeds on the test plant, suggesting that the history of host shifts in Ophraella has been guided in part by restrictions on genetic variation. It was also correlated with the propinquity of relationship between a test plant and the beetle's natural host. The contributions of plant relationships and insect relationships, themselves correlated in part, to the pattern of genetic variation, are not readily distinguishable, but together accord with phylogenetic evidence that these and other phytophagous insects adapt most readily to related plants. In this instance, therefore, the macroevolution of an ecologically important character appears to have been influenced by genetic constraints. We hypothesize that absence of the structural prerequisites for genetic variation in complex characters may affect genetic variation and the trajectory of evolution.     

The Influence of the Mating System on the Maintenance of Genetic Variability in Polygenic Characters

The traditional models of the effect of assortative mating and inbreeding on the genetic variance of polygenic characters (Fisher 1918; Wright 1921) presume that there is no natural selection or mutation. In a large population, the genetic variance determined by additive genes may then increase by up to a factor of two with local inbreeding, and even more with assortative mating. The classical models are still used to interpret data from natural populations. But contrary to their assumptions, most metrical characters in natural populations are usually thought to be under a type of selection which depletes polygenic variation. Mutation is then necessary to maintain genetic variation. The present models show that with the additional features of mutation and selection, in a large population, the mating system has no influence on the amount of genetic variability maintained by additive genes.     

THE EVOLUTIONARY GENETICS OF MALE LIFE-HISTORY CHARACTERS IN DROSOPHILA MELANOGASTER

Alternative models of the maintenance of genetic variability, theories of life-history evolution, and theories of sexual selection and mate choice can be tested by measuring additive and nonadditive genetic variances of components of fitness. A quantitative genetic breeding design was used to produce estimates of genetic variances for male life-history traits in Drosophila melanogaster. Additive genetic covariances and correlations between traits were also estimated. Flies from a large, outbred, laboratory population were assayed for age-specific competitive mating ability, age-specific survivorship, body mass, and fertility. Variance-component analysis then allowed the decomposition of phenotypic variation into components associated with additive genetic, nonadditive genetic, and environmental variability. A comparison of dominance and additive components of genetic variation provides little support for an important role for balancing selection in maintaining genetic variance in this suite of traits. The results provide support for the mutation-accumulation theory, but not the antagonistic-pleiotropy theory of senescence. No evidence is found for the positive genetic correlations between mating success and offspring quality or quantity that are predicted by “good genes” models of sexual selection. Additive genetic coefficients of variation for life-history characters are larger than those for body weight. Finally, this set of male life-history characters exhibits a very low correspondence between estimates of genetic and phenotypic correlations.     

Chromosome Rearrangements Recovered following Transformation of Neurospora Crassa

Analyses of evolution and maintenance of quantitative genetic variation depend on the mutation models assumed. Currently two polygenic mutation models have been used in theoretical analyses. One is the random walk mutation model and the other is the house-of-cards mutation model. Although in the short term the two models give similar results for the evolution of neutral genetic variation within and between populations, the predictions of the changes of the variation are qualitatively different in the long term. In this paper a more general mutation model, called the regression mutation model, is proposed to bridge the gap of the two models. The model regards the regression coefficient, γ, of the effect of an allele after mutation on the effect of the allele before mutation as a parameter. When γ = 1 or 0, the model becomes the random walk model or the house-of-cards model, respectively. The additive genetic variances within and between populations are formulated for this mutation model, and some insights are gained by looking at the changes of the genetic variances as γ changes. The effects of γ on the statistical test of selection for quantitative characters during macroevolution are also discussed. The results suggest that the random walk mutation model should not be interpreted as a null hypothesis of neutrality for testing against alternative hypotheses of selection during macroevolution because it can potentially allocate too much variation for the change of population means under neutrality.