Hardy-Weinberg Frequencies Research Articles

874 Is Idiopathic Pancreatitis (Acute, Recurrent Acute and Chronic) in Children Genetically Predisposed?

ism of them is also relevant to pancreatic steatosis in alcoholics. Objective: to find out the possible genetic background of alcohol-induced pancreatic steatosis in alcoholics by analyzing genetic polymorphism in ADH2 and ALDH2. Methods: 163 alcoholic male aged 20~70 years with a normal body mass index were recruited into this study. The alcoholics were defined as the drinkers with an alcohol intake of >80g/day, a duration of >5 years, and abstinence from alcohol within 2 years. They received magnetic resonance scanning in the epigastric region by using double-echo chemical shift magnetic resonance technique. PCRrestriction fragment length polymorphism was used for ADH2 and ALDH2 genotype detection. The drinkers with pancreatic fat content higher than 4.2%, 8.0% in alcoholics younger and older than 50 years respectively were diagnosed as alcohol-induced pancreatic steatosis. This study was approved by the Chinese Clinical Trial Registry Clinical Trial Ethics Committee (registration number:ChiCTR-CCH-00000147) and the Ethics Committee of West China Hospital of Sichuan University. And it conformed to the principles of the Declaration of Helsinki of the World Medical Association. Informed consent was obtained from each participant before enrollment. Results: The distribution of the different ADH2 and ALDH2 genotypes among the 163 alocholics closely conformed to expected Hardy-Weinberg frequencies (p>0.05). In drinkers, compared with ADH2*2/*2 carriers, ADH2*1/*1 carriers showed a significantly elevated risk of developing pancreatic steatosis ( 50 years, OR=5.34). No association was found between ALDH2 genotypes and risk of pancreatic steatosis. Conclusion: In drinkers, ADH2*l/*1 carriers had a significantly higher risk to develop alcohol-induced pancreatic steatosis. ADH2*1/*1 genotypemay be related to alcoholinduced pancreatic steatosis.

Studies on isozyme variation in marginal and central populations of Picea abies.

Two delimited populations of Picea abies, each comprising about 50 individuals have been analysed with regard to three different enzyme systems, esterase (EST), leucine-amino-peptidase (LAP) and acid phosphatase (PHOS). Female gametophytic endosperm tissue dissected from mature seed has been used for all three isozyme analyses. As this tissue is haploid, a novel method for distinguishing heterozygotes and homozygotes has been used. The spatial mapping of genotypes in their habitat indicates complete randomness of gene distribution within stands. In two cases (LAP and PHOS), enzyme analyses also indicate strict conformity of allozymes to expected Hardy-Weinberg frequencies. Allele frequencies in the range of 0.3–0.7 for two or more allozymes suggest heavy gene flow, frequency-dependent selection or, possibly, founder effects. In the third enzyme system analysed (EST), there is indication of balanced heterozygosity. There appears to be plenty of genetic variability of allozymes even at the species margin. The adaptive significance of different enzyme systems is briefly discussed.

Esterase-3 polymorphism in the sugarcane borer Diatraea saccharalis (Lepidoptera, Pyralidae)

The migration rate of esterases and their substrate specificity for 4-methylumbelliferyl esters (acetate, propionate, and butyrate) and alpha- and beta-naphthyl esters were analyzed in Diatraea saccharalis by starch gel electrophoresis. Substrate preference of esterases was observed with Est-2 and Est-8 isozymes showing substrate specificity for 4-methylumbelliferyl esters and Est-4 isozyme showing specificity for 4-methylumbelliferyl butyrate and alpha-naphthyl butyrate. Allele variation was detected at the Est-3 locus. Two alleles, Est-3F and Est-3S, were identified in pupae with fluorogenic and ester-naphthyl substrates. Chi-square analysis showed no differences between the observed genotypic frequencies and those expected on the basis of Hardy-Weinberg frequencies for the Est-3 locus (chi² = 2.4; p < 0.01). The negative value for the Wright's fixation index (F = -0.2096) calculated for the D. saccharalis population maintained under laboratory conditions indicates an excess of heterozygotes, however, the observed Hardy-Weinberg equilibrium indicates that in the laboratory the population of D. saccharalis behaved as if the moth were randomly mating in nature. The high level of heterozygosity at the Est-3 locus indicates also that this esterase may be a good genetic marker for studies of natural D. saccharalis populations.

Structuration génétique des populations de tétras-lyre (Tetrao tetrix) des Alpes françaises

Allelic variation at eight microsatellite loci was used to assess the levels of genetic differentiation between seven natural populations of black grouse (Tetrao tetrix) in the French Alps spaced along a 250 km south-north transect. Whatever the population or locus, genotype frequencies did not deviate significantly from expected Hardy-Weinberg frequencies and no significant between-locus linkage desequilibrium was detected. Observed levels of genotypic variation were statistically significant with maximum Fst values reaching 10% for the most distant populations (250 km). An isolation-by-distance effect was detected suggesting, as expected from data on marked birds, that black grouse populations in the French Alps are interconnected by dispersal.

Spatial population genetic structure in Trillium grandiflorum: the roles of dispersal, mating, history, and selection.

The roles of the various potential ecological and evolutionary causes of spatial population genetic structure (SPGS) cannot in general be inferred from the extant structure alone. However, a stage-specific analysis can provide clues as to the causes of SPGS. We conducted a stage-specific SPGS analysis of a mapped population of about 2000 Trillium grandiflorum (Liliaceae), a long-lived perennial herb. We compared SPGS for juvenile (J), nonreproductive (NR), and reproductive (R) stages. Fisher's exact test showed that genotypes had Hardy-Weinberg frequencies at all loci and stage classes. Allele frequencies did not differ between stages. Bootstrapped 99% confidence intervals (99%CI) indicate that F-statistic values are indistinguishable from zero, (except for a slightly negative FIT for the R stage). Spatial autocorrelation was used to calculate f the average kinship coefficient between individuals within distance intervals. Null hypothesis 99%CIs for f were constructed by repeatedly randomizing genotypic locations. Significant positive fine-scale genetic structure was detected in the R and NR stages, but not in the J stage. This structure was most pronounced in the R stage, and declined by about half in each remaining stage: near-neighbor f = 0.122, 0.065, 0.027, for R, NR, and J, respectively. For R and NR, the near-neighbor f lies outside the null hypothesis 99%CI, indicating kinship at approximately the level of half-sibs and first cousins, respectively. We also simulated the expected SPGS of juveniles post dispersal, based on measured R-stage SPGS, the mating system, and measured pollen and seed dispersal properties. This provides a null hypothesis expectation (as a 99%CI) for the J-stage correlogram, against which to test the likelihood that post-dispersal events have influenced J-stage SPGS. The actual J correlogram lies within the null hypothesis 99%CI for the shortest distance interval and nearly all other distance intervals indicating that the observed low recruitment, random mating and seed dispersal patterns are sufficient to account for the disappearance of SPSG between the R and the J stages. The observed increase in SPGS between J and R stages has two potential explanations: history and local selection. The observed low total allelic diversity is consistent with a past bottleneck: a possible historical explanation. Only a longitudinal stage-specific study of SPGS structure can distinguish between historical events and local selection as causes of increased structure with increasing life history stage.

SPATIAL POPULATION GENETIC STRUCTURE IN TRILLIUM GRANDIFLORUM: THE ROLES OF DISPERSAL, MATING, HISTORY, AND SELECTION

The roles of the various potential ecological and evolutionary causes of spatial population genetic structure (SPGS) cannot in general be inferred from the extant structure alone. However, a stage-specific analysis can provide clues as to the causes of SPGS. We conducted a stage-specific SPGS analysis of a mapped population of about 2000 Trillium grandiflorum (Liliaceae), a long-lived perennial herb. We compared SPGS for juvenile (J), nonreproductive (NR), and reproductive (R) stages. Fisher's exact test showed that genotypes had Hardy-Weinberg frequencies at all loci and stage classes. Allele frequencies did not differ between stages. Bootstrapped 99% confidence intervals (99%CI) indicate that F-statistic values are indistinguishable from zero, (except for a slightly negative FIT for the R stage). Spatial autocorrelation was used to calculate f, the average kinship coefficient between individuals within distance intervals. Null hypothesis 99%CIs for f were constructed by repeatedly randomizing genotypic locations. Significant positive fine-scale genetic structure was detected in the R and NR stages, but not in the J stage. This structure was most pronounced in the R stage, and declined by about half in each remaining stage: near-neighbor f = 0.122, 0.065, 0.027, for R, NR, and J, respectively. For R and NR, the near-neighbor f lies outside the null hypothesis 99%CI, indicating kinship at approximately the level of half-sibs and first cousins, respectively. We also simulated the expected SPGS of juveniles post dispersal, based on measured R-stage SPGS, the mating system, and measured pollen and seed dispersal properties. This provides a null hypothesis expectation (as a 99%CI) for the J-stage correlogram, against which to test the likelihood that post-dispersal events have influenced J-stage SPGS. The actual J correlogram lies within the null hypothesis 99%CI for the shortest distance interval and nearly all other distance intervals indicating that the observed low recruitment, random mating and seed dispersal patterns are sufficient to account for the disappearance of SPSG between the R and the J stages. The observed increase in SPGS between J and R stages has two potential explanations: history and local selection. The observed low total allelic diversity is consistent with a past bottleneck: a possible historical explanation. Only a longitudinal stage-specific study of SPGS structure can distinguish between historical events and local selection as causes of increased structure with increasing life history stage.Corresponding Editor: O. Savolainen

Hardy–Weinberg quality control

An efficient test of deviation from Hardy–Weinberg frequencies with one degree of freedom was applied to 44 marker loci in a genome scan, and 7 loci had a significant excess of apparent homozygotes (χ2(1) &gt; 6) suggestive of typing error. In this example evidence for linkage did not increase when outliers were censored. Statistical quality control is an essential part of genotyping, and the effect of mistyping and map error should be considered in evaluating any genome scan.

Genetic diversity at a single locus under viability selection and facultative apomixis: equilibrium structure and deviations from Hardy-Weinberg frequencies.

We extensively analyze the maintenance of genetic variation and deviations from Hardy-Weinberg frequencies at a diallelic locus under mixed mating with apomixis and constant viability selection. Analytical proofs show that: (1) at most one polymorphic equilibrium exists, (2) polymorphism requires overdominant or underdominant selection, and (3) a simple, modified overdominance condition is sufficient to maintain genetic variation. In numerical analyses, only overdominant polymorphic equilibria are stable, and these are stable whenever they exist, which happens for approximately 78% of random fitness and mating parameters. The potential for maintaining both alleles increases with increasing apomixis or outcrossing and decreasing selfing. Simulations also indicate that equilibrium levels of heterozygosity will often be statistically indistinguishable from Hardy-Weinberg frequencies and that adults, not seeds, should usually be censused to maximize detecting deviations. Furthermore, although both censuses more often have an excess rather than a deficit of heterozygotes, analytical sign analyses of the fixation indices prove that, overall, adults are more likely to have an excess and seeds a deficit at equilibrium.

An index of information content for genotype probabilities derived from segregation analysis.

A genotype probability index (GPI) is proposed to indicate the information content of genotype probabilities derived from a segregation analysis. Typically, some individuals are genotyped at a marker locus or a quantitative trait locus, and segregation analysis is used to make genotype inferences about ungenotyped relatives. Genotype probabilities for a two-allele autosomal locus are plotted on a triangular surface. The GPI has a value of zero at the point corresponding to Hardy-Weinberg frequencies, and a value of 100% at the vertices of the triangle. Trigonometric functions are used to help calculate intermediate index values. It is proposed that such an index can be useful to help identify which ungenotyped individuals or loci should be genotyped to maximize the benefit/cost of genotyping operations.

Allozyme variation among natural populations of Holopedium gibberum (Crustacea; Cladocera)

SUMMARY Holopedium gibberum, from twenty lakes in Rhode Island and Maine, were examined for allozyme variation at five loci to determine the pattern and degree of generic variation among sites and the genetic structure within individual lakes. There were significant differences in allele frequencies among sites. Most populations were fixed for a particular allele at each locus. Only five lakes had polymorphic populations. Polymorphic populations showed significant deviation from expected Hardy‐Weinberg genotype frequencies. In each case, there was an excess of homozygotes. Two lakes were examined for intra‐lake allele frequency differences. In one lake there were no differences. The other lake exhibited significant allele frequency differences between stations at the north and south ends of the lake. Populations were examined for the frequency distribution of composite genotypes over three loci. Most populations were dominated by one or two genotypes. The results suggest sporadic sexual recruitment and a high degree of genetic isolation among these populations of H. gibberum. In these respects they resemble the permanent pond populations of Daphnia magna examined by Hebert (1974a).

Density-Regulated Selection in a Heterogeneous Environment

A model is developed for density-regulated selection in a heterogeneous environment, analogous to Levene's model for selection in a subdivided environment. The population is polymorphic for two alleles at an autosomal locus. Before selection the three genotypes are in Hardy-Weinberg frequencies, and a constant fraction of newborn offspring go to habitat k to live. Genotypes differ in their selective values because of genotypic and habitat differences in intrinsic rates of increase and carrying capacities, and selective values are parameterized in terms of these ecological fitness parameters so that the growth of the whole population is logistic. All selection occurs in the habitats, and at the end of each generation adults emerge from the habitats and join a mating pool to mate at random. In the Levene model, individuals in the mating pool from each habitat make a constant contribution to the gametic pool from which individuals of the next generation develop. In our model, however, the gametic contribution from a habitat is proportional to the number of organisms remaining in the habitat after selection has taken place, and thus to the average selective value of individuals from the habitat. As a consequence, the gametic contributions change with allele frequency. Sufficient conditions for a protected polymorphism under this more realistic assumption are derived, and remarkably enough take a form analogous to Levene's, with the same increased opportunity for genetic polymorphism which is the major result of his model. A protected polymorphism occurs provided that a harmonic mean over habitats of the adjusted carrying capacities of each homozygote are less than a corresponding mean for the heterozygote; the adjusted carrying capacity of a genotype in a habitat is just an extension to the population level of the carrying capacity for a single habitat. The population's carrying capacity, a weighted harmonic mean of the adjusted carrying capacities of the genotypes, is maximized near population size equilibrium. Sufficient conditions for a protected polymorphism under a more general form of density-regulated selection, with the genotypic fitnesses any smooth, strictly decreasing function of population size, are also outlined.

Density-Regulated Selection with Genotypic Interactions

A deterministic model of density-regulated selection with genotypic interactions is developed for a diploid population with discrete, nonoverlapping generations. The population is polymorphic for two alleles at an autosomal locus. Before selection in each generation, the three genotypes are in Hardy-Weinberg frequencies, but genotypes differ in their selective values because of genotypic differences in their intrinsic rates of increase, carrying capacities, and genotypic interactions. The genotypic interactions specify the effect of an individual of one genotype on the fitness of another genotype. By analogy to the Lotka-Volterra model for interspecific competition, our model for intraspecific competition assumes that the selective value of a genotype strictly decreases with numbers of each genotype; therefore, selective values depend on both density and gene frequency. Sufficient conditions for a protected polymorphism are surprisingly simple: the heterozygote must have a carrying capacity greater than that of either homozygote multiplied by the interaction coefficient which expresses the effect of that homozygote on the heterozygote; or, alternatively each homozygous individual must inhibit the fitness of its own genotype, and hence its contribution to population growth, more than it inhibits the fitness of the heterozygote.

A note on the island model with sex dependent migration

A theoretical calculation is presented which extends Wright's island model of drift and migration to differential migration between the two sexes. In this circumstance, local demes no longer have Hardy-Weinberg frequencies. There may be local heterozygote excess or deficiency depending, respectively, on whether migration occurs before or after mating. The magnitude of the local departure from Hardy-Weinberg is directly proportional to the difference between the migration parameters of the two sexes. These results could have important implications for studies where genetic markers are used for inferring population structure. An example from a study of Marmot colonies is cited.

ALLOZYMIC VARIATION AND LINKAGE DISEQUILIBRIUM IN SOME LABORATORY POPULATIONS OF DROSOPHILA MELANOGASTER

Nine laboratory populations of D. melanogaster were surveyed by starch gel electrophoresis for variation at 17 enzyme loci. A single-fly extract could be assayed for all 17 enzymes, so that the data consist of 17-locus genotypes.--Pairwise linkage disequilibria were estimated from the multilocus genotypic frequencies, using both Burrows' and Hill's methods. Large amounts of linkage disequilibrium were found, in contrast to the results reported for natural populations.-Knowledge of the approximate sizes of these populations was used to compare the observed heterozygosities and linkage disequilibria with predictions of the neutral allele hypothesis. The relatively large amount of linkage disequilibrium is consistent with the small sizes of the populations. However, the levels of heterozygosity in at least some populations suggest that some mechanism has been operating to retard the rate of decay by random drift. Several examples of significant deviation from Hardy-Weinberg frequencies and the large amount of linkage disequilibrum present in these populations indicate that a likely mechanism is selective effects associated with neutral alleles because of linkage disequilibrium with selected loci (e.g., "associative overdominance"). The results are therefore consistent with both neutralist, and selectionist hypotheses, but suggest the importance of considering linkage disequilibrium between neutral and selected loci when attempting to explain the dynamics of enzyme polymorphisms.

The sampling variance of the linkage disequilibrium parameter in multi-allele loci

The linkage disequilibrium parameter Δ between two loci has been evaluated for multiple alleles. It shows that when there is random mating and chromosome pairs satisfy Hardy-Weinberg frequencies the disequilibrium between two multi-allele loci is due to unequal frequencies between coupling and repulsion phases in the double heterozygote. The maximum likelihood estimators of Δ and the approximate variance of Δ are given for a large size of sample. A numerical example is also given.

MATING PATTERN AND MATING SUCCESS OF DROSOPHILA PSEUDOOBSCURA KARYOTYPES IN LARGE EXPERIMENTAL POPULATIONS.

The pattern of matings between genotypes is the bridge connecting genotypic frequencies at the end of one generation with those at the beginning of the next. It is consequently an essential part of models in population genetics. The simplest assumption is that mating is random. The mating process in higher animals such as vertebrates and arthropods involves the pairing of diploid males and females and is random when the pairing occurs without regard to genotype. When mating is random and forces such as selection are absent, the genotypic frequencies among zygotes are the familiar Hardy-Weinberg frequencies. Most tests for randomness of mating are based on this fact. The usual procedure is to perform a chi-square test for goodness-of-fit between the frequencies of genotypes observed among zygotes and the Hardy-Weinberg expectations. However, such tests are indirect because they are based on genotypic frequencies which are the consequences of matings among adults of the previous generation, rather than on the frequencies of the matings themselves. And it is well known that the power of the chi-square test to detect departures from Hardy-Weinberg frequencies due to inbreeding (Ward and Sing, 1970) or selection (Lewontin and Cockerham, 1959) is severely limited. A stronger means of testing the randomness of mating is by direct analysis of the mating pattern-that is, by determination of the frequencies of matings between spe-

The Implications of Density-Dependent Population Growth for Frequency- and Density-Dependent Selection

The relationship between density-dependent population growth and frequency- and density-dependent selection was investigated. For the haploid asexual case, Malthusian growth leads to constant birth and death rates and constant fitness values. A more general Lotka-Volterra formulation leads to both density- and frequency-dependent selection. The more general formulation is necessary but not sufficient for polymorphic coexistence in asexual forms. For the diploid sexual case, Malthusian growth leads to frequency-dependent population trajectories, but the basic birth and death rates are constant. A density-dependent model, analogous to the Lotka-Volterra model of the asexual case, leads to both frequency- and density-dependent fitness values and selection differentials. If selective differentials are solely reproductive in origin, whether density dependent or independent, Hardy-Weinberg frequencies characterize the polymorphic equilibrium, when it exists. This is not the case when selection differentials inv...

392: A Differential Viability Model for Twin-Pair Blood Group Data

Much interest in human genetics studies of blood systems is focussed on the possible incompatibility of discordant twin pairs. Here we discuss a differential viability model which accounts for deviations from the standard multinomial model for twin pair data based on the Hardy-Weinberg frequencies. We discuss related estimation and testing problems, illustrating the techniques with data from the Louisville Twin Study.

Deviations from Hardy-Weinberg frequencies caused by assortative mating in hybrid populations

Deviations from Hardy-Weinberg frequencies caused by assortative mating in hybrid populations

Deviations from Hardy-Weinberg frequencies caused by assortative mating in hybrid populations.

The conventional formulas for genotype frequencies in a hybrid population H produced by interbreeding from ancestral populations P(1) and P(2) involve only one hybrid parameter M, equal to the fraction of alleles derived from P(2). For the one-parameter model to be accurate, all individuals of H must have probabilities for alleles determined by one and the same M. When H contains subpopulations that have different values of M, the correct genotype frequencies can be predicted by use of two parameters: (i) M(H), the average of M for all individuals of H and (ii) eta(H), defined like the eta devised by C. A. B. Smith for testing the Hardy-Weinberg Law and computed with a formula like G. R. Price's eta, which involves assortative mating covariance-in this case for the M values of the parents of H. If parents of H have equal average M values for males and females, and mate at random, eta(H) vanishes. For perfect assortative mating, eta(H) is the variance of M for H. As for Smith's eta, eta(H) provides a test of fit of prediction to observed that is sensitive to signs of deviations. Using eta(H) with T. E. Reed's data for Gm in Oakland, California Negroes, his one-parameter fit ("good" by his chi-square test) is significantly rejected (P = 0.04). A simultaneous good fit of Reed's Gm data and his Duffy data results (chi-square, 1 df = 0.88, P > 0.30) from the use of previously published values of 0.23 and 0.047 for M(H) and eta(H). It is concluded that Reed's conclusion that these values were in error is itself in error, as is also his view that differences between M values from different genes and deviations from frequencies expected within genes are not likely to give significant information about variance of M.