The Age of a Neutral Mutant Persisting in a Finite Population

Formulae for the mean and the mean square age of a neutral allele which is segregating with frequency x in a population of effective size N(e) have been obtained using the diffusion equation method, for the case of 4N(e)v<1 where v is the mutation rate. It has been shown that the average ages of neutral alleles, even if their frequencies are relatively low, are quite old. For example, a neutral mutant whose current frequency is 10% has the expected age roughly equal to the effective population size N(e) and the standard deviation 1.4N(e) (in generations), assuming that this mutant has increased by random drift from a very low frequency. Also, formulae for the mean "first arrival time" of a neutral mutant to a certain frequency x have been presented. In addition, a new, approximate method has been developed which enables us to obtain the condition under which frequencies of "rare" polymorphic alleles among local populations are expected to be uniform if the alleles are selectively neutral.-It was concluded that exchange of only a few individuals on the average between adjacent colonies per generation is enough to bring about such a uniformity of frequencies.     

Analyses of the age of genes and the first arrival times in a finite population

The age of a mutant gene is studied using the infinite allele model in which every mutant is new and selectively neutral. Based on a time reversal theory of Markov processes, we develop a method of mathematical analysis that is considerably simpler for calculating the various statistics of the age than previous methods. Formulas for the mean and variance and for the distribution of age are presented together with some examples of relevance to cases in natural populations.—Theoretical studies of the first arrival time of an allele to a specified frequency, given an initially monomorphic condition of the locus, are presented. It is shown that, beginning with an allele that has frequency p = 1 or an allele with frequency p = 1/2N, there is an initial lag phase in which there is virtually no chance of an allele with a specified intermediate frequency appearing in the population. The distribution of the first arrival time is also presented. The distribution shows several characteristics that are not immediately obvious from a consideration of only the mean and variance of first arrival time. Especially noteworthy is the existence of a very long tail to the distribution. We have also studied the distribution of the age of an allele in the population. Again, the distribution of this measure is shown to be more informative for several questions than are the mean and variance alone.     

Increased Selection Response in Larger Populations. I. Selection for Wing-Tip Height in Drosophila Melanogaster at Three Population Sizes

The effect of population size on selection response was investigated with replicated selection lines of 40, 200 and 1000 selected parents, using Drosophila melanogaster homozygous for the mutant raised. Selection for increased wing-tip height was carried out for 55 generations, with an average selection intensity of 0.6 standard deviation. The rank order of responses in the seven individual lines was significantly in order of population size, and the variance of response among lines showed a significant effect of population size. The final mean responses (selected - controls, +/- standard errors) in the three treatments, in order of increasing population size, were 8.6 +/- 1.8 mils (three small lines), 15.1 +/- 1.3 mils (two medium lines), and 19.8 +/- 1.5 mils (two large lines). The differences between treatments seem to have emerged too rapidly to be the result of mutations, and are probably due mainly to the utilization of existing variation with greater efficiency by selection in larger populations.     

Towards an understanding of the nature and fitness of induced mutations in germ cells of mice: homozygous viability and heterozygous fitness effects of induced specific-locus, dominant cataract and enzyme-activity mutations

A total of 219 specific-locus, 35 dominant cataract and 44 enzyme-activity mutations induced in spermatogonia of mice by radiation or ethylnitrosourea (ENU) treatment were characterized for homozygous viability as well as fitness effects on heterozygous carriers. For all 3 genetic endpoints, the frequency of homozygous lethal mutations was higher in the group of radiation-induced mutations than in the ENU-treatment group. These observations are consistent with the hypothesis that radiation-induced mutations recovered in the mouse are mainly due to small deletions while ENU induces mainly intragenic mutations. The overall fitness of mutant heterozygotes was reduced for the group of radiation-induced specific-locus, dominant cataract and enzyme-activity mutations while the ENU-induced mutations exhibited no reduction in fitness. The fitness reduction of heterozygous carriers for a newly occurring mutation in a population is important in determining the persistence of the mutation in a population, and thus the total number of individuals affected before a mutation is eventually eliminated from the population. For the present results a maximal persistence of 12 generations and a minimal persistence of 3 generations is estimated. These results are consistent with the 6-7-generation persistence time assumed by UNSCEAR (1982) in an estimate of the overall effects of radiation-induced mutations in man.     

Prevalence of factor V G1691A (Leiden) and prothrombin G20210A polymorphisms among apparently healthy Jordanians

Factor V Leiden and prothrombin G20210A are related genetic risk factors for venous thromboembolism (VTE). Analysis for both mutations is increasingly being performed on patients exhibiting hypercoagulability. The objective of this study was to determine the prevalence of factor V Leiden (FVL), prothrombin-G20210A (PT-G20210A) polymorphisms and their coexistence among apparently healthy Jordanians. One thousand apparently healthy individuals from representative regions of Jordan with no previous history of VTE participated in this study. The mean age of participants was 28.5+/-6.4 years (age range 18-45 years). Two hundred and eighteen subjects were APC resistant with an APC-R mean of 85.52+/-15.35 seconds; the non-resistant subjects had an APC-R mean of 159.90+/-26.96 seconds. A multiplex polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP) for the simultaneous detection of FVL and prothrombin G20210A was used to analyze the 218 DNA samples that were APC-R resistant. Both mutations generate HindIII RFLPs and the prothrombin amplicon contains an invariant HindIII recognition sites. The multiplex PCR-RFLP of Factor V for those 218-samples was: 41 wild-type, 169 heterozygous mutant, and eight homozygous mutant individuals. For prothrombin G20210A, the multiplex PCR-RFLP identified 215 wild-type and three heterozygous mutant individuals. Factor V positive individuals (n=50) had a mean F-V activity of 78.04%+/-25.81. F-V activity among wild type (n=41), F-V Leiden heterozygous (n=169) and F-V Leiden homozygous (n=8) were 92.93%+/-16.17, 87.02%+/-15.21 and 96.14%+/-12.32, respectively. Factor II positive subjects (n=47) had a mean factor II activity of 127.96%+/-21.37. F-II activity among carriers (heterozygous, n=3) and non-carriers (normal, n=215) of PT-G20210A mutation were 107.67%+/-9.29 and 105.00%+/-17.79, respectively. The prevalence of FVL was 21.8% and there is a little likelihood of the co-inheritance of the FVL and PT-G20210A among healthy young adults, since only few cases were found to be carriers for the two alleles.     

On the Genealogy of a Rare Allele

The gene genealogy is derived for a rare allele that is descended from a mutant ancestor that arose at a fixed time in the past. Following Thompson (1976,Amer. J. Human Genet.28, 442–452), the fractional linear branching process is used as a model of the demography of a rare allele. The model does not require the total population size to be constant or the mutant class to be neutral; so long as individuals in the class are selectively equivalent, the class as a whole may have a selective advantage, or disadvantage, relative to other alleles in the population. An exact result is given for the joint probability distribution of the coalescence times among a sample of alleles descended from the mutant. A method is described for rapidly simulating these coalescence times. The relationship between the genealogical structure of a discrete generation branching process and a continuous generation birth–death process is elucidated. The theory may be applied to the problem of estimating the ages of rare nonrecurrent mutations.     

The consequences of the variance-mean rescaling effect on effective population size

The effective population size (N_e), and the ratio between N_e and census population size (N) are often used as measures of population viability. We show that using the harmonic mean of population sizes over time – a common proxy for N_e– has some important evolutionary consequences and implications for conservation management. This stems from the fact that there is no unambiguous relationship between the arithmetic and harmonic means for populations fluctuating in size. As long as the variance of population size increases moderately with increasing arithmetic mean population size, the harmonic mean also increases. However, if the variance of population size increases more rapidly, which existing data often suggest, then the harmonic mean may actually decrease with increasing arithmetic mean. Thus maximizing N may not maximize N_e, but could instead lower the adaptive potential and hence limit the evolutionary response to environmental change. Large census size has the clear advantage of lowering demographic stochasticity, and hence extinction risk, and under certain conditions large census size also minimizes the loss of genetic variation. Consequently, maximising census size has served as a useful dogma in ecology, genetics and conservation. Nonetheless, due to the intricate relationships among N_e, population viability and the properties of population fluctuations, we suggest that this dogma should be taken only as a rule of thumb.     

The anomalous effects of biased mutation revisited: mean-optimum deviation and apparent directional selection under stabilizing selection

Empirical evidence indicates that the distribution of the effects of mutations on quantitative traits is not symmetric about zero. Under stabilizing selection in infinite populations with normally distributed mutant effects having a nonzero mean, Waxman and Peck showed that the deviation of the population mean from the optimum is expected to be small. We show by simulation that genetic drift, leptokurtosis of mutational effects, and pleiotropy can increase the mean-optimum deviation greatly, however, and that the apparent directional selection thereby caused can be substantial.     

Age-related accumulation of autosomal mutations in solid tissues of the mouse is gender and cell type specific

Most cancers in solid tissues increase with age and invariably contain causal mutations eliminating expression of one or more autosomal tumor suppressor genes. However, very little is known about the effect of age on autosomal mutations, often large in size, in cells of solid tissues. In this study, the frequency and spectrum of autosomal mutations were examined as a function of age for kidney epithelial cells and ear mesenchymal cells in B6D2F1 mice heterozygous for the selectable Aprt locus. Aprt mutant frequencies were found to increase with age in the kidneys of both male and female mice, but at all ages the mutant frequencies were approximately twice as high in the females, which in this strain have shorter lifespans than the males. An age-related increase in Aprt mutant frequencies was also observed for ear cells from female mice, but no significant increases in mutant frequencies were observed for the ear cells of male mice. A molecular analysis showed that the kidney and ear mutational spectra were distinct and that the age-related increases in mutant frequencies did not involve significant shifts in the mutational spectra. In total, the results demonstrate both gender and cell-type-specific patterns of autosomal mutational accumulation as a function of age in two solid tissues of the mouse.     

Clusters of identical new mutation in the evolutionary landscape

In contrast to the common assumption that each new mutant results from a unique, independent mutation event, clusters of identical premeiotic mutant alleles are common. Clusters can produce large numbers of related individuals carrying identical copies of the same new genetic change. By entering the gene pool in multiple copies at one time, clusters can influence fundamental processes of population genetics. Here we report evidence that clusters can increase the arrival and fixation probabilities and can lengthen the average time to extinction of new mutations. We also suggest it may be necessary to reconsider other fundamental elements of population genetic theory.     

Age-related instability in spermatogenic cell nuclear and mitochondrial DNA obtained from Apex1 heterozygous mice

The prevalence of spontaneous mutations increases with age in the male germline; consequently, older men have an increased risk of siring children with genetic disease due to de novo mutations. The lacI transgenic mouse can be used to study paternal age effects, and in this system, the prevalence of de novo mutations increases in the male germline at old ages. Mutagenesis is linked with DNA repair capacity, and base excision repair (BER), which can ameliorate spontaneous DNA damage, decreases in nuclear extracts of spermatogenic cells from old mice. Mice heterozygous for a null allele of the Apex1 gene, which encodes apurinic/apyrimidinic endonuclease I (APEN), an essential BER enzyme, display an accelerated increase in spontaneous germline mutagenesis early in life. Here, the consequences of lifelong reduction of APEN on genetic instability in the male germline were examined, for the first time, at middle and old ages. Mutant frequency increased earlier in spermatogenic cells from Apex1(+/-) mice (by 6 months of age). Nuclear DNA damage increased with age in the spermatogenic lineage for both wild-type and Apex1(+/-) mice. By old age, mutant frequencies were similar for wild-type and APEN-deficient mice. Mitochondrial genome repair also depends on APEN, and novel analysis of mitochondrial DNA (mtDNA) damage revealed an increase in the Apex1(+/-) spermatogenic cells by middle age. Thus, Apex1 heterozygosity results in accelerated damage to mtDNA and spontaneous mutagenesis, consistent with an essential role for APEN in maintaining nuclear and mtDNA integrity in spermatogenic cells throughout life.     

Optimal bacteriophage mutation rates for phage therapy

The mutability of bacteriophages offers a particular advantage in the treatment of bacterial infections not afforded by other antimicrobial therapies. When phage-resistant bacteria emerge, mutation may generate phage capable of exploiting and thus limiting population expansion among these emergent types. However, while mutation potentially generates beneficial variants, it also contributes to a genetic load of deleterious mutations. Here, we model the influence of varying phage mutation rate on the efficacy of phage therapy. All else being equal, phage types with historical mutation rates of approximately 0.1 deleterious mutations per genome per generation offer a reasonable balance between beneficial mutational diversity and deleterious mutational load. We determine that increasing phage inoculum density can undesirably increase the peak density of a mutant bacterial class by limiting the in situ production of mutant phage variants. For phage populations with minimal genetic load, engineering mutation rate increases beyond the mutation-selection balance optimum may provide even greater protection against emergent bacterial types, but only with very weak selective coefficients for de novo deleterious mutations (below approximately 0.01). Increases to the mutation rate beyond the optimal value at mutation-selection balance may therefore prove generally undesirable.     

The stromal processing peptidase of chloroplasts is essential in Arabidopsis, with knockout mutations causing embryo arrest after the 16-cell stage

Stromal processing peptidase (SPP) is a metalloendopeptidase located in the stroma of chloroplasts, and it is responsible for the cleavage of transit peptides from preproteins upon their import into the organelle. Two independent mutant Arabidopsis lines with T-DNA insertions in the SPP gene were analysed (spp-1 and spp-2). For both lines, no homozygous mutant plants could be detected, and the segregating progeny of spp heterozygotes contained heterozygous and wild-type plants in a ratio of 2∶1. The siliques of heterozygous spp-1 and spp-2 plants contained many aborted seeds, at a frequency of ～25%, suggesting embryo lethality. By contrast, transmission of the spp mutations through the male and female gametes was found to be normal, and so gametophytic effects could be ruled out. To further elucidate the timing of the developmental arrest, mutant and wild-type seeds were cleared and analysed by Nomarski microscopy. A significant proportion (～25%) of the seeds in mutant siliques exhibited delayed embryogenesis compared to those in wild type. Moreover, the mutant embryos never progressed normally beyond the 16-cell stage, with cell divisions not completing properly thereafter. Heterozygous spp mutant plants were phenotypically indistinguishable from the wild type, indicating that the spp knockout mutations are completely recessive and suggesting that one copy of the SPP gene is able to produce sufficient SPP protein for normal development under standard growth conditions.     

Survival rates of mutant genes under artificial selection using individual and family information

We have used diffusion and branching process methods to investigate fixation rates, probabilities of survival per generation, and times to fixation of mutant genes under different selection methods incorporating individual and family information. Diffusion approximations fit well to simulated results even for large selection coefficients. Methods that give much weight to family information, such as BLUP evaluation which is widely used in animal breeding, reduce fixation rates of mutant genes because of the reduced effective population sizes. In general, it is observed that even mutants with relatively small heterozygous effects (say 0.1 phenotypic standard deviation) are practically ‘safe’ (i.e. their probability of loss from one generation to the next is smaller than, say, 10%) after just a few generations, typically less than 10. For methods of selection with larger effective size, such as within-family selection, the mutant is ‘safe’ in the population somewhat earlier but eventual fixation takes a longer time. Finally we evaluate the amount by which the use of marker assisted selection reduces the fixation probability of newly arisen mutants.     

Ethyl methanesulfonate-induced mutations of major genes for quantitative phenotypes: mutant alleles for altered activity of brain or liver enzymes in C57BL/6J mice and their inheritance across several generations

We recently identified and confirmed 8 induced mutations in the N2 and N3 progeny of ethyl methanesulfonate (EMS) treated C57BL/6J mice. Each of these mutations altered specific enzyme activities. These separate mutant sublines have been maintained through several generations as heterozygous mutant carriers. The percent decrease of the specific enzyme activity from normal in each subline was calculated for each generation. Additionally, the percentage of breeders within each mutant subline producing abnormal progeny and the fraction of such breeders' total progeny possessing abnormal activity were determined. The aberrant activity values observed in progeny of a confirmed mutant carrier were all lower than normal. 4 of the mutant sublines had decreases in enzyme activities which were constant across the generations analyzed. 3 of the mutant sublines had decreases in activities which were consistent over early generations but changed significantly in later generations. Another subline with decreased enzyme activity was lost. For 7 of the sublines, the number of progeny having altered activity and the number of breeders producing mutant progeny approximated that expected for single gene inheritance. In the remaining subline, a change in the decrease in enzyme activity probably accounts for the deviation from expected inheritance. Although the phenotypes for these quantitative traits are considered to be quasi-continuous, the data indicate that the mutations are probably of major genes.     

Factors influencing plasticity in the arrival‐breeding interval in a migratory species reacting to climate change

Climate change is profoundly affecting the phenology of many species. In migratory birds, there is evidence for advances in their arrival time at the breeding ground and their timing of breeding, yet empirical studies examining the interdependence between arrival and breeding time are lacking. Hence, evidence is scarce regarding how breeding time may be adjusted via the arrival‐breeding interval to help local populations adapt to local conditions or climate change. We used long‐term data from an intensively monitored population of the northern wheatear (Oenanthe oenanthe) to examine the factors related to the length of 734 separate arrival‐to‐breeding events from 549 individual females. From 1993 to 2017, the mean arrival and egg‐laying dates advanced by approximately the same amount (~5–6 days), with considerable between‐individual variation in the arrival‐breeding interval. The arrival‐breeding interval was shorter for: (a) individuals that arrived later in the season compared to early‐arriving birds, (b) for experienced females compared to first‐year breeders, (c) as spring progressed, and (d) in later years compared to earlier ones. The influence of these factors was much larger for birds arriving earlier in the season compared to later arriving birds, with most effects on variation in the arrival‐breeding interval being absent in late‐arriving birds. Thus, in this population it appears that the timing of breeding is not constrained by arrival for early‐ to midarriving birds, but instead is dependent on local conditions after arrival. For late‐arriving birds, however, the timing of breeding appears to be influenced by arrival constraints. Hence, impacts of climate change on arrival dates and local conditions are expected to vary for different parts of the population, with potential negative impacts associated with these factors likely to differ for early‐ versus late‐arriving birds.     

Aneuploidy in metaphases II of spermatocytes of wild house mice from a hybrid zone between a Robertsonian population (CD: 2n = 22) and a population with the standard karyotype (2n = 40)

Meiotic metaphases II from archival slides were studied of male house mice caught in a hybrid zone between a population monomorphic for nine centric fusions (2n = 22) and a population with the standard karyotype (2n = 40), near Rome. The frequency of aneuploidy increases, up to 50%, with increasing number of heterozygous centric fusions (1–4). This revised version was published online in July 2006 with corrections to the Cover Date.     

Competition Between the Sperm of a Single Male Can Increase the Evolutionary Rate of Haploid Expressed Genes

The population genetic behavior of mutations in sperm genes is theoretically investigated. We modeled the processes at two levels. One is the standard population genetic process, in which the population allele frequencies change generation by generation, depending on the difference in selective advantages. The other is the sperm competition during each genetic transmission from one generation to the next generation. For the sperm competition process, we formulate the situation where a huge number of sperm with alleles A and B, produced by a single heterozygous male, compete to fertilize a single egg. This “minimal model” demonstrates that a very slight difference in sperm performance amounts to quite a large difference between the alleles’ winning probabilities. By incorporating this effect of paternity-sharing sperm competition into the standard population genetic process, we show that fierce sperm competition can enhance the fixation probability of a mutation with a very small phenotypic effect at the single-sperm level, suggesting a contribution of sperm competition to rapid amino acid substitutions in haploid-expressed sperm genes. Considering recent genome-wide demonstrations that a substantial fraction of the mammalian sperm genes are haploid expressed, our model could provide a potential explanation of rapid evolution of sperm genes with a wide variety of functions (as long as they are expressed in the haploid phase). Another advantage of our model is that it is applicable to a wide range of species, irrespective of whether the species is externally fertilizing, polygamous, or monogamous. The theoretical result was applied to mammalian data to estimate the selection intensity on nonsynonymous mutations in sperm genes.     

Mutation Rate and Dominance of Genes Affecting Viability in DROSOPHILA MELANOGASTER

Spontaneous mutations were allowed to accumulate in a second chromosome that was transmitted only through heterozygous males for 40 generations. At 10-generation intervals the chromosomes were assayed for homozygous effects of the accumulated mutants. From the regression of homozygous viability on the number of generations of mutant accumulation and from the increase in genetic variance between replicate chromosomes it is possible to estimate the mutation rate and average effect of the individual mutants. Lethal mutations arose at a rate of 0.0060 per chromosome per generation. The mutants having small effects on viability are estimated to arise with a frequency at least 10 times as high as lethals, more likely 20 times as high, and possibly many more times as high if there is a large class of very nearly neutral mutations.-The dominance of such mutants was measured for chromosomes extracted from a natural population. This was determined from the regression of heterozygous viability on that of the sum of the two constituent homozygotes. The average dominance for minor viability genes in an equilibrium population was estimated to be 0.21. This is lower than the value for new mutants, as expected since those with the greatest heterozygous effect are most quickly eliminated from the population. That these mutants have a disproportionately large heterozygous effect on total fitness (as well as on the viability component thereof) is shown by the low ratio of the genetic load in equilibrium homozygotes to that of new mutant homozygotes.     

Phenotypic expression of a genetic property introduced by deoxyribonucleate

The time course of the appearance of cells showing a new phenotype, following treatment with a specific DNA, has been analyzed. A plot as a function of time of the number of cells showing the new property closely resembles the summation under a normal distribution curve. Describing the appearance of the new phenotype in these terms permits the definition of two parameters, the mean time, and the standard deviation of the distribution curve. This distribution is not affected either by the DNA concentration with which the transformable population has been treated, or by the streptomycin concentration with which the transformed population has been challenged. Interruptions of the expression process, by cooling to 20° or 0°C., serve only to displace the expression curves, without changing their shape, while small reductions in temperature change both the mean time of expression and the standard deviation of the distribution curve. On the basis of these observations a number of hypotheses have been examined concerning the mechanism whereby transforming DNA manifests a phenotypic alteration in the transformed cells. It can be concluded that there exist at least two stages in the process of expression. The completion of the first stage, causing the randomization, occurs with a mean time of about 60 minutes, and a terminal step, that of the transition of phenotype, occurs in less than 3 minutes.