Simultaneous estimation of all the parameters of a stepwise mutation model.

Minisatellite and microsatellite are short tandemly repetitive sequences dispersed in eukaryotic genomes, many of which are highly polymorphic due to copy number variation of the repeats. Because mutation changes copy numbers of the repeat sequences in a generalized stepwise fashion, stepwise mutation models are widely used for studying the dynamics of these loci. We propose a minimum chi-square (MCS) method for simultaneous estimation of all the parameters in a stepwise mutation model and the ancestral allelic type of a sample. The MCS estimator requires knowing the mean number of alleles of a certain size in a sample, which can be estimated using Monte Carlo samples generated by a coalescent algorithm. The method is applied to samples of seven (CA)n repeat loci from eight human populations and one chimpanzee population. The estimated values of parameters suggest that there is a general tendency for microsatellite alleles to expand in size, because (1) each mutation has a slight tendency to cause size increase and (2) the mean size increase is larger than the mean size decrease for a mutation. Our estimates also suggest that most of these CA-repeat loci evolve according to multistep mutation models rather than single-step mutation models. We also introduced several quantities for measuring the quality of the estimation of ancestral allelic type, and it appears that the majority of the estimated ancestral allelic types are reasonably accurate. Implications of our analysis and potential extensions of the method are discussed.SINCE the discovery that a large number of loci with tandemly repeated sequences in human and many eukaryote species are highly polymorphic because of copy number variation of the repeats in different individuals (Jeffreys 1985; Litt and Luty 1989; Weber and May 1989), allele size data from such loci are rapidly becoming the dominant source of genetic markers for genome mapping, forensic testing, and population studies. Loci with repeat sequences longer than 5 bp are generally referred to as minisatellite or variable number tandem repeat loci, and those with repeat sequences between 2 to 5 bp are referred to as microsatellite or short tandem repeat loci (Tautz 1993). Because mutations change the copy number of such loci in a stepwise fashion, rapid accumulation of population samples from minisatellite and microsatellite loci has resurrected the interest of the stepwise mutation model (SMM), which was popular in the 1970s.     

Precision and accuracy of divergence time estimates from STR and SNPSTR variation

Inference of intraspecific population divergence patterns typically requires genetic data for molecular markers with relatively high mutation rates. Microsatellites, or short tandem repeat (STR) polymorphisms, have proven informative in many such investigations. These markers are characterized, however, by high levels of homoplasy and varying mutational properties, often leading to inaccurate inference of population divergence. A SNPSTR is a genetic system that consists of an STR polymorphism closely linked (typically < 500 bp) to one or more single-nucleotide polymorphisms (SNPs). SNPSTR systems are characterized by lower levels of homoplasy than are STR loci. Divergence time estimates based on STR variation (on the derived SNP allele background) should, therefore, be more accurate and precise. We use coalescent-based simulations in the context of several models of demographic history to compare divergence time estimates based on SNPSTR haplotype frequencies and STR allele frequencies. We demonstrate that estimates of divergence time based on STR variation on the background of a derived SNP allele are more accurate (3% to 7% bias for SNPSTR versus 11% to 20% bias for STR) and more precise than STR-based estimates, conditional on a recent SNP mutation. These results hold even for models involving complex demographic scenarios with gene flow, population expansion, and population bottlenecks. Varying the timing of the mutation event generating the SNP revealed that estimates of divergence time are sensitive to SNP age, with more recent SNPs giving more accurate and precise estimates of divergence time. However, varying both mutational properties of STR loci and SNP age demonstrated that multiple independent SNPSTR systems provide less biased estimates of divergence time. Furthermore, the combination of estimates based separately on STR and SNPSTR variation provides insight into the age of the derived SNP alleles. In light of our simulations, we interpret estimates from data for human populations.     

Demographic reductions and genetic bottlenecks in humans: minisatellite allele distributions in oceania

Polynesians have lower heterozygosities at minisatellite VNTR (Variable Number of Tandem Repeat) loci than have Melanesians; this has been taken as evidence of population-size bottlenecks during the colonisation of Polynesia. We have analysed the allelic distribution of several minisatellite loci in the population of Rapa, a Polynesian island that is known to have undergone a demographic reduction of approximately 95% since first contact with European explorers 200 years ago, leaving a surviving population of 120. We found that the minisatellite diversity of this population does not differ significantly from that of other Polynesian populations, and appears consistent with the neutral expectation of diversity assuming the infinite alleles model. This suggests that the demographic crisis that Rapa underwent did not perturb the allele distribution to the extent that the tests used here could detect. Thus we cannot say that a demographic change of this magnitude constitutes a genetic bottleneck detectable at these loci. The reduced diversity seen in Polynesia must therefore be explained either by more severe bottlenecks as might be expected during colonisation, or else by other causes.     

Mutation and evolution of microsatellite loci in Neurospora

The patterns of mutation and evolution at 13 microsatellite loci were studied in the filamentous fungal genus Neurospora. First, a detailed investigation was performed on five microsatellite loci by sequencing each microsatellite, together with its nonrepetitive flanking regions, from a set of 147 individuals from eight species of Neurospora. To elucidate the genealogical relationships among microsatellite alleles, repeat number was mapped onto trees constructed from flanking-sequence data. This approach allowed the potentially convergent microsatellite mutations to be placed in the evolutionary context of the less rapidly evolving flanking regions, revealing the complexities of the mutational processes that have generated the allelic diversity conventionally assessed in population genetic studies. In addition to changes in repeat number, frequent substitution mutations within the microsatellites were detected, as were substitutions and insertion/deletions within the flanking regions. By comparing microsatellite and flanking-sequence divergence, clear evidence of interspecific allele length homoplasy and microsatellite mutational saturation was observed, suggesting that these loci are not appropriate for inferring phylogenetic relationships among species. In contrast, little evidence of intraspecific mutational saturation was observed, confirming the utility of these loci for population-level analyses. Frequency distributions of alleles within species were generally consistent with the stepwise mutational model. By comparing variation within species at the microsatellites and the flanking-sequence, estimated microsatellite mutation rates were approximately 2500 times greater than mutation rates of flanking DNA and were consistent with estimates from yeast and fruit flies. A positive relationship between repeat number and variance in repeat number was significant across three genealogical depths, suggesting that longer microsatellite alleles are more mutable than shorter alleles. To test if the observed patterns of microsatellite variation and mutation could be generalized, an additional eight microsatellite loci were characterized and sequenced from a subset of the same Neurospora individuals.     

Microsatellite size homoplasy, SSCP, and population structure: a case study in the freshwater snail Bulinus truncatus

The extent of microsatellite size homoplasy, as well as its effect on several population genetics statistics, was investigated in natural populations using the single-strand conformation polymorphism (SSCP) method. The analysis was conducted using 240 individuals from 13 populations of the freshwater snail Bulinus truncatus at a GT(n)CT(m) compound microsatellite locus. We showed that SSCP can be used to uncover, at least partly, size homoplasy in the core sequence of this category of loci. Eight conformers (SSCP variants) were detected among the three size variants (electromorphs). Sequencing revealed that each conformer corresponded to a different combination of repeats in the GT(n) and CT(m) arrays. Part of this additional variability was detected within populations, resulting in a substantial increase in gene diversity in four populations. Additional variability also changed the values of parameters used to analyze population differentiation among populations: pairwise tests of differentiation were significant much more often with conformers than with electromorphs. On the other hand, pairwise estimates of F(st) were either smaller or larger with conformers than with electromorphs, depending on whether or not electromorphs were shared among populations. However, estimates of F(st) (or analogs) over all populations were very similar, ranging between 0.66 and 0.75. Our results were consistent with the theoretical prediction that homoplasy should not always lead to stronger population structure. Finally, conformer sequences and electromorph size distribution suggested that single-point and/or stepwise mutations occurring simultaneously in the different repeated arrays of compound microsatellites produce sequence variation without size variation and hence generate more size homoplasy than expected under a simple stepwise mutation model.     

Effects of Interference Between Selected Loci on the Mutation Load,Inbreeding Depression,and Heterosis

A classical prediction from single-locus models is that inbreeding increases the efficiency of selection against partially recessive deleterious alleles (purging), thereby decreasing the mutation load and level of inbreeding depression. However, previous multilocus simulation studies found that increasing the rate of self-fertilization of individuals may not lead to purging and argued that selective interference among loci causes this effect. In this article, I derive simple analytical approximations for the mutation load and inbreeding depression, taking into account the effects of interference between pairs of loci. I consider two classical scenarios of nonrandomly mating populations: a single population undergoing partial selfing and a subdivided population with limited dispersal. In the first case, correlations in homozygosity between loci tend to reduce mean fitness and increase inbreeding depression. These effects are stronger when deleterious alleles are more recessive, but only weakly depend on the strength of selection against deleterious alleles and on recombination rates. In subdivided populations, interference increases inbreeding depression within demes, but decreases heterosis between demes. Comparisons with multilocus, individual-based simulations show that these analytical approximations are accurate as long as the effects of interference stay moderate, but fail for high deleterious mutation rates and low dominance coefficients of deleterious alleles.     

Vntr Allele Frequency Distributions under the Stepwise Mutation Model: A Computer Simulation Approach

Variable numbers of tandem repeats (VNTRs) are a class of highly informative and widely dispersed genetic markers. Despite their wide application in biological science, little is known about their mutational mechanisms or population dynamics. The objective of this work was to investigate four summary measures of VNTR allele frequency distributions: number of alleles, number of modes, range in allele size and heterozygosity, using computer simulations of the one-step stepwise mutation model (SMM). We estimated these measures and their probability distributions for a wide range of mutation rates and compared the simulation results with predictions from analytical formulations of the one-step SMM. The average heterozygosity from the simulations agreed with the analytical expectation under the SMM. The average number of alleles, however, was larger in the simulations than the analytical expectation of the SMM. We then compared our simulation expectations with actual data reported in the literature. We used the sample size and observed heterozygosity to determine the expected value, 5th and 95th percentiles for the other three summary measures, allelic size range, number of modes and number of alleles. The loci analyzed were classified into three groups based on the size of the repeat unit: microsatellites (1-2 base pair (bp) repeat unit), short tandem repeats [(STR) 3-5 bp repeat unit], and minisatellites (15-70 bp repeat unit). In general, STR loci were most similar to the simulation results under the SMM for the three summary measures (number of alleles, number of modes and range in allele size), followed by the microsatellite loci and then by the minisatellite loci, which showed deviations in the direction of the infinite allele model (IAM). Based on these differences, we hypothesize that these three classes of loci are subject to different mutational forces.     

Joint estimation of migration rate and effective population size using the island model

Using the island model of population demography, I report that the demographic parameters migration rate and effective population size can be jointly estimated with equilibrium probabilities of identity in state calculated using a sample of genotypes collected at a single point in time from a single generation. The method, which uses moment-type estimators, applies to dioecious populations in which females and males have identical demography and monoecious populations with no selfing and requires that offspring genotypes are sampled following reproduction and prior to migration. I illustrate the estimation procedure using the infinite-island model with no mutation and the finite-island model with three kinds of mutation models. In the infinite-island model with no mutation, the estimators can be expressed as simple functions of estimates of the F-statistic parameters F(IT) and F(ST). In the finite-island model with mutation among k alleles, mutation rate, migration rate, and effective population size can be simultaneously estimated. The estimates of migration rate and effective population size are somewhat robust to violations in assumptions that may arise in empirical applications such as different kinds of mutation models and deviations from temporal equilibrium.     

Evolutionary and statistical properties of three genetic distances

Many genetic distances have been developed to summarize allele frequency differences between populations. I review the evolutionary and statistical properties of three popular genetic distances: DS, DA, and theta;, using computer simulation of two simple evolutionary histories: an isolation model of population divergence and an equilibrium migration model. The effect of effective population size, mutation rate, and mutation mechanism upon the parametric value between pairs of populations in these models explored, and the unique properties of each distance are described. The effect of these evolutionary parameters on study design is also investigated and similar results are found for each genetic distance in each model of evolution: large sample sizes are warranted when populations are relatively genetically similar; and loci with more alleles produce better estimates of genetic distance.     

A genome-wide departure from the standard neutral model in natural populations of Drosophila

We analyze nucleotide polymorphism data for a large number of loci in areas of normal to high recombination in Drosophila melanogaster and D. simulans (24 and 16 loci, respectively). We find a genome-wide, systematic departure from the neutral expectation for a panmictic population at equilibrium in natural populations of both species. The distribution of sequence-based estimates of 2Nc across loci is inconsistent with the assumptions of the standard neutral theory, given the observed levels of nucleotide diversity and accepted values for recombination and mutation rates. Under these assumptions, most estimates of 2Nc are severalfold too low; in other words, both species exhibit greater intralocus linkage disequilibrium than expected. Variation in recombination or mutation rates is not sufficient to account for the excess of linkage disequilibrium. While an equilibrium island model does not seem to account for the data, more complicated forms of population structure may. A proper test of alternative demographic models will require loci to be sampled in a more consistent fashion.     

Complex mutations in a high proportion of microsatellite loci from the protozoan parasite Plasmodium falciparum

Microsatellite loci are generally assumed to evolve via a stepwise mutational process and a battery of statistical techniques has been developed in recent years based on this or related mutation models. It is therefore important to investigate the appropriateness of these models in a wide variety of taxa. We used two approaches to examine mutation patterns in the malaria parasite Plasmodium falciparum: (i) we examined sequence variation at 12 tri-nucleotide repeat loci; and (ii) we analysed patterns of repeat structure and heterozygosity at 114 loci using data from 12 laboratory parasite lines. The sequencing study revealed complex patterns of mutation in five of the 12 loci studied. Alleles at two loci contain indels of 24 bp and 57 bp in flanking regions, while in the other three loci, blocks of imperfect microsatellites appear to be duplicated or inserted; these loci essentially consist of minisatellite repeats, with each repeat unit containing four to eight microsatellites. The survey of heterozygosity revealed a positive relationship between repeat number and microsatellite variability for both di- and trinucleotides, indicating a higher mutation rate in loci with longer repeat arrays. Comparisons of levels of variation in different repeat types indicate that the mutation rate of dinucleotide-bearing loci is 1.6-2.1 times faster than trinucleotides, consistent with the lower mean number of repeats in trinucleotide-bearing loci. However, despite the evidence that microsatellite arrays themselves are evolving in a manner consistent with stepwise mutation model in P. falciparum, the high frequency of complex mutations precludes the use of analytical tools based on this mutation model for many microsatellite-bearing loci in this protozoan. The results call into question the generality of models based on stepwise mutation for analysing microsatellite data, but also demonstrate the ease with which loci that violate model assumptions can be detected using minimal sequencing effort.     

Using molecular markers with high mutation rates to obtain estimates of relative population size and to distinguish the effects of gene flow and mutation: a demonstration using data from endemic Mauritian skinks

We propose a method of analysing genetic data to obtain separate estimates of the size (N(p)) and migration rate (m(p)) for the sampled populations, without precise prior knowledge of mutation rates at each locus ( micro(L)). The effects of migration and mutation can be distinguished because high migration has the effect of reducing genetic differentiation across all loci, whereas a high mutation rate will only affect the locus in question. The method also takes account of any differences between the spectra of immigrant alleles and of new mutant alleles. If the genetic data come from a range of population sizes, and the loci have a range of mutation rates, it is possible to estimate the relative sizes of the different N(p) values, and likewise the m(p) and the micro(L). Microsatellite loci may also be particularly appropriate because loci with a high mutation rate can reach mutation-drift-migration equilibrium more quickly, and because the spectra of mutants arriving in a population can be particularly distinct from the immigrants. We demonstrate this principle using a microsatellite data set from Mauritian skinks. The method identifies low gene flow between a putative new species and populations of its sister species, whereas the differentiation of two other populations is attributed to small population size. These distinct interpretations were not readily apparent from conventional measures of genetic differentiation and gene diversity. When the method is evaluated using simulated data sets, it correctly distinguishes low gene flow from small population size. Loci that are not at mutation-migration-drift equilibrium can distort the parameter estimates slightly. We discuss strategies for detecting and overcoming this effect.     

Cis-regulation of inter-allelic exchanges in mutation at human minisatellite MS205 in yeast.

Tandemly repeated DNA is a major component of the human genome, and includes loci contributing to human disease. Minisatellites include the most variable human loci described to date, and the mechanisms by which this variation is generated in humans have been studied in detail. Integration of human minisatellites into yeast not only provides a model for further dissecting the molecular basis of length change mutation at these loci, but also more generally allows the study of complex recombinational events in yeast. We have used human minisatellite MS205 integrated into yeast to study the structural details of length change mutations. Apart from showing that mutation at this locus in yeast has features similar to those observed at some minisatellites in humans, including meiosis-specificity, and polarity, in which exchange events are localised to one extremity of the array, we here, for the first time, directly demonstrate that a flanking element in yeast regulates the mutation process. The results therefore support the hypothesis that flanking initiators are involved in minisatellite mutation in humans. Furthermore, mutant alleles showed more complex rearrangements in one orientation than the other. The data also suggest that the mutational pathway for deletions might be different from the pathway generating inter-allelic exchanges and duplications.     

Mechanisms of human minisatellite mutation in yeast

Minisatellites are tandem repeat loci, with repeat units ranging in size from 5 bp to 100 bp. The total lengths of repeat arrays vary from about 0.5 kb to 30 kb, and excessive variability in allele length at human minisatellite loci is the result of germline-specific complex recombination events generating new length alleles. Minisatellite alleles also mutate to new lengths in somatic cells, but this occurs at a much lower rate than in the germline. Since recombination is involved in minisatellite mutation, the yeast Saccharomyces cerevisiae is a suitable model organism that has been employed to further dissect the molecular basis of mutation events at human minisatellites. These studies have shown that the mutational behaviour of a minisatellite in meiosis is not determined by the intrinsic properties of the repeat array, but are highly dependent on the position of the minisatellite in the genome. The processes for minisatellite mutation in yeast and humans are identical in the sense that mutation is indeed driven by meiotic recombination, but differ with regard to the types of structural changes that are generated by the recombination events. Tetrad analyses showed that inter-allelic transfers of repeats occur by conversion and not crossing over, and that several chromatids can be involved in successive recombination events in one meiosis, resulting in mutant alleles in several spores. It has been demonstrated that the genes SPO11 and RAD50, involved in the initiation of recombination events, are required for human minisatellite mutation in yeast meiosis. Intrinsic properties of the repeat array appear to determine the stability of human minisatellites in yeast mitosis, since mitotic mutation rates in yeast are highly variable between minisatellites. The repair genes RAD27 and DNA2 stabilise human minisatellites in yeast mitosis, while RAD5 has no effect on mitotic stability. MSH2 depresses human minisatellite frequency in meiotic cells of yeast.     

Genetic variation at minisatellite loci D1S7, D4S139, D5S110 and D17S79 among three population groups of eastern India

Genetic variation at four minisatellite loci D1S7, D4S139, D5S110 and D17S79 in three predominant population groups of eastern India, namely Brahmin, Kayastha and Garo, are reported in this study. The Brahmin and Kayastha are of Indo-Caucasoid origin while the Garo community represents the Indo-Mongoloid ethnic group. The methodology employed comprised generation of HaeIII-restricted fragments of isolated DNA, Southern blotting, and hybridization using chemiluminescent probes MS1, pH30, LH1 and V1 for the four loci. All four loci were highly polymorphic in the population groups. Heterozygosity values for the four loci ranged between 0.68 and 0.95. Neither departure from Hardy-Weinberg expectations nor evidence of any association across alleles among the selected loci was observed. The gene differentiation value among the loci is moderate (G_ST = 0.027). A neighbour-joining tree constructed on the basis of the generated data shows very low genetic distance between the Brahmin and Kayastha communities in relation to the Garo. Our results based on genetic distance analysis are consistent with results of earlier studies based on serological markers and linguistic as well as morphological affiliations of these populations and their Indo-Caucasoid and Indo-Mongoloid origin. The minisatellite loci studied here were found to be not only useful in showing significant genetic variation between the populations but also to be suitable for human identity testing among eastern Indian populations.     

Mutation Patterns at Dinucleotide Microsatellite Loci in Humans

Microsatellites are a major type of molecular markers in genetics studies. Their mutational dynamics are not clear. We investigated the patterns and characteristics of 97 mutation events unambiguously identified, from 53 multigenerational pedigrees with 630 subjects, at 362 autosomal dinucleotide microsatellite loci. A size-dependent mutation bias (in which long alleles are biased toward contraction, whereas short alleles are biased toward expansion) is observed. There is a statistically significant negative relationship between the magnitude (repeat numbers changed during mutation) and direction (contraction or expansion) of mutations and standardized allele size. Contrasting with earlier findings in humans, most mutation events (63%) in our study are multistep events that involve changes of more than one repeat unit. There was no correlation between mutation rate and recombination rate. Our data indicate that mutational dynamics at microsatellite loci are more complicated than the generalized stepwise mutation models.     

Microsatellites and the Genetics of Highly Selfing Populations in the Freshwater Snail Bulinus Truncatus

Hermaphrodite tropical freshwater snails provide a good opportunity to study the effects of mating system and genetic drift on population genetic structure because they are self-fertile and they occupy transient patchily distributed habitats (ponds). Up to now the lack of detectable allozyme polymorphism prevented any intrapopulation studies. In this paper, we examine the consequences of selfing and bottlenecks on genetic polymorphism using microsatellite markers in 14 natural populations (under a hierarchical sampling design) of the hermaphrodite freshwater snail Bulinus truncatus. These population genetics data allowed us to discuss the currently available mutation models for microsatellite sequences. Microsatellite markers revealed an unexpectedly high levels of genetic variation with <=41 alleles for one locus and gene diversity of 0.20-0.75 among populations. The values of any estimator of F(is) indicate high selfing rates in all populations. Linkage disequilibria observed at all loci for some populations may also indicate high levels of inbreeding. The large extent of genetic differentiation measured by F(st), R(st) or by a test for homogeneity between genic distributions is explained by both selfing and bottlenecks. Despite a limited gene flow, migration events could be detected when comparing different populations within ponds.     

Inverse relationship between F and microsatellite polymorphism in the marine fish, walleye pollock (Theragra chalcogramma): implications for resolving weak population structure

Microsatellites have proved to be useful for the detection of weak population structure in marine fishes and other species characterized by large populations and high gene flow. None the less, uncertainty remains about the net effects of the particular mutational properties of these markers, and the wide range of locus polymorphism they exhibit, on estimates of differentiation. We examined the effect of varying microsatellite polymorphism on the magnitude of observed differentiation in a population survey of walleye pollock, Theragra chalcogramma. Genetic differentiation at 14 microsatellite loci among six putative populations from across the North Pacific Ocean and Bering Sea was weak but significant on large geographical scales and conformed to an isolation-by-distance pattern. A negative relationship was found between locus variability and the magnitude of estimated population subdivision. Estimates of F(ST) declined with locus polymorphism, resulting in diminished power to discriminate among samples, and we attribute this loss to the effects of size homoplasy. This empirical result suggests that mutation rates of some microsatellite loci are sufficiently high to limit resolution of weak genetic structure typical of many marine fishes.     

Meiotic interallelic conversion at the human minisatellite MS32 in yeast triggers recombination in several chromatids

Tandem repetitive DNA sequences such as minisatellites include the most polymorphic loci yet identified in the human genome. The high mutation rates at many of these loci are driven by incompletely understood recombination-based mechanisms that operate in the germline. To analyse aspects of minisatellite mutation processes and general eukaryotic recombination in meiosis that cannot be studied in humans or other mammals, including crosstalk and interplay between all four chromatids, we have previously constructed a eukaryotic model system, enabling the analysis of all four products of meiosis. In this system we have integrated alleles of the human minisatellite MS32, flanked by synthetic markers, in the vicinity of a meiotic recombination hot spot in chromosome III of Saccharomyces cerevisiae. In the present study, tetrad analysis showed that gene conversion is the predominant and possibly the universal pathway leading to interallelic transfer of repeats, with or without exchange of flanking regions. The data also suggest a hyper-recombinogenic state, triggered by interallelic mutation processes which generate a cascade of mutant alleles in the same meiosis. A number of tetrads contained identical mutant alleles of meiotic origin. Several tetrads could not be explained by the current models for minisatellite mutation. Accordingly, we here present a modified model based on the successive repair of multiple double-strand breaks.     

No evidence of radiation effect on mutation rates at hypervariable minisatellite loci in the germ cells of atomic bomb survivors

Human minisatellites consist of tandem arrays of short repeat sequences, and some are highly polymorphic in numbers of repeats among individuals. Since these loci mutate much more frequently than coding sequences, they make attractive markers for screening populations for genetic effects of mutagenic agents. Here we report the results of our analysis of mutations at eight hypervariable minisatellite loci in the offspring (61 from exposed families in 60 of which only one parent was exposed, and 58 from unexposed parents) of atomic bomb survivors with mean doses of >1 Sv. We found 44 mutations in paternal alleles and eight mutations in maternal alleles with no indication that the high doses of acutely applied radiation had caused significant genetic effects. Our finding contrasts with those of some other studies in which much lower radiation doses, applied chronically, caused significantly increased mutation rates. Possible reasons for this discrepancy are discussed.