The evolution of the chemical isotopes as an analog of biological evolution

A comparison is made between a biological adaptive landscape and the chemical isotopic landscape defined with three dimensions: the number of protons, the number of neutrons, and the stability of each isotopic nucleus. The courses of both biological and elemental evolution have been stochastic, leading from the simple to the complex; this is in agreement with statistical thermodynamic predictions. Analogs of mutation and natural selection occur in elementary evolution. The isotopic landscape can be assumed to have an a priori existence; at least the general features of the biological adaptive landscape also have an a priori existence. Both landscapes were occupied by spontaneous processes, analogous to diffusion.     

Male and female recombination landscapes of diploid Arabidopsis arenosa

The number and placement of meiotic crossover events during meiosis have important implications for the fidelity of chromosome segregation as well as patterns of inheritance. Despite the functional importance of recombination, recombination landscapes vary widely among and within species, and this can have a strong impact on evolutionary processes. A good knowledge of recombination landscapes is important for model systems in evolutionary and ecological genetics, since it can improve interpretation of genomic patterns of differentiation and genome evolution, and provides an important starting point for understanding the causes and consequences of recombination rate variation. Arabidopsis arenosa is a powerful evolutionary genetic model for studying the molecular basis of adaptation and recombination rate evolution. Here, we generate genetic maps for 2 diploid A. arenosa individuals from distinct genetic lineages where we have prior knowledge that meiotic genes show evidence of selection. We complement the genetic maps with cytological approaches to map and quantify recombination rates, and test the idea that these populations might have distinct patterns of recombination. We explore how recombination differs at the level of populations, individuals, sexes and genomic regions. We show that the positioning of crossovers along a chromosome correlates with their number, presumably a consequence of crossover interference, and discuss how this effect can cause differences in recombination landscape among sexes or species. We identify several instances of female segregation distortion. We found that averaged genome-wide recombination rate is lower and sex differences subtler in A. arenosa than in Arabidopsis thaliana.     

A model-based Bayesian estimation of the rate of evolution of VNTR loci in Mycobacterium tuberculosis

Variable numbers of tandem repeats (VNTR) typing is widely used for studying the bacterial cause of tuberculosis. Knowledge of the rate of mutation of VNTR loci facilitates the study of the evolution and epidemiology of Mycobacterium tuberculosis. Previous studies have applied population genetic models to estimate the mutation rate, leading to estimates varying widely from around to per locus per year. Resolving this issue using more detailed models and statistical methods would lead to improved inference in the molecular epidemiology of tuberculosis. Here, we use a model-based approach that incorporates two alternative forms of a stepwise mutation process for VNTR evolution within an epidemiological model of disease transmission. Using this model in a Bayesian framework we estimate the mutation rate of VNTR in M. tuberculosis from four published data sets of VNTR profiles from Albania, Iran, Morocco and Venezuela. In the first variant, the mutation rate increases linearly with respect to repeat numbers (linear model); in the second, the mutation rate is constant across repeat numbers (constant model). We find that under the constant model, the mean mutation rate per locus is (95% CI: ,)and under the linear model, the mean mutation rate per locus per repeat unit is (95% CI: ,). These new estimates represent a high rate of mutation at VNTR loci compared to previous estimates. To compare the two models we use posterior predictive checks to ascertain which of the two models is better able to reproduce the observed data. From this procedure we find that the linear model performs better than the constant model. The general framework we use allows the possibility of extending the analysis to more complex models in the future.     

Molecular evolution of the meiotic recombination pathway in mammals

Meiotic recombination shapes evolution and helps to ensure proper chromosome segregation in most species that reproduce sexually. Recombination itself evolves, with species showing considerable divergence in the rate of crossing‐over. However, the genetic basis of this divergence is poorly understood. Recombination events are produced via a complicated, but increasingly well‐described, cellular pathway. We apply a phylogenetic comparative approach to a carefully selected panel of genes involved in the processes leading to crossovers—spanning double‐strand break formation, strand invasion, the crossover/non‐crossover decision, and resolution—to reconstruct the evolution of the recombination pathway in eutherian mammals and identify components of the pathway likely to contribute to divergence between species. Eleven recombination genes, predominantly involved in the stabilization of homologous pairing and the crossover/non‐crossover decision, show evidence of rapid evolution and positive selection across mammals. We highlight TEX11 and associated genes involved in the synaptonemal complex and the early stages of the crossover/non‐crossover decision as candidates for the evolution of recombination rate. Evolutionary comparisons to MLH1 count, a surrogate for the number of crossovers, reveal a positive correlation between genome‐wide recombination rate and the rate of evolution at TEX11 across the mammalian phylogeny. Our results illustrate the power of viewing the evolution of recombination from a pathway perspective.     

Meiotic,genomic and evolutionary properties of crossover distribution in Drosophila yakuba

The number and location of crossovers across genomes are highly regulated during meiosis, yet the key components controlling them are fast evolving, hindering our understanding of the mechanistic causes and evolutionary consequences of changes in crossover rates. Drosophila melanogaster has been a model species to study meiosis for more than a century, with an available high-resolution crossover map that is, nonetheless, missing for closely related species, thus preventing evolutionary context. Here, we applied a novel and highly efficient approach to generate whole-genome high-resolution crossover maps in D. yakuba to tackle multiple questions that benefit from being addressed collectively within an appropriate phylogenetic framework, in our case the D. melanogaster species subgroup. The genotyping of more than 1,600 individual meiotic events allowed us to identify several key distinct properties relative to D. melanogaster. We show that D. yakuba, in addition to higher crossover rates than D. melanogaster, has a stronger centromere effect and crossover assurance than any Drosophila species analyzed to date. We also report the presence of an active crossover-associated meiotic drive mechanism for the X chromosome that results in the preferential inclusion in oocytes of chromatids with crossovers. Our evolutionary and genomic analyses suggest that the genome-wide landscape of crossover rates in D. yakuba has been fairly stable and captures a significant signal of the ancestral crossover landscape for the whole D. melanogaster subgroup, even informative for the D. melanogaster lineage. Contemporary crossover rates in D. melanogaster, on the other hand, do not recapitulate ancestral crossovers landscapes. As a result, the temporal stability of crossover landscapes observed in D. yakuba makes this species an ideal system for applying population genetic models of selection and linkage, given that these models assume temporal constancy in linkage effects. Our studies emphasize the importance of generating multiple high-resolution crossover rate maps within a coherent phylogenetic context to broaden our understanding of crossover control during meiosis and to improve studies on the evolutionary consequences of variable crossover rates across genomes and time.     

Natural selection fails to optimize mutation rates for long-term adaptation on rugged fitness landscapes

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms.     

Why sampling scheme matters: the effect of sampling scheme on landscape genetic results

There has been a recent trend in genetic studies of wild populations where researchers have changed their sampling schemes from sampling pre-defined populations to sampling individuals uniformly across landscapes. This reflects the fact that many species under study are continuously distributed rather than clumped into obvious “populations”. Once individual samples are collected, many landscape genetic studies use clustering algorithms and multilocus genetic data to group samples into subpopulations. After clusters are derived, landscape features that may be acting as barriers are examined and described. In theory, if populations were evenly sampled, this course of action should reliably identify population structure. However, genetic gradients and irregularly collected samples may impact the composition and location of clusters. We built genetic models where individual genotypes were either randomly distributed across a landscape or contained gradients created by neighbor mating for multiple generations. We investigated the influence of six different sampling protocols on population clustering using program STRUCTURE, the most commonly used model-based clustering method for multilocus genotype data. For models where individuals (and their alleles) were randomly distributed across a landscape, STRUCTURE correctly predicted that only one population was being sampled. However, when gradients created by neighbor mating existed, STRUCTURE detected multiple, but different numbers of clusters, depending on sampling protocols. We recommend testing for fine scale autocorrelation patterns prior to sample clustering, as the scale of the autocorrelation appears to influence the results. Further, we recommend that researchers pay attention to the impacts that sampling may have on subsequent population and landscape genetic results. The U.S. Government's right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

The effect of phenotypic plasticity on evolution in multipeaked fitness landscapes

When facing the challenge of developing an individual that best fits its environment, nature demonstrates an interesting combination of two fundamentally different adaptive mechanisms: genetic evolution and phenotypic plasticity. Following numerous computational models, it has become the accepted wisdom that lifetime acclimation (e.g. via learning) smooths the fitness landscape and consequently accelerates evolution. However, analytical studies, focusing on the effect of phenotypic plasticity on evolution in simple unimodal landscapes, have often found that learning hinders the evolutionary process rather than accelerating it. Here, we provide a general framework for studying the effect of plasticity on evolution in multipeaked landscapes and introduce a rigorous mathematical analysis of these dynamics. We show that the convergence rate of the evolutionary process in a given arbitrary one-dimensional fitness landscape is dominated by the largest descent (drawdown) in the landscape and provide numerical evidence to support an analogous dominance also in multidimensional landscapes. We consider several schemes of phenotypic plasticity and examine their effect on the landscape drawdown, identifying the conditions under which phenotypic plasticity is advantageous. The lack of such a drawdown in unimodal landscapes vs. its dominance in multipeaked landscapes accounts for the seemingly contradictory findings of previous studies.     

Mutation and the experimental evolution of outcrossing in Caenorhabditis elegans

An understanding of the forces that contribute to the phylogenetically widespread phenomenon of sexual reproduction has posed a longstanding problem in evolutionary biology. Mutational theories contend that sex can be maintained when the deleterious mutation rate is sufficiently high, although empirical evidence is equivocal and experimental studies are rare. To test the influence of mutation on the evolution of obligate outcrossing, I introduced a genetic polymorphism for breeding system into populations of the nematode Caenorhabditis elegans with high- and low-mutation rate genetic backgrounds and tracked the change in frequency of females, hermaphrodites, and males over approximately 21 generations. Hermaphrodites invaded all populations, regardless of mutational background. However, experimental populations with elevated mutation rates experienced more outcrossing and greater retention of females. This provides experimental evidence consistent with deleterious mutational explanations for the evolution of sex in principle, but the action of other processes is required to explain the evolution of sex in entirety.     

The evolution of bacterial mutation rates under simultaneous selection by interspecific and social parasitism

Many bacterial populations harbour substantial numbers of hypermutable bacteria, in spite of hypermutation being associated with deleterious mutations. One reason for the persistence of hypermutators is the provision of novel mutations, enabling rapid adaptation to continually changing environments, for example coevolving virulent parasites. However, hypermutation also increases the rate at which intraspecific parasites (social cheats) are generated. Interspecific and intraspecific parasitism are therefore likely to impose conflicting selection pressure on mutation rate. Here, we combine theory and experiments to investigate how simultaneous selection from inter- and intraspecific parasitism affects the evolution of bacterial mutation rates in the plant-colonizing bacterium Pseudomonas fluorescens. Both our theoretical and experimental results suggest that phage presence increases and selection for public goods cooperation (the production of iron-scavenging siderophores) decreases selection for mutator bacteria. Moreover, phages imposed a much greater growth cost than social cheating, and when both selection pressures were imposed simultaneously, selection for cooperation did not affect mutation rate evolution. Given the ubiquity of infectious phages in the natural environment and clinical infections, our results suggest that phages are likely to be more important than social interactions in determining mutation rate evolution.     

On the evolution of dispersal via heterogeneity in spatial connectivity

Dispersal has long been recognized as a mechanism that shapes many observed ecological and evolutionary processes. Thus, understanding the factors that promote its evolution remains a major goal in evolutionary ecology. Landscape connectivity may mediate the trade-off between the forces in favour of dispersal propensity (e.g. kin-competition, local extinction probability) and those against it (e.g. energetic or survival costs of dispersal). It remains, however, an open question how differing degrees of landscape connectivity may select for different dispersal strategies. We implemented an individual-based model to study the evolution of dispersal on landscapes that differed in the variance of connectivity across patches ranging from networks with all patches equally connected to highly heterogeneous networks. The parthenogenetic individuals dispersed based on a flexible logistic function of local abundance. Our results suggest, all else being equal, that landscapes differing in their connectivity patterns will select for different dispersal strategies and that these strategies confer a long-term fitness advantage to individuals at the regional scale. The strength of the selection will, however, vary across network types, being stronger on heterogeneous landscapes compared with the ones where all patches have equal connectivity. Our findings highlight how landscape connectivity can determine the evolution of dispersal strategies, which in turn affects how we think about important ecological dynamics such as metapopulation persistence and range expansion.     

Adaptive Landscape by Environment Interactions Dictate Evolutionary Dynamics in Models of Drug Resistance

The adaptive landscape analogy has found practical use in recent years, as many have explored how their understanding can inform therapeutic strategies that subvert the evolution of drug resistance. A major barrier to applications of these concepts is a lack of detail concerning how the environment affects adaptive landscape topography, and consequently, the outcome of drug treatment. Here we combine empirical data, evolutionary theory, and computer simulations towards dissecting adaptive landscape by environment interactions for the evolution of drug resistance in two dimensions—drug concentration and drug type. We do so by studying the resistance mediated by Plasmodium falciparum dihydrofolate reductase (DHFR) to two related inhibitors—pyrimethamine and cycloguanil—across a breadth of drug concentrations. We first examine whether the adaptive landscapes for the two drugs are consistent with common definitions of cross-resistance. We then reconstruct all accessible pathways across the landscape, observing how their structure changes with drug environment. We offer a mechanism for non-linearity in the topography of accessible pathways by calculating of the interaction between mutation effects and drug environment, which reveals rampant patterns of epistasis. We then simulate evolution in several different drug environments to observe how these individual mutation effects (and patterns of epistasis) influence paths taken at evolutionary “forks in the road” that dictate adaptive dynamics in silico. In doing so, we reveal how classic metrics like the IC₅₀ and minimal inhibitory concentration (MIC) are dubious proxies for understanding how evolution will occur across drug environments. We also consider how the findings reveal ambiguities in the cross-resistance concept, as subtle differences in adaptive landscape topography between otherwise equivalent drugs can drive drastically different evolutionary outcomes. Summarizing, we discuss the results with regards to their basic contribution to the study of empirical adaptive landscapes, and in terms of how they inform new models for the evolution of drug resistance.     

Crossover Heterogeneity in the Absence of Hotspots in Caenorhabditis elegans

Crossovers play mechanical roles in meiotic chromosome segregation, generate genetic diversity by producing new allelic combinations, and facilitate evolution by decoupling linked alleles. In almost every species studied to date, crossover distributions are dramatically nonuniform, differing among sexes and across genomes, with spatial variation in crossover rates on scales from whole chromosomes to subkilobase hotspots. To understand the regulatory forces dictating these heterogeneous distributions a crucial first step is the fine-scale characterization of crossover distributions. Here we define the wild-type distribution of crossovers along a region of the C. elegans chromosome II at unprecedented resolution, using recombinant chromosomes of 243 hermaphrodites and 226 males. We find that well-characterized large-scale domains, with little fine-scale rate heterogeneity, dominate this region’s crossover landscape. Using the Gini coefficient as a summary statistic, we find that this region of the C. elegans genome has the least heterogeneous fine-scale crossover distribution yet observed among model organisms, and we show by simulation that the data are incompatible with a mammalian-type hotspot-rich landscape. The large-scale structural domains—the low-recombination center and the high-recombination arm—have a discrete boundary that we localize to a small region. This boundary coincides with the arm-center boundary defined both by nuclear-envelope attachment of DNA in somatic cells and GC content, consistent with proposals that these features of chromosome organization may be mechanical causes and evolutionary consequences of crossover recombination.     

Landscape-level comparison of genetic diversity and differentiation in a small mammal inhabiting different fragmented landscapes of the Brazilian Atlantic Forest

Habitat loss and fragmentation can have detrimental effects on all levels of biodiversity, including genetic variation. Most studies that investigate genetic effects of habitat loss and fragmentation focus on analysing genetic data from a single landscape. However, our understanding of habitat loss effects on landscape-wide patterns of biodiversity would benefit from studies that are based on quantitative comparisons among multiple study landscapes. Here, we use such a landscape-level study design to compare genetic variation in the forest-specialist marsupial Marmosops incanus from four 10,000-hectare Atlantic forest landscapes which differ in the amount of their remaining native forest cover (86, 49, 31, 11 %). Additionally, we used a model selection framework to evaluate the influence of patch characteristics on genetic variation within each landscape. We genotyped 529 individuals with 12 microsatellites to statistically compare estimates of genetic diversity and genetic differentiation in populations inhabiting different forest patches within the landscapes. Our study indicates that before the extinction of the specialist species (here in the 11 % landscape) genetic diversity is significantly reduced in the 31 % landscape, while genetic differentiation is significantly higher in the 49 and 31 % landscapes compared to the 86 % landscape. Results further provide evidence for non-proportional responses of genetic diversity and differentiation to increasing habitat loss, and suggest that local patch isolation impacts gene flow and genetic connectivity only in the 31 % landscape. These results have high relevance for analysing landscape genetic relationships and emphasize the importance of landscape-level study designs for understanding habitat loss effects on all levels of biodiversity.     

Theoretical perspectives on the statics and dynamics of species' borders in patchy environments

Understanding range limits is a fundamental problem in ecology and evolutionary biology. In 1963, Mayr argued that "contaminating" gene flow from central populations constrained adaptation in marginal populations, preventing range expansion, while in 1984, Bradshaw suggested that absence of genetic variation prevented species from occurring everywhere. Understanding stability of range boundaries requires unraveling the interplay of demography, gene flow, and evolution of populations in concrete landscape settings. We walk through a set of interrelated spatial scenarios that illustrate interesting complexities of this interplay. To motivate our individual-based model results, we consider a hypothetical zooplankter in a landscape of discrete water bodies coupled by dispersal. We examine how patterns of dispersal influence adaptation in sink habitats where conditions are outside the species' niche. The likelihood of observing niche evolution (and thus range expansion) over any given timescale depends on (1) the degree of initial maladaptation; (2) pattern (pulsed vs. continuous, uni- vs. bidirectional), timing (juvenile vs. adult), and rate of dispersal (and hence population size); (3) mutation rate; (4) sexuality; and (5) the degree of heterogeneity in the occupied range. We also show how the genetic architecture of polygenic adaptation is influenced by the interplay of selection and dispersal in heterogeneous landscapes.     

Parasite-mediated evolution of the functional part of the MHC in primates

The major histocompatibility complex (MHC) is a key model of genetic polymorphism, but the mechanisms underlying its extreme variability are debated. Most hypotheses for MHC diversity focus on pathogen-driven selection and predict that MHC polymorphism evolves under the pressure of a diverse parasite fauna. Several studies reported that certain alleles offer protection against certain parasites, yet it remains unclear whether variation in parasite pressure more generally covaries with allelic diversity and rates of molecular evolution of MHC across species. We tested this prediction in a comparative study of 41 primate species. We characterized polymorphism of the exon 2 of DRB region of the MHC class II. Our phylogenetic analyses controlled for the potential effects of neutral mutation rate, population size, geographic origin and body mass and revealed that nematode species richness associates positively with nonsynonymous nucleotide substitution rate at the functional part of the molecule. We failed to find evidence for allelic diversity being strongly related to parasite species richness. Continental distribution was a strong predictor of both allelic diversity and substitution rate, with higher values in Malagasy and Neotropical primates. These results indicate that parasite pressure can influence the different estimates of MHC polymorphism, whereas geography plays an independent role in the natural history of MHC.     

The experimental evolution of specialists,generalists, and the maintenance of diversity

Environmental heterogeneity may be a general explanation for both the quantity of genetic variation in populations and the ecological niche width of individuals. To evaluate this hypothesis, I review the literature on selection experiments in heterogeneous environments. The niche width usually – but not invariably – evolves to match the amount of environmental variation, specialists evolving in homogeneous environments and generalists evolving in heterogeneous environments. The genetics of niche width are more complex than has previously been recognized, particularly with respect to the magnitude of costs of adaptation and the putative constraints on the evolution of generalists. Genetic variation in fitness is more readily maintained in heterogeneous environments than in homogeneous environments and this diversity is often stably maintained through negative frequency‐dependent selection. Moreover environmental heterogeneity appears to be a plausible mechanism for at least two well‐known patterns of species diversity at the landscape scale. I conclude that environmental heterogeneity is a plausible and possibly very general explanation for diversity across the range of scales from individuals to landscapes.     

Weak selection and protein evolution

The "nearly neutral" theory of molecular evolution proposes that many features of genomes arise from the interaction of three weak evolutionary forces: mutation, genetic drift, and natural selection acting at its limit of efficacy. Such forces generally have little impact on allele frequencies within populations from generation to generation but can have substantial effects on long-term evolution. The evolutionary dynamics of weakly selected mutations are highly sensitive to population size, and near neutrality was initially proposed as an adjustment to the neutral theory to account for general patterns in available protein and DNA variation data. Here, we review the motivation for the nearly neutral theory, discuss the structure of the model and its predictions, and evaluate current empirical support for interactions among weak evolutionary forces in protein evolution. Near neutrality may be a prevalent mode of evolution across a range of functional categories of mutations and taxa. However, multiple evolutionary mechanisms (including adaptive evolution, linked selection, changes in fitness-effect distributions, and weak selection) can often explain the same patterns of genome variation. Strong parameter sensitivity remains a limitation of the nearly neutral model, and we discuss concave fitness functions as a plausible underlying basis for weak selection.     

Linked selection,demography and the evolution of correlated genomic landscapes in birds and beyond

Selection has a deep impact on the distribution of genetic diversity and population differentiation along the genome (the genomic landscapes of diversity and differentiation), reducing diversity and elevating differentiation not only at the sites it targets, but also at linked neutral sites. Fuelled by the high‐throughput sequencing revolution, these genomic footprints of selection have been extensively exploited over the past decade with the aim to identify genomic regions involved in adaptation and speciation. However, while this research has shown that the genomic landscapes of diversity and differentiation are usually highly heterogeneous, it has also led to the increasing realization that this heterogeneity may evolve under processes other than adaptation or speciation. In particular, instead of being an effect of selective sweeps or barriers to gene flow, accentuated differentiation can evolve by any process reducing genetic diversity locally within the genome (Charlesworth, 1998 ), including purifying selection at linked sites (background selection). In particular, in genomic regions where recombination is infrequent, accentuated differentiation can evolve as a by‐product of diversity reductions unrelated to adaptation or speciation (Cruickshank & Hahn, 2014 ; Nachman & Payseur, 2012 ; Noor & Bennett, 2009 ). In such genomic regions, linkage extends over physically larger genome stretches, and selection affects a particularly high number of linked neutral sites. Even though the effects of selection on linked neutral diversity (linked selection) within populations are well documented (Cutter & Payseur, 2013 ), recent observations of diversity and differentiation landscapes that are highly correlated even among independent lineages suggest that the effects of long‐term linked selection may have a deeper impact on the evolution of the genomic landscapes of diversity and differentiation than previously anticipated. The study on Saxicola stonechats by Van Doren et al. ( 2017 ) reported in the current issue of Molecular Ecology lines in with a rapidly expanding body of evidence in this direction. Correlations of genomic landscapes extending from within stonechats to comparisons with Ficedula flycatchers add to recent insights into the timescales across which the effects of linked selection persist. Absent and inverted correlations of genomic landscapes in comparisons involving an island taxon, on the other hand, provide important empirical clues about the role of demographic constraints in the evolution of the genomic landscapes of diversity and differentiation.     

Molecular evolution, mutation size and gene pleiotropy: a geometric reexamination

The influence of phenotypic effects of genetic mutations on molecular evolution is not well understood. Neutral and nearly neutral theories of molecular evolution predict a negative relationship between the evolutionary rate of proteins and their functional importance; nevertheless empirical studies seeking relationships between evolutionary rate and the phenotypic role of proteins have not produced conclusive results. In particular, previous studies have not found the expected negative correlation between evolutionary rate and gene pleiotropy. Here, we studied the effect of gene pleiotropy and the phenotypic size of mutations on the evolutionary rate of genes in a geometrical model, in which gene pleiotropy was characterized by n molecular phenotypes that affect organismal fitness. For a nearly neutral process, we found a negative relationship between evolutionary rate and mutation size but pleiotropy did not affect the evolutionary rate. Further, for a selection model, where most of the substitutions were fixed by natural selection in a randomly fluctuating environment, we also found a negative relationship between evolutionary rate and mutation size, but interestingly, gene pleiotropy increased the evolutionary rate as √n. These findings may explain part of the disagreement between empirical data and traditional expectations.