Genetics of Parthenogenesis in DROSOPHILA MELANOGASTER. II. Characterization of a Gynogenetically Reproducing Strain

A strain of Drosophila melanogaster, named gyn-F9, can reproduce by gynogenesis. On mating with a male sterile mutant, ms( 3)K81, gyn-F9 females produced impaternate progeny at a rate of about 15 flies per female, which was almost 2000 times as frequent as that of the control. When the females were mated with normally fertile males, the number of offspring varied extremely from parent to parent, with average fertility being much lower than that of normal females. Nearly one-third of these bisexual progeny were either triploid females or intersexes. Among the rest of the progeny, some were diploid impaternates having developed without syngamy. The gynogenetic property of gyn-F9 is primarily governed by a few genes, most likely two recessive genes, one each located on the second and third chromosomes. The impaternates were found to restore their diploidy by the fusion of two nonsister nuclei out of the four egg pronuclei which result from the second meiotic division (central fusion). Although nondisjunction occurs frequently in the meiosis of gyn-F9, this is unlikely to bring about an appreciable number of diploid gametes developing into impaternates. Possible mechanisms of the evolutionary origin of parthenogenesis are discussed in relation to these findings.     

Cytological Investigation of the Mechanism of Parthenogenesis in Drosophila mercatorum

Thelytokous parthenogenesis (female progeny only) in animals is believed to arise initially in unfertilized eggs produced by bisexual females via the fusion of two haploid nuclei following meiosis, to produce diploid female progeny. The transition from sexual to parthenogenetic mechanisms of reproduction requires that the egg replace the paternal contributions of a haploid genetic complement and the basal body, which is thought to be essential for centrosome formation. The transitional facultative parthenogenetic stage is usually associated with a high rate of failed or abortive development, but the molecular and mechanistic reasons for this failure remain unclear. We show that a facultatively parthenogenetic strain of Drosophila mercatorum produces a high percentage of unfertilized eggs competent to restore diploidy and form centrosomes de novo following meiosis. The female meiotic products replicate and divide by an acentrosomal mechanism in most oocytes and cytoplasmic centrosomes form in 35% of the oocytes. However, after pronuclear replication the cytoplasmic centrosomes must "capture" two haploid nuclei in order to restore diploidy. In practice, this process frequently fails due to centrosome-mediated capture events of single or more than two haploid nuclei, as well as multiple nuclear capture events in a single embryo when excess free centrosomes are not inactivated following formation of the first zygotic nucleus. Additionally, as development proceeds, many of the centrosomes that initiate syncytial development do not remain functional, possibly due to centrosome maturation defects, and later stages of syncytial development fail. The combined effect of the high error rate associated with nuclear capture and the failure of centrosome maturation during later developmental prevents successful parthenogenesis in most of the eggs that initiate development. This shows that the high rate of failed development associated with the transition from sexual to parthenogenetic reproduction is limited by the low probability of the formation of a diploid zygotic nucleus with the correct complement of centrosomes in D. mercatorum.     

Cytological investigation of the mechanism of parthenogenesis in Drosophila mercatorum

Thelytokous parthenogenesis (female progeny only) in animals is believed to arise initially in unfertilized eggs produced by bisexual females via the fusion of two haploid nuclei following meiosis, to produce diploid female progeny. The transition from sexual to parthenogenetic mechanisms of reproduction requires that the egg replace the paternal contributions of a haploid genetic complement and the basal body, which is thought to be essential for centrosome formation. The transitional facultative parthenogenetic stage is usually associated with a high rate of failed or abortive development, but the molecular and mechanistic reasons for this failure remain unclear. We show that a facultative parthenogenetic strain of Drosophila mercatorum produces a high percentage of unfertilized eggs competent to restore diploidy and form centrosomes de novo following meiosis. The female meiotic products replicate and divide by an acentrosomal mechanism in most oocytes and cytoplasmic centrosomes form in 35% of the oocytes. However, after pronuclear replication the cytoplasmic centrosomes must "capture" two haploid nuclei in order to restore diploidy. In practice, this process frequently fails due to centrosome-mediated capture events of single or more than two haploid nuclei, as well as multiple nuclear capture events in a single embryo when excess free centrosomes are not inactivated following formation of the first zygotic nucleus. Additionally, as development proceeds, many of the centrosomes that initiate syncytial development do not remain functional, possibly due to centrosome maturation defects, and later stages of syncytial development fail. The combined effect of the high error rate associated with nuclear capture and the failure of centrosome maturation during later developmental prevents successful parthenogenesis in most of the eggs that initiate development. This shows that the high rate of failed development associated with the transition from sexual to parthenogenetic reproduction is limited by the low probability of the formation of a diploid zygotic nucleus with the correct complement of centrosomes in D. mercatorum.     

Evidence for dosage compensation in parthenogenetic Hymenoptera

Amount of DNA-Feulgen staining in individual somatic nuclei and mature sperm of the parthenogenetic wasps, Habrobracon juglandis, H. serinopae, and Mormoniella vitripennis, were determined with a scanning microdensitometer. The haploid genome for both species of Habrobracon was estimated to be 0.15–0.16×10^–12 g DNA, corresponding to a molecular weight of roughly 10×10¹⁰ daltons. The haploid genome of M. vitripennis is approximately twice this value, 0.33–0.34×10^–12 g, or about 20×10¹⁰ daltons. Measurements made on dividing nuclei from syncytial preblastoderm embryos of H. juglandis and M. vitripennis showed that the chromosomes of impaternate males were present in the haploid number and contained the C amount of DNA; whereas nuclei from female preblastoderm embryos contained the diploid number of chromosomes and the 2C amount of DNA. However, hemocyte and brain cell nuclei from either male or female adult wasps contained 2C and 4C amounts of DNA. Both sexes also showed equivalent levels of polyploidy (8C, 16C, or 32C) in Malpighian tubule nuclei. Therefore, in these parthenogenetic species, a mechanism must exist that compensates during later development for the initial two-fold difference in the chromatin content of somatic nuclei in haploid male and diploid female embryos. Hemocytes from impaternate Mormoniella diploid males and triploid females contain the 2C and 3C amounts of DNA, respectively. Therefore dosage compensation involves an additional cycle of DNA replication only in haploid cells, and it insures that a certain minimum quantity of DNA is received by each somatic cell.     

Evaluating the transferability of Hapmap SNPs to a Singapore Chinese population

Background

Sexual reproduction relies on two key events: formation of cells with a haploid genome (the gametes) and restoration of diploidy after fertilization. Therefore the underlying mechanisms must have been evolutionary linked and there is a need for evidence that could support such a model.

Results

We describe the identification and the characterization of yem ¹ , the first yem-alpha mutant allele (V478E), which to some extent affects diploidy reduction and its restoration. Yem-alpha is a member of the Ubinuclein/HPC2 family of proteins that have recently been implicated in playing roles in chromatin remodeling in concert with HIRA histone chaperone. The yem ¹ mutant females exhibited disrupted chromosome behavior in the first meiotic division and produced very low numbers of viable progeny. Unexpectedly these progeny did not display paternal chromosome markers, suggesting that they developed from diploid gametes that underwent gynogenesis, a form of parthenogenesis that requires fertilization.

Conclusions

We focus here on the analysis of the meiotic defects exhibited by yem ¹ oocytes that could account for the formation of diploid gametes. Our results suggest that yem ¹ affects chromosome segregation presumably by affecting kinetochores function in the first meiotic division. This work paves the way to further investigations on the evolution of the mechanisms that support sexual reproduction.     

Recovery and development of parasexual fusion products inEnteromorpha linza (L.) J. Ag. (Ulvales,Chlorophyta)

Newly released zoospores fromEnteromorpha linza (L.) J. Ag. lack significant cellulose cell wall material and are suitable for treatment as protoplasts in a parasexual fusion process using high pH-Ca^{+ +}, PEG and centrifugation. Treated zoospores settled on glass cover slips within 3 h and were examined microscopically at 1000 ×. Presumptive fusion products were identified by their larger size and presence of twin chloroplasts and eyespots. Unfused zoospores adjacent to fusion cells were killed by 2–3 min exposure to blue light (410–490 nm) from a high pressure mercury illuminator. Unexposed fusion cells developed into uniseriate germlings within 10 days at which stage they could be readily identified at 60 × with a dissecting microscope and isolated by micropipette. Ten-day germlings from both unfused zoospores and fusion cells were stained with the DNA-localizing fluorochrome hydroethidine and relative nuclear DNA content determined with epi-(incident) UV illumination. All germlings were found to be uninucleate. Germlings from unfused zoospores had haploid nuclei with 1N = 10 and 1C and 2C levels of DNA, while germlings from fusion cells had diploid nuclei with 2N = 20 and 2C and 4C levels of DNA. These result are interpreted as evidence of karyogamy following parasexual zoospore fusions. Isolated diploid germlings, cultured for 10 weeks were found to conserve their 2N chromosome complements and elevated levels of nuclear DNA. Although most diploid germlings were morphologically similar to haploid control plants, some exhibited ‘gigas’ characteristics, including larger cells, chloroplasts, and nuclei. These results are discussed in terms of unique phenotypes that result when nuclear and organellar genes are combined in different ways.     

Experiments inducing prospective polar body nuclei to participate in embryogenesis of the sawfly Athalia rosae (Hymenoptera)

Summary Mature eggs dissected from ovaries of unmated females of Athalia rosae (Hymenoptera: Tenthredinidae), if placed on a filter-paper soaked with distilled water, are activated and develop to haploid males. Occasionally, however, diploid females develop from these artificially activated eggs. Treatment of mature unfertilized eggs dissected from diploid females with ice-cold temperatures immediately before activation and with a high temperature (36° C) upon and immediately after activation resulted in the production of diploid males, diploid females, triploid females and gynandromorphs at high frequency. The same treatment of mature unfertilized eggs dissected from triploid females resulted in the production of only triploid survivors. These results, together with the results on the segregation of a marker mutation, yellow fatbody (yfb), appear to indicate that meiotic divisions were complete in the treated eggs, and that all four nuclei became potentially capable of participating in development with or without automictic fusion.Studies on the sawfly, Athalia rosae (Insecta, Hymenoptera, Tenthredinidae), part V     

Analysis of haploid mosaics in Drosophila

Adult chimeric epidermal structures were obtained following transplantation of haploid nuclei from haploid donor embryos of Drosophila into genetically marked diploid embryos. The haploid nuclei either remained haploid or became diploid. Where possible, physical measurements indicated that the haploid cells were smaller and produced smaller cuticular structures than did diploid cells. An increase in the number of pattern elements was observed in many patches which, by various criteria, were judged to be formed by haploid cells. The observation of altered pattern element spacing in haploid patches is in agreement with the conclusion, reached by L. I. Held (1979, Wilhelm Roux's Arch.187, 105–127) in triploid flies, that bristle spacing is a function of cell size.     

Initiation of Meiotic Recombination in Ustilago maydis

A central feature of meiosis is the pairing and recombination of homologous chromosomes. Ustilago maydis, a biotrophic fungus that parasitizes maize, has long been utilized as an experimental system for studying recombination, but it has not been clear when in the life cycle meiotic recombination initiates. U. maydis forms dormant diploid teliospores as the end product of the infection process. Upon germination, teliospores complete meiosis to produce four haploid basidiospores. Here we asked whether the meiotic process begins when teliospores germinate or at an earlier stage in development. When teliospores homozygous for a cdc45 mutation temperature sensitive for DNA synthesis were germinated at the restrictive temperature, four nuclei became visible. This implies that teliospores have already undergone premeiotic DNA synthesis and suggests that meiotic recombination initiates at a stage of infection before teliospores mature. Determination of homologous recombination in plant tissue infected with U. maydis strains heteroallelic for the nar1 gene revealed that Nar⁺ recombinants were produced at a stage before teliospore maturation. Teliospores obtained from a spo11Δ cross were still able to germinate but the process was highly disturbed and the meiotic products were imbalanced in chromosomal complement. These results show that in U. maydis, homologous recombination initiates during the infection process and that meiosis can proceed even in the absence of Spo11, but with loss of genomic integrity.     

Meiotic mutations from natural populations ofDrosophila melanogaster

Two meiotic genes from natural populations are described. A female meiotic mutation,mei(1)g13, mapped to 17.4 on the X chromosome, causes nondisjunction of all homologs except for the fourth chromosomes. In addition, it reduces recombination by 10% in the homozygotes and causes 18% increased recombination in the heterozygotes. A male meiotic mutation,mei-1223 ^m144 , is located on the third chromosome. Although this mutation causes nondisjunction of all chromosomes, each chromosome pair exhibits a different nondisjunction frequency. Large variations in the sizes of the premature sperm heads observed in the homozygotes may reflect irregular meiotic pairing and the subsequent abnormal segregation, resulting in aneuploid chromosome complements.     

The Utilization during Mitotic Cell Division of Loci Controlling Meiotic Recombination and Disjunction in DROSOPHILA MELANOGASTER

To inquire whether the loci identified by recombination-defective and disjunction-defective meiotic mutants in Drosophila are also utilized during mitotic cell division, the effects of 18 meiotic mutants (representing 13 loci) on mitotic chromosome stability have been examined genetically. To do this, meiotic-mutant-bearing flies heterozygous for recessive somatic cell markers were examined for the frequencies and types of spontaneous clones expressing the cell markers. In such flies, marked clones can arise via mitotic recombination, mutation, chromosome breakage, nondisjunction or chromosome loss, and clones from these different origins can be distinguished. In addition, meiotic mutants at nine loci have been examined for their effects on sensitivity to killing by UV and X rays.—Mutants at six of the seven recombination-defective loci examined (mei-9, mei-41, c(3)G, mei-W68, mei-S282, mei-352, mei-218) cause mitotic chromosome instability in both sexes, whereas mutants at one locus (mei-218) do not affect mitotic chromosome stability. Thus many of the loci utilized during meiotic recombination also function in the chromosomal economy of mitotic cells.—The chromosome instability produced by mei-41 alleles is the consequence of chromosome breakage, that of mei-9 alleles is primarily due to chromosome breakage and, to a lesser extent, to an elevated frequency of mitotic recombination, whereas no predominant mechanism responsible for the instability caused by c(3)G alleles is discernible. Since these three loci are defective in their responses to mutagen damage, their effects on chromosome stability in nonmutagenized cells are interpreted as resulting from an inability to repair spontaneous lesions. Both mei-W68 and mei-S282 increase mitotic recombination (and in mei-W68, to a lesser extent, chromosome loss) in the abdomen but not the wing. In the abdomen, the primary effect on chromosome stability occurs during the larval period when the abdominal histoblasts are in a nondividing (G2) state.—Mitotic recombination is at or above control levels in the presence of each of the recombination-defective meiotic mutants examined, suggesting that meiotic and mitotic recombination are under separate genetic control in Drosophila.—Of the six mutants examined that are defective in processes required for regular meiotic chromosome segregation, four (l(1)TW-6^cs, ca^nd, mei-S332, ord) affect mitotic chromosome behavior. At semi-restrictive temperatures, the cold sensitive lethal l(1)TW-6^cs causes very frequent somatic spots, a substantial proportion of which are attributable to nondisjunction or loss. Thus, this locus specifies a function essential for chromosome segregation at mitosis as well as at the first meiotic division in females. The patterns of mitotic effects caused by ca^nd, mei-S332, and ord suggest that they may be leaky alleles at essential loci that specify functions common to meiosis and mitosis. Mutants at the two remaining loci (nod, pal) do not affect mitotic chromosome stability.     

Corn Smut Dikaryon in Culture

A TYPICAL smut life cycle has three phases—diploid, haploid and dikaryon¹. Diploid spores (teliospores) formed in the host tissue are a resting phase. They undergo meiosis at germination to form haploid vegetative cells which are usually yeast-like. The dikaryon is the pathogenic phase and is made up of cells with two haploid nuclei. It is initiated by the fusion of two compatible non-pathogenic haploid cells and the formation of an infection hypha by the fusion product.     

Diploid arrhenotoky and automictic thelytoky in soft scale insects (Lecaniidae: Coccoidea: Homoptera)

Parthenogenesis is reported in three soft scales with 2n=16. In the unfertilized eggs of all three, oogenesis is normal and diploidy is restored by the fusion of the division products of the haploid female pronucleus. In Lecanium putmani Phillips 12 of 13 uninseminated females collected in the wild produced only males. The 21 inseminated females produced 15% males. The males were diploid but contained one euchromatic (E) and one heterochromatic (H) chromosome set. Most of the eggs produced by the inseminated females contained sperm but a few did not. It was concluded, therefore, that females develop from fertilized eggs and males from unfertilized eggs and that the species was diploid arrhenotokous. In L. cerasifex Fitch only 18 of 56 females collected in the wild had been inseminated. The frequency of males among their embryos was 22%. The males were again diploid with one E and one H set of chromosomes. Among the 38 uninseminated females, 27 produced only males, and 10 produced only females. All the female producers contained needle-like bacterial symbionts. Most of the male producers, and most of the inseminated females contained no symbionts; the rest contained rod-like symbionts. It was concluded, therefore, that the females of L. cerasifex studied belonged to two races, a diploid arrhenotokous race and an obligate automictic thelytokous race. Eucalymantus tessellatus (Signoret) is obligate automictic thelytokous. All the females examined were uninseminated and produced only females.Supported by Grant GB 23665 from the National Science Foundation, Washington, D.C.     

Meiotic Nondisjunction and Aneuploids in Intersyngenic Hybrids of PARAMECIUM CAUDATUM

Artificially induced intersyngenic crosses in Paramecium caudatum can produce viable and fertile hybrids. When F₁ hybrids of double E mating type (Mt¹/Mt³ or Mt¹²/Mt³) were crossed with mating type O (mt/mt), aberrant segregants of double E and single O type were produced. This segregation was not explained by ordinary equal or unequal crossing over. Breeding analyses of these segregants by using linkage between Mt and cnrA (a behavioral mutant) revealed that they were produced by meiotic nondisjunction of bivalent chromosomes carrying Mt genes, and thus the double E and single O segregants were aneuploids: trisomics ( Mt¹/Mt³/mt or Mt ¹²/Mt³/mt) and monosomics (mt), respectively. An aberrant segregant was also obtained for another locus, tnd 2, independent of both Mt and cnrA, suggesting the occurrence of meiotic nondisjunction throughout hybrid genomes. These aneuploids will be useful for genetic study in this species. The occurrence of meiotic nondisjunction in the intersyngenic hybrids also suggests that syngens of P. caudatum have been reproductively isolated for long enough to develop chromosomal incompatibility in their meiotic process.     

Further Studies on the Role of Polyploidy in the Evolution of Meloidogyne

Two tetraploid isolates of Meloidogyne hapla, 86P and E289P, with haploid chromosome numbers of 34 and 28, respectively, were studied cytogenetically and biologically in relation to the diploid populations, 86-Va (n = 17) and E289-Taiwan (n = 14), from which they had been originally isolated. Both isolates were quite stable, converting to diploidy at the low rate of about 2.5%. The tetraploid isolate 86P maintained itself in competition with its diploid counterpart in mixed cultures, although an initial frequency of 50% polyploidy was reduced to about 9% at the end of the sixth generation. Both tetraploid isolates could maintain themselves in greenhouse cultures without artificial selection for at least 2 years. Crosses between diploid females and tetraploid males resulted in a few triploid females that produced mostly nonviable eggs, suggesting partial reproductive isolation between the two ploidy forms. Ten generations of propagation of only polyploid females of isolate 86P that were associated with males failed to yield an obligatorily amphimictic isolate that would not convert at all to diploidy. If one accepts a previous assumption that the present day amphimictic root-knot nematodes are tetraploids derived from diploid ancestors, results of the present study are not inconsistent with an evolutionary trend toward an even higher level of ploidy in Meloidogyne, presumably octaploidy.     

Sex Chromosome Meiotic Drive Systems in DROSOPHILA MELANOGASTER I. Abnormal Spermatid Development in Males with a Heterochromatin-Deficient X Chromosome (sc4sc8)

The meiotic drive characteristics of the In(1)sc^4Lsc^8R/Y system have been examined by genetic analysis and by light and electron microscopy. sc⁴sc⁸/Y males show a direct correlation between nondisjunction frequency and meiotic drive. Temperature-shift experiments reveal that the temperature-sensitive period for nondisjunction is at meiosis, whereas that for meiotic drive has both meiotic and post-meiotic components. Cytological analyses in the light and electron microscopes reveal failures in spermiogenesis in the testes of sc⁴sc⁸ males. The extent of abnormal spermatid development increases as nondisjunction becomes more extreme.     

Chromosomal loci of genes controlling site-specific restriction endonucleases of Bacillus subtilis

Summary In Saccharomyces cerevisiae, diploid strains which are respiratory deficient (e.g., rho^–) or are homozygous for the mating-type locus (i.e., either a/a or /) are unable to sporulate. In order to induce sporulation in these nonsporulating strains, the technique of protoplast fusion mediated by polyethylene glycol was adopted. In this study, the products of protoplast fusion were induced to sporulate without reversion to normal cells.Protoplasts from a respiratory-deficient diploid strain were mixed with those from a respiratory-competent haploid one carrying mitochondrial drug resistance markers, treated with 30% polyethylene glycol-4000 and 25 mM CaCl₂, and incubated in 0.1 M potassium acetate containing 0.8 M sorbitol as an osmotic stabilizer. After two days' incubation, asci with three to eight spores were formed at a frequency of 1×10^–3 to 2×10^–4. Sporulation was also observed in products of fusion between an a/a diploid and haploid strains and between an / diploid and a haploid strains. The analysis of the genotypes of spores revealed that when fusion products were cultured under conditions for sporulation, karyogamy did not take place, diploid nuclei underwent meiosis, and both diploid and haploid nuclei were able to develop into spores.     

Statistical Analysis of Nondisjunction Assays in Drosophila

Many advances in the understanding of meiosis have been made by measuring how often errors in chromosome segregation occur. This process of nondisjunction can be studied by counting experimental progeny, but direct measurement of nondisjunction rates is complicated by not all classes of nondisjunctional progeny being viable. For X chromosome nondisjunction in Drosophila female meiosis, all of the normal progeny survive, while nondisjunctional eggs produce viable progeny only if fertilized by sperm that carry the appropriate sex chromosome. The rate of nondisjunction has traditionally been estimated by assuming a binomial process and doubling the number of observed nondisjunctional progeny, to account for the inviable classes. However, the correct way to derive statistics (such as confidence intervals or hypothesis testing) by this approach is far from clear. Instead, we use the multinomial-Poisson hierarchy model and demonstrate that the old estimator is in fact the maximum-likelihood estimator (MLE). Under more general assumptions, we derive asymptotic normality of this estimator and construct confidence interval and hypothesis testing formulae. Confidence intervals under this framework are always larger than under the binomial framework, and application to published data shows that use of the multinomial approach can avoid an apparent type 1 error made by use of the binomial assumption. The current study provides guidance for researchers designing genetic experiments on nondisjunction and improves several methods for the analysis of genetic data.MEIOSIS is a specialized cell division, where a diploid cell undergoes a single round of replication followed by two rounds of segregation to produce four haploid gametes. During this segregation, chromosomes must correctly separate (or disjoin) from their homologs at meiosis I, followed by sister chromatids disjoining at meiosis II. When chromosomes fail to disjoin from their partners, the resultant nondisjunction produces aneuploid gametes with the wrong number of chromosomes. The study of meiotic nondisjunction in Drosophila has a long and distinguished history of publication in genetics, with the inaugural article published in this journal being Calvin Bridges'' use of nondisjunction to prove the chromosome theory of heredity (Bridges 1916). The first study that screened variants isolated from natural populations used nondisjunction to identify meiotic mutants (Sandler et al. 1968), as did the first EMS-induced mutant screen (Baker and Carpenter 1972). Subsequent screens using new mutagens or techniques have also relied on measuring nondisjunction to identify mutants of interest (Sekelsky et al. 1999). Indeed, much of the progress that has been made in the study of meiosis would not have been possible without the use of nondisjunction to identify new mutations that are defective at some step in chromosome segregation.However, one difficulty in estimating nondisjunction rates is that in most instances the resulting aneuploid progeny cannot survive. Fortunately, in Drosophila it is possible to design crosses to recover them. Sex determination in flies is based on the number of X chromosomes, rather than a masculinizing Y chromosome as in mammals. This means that XO flies are viable (but sterile) males, while XXY flies are viable females. Therefore, it is possible to recover both normal and nondisjunctional progeny, as a nullo-X egg fertilized by an X-bearing sperm will survive as an XO male, while a diplo-X egg fertilized by a sperm lacking an X will be female (XXY). By using visible markers on the sex chromosomes, these exceptional progeny are straightforward to identify. However, if those eggs are fertilized by the other class of sperm, the resulting OY or XXX progeny are inviable. Therefore, the nondisjunction rate that occurs during meiosis is not equal to the proportion of nondisjunctional progeny, as only 50% of nondisjunctional eggs receive sperm compatible with viability, while all normal eggs are viable.Given this experimental limitation, what is the correct method to calculate the error rate during meiosis? For this discussion, let N be the total number of progeny produced in an experiment, let X₁ be the number of inviable nondisjunctional progeny (OY and XXX), let X₂ be the number of viable nondisjunctional progeny (XO and XXY), and let X₃ be the number of normal progeny (XY and XX), such that N = X₁ + X₂ + X₃. If all progeny could be counted, then the nondisjunction rate would simply be (X₁ + X₂)/N.However, only flies that survive to adulthood can be counted, and therefore both X₁ and N are unknown. As X- and Y-bearing sperm are produced in equal numbers, live and dead nondisjunctional progeny are also expected in equal numbers. Therefore, K.W. Cooper (Cooper 1948) proposed the widely used estimator for the X chromosome nondisjunction rate, where X₂ is substituted for X₁ in the above formula, giving the rate as:(1)While this estimator works, the statistical properties of this estimator are not clear. Instead of following the early literature to combine X₁ and X₂ and use a binomial distribution, we go back to the three original categories and model the process as a multinomial distribution with latent number of progeny N, considering all three possible phenotypes for each progeny (nondisjunctional dead, nondisjunctional living, and normal). Whether a nondisjunctional oocyte becomes a nondisjunctional dead or nondisjunctional living progeny depends on the sex chromosome content of the sperm that fertilized it. As X- and Y-bearing sperm are produced in equal numbers during male meiosis, the usual genetic expectation for the rates of nondisjunctional dead and living progeny will be . However, even assuming that the rates of nondisjunctional dead and living progeny are different, with a Poisson assumption of N, we can derive the maximum-likelihood estimators (MLEs) for the nondisjunctional dead and nondisjunctional living rates. Under the usual genetic expectation of equality, the MLE of the nondisjunctional rate coincides with Cooper''s estimator, and we furthermore derive the exact distribution of . Under another set of reasonable assumptions, we show the consistency and asymptotic normality of Cooper''s estimator, and derive asymptotic results when comparing two nondisjunction rates. All these distributional results enable us to develop confidence interval and hypothesis testing related to p, or p_x − p_y in the case of comparing two nondisjunction rates from populations x and y.     

Viability of Physarum polycephalum spores and ploidy of plasmodial nuclei.

Amoebae of Physarum polycephalum carrying the mth mating-type allele may differentiate into plasmodia in the absence of mating. Such plasmodia are haploid and, upon sporulation, produce mainly inviable spores. We have asked whether the viable spores arise from meiotic or mitotic divisions. Using a microfluorometric measurement of the deoxyribonucleic acid content of individual nuclei, we found the fraction of viable spores to be correlated with the proportion of rare, diploid nuclei containing in the generally haploid plasmodium. When homozygous diploid plasmodia were created by heat shocking, spore viability increased dramatically. We suggest that viable spores are produced via meiosis in mth plasmodia, that the mth allele has no effect on sporulation per se, and that the normal source of viable haploid spores is a small fraction of diploid nuclei ubiquitous in haploid plasmodia.     

Delayed sperm injection and fertilization in parthenogenetically activated insect egg (Athalia rosae,Hymenoptera)

Summary Mature eggs dissected from the ovary of unmated females of Athalia rosae ruficornis Jakovlev (Hymenoptera, Tenthredinidae) can be activated to develop (into haploid parthenogenetic males) simply by exposing them to distilled water. These eggs, which are primary oocytes arrested at the first meiotic metaphase, resume meiosis upon activation and reach the first meiotic telophase in 20 min. Mature eggs immediately upon dissection have previously been shown to complete karyogamy and develop as fertilized diploid females if injected with sperm. We show here that the eggs activated in water for 20 min have a much higher rate of successful fertilization if injected with sperm, and that the eggs activated for 40 min, upon sperm injection, though at a reduced frequency still develop as diploid fertilized females. Eggs left in water for 60 min, however, are no longer fertilized upon sperm injection and develop as haploid males.