Methodologies for estimating the sample size required for genetic conservation of outbreeding crops

Summary The main purpose of germplasm banks is to preserve the genetic variability existing in crop species. The effectiveness of the regeneration of collections stored in gene banks is affected by factors such as sample size, random genetic drift, and seed viability. The objective of this paper is to review probability models and population genetics theory to determine the choice of sample size used for seed regeneration. A number of conclusions can be drawn from the results. First, the size of the sample depends largely on the frequency of the least common allele or genotype. Genotypes or alleles occurring at frequencies of more than 10% can be preserved with a sample size of 40 individuals. A sample size of 100 individuals will preserve genotypes (alleles) that occur at frequencies of 5%. If the frequency of rare genotypes (alleles) drops below 5%, larger sample sizes are required. A second conclusion is that for two, three, and four alleles per locus the sample size required to include a copy of each allele depends more on the frequency of the rare allele or alleles than on the number. Samples of 300 to 400 are required to preserve alleles that are present at a frequency of 1%. Third, if seed is bulked, the expected number of parents involved in any sample drawn from the bulk will be less than the number of parents included in the bulk. Fourth, to maintain a rate of breeding (F) of 1 %, the effective population size (N _e) should be at least 150 for three alleles, and 300 for four alleles. Fifth, equalizing the reproductive output of each family to two progeny doubles the effective size of the population. Based on the results presented here, a practical option is considered for regenerating maize seed in a program constrained by limited funds.Part of this paper was presented at the Global Maize Germplasm Workshop, CIMMYT, El Batan, Mexico, March 6–12, 1988     

Genetic control of in vitro shoot regeneration from leaf explants inSolanum chacoense Bitt.

Although the heritable nature of plant tissue culture responses is now well documented in many species, only a few studies have been conducted to elucidate complete inheritance patterns. Genetic control of in vitro shoot regeneration from leaf explants was investigated inSolanum chacoense using parental, F₁ and F₂ generations. Broad-sense heritability estimates were high for frequency (percentage) of responsive leaf explants (61–83%) and number of shoots regenerated per responsive explant (53–75%). Consistent with high heritability estimates, a hypothesis involving three genes could be formulated to explain the variability in the response observed in this study. This model implies that homozygous recessive alleles at any two (out of three) loci are required for the highest response, i.e., more than two shoots per explant in more than 40% of the explants. The presence of homozygous recessive alleles at any one of the three loci produces an intermediate response, i.e., fewer than 40% of the explants regenerating fewer than two shoots per explant, and a dominant allele at all the three loci results in non-responsiveness. Additional minor modifier genes, each with a small effect, would also be required to account for the variable intensity of regeneration within groups. Such a relatively simple genetic control of in vitro regenerability suggests that incorporation of this trait should be easy in potato improvement programmes.     

Investigations on the population genetics of the α1-antitrypsin polymorphism

Summary The results of Pi-typing on 2647 individuals from 9 populations are reported. Of the 17 phenotypes and 9 alleles described in literature, we found 12 phenotypes and 8 alleles. The population smaples differ characteristically in their allele frequencies. The allle Pi^M appears constantly in all populations tested with a frequency of more than 0.85. The alleles Pi^F (0.01–0.11), Pi^S (0.01–0.02) and Pi^Z (0.01–0.02) were also relatively frequent in all samples. All the other alleles remain below 0.01. A great increase in the number of Pi-variants was observed in the Central European area. The frequency of ₁-at variants in various populations is discussed.Supported by the Deutsche Forschungsgemeinschaft.Dedicated to Prof. W. Lehmann, Kiel, on his 65th birthday.     

Population genetic structure of Nantucket pine tip moth

Summary Variation at polymorphic isozyme loci was analyzed in Nantucket pine tip moth (NPTM) populations from 5 geographic locations. At the North Carolina location, populations representing 3 generations at 3 local sites were also studied. Four of the loci investigated (LAP, MDH, -GPDH and AK), although variable, had few alleles per locus (3–5) and few differences among populations in allele frequencies. At each locus, all populations had the same allele at a high frequency.At the PGM locus, fifteen alleles were identified and allelic frequencies varied among populations. At least eight alleles were present within a population and, in most populations, two or more alleles had high frequencies that differed among populations. An excess of homozygotes over Hardy-Weinberg expectations was found for 7 out of the 10 populations studied, indicating the probable existence of some form of inbreeding structure or populational subdivision within sampled stands.Joint consideration of the results observed for PGM and the other four loci is counterindicative of neutrality at all loci and strongly indicative of genetic differentiation among locally disjunct populations.Published as Paper No. 6751 of the Journal Series of the North Carolina Agricultural Research Service     

Migration and mutation in stochastic models of gene frequency change

Summary Migration has in the past been introduced deterministically into stochastic gene frequency models. Migration at rate m then reduces the between-population variability by a factor of (1 – m)² each generation. We show that with stochastic migration, whether of fixed or variable numbers of individuals, a positive term _m is added to the variance. As a result of the _m term, the equilibrium value of the between-population variability is increased compared to the corresponding value for deterministic migration by a factor of approximately (1 – m)^–2 for small m. An equivalent result is derived for mutation, using the infinite allele model for a single population. We show in addition that these results may be derived much more simply by use of identity-by-descent probability methods, but only if a modified definition of the probability of identity-by-descent is used, involving the sampling with instead of without replacement of pairs of genes from the population.     

Rate of Gene Silencing at Duplicate Loci: A Theoretical Study and Interpretation of Data from Tetraploid Fishes

A large-scale simulation has been conducted on the rate of gene loss at duplicate loci under irreversible mutation. It is found that tight linkage does not provide a strong sheltering effect, as thought by previous authors; indeed, the mean loss time for the case of tight linkage is of the same order of magnitude as that for no linkage, as long as Nu is not much larger than 1, where N is the effective population size and u the mutation rate. When Nu is 0.01 or less, the two loci behave almost as neutral loci, regardless of linkage, and the mean loss time is about only half the mean extinction time for a neutral allele under irreversible mutation. However, the former becomes two or more times larger than the latter when Nu ≥ 1.——In the simulation, the sojourn times in the frequency intervals (0, 0.01) and (0.99, 1) and the time for the frequency of the null allele to reach 0.99 at one of the two loci have also been recorded. The results show that the population is monomorphic for the normal allele most of the time if Nu ≤ 0.01, but polymorphic for the null and the normal alleles most of the time if Nu ≥ 0.1.——The distribution of the frequency of the null allele in an equilibrium tetraploid population has been studied analytically. The present results have been applied to interpret data from some fish groups that are of tetraploid origin, and a model for explaining the slow rate of gene loss in these fishes is proposed.     

Detection of linkage between marker loci and loci affecting quantitative traits in crosses between segregating populations

Summary By making use of pedigree information and information on marker-genotypes of the parent and F-1 individuals crossed to form an F-2 population, it is possible to carry out a linkage analysis between marker loci and loci affecting quantitative traits in a cross between segregating parent populations that are at fixation for alternative alleles at the QTL, but share the same alleles at the marker loci. For two-allele systems, depending on marker allele frequencies in the parent populations, 2–4 times as many F-2 offspring will have to be raised and scored for markers and quantitative traits in order to provide power equivalent to that obtained in a cross between fully inbred lines. Major savings in number of F-2 offspring raised can be achieved by scoring each parent pair for a large number of markers in each chromosomal region and scoring F-1 and F-2 offspring only for those markers for which the parents were homozygous for alternative alleles. For multiple allele systems, particularly when dealing with hypervariable loci, only 10%–20% additional F-2 offspring will have to be raised and scored to provide power equivalent to that obtained in a cross between inbred lines. When a resource population contains novel favorable alleles at quantitative trait loci that are not present (or rare) in a commercial population, analyses of this sort will enable the loci of interest to be identified, mapped and manipulated effectively in breeding programs.Contribution no. 2124-E, 1987 series from The Agricultural Research Organization, The Volcani Center, Bet Dagan, Israel     

The Evolution of Recombination: Removing the Limits to Natural Selection

One of the oldest hypotheses for the advantage of recombination is that recombination allows beneficial mutations that arise in different individuals to be placed together on the same chromosome. Unless recombination occurs, one of the beneficial alleles is doomed to extinction, slowing the rate at which adaptive mutations are incorporated within a population. We model the effects of a modifier of recombination on the fixation probability of beneficial mutations when beneficial alleles are segregating at other loci. We find that modifier alleles that increase recombination do increase the fixation probability of beneficial mutants and subsequently hitchhike along as the mutants rise in frequency. The strength of selection favoring a modifier that increases recombination is proportional to λ(2)Sδr/r when linkage is tight and λ(2)S(3)δ r/N when linkage is loose, where λ is the beneficial mutation rate per genome per generation throughout a population of size N, S is the average mutant effect, r is the average recombination rate, and δr is the amount that recombination is modified. We conclude that selection for recombination will be substantial only if there is tight linkage within the genome or if many loci are subject to directional selection as during periods of rapid evolutionary change.     

Genetic relatedness in open-pollinated families of two leguminous tree species,Robinia pseudoacacia L. and Gleditsia triacanthos L.

Summary When conducting tree breeding experiments, geneticists often assume that individuals from open-pollinated families are halfsibs. The reliability of this assumption was tested using data from enzyme electrophoresis to estimate the genetic relatedness among progeny within 22 open-pollinated families of Robinia pseudoacacia L. (black locust) and 34 open-pollinated families of Gleditsia triacanthos L. (honey locust) from natural stands. An algorithm employing population estimates of fixation indices, pollen allele frequencies, and selfing rates was used to calculate the mean expected number of alleles in common across loci under assumptions of either full-sib (i.e., a single pollen parent) or half-sib (i.e., random mating) relationships. For each open-pollinated family, the average coefficient of relationship among progeny was calculated by linear interpolation from the observed number of alleles in common. For most families of both species, coefficients were significantly higher than 0.25 (half-sib relation), but were significantly lower than 0.50 (full-sib relation). These results suggest that the assumption of a half-sib relationship among progeny of open-pollinated families is violated for these tree species. More critical to the estimation of heritabilities and the prediction of genetic gains was the observation that estimates of the coefficient of relationship varied widely among open-pollinated families (for R. pseudoacacia r ₀=0.20–0.43, mean=0.34; for G. triacanthos r ₀=0.29–0.55, mean=0.36).     

Sampling for Microsatellite-Based Population Genetic Studies: 25 to 30 Individuals per Population Is Enough to Accurately Estimate Allele Frequencies

One of the most common questions asked before starting a new population genetic study using microsatellite allele frequencies is “how many individuals do I need to sample from each population?” This question has previously been answered by addressing how many individuals are needed to detect all of the alleles present in a population (i.e. rarefaction based analyses). However, we argue that obtaining accurate allele frequencies and accurate estimates of diversity are much more important than detecting all of the alleles, given that very rare alleles (i.e. new mutations) are not very informative for assessing genetic diversity within a population or genetic structure among populations. Here we present a comparison of allele frequencies, expected heterozygosities and genetic distances between real and simulated populations by randomly subsampling 5–100 individuals from four empirical microsatellite genotype datasets (Formica lugubris, Sciurus vulgaris, Thalassarche melanophris, and Himantopus novaezelandia) to create 100 replicate datasets at each sample size. Despite differences in taxon (two birds, one mammal, one insect), population size, number of loci and polymorphism across loci, the degree of differences between simulated and empirical dataset allele frequencies, expected heterozygosities and pairwise F_ST values were almost identical among the four datasets at each sample size. Variability in allele frequency and expected heterozygosity among replicates decreased with increasing sample size, but these decreases were minimal above sample sizes of 25 to 30. Therefore, there appears to be little benefit in sampling more than 25 to 30 individuals per population for population genetic studies based on microsatellite allele frequencies.     

Physical Activity Attenuates the Genetic Predisposition to Obesity in 20,000 Men and Women from EPIC-Norfolk Prospective Population Study

Background

We have previously shown that multiple genetic loci identified by genome-wide association studies (GWAS) increase the susceptibility to obesity in a cumulative manner. It is, however, not known whether and to what extent this genetic susceptibility may be attenuated by a physically active lifestyle. We aimed to assess the influence of a physically active lifestyle on the genetic predisposition to obesity in a large population-based study.

Methods and Findings

We genotyped 12 SNPs in obesity-susceptibility loci in a population-based sample of 20,430 individuals (aged 39–79 y) from the European Prospective Investigation of Cancer (EPIC)-Norfolk cohort with an average follow-up period of 3.6 y. A genetic predisposition score was calculated for each individual by adding the body mass index (BMI)-increasing alleles across the 12 SNPs. Physical activity was assessed using a self-administered questionnaire. Linear and logistic regression models were used to examine main effects of the genetic predisposition score and its interaction with physical activity on BMI/obesity risk and BMI change over time, assuming an additive effect for each additional BMI-increasing allele carried. Each additional BMI-increasing allele was associated with 0.154 (standard error [SE] 0.012) kg/m² (p = 6.73×10⁻³⁷) increase in BMI (equivalent to 445 g in body weight for a person 1.70 m tall). This association was significantly (p _interaction = 0.005) more pronounced in inactive people (0.205 [SE 0.024] kg/m² [p = 3.62×10⁻¹⁸; 592 g in weight]) than in active people (0.131 [SE 0.014] kg/m² [p = 7.97×10⁻²¹; 379 g in weight]). Similarly, each additional BMI-increasing allele increased the risk of obesity 1.116-fold (95% confidence interval [CI] 1.093–1.139, p = 3.37×10⁻²⁶) in the whole population, but significantly (p _interaction = 0.015) more in inactive individuals (odds ratio [OR] = 1.158 [95% CI 1.118–1.199; p = 1.93×10⁻¹⁶]) than in active individuals (OR = 1.095 (95% CI 1.068–1.123; p = 1.15×10⁻¹²]). Consistent with the cross-sectional observations, physical activity modified the association between the genetic predisposition score and change in BMI during follow-up (p _interaction = 0.028).

Conclusions

Our study shows that living a physically active lifestyle is associated with a 40% reduction in the genetic predisposition to common obesity, as estimated by the number of risk alleles carried for any of the 12 recently GWAS-identified loci. Please see later in the article for the Editors'' Summary     

Genetic variation and hybridization in SwedishSchoenus (Cyperaceae)

Schoenus ferrugineus andS. nigricans have restricted distributions in Sweden and are almost exclusively confined to calcareous fen habitats. AtS. nigricans sites,S. ferrugineus is usually also present, and hybrids are frequently found. In this report, I used allozymes to estimate the amount of gene flow between the two species, and to compare the partitioning of genetic diversity in each of them. Thirteen loci were analysed at eight different enzyme systems. Seven loci were variable between or within the species. The two species had completely different alleles at two of the seven variable loci, whereas there was overlap at five loci. In all, 22 different alleles were found. Six of these alleles were confined toS. nigricans, and five alleles were confined toS. ferrugineus. Nei's genetic identity was 0.55.—InS. ferrugineus, three loci (23%) were polymorphic, and the average number of alleles per polymorphic locus was 2.0 (each polymorphic locus had two alleles). InS. nigricans, three loci (23%) were polymorphic, and the average number of alleles per polymorphic locus was 2.3.—The proportion of genetic diversity due to variation among sites (G _ST) was fairly similar in the two species, mean over loci = 0.12 inS. ferrugineus and 0.15 inS. nigricans. However, the proportion of genetic diversity due to variation among individuals within sites (G _IS) differed markedly between the two species, mean over loci = 0.54 inS. ferrugineus and 0.17 inS. nigricans. Accordingly, there was a much higher individual heterozygosity inS. nigricans than inS. ferrugineus. — Most hybrids were interpreted as F₁ hybrids. However, a small proportion, 0.5–1.6 %, were F_n hybrids or back-crosses.—On the Swedish mainland, all former occurrences ofS. nigricans are extinct, but viable hybrids are still present at a few sites in southernmost Sweden.     

Biochemical genetics of some seed proteins of Pinus radiata

In a high-salt soluble fraction of the total protein from single seeds of Pinus radiata, up to 45 polypeptides were resolved on SDS-polyacrylamide gels. At least one-fifth of these polypeptides showed variation between seeds. In the 27,000–29,000 dalton region, two polypeptides were inherited as codominant alleles at a single locus and were shown to assort independently of another seed protein locus and three allozyme loci. A survey of 120 individuals from the five known native populations of P. radiata in California detected only the 27K and 29K alleles at the locus. In all populations, the 29K allele predominated, and the two island populations were monomorphic for the 29K allele. The 27 and 29 kdalton polypeptides were shown to have very similar amino acid sequences, and the allelic difference at this locus is most probably in the gene sequence for the polypeptide.     

Five genetic loci involved in the synthesis of acidic exopolysaccharides are closely linked in the genome of Rhizobium sp strain NGR234

Summary R-prime plasmids were constructed from a derivative of Rhizobium strain NGR234 (ANU280) and were shown to contain overlapping genomic DNA segments involved in biosynthesis of exopolysaccharides (EPS). The R-primes originally constructed carried the mutant allele from Tn5-induced EPS-deficient (Exo^–) mutant ANU2811. This plasmid-located mutant allele was dominant to the corresponding wild-type allele as merodiploid strains were Exo^–. Exo⁺ revertants occurred at a low rate (1×10^-7) and these were shown to result from double reciprocal recombination events, which led to the isolation of R-prime plasmids carrying functional wild-type exo alleles. R-prime plasmids that carry overlapping segments of DNA from parental strain ANU280 complemented 28 of the 30 group 2 Exo^– mutants of strain ANU280. Complementation of these Exo^– mutants also restored their symbiotic abilities of effective nodulation. Subsequent in vivo recombination between the wild-type alleles located on the R-prime and the corresponding mutated allele on the genome, was used to generate a new family of R-primes, which carried mutations in the exo genes. The 30 group 2 Exo^– mutants were classified into 7 distinct genetic groups based upon complementation and physical mapping data. Five of the seven exo loci were gentically linked and located on a 15-kb region of DNA. Mutations at two loci were dominant only when the mutations were R-prime plasmid-located while a mutation at a second locus was cis-dominant to two other exo loci. At least five genes involved in the synthesis of acidic exopolysaccharide synthesis have been identified.     

Development of Novel Microsatellite DNA Markers from the Pacific Oyster Crassostrea gigas

We document the potential of novel microsatellites as a genetic tool in furthering our understanding of the Crassostrea gigas genetic structure. From the microsatellite-enriched libraries we constructed, 123 repeat regions that had sufficient sequence information to design polymerase chain reaction primer sets were isolated. From these, 9 primer pairs were screened in a C. gigas population of 67 individuals to evaluate the genetic variability. All but 1 of the 9 loci showed allelic variation (number of alleles, 2–20; observed heterozygosity, 0.119–0.925; unbiased expected heterozygosity, 0.139–0.914). Considerable discrepancy of genotypic proportions from the Hardy-Weinberg equilibrium was observed at 1 locus with an apparent heterozygote deficiency. Several loci were successfully amplified in 3 other related species with the appropriate allele size: 6 loci in C. sikamea, 4 loci in C. ariakensis, and 5 loci in C. nippona.     

Genetic Analysis of Group Composition and Breeding System in a Wild Common Marmoset (Callithrix jacchus) Population

We established pedigree relations in three wild common marmoset social groups for which observational data were available, together with genotypes of some individuals from neighboring groups. Relatedness of 40 individuals were based on 11 microsatellite loci amplified from nDNA obtained noninvasively from plucked hair. The wild marmosets were only half as variable as a captive population characterized previously: 2–6 alleles/locus; H_O = 0.41 and H_E = 0.35. Parentage exclusion probabilities were 61.8% for an offspring and one alleged parent and 90.7% for an offspring with one confirmed and one alleged parent. Each group (n = 5–14 individuals) had two breeding females and 2 adult males. Within each group the infants and reproductively inactive adults were closely related to at least the breeding females; the latter were related to each other as closely as mother/infant pairs or sisters. Relatedness of adult males was lower, indicating recent intergroup dispersal. Genetic data confirm Callithrix jacchus live in relatively stable extended family groups of closely related individuals. Matings occurred preferentially among the least related adults and most infants were fathered by the dominant male. The genetic data are consistent with polygynmonandry as are the field observations. Callithrix have variable mating systems, ranging from monogamy to polyandry to polygyny within social groups plus extragroup copulations; our data provide no evidence for polyandry and are inconclusive with respect to extragroup paternity. Nevertheless, noninvasive multilocus genotyping methods will resolve these questions when longer-term studies of entire populations are undertaken.     

Persistence of Common Alleles in Two Related Populations or Species

Mathematical studies are conducted on three problems that arise in molecular population genetics. (1) The time required for a particular allele to become extinct in a population under the effects of mutation, selection, and random genetic drift is studied. In the absence of selection, the mean extinction time of an allele with an initial frequency close to 1 is of the order of the reciprocal of the mutation rate when 4Nv << 1, where N is the effective population size and v is the mutation rate per generation. Advantageous mutations reduce the extinction time considerably, whereas deleterious mutations increase it tremendously even if the effect on fitness is very slight. (2) Mathematical formulae are derived for the distribution and the moments of extinction time of a particular allele from one or both of two related populations or species under the assumption of no selection. When 4Nv << 1, the mean extinction time is about half that for a single population, if the two populations are descended from a common original stock. (3) The expected number as well as the proportion of common neutral alleles shared by two related species at the tth generation after their separation are studied. It is shown that if 4Nv is small, the two species are expected to share a high proportion of common alleles even 4N generations after separation. In addition to the above mathematical studies, the implications of our results for the common alleles at protein loci in related Drosophila species and for the degeneration of unused characters in cave animals are discussed.     

Polymorphism of Trinucleotide Repeats at Loci FRAXA and FRAXE in the Population of Tomsk

Polymorphism of CGG and GCC trinucleotide repeats, whose expansions at the FRAXA and FRAXE loci have been identified as causative mutations in two forms of mental retardation, was studied in Slavic population of Tomsk. At the FRAXA locus a total of 31 allelic variants ranging from 8 to 56 copies of CGG repeat with two modal classes of 28–29 and 18–20 repeat units (with the frequencies of 24.6 and 11.5% respectively) were revealed. Compared to other populations, this locus was characterized by unusually high frequency of intermediate alleles with the sizes of more than 40 CGG repeat units (12.4%). Since intermediate repeats of the FRAXAlocus were more prone to instability than normal alleles, it was suggested that Slavic population of Siberia had higher risk of the development of FMR1 dynamic mutations, giving rise to the Martin–Bell syndrome. The FRAXE allele frequency distribution was demonstrated to be normal with 18 allelic variants ranging from 9 to 27 GCC repeat units. In the population of Tomsk this locus had higher than in other populations frequency (26.7%) of short (less than 15 repeat units in size) alleles. In addition, in the Tomsk population both loci were characterized by high level of heterozygosity and low frequencies of modal allele classes. These results can be explained by the high level of outbreeding typical of the population of Siberia.     

Genic Variation in Male Haploids under Deterministic Selection

Genic variation in male haploids and male diploids was compared assuming constant fitnesses (derived from computer-generated random numbers) and infinite population size. Several models were studied, differing by the fitness correlation between the sexes (r_s) and genotypes (r_g), and by the intensity of selection as measured by the coefficient of variation (CV) of the fitness distribution. Genic variation was quantified using the proportion of polymorphic loci, P, the gene diversity at polymorphic loci, H_p, and the gene diversity over all loci, H_a. The two genetic systems were compared via variation ratios: variation in male haploidy/variation in male diploidy.—P and H_a were markedly lower for male-haploids than for male diploids, the variation ratios declining with increasing r_s, r_g and CV, but the two genetic systems were similar for H_p. Except for male diploids with r_s = 1, the two sexes had different equilibrium gene frequencies but the sample sizes required to detect such differences reliably were larger than usually possible in surveys of natural populations.—Data from natural populations fit the above trends qualitatively, but the variation ratios are much lower than those from our analyses, except that for H_p, which is higher when Drosophila is excluded. Also, the frequency distribution of most common alleles from electrophoretic data has a deficiency of intermediate frequencies compared to that from the computer-generated sets of fitnesses, possibly reflecting either the influence of stochastic processes shifting frequencies away from equilibrium or the involvement of alleles under selection-mutation balance.——While electrophoretic data suggest that Drosophila has unusually high levels of genic variation, unusually low levels of genic variation in male haploids compared with male diploids are not strongly indicated. However, if further data confirm male haploids as having low levels of genic variation, likely explanations are that the bulk of electrophoretically detected variation involves fixed-fitness balancing selection, selection-mutation balance involving slightly deleterious recessive alleles, new favorable male haploid alleles moving more rapidly to fixation than under male diploidy and thus carrying linked loci to fixation faster, or some combination of these possible factors.     

Estimation of Allele Frequencies at Isoloci

In some polyploid animals and plants, pairs of duplicated loci occur that share alleles encoding proteins with identical electrophoretic mobilities. Except in cases where these ``isoloci' are known to be inherited tetrasomically, individual genotypes cannot be determined unambiguously, and there is no direct way to assign observed variation to a particular locus of the pair. For a pair of diallelic isoloci, nine genotypes are possible but only five phenotypes can be identified, corresponding to individuals with 0-4 doses of the variant allele. A maximum likelihood (ML) approach is used here to identify the set of allele frequencies (p, q) at the individual gene loci with the highest probability of producing the observed phenotypic distribution. A likelihood ratio test is used to generate the asymmetrical confidence intervals around ML estimates. Simulations indicate that the standard error of p is typically about twice the binomial sampling error associated with single locus allele frequency estimates. ML estimates can be used in standard indices of genetic diversity and differentiation and in goodness-of-fit tests of genetic hypotheses. The noncentral χ(2) distribution is used to evaluate the power of a test of apparent heterozygote deficiency that results from attributing all variation to one locus when both loci are polymorphic.