Do-it-yourself statistics: A computer-assisted likelihood approach to analysis of data from genetic crosses

Graduate school programs in genetics have become so full that courses in statistics have often been eliminated. In addition, typical introductory statistics courses for the "statistics user" rather than the nascent statistician are laden with methods for analysis of measured variables while genetic data are most often discrete numbers. These courses are often seen by students and genetics professors alike as largely irrelevant cookbook courses. The powerful methods of likelihood analysis, although commonly employed in human genetics, are much less often used in other areas of genetics, even though current computational tools make this approach readily accessible. This article introduces the MLIKELY.PAS computer program and the logic of do-it-yourself maximum-likelihood statistics. The program itself, course materials, and expanded discussions of some examples that are only summarized here are available at http://www.unisi. it/ricerca/dip/bio_evol/sitomlikely/mlikely.h tml.

Are unpaired chromosomes spermicidal?: A maximum-likelihood analysis of segregation and meiotic drive in Drosophila melanogaster males deficient for the ribosomal-dna

Meiosis in Drosophila melanogaster males is achiasmate and requires special systems to ensure normal segregation. Several situations that yield frequent nondisjunction also produce high levels of chromatin-dependent sperm lethality, suggesting the possibility of a simple and direct connection between defective disjunction and defective sperm development. One hypothesis that has been offered is that pairing not only ensures disjunction, but also changes the physical state of chromosomes so that they can be packaged in sperm. Here, I present an analysis of extensive data on disjunction and sperm survival in rDNA-deficient males collected by B. McKee and D. Lindsley. This analysis demonstrates that, although nondisjunction and sperm lethality are indeed correlated, the basis of this is not the presence of unpaired chromosomes in the sperm. Chromosomes that have failed to disjoin are not themselves spermicidal.

The incidence of deafness is non-randomly distributed among families segregating for Waardenburg syndrome type 1 (WS1)

Waardenburg syndrome (WS) is caused by autosomal dominant mutations, and is characterised by pigmentary anomalies and various defects of neural crest derived tissues. It accounts for over 2% of congenital deafness. WS shows high variability in expressivity within families and differences in penetrance of clinical traits between families. While mutations in the gene PAX3 seem to be responsible for most, if not all, WS type 1, it is still not clear what accounts for the reduced penetrance of deafness. Stochastic events during development may be the factors that determine whether a person with a PAX3 mutation will be congenitally deaf or not. Alternatively, genetic background or non-random environmental factors or both may be significant. We compared the likelihoods for deafness in affected subjects from 24 families with reported PAX3 mutations, and in seven of the families originally described by Waardenburg. We found evidence that stochastic variation alone does not explain the differences in penetrances of deafness among WS families. Our analyses suggest that genetic background in combination with certain PAX3 alleles may be important factors in the aetiology of deafness in WS.

Specificity of chromosome damage caused by the Rex element of Drosophila melanogaster

Rex is a multicopy genetic element that maps within an X-linked ribosomal RNA gene (rDNA) array of D. melanogaster. Acting maternally, Rex causes recombination between rDNA arrays in a few percent of early embryos. With target chromosomes that contain two rDNA arrays, the exchanges either delete all of the material between the two arrays or invert the entire intervening chromosomal segment. About a third of the embryos produced by Rex homozygotes have cytologically visible chromosome damage, nearly always involving a single chromosome. Most of these embryos die during early development, displaying a characteristic apoptosis-like phenotype. An experiment that tests whether the cytologically visible damage is rDNA-specific is reported here. In this experiment, females heterozygous for Rex and an rDNA-deficient X chromosome were crossed to males of two genotypes. Some of the progeny from the experimental cross entirely lacked rDNA, while all of the progeny from the control cross had at least one rDNA array. A significantly lower frequency of early-lethal embryos in the experimental cross, proportionate to the fraction of rDNA-deficient embryos, demonstrates that Rex preferentially damages rDNA.

Genetic analysis of Stellate elements of Drosophila melanogaster

Repeated elements are remarkably important for male meiosis and spermiogenesis in Drosophila melanogaster. Pairing of the X and Y chromosomes is mediated by the ribosomal RNA genes of the Y chromosome and X chromosome heterochromatin, spermiogenesis depends on the fertility factors of the Y chromosome. Intriguingly, a peculiar genetic system of interaction between the Y-linked crystal locus and the X-linked Stellate elements seem to be also involved in male meiosis and spermiogenesis. Deletion of the crystal element of the Y, via an interaction with the Stellate elements of the X, causes meiotic abnormalities, gamete-genotype dependent failure of sperm development (meiotic drive), and deposition of protein crystals in spermatocytes. The current hypothesis is that the meiotic abnormalities observed in cry- males is due to an induced overexpression of the normally repressed Ste elements. An implication of this hypothesis is that the strength of the abnormalities would depend on the amount of the Ste copies. To test this point we have genetically and cytologically examined the relationship of Ste copy number and organization to meiotic behavior in cry- males. We found that heterochromatic as well as euchromatic Ste repeats are functional and that the abnormality in chromosome condensation and the frequency of nondisjunction are related to Ste copy number. Moreover, we found that meiosis is disrupted after synapsis and that cry-induced meiotic drive is probably not mediated by Ste.

Chromosome damage and early developmental arrest caused by the Rex element of Drosophila melanogaster

Rex (Ribosomal exchange) is a genetically identified repeated element within the ribosomal DNA (rDNA) of Drosophila melanogaster. Rex has a semidominant maternal effect that promotes exchange between and within rDNA arrays in the first few embryonic mitoses. Several of Rex's genetic properties suggest that its primary effect is rDNA-specific chromosome breakage that is resolved by recombination. We report here that rDNA crossovers are only a small, surviving minority of Rex-induced events. Cytology of embryos produced by Rex-homozygous females reveals obvious chromosome damage in at least a quarter of the embryos within the first three mitotic divisions. More than half of the embryos produced by Rex females die, and the developmental arrest is among the earliest reported for any maternal-effect lethal. The striking lethal phenotype suggests that embryos with early chromosome damage could be particularly fruitful subjects for analysis of the cell biology of early embryos.

Molecular genetic analysis of Drosophila rDNA arrays

Large repeated DNA arrays are a major component of the eukaryotic genome, but we know little about their internal organization. Understanding their architecture, however, is critical for describing genome structure and for inferring the mechanisms that shape it. One repeated family that is yielding a picture of how structure, function and recombination mechanisms come together is the ribosomal DNA (rDNA) of Drosophila melanogaster.

Rex and a suppressor of Rex are repeated neomorphic loci in the Drosophila melanogaster ribosomal DNA

The Rex locus of Drosophila melanogaster induces a high frequency of mitotic exchange between two separated ribosomal DNA arrays on a single chromosome. The exchanges take place in the progeny of Rex mothers and occur very early, before the third mitotic division. A number of common laboratory stocks have also been found to carry dominant suppressors of Rex (Su(Rex)). Rex was mapped to the X centric heterochromatin, proximal to su(f), by genetic and molecular analysis of two spontaneous recombinants. Using deficiencies and duplications of the heterochromatin, both Rex and one Su(Rex) were shown to behave as neomorphs. Rex-induced exchange in a target chromosome bearing both Rex and Su(Rex) was then used to map these functions to the bb locus itself. Molecular analysis of the recombinants, using length variants of the ribosomal DNA intergenic spacer as genetic markers, mapped Su(Rex) and Rex within the bb locus and demonstrated that both are repeated elements.

The use of maternally coded gene products in Drosophila

Both maternal and zygotic expression of many essential genes are required for normal development. For some of these genes, absence of maternal function yields striking embryonic defects. The experiments reported here examine two questions about such genes: (1) Are embryonic effects of maternal deficits a common property of maternally-and-zygotically active genes? and (2) Is use of the maternal products of these genes restricted to early embryogenesis? A comparison of times of lethality of mutant sons of normal and mutant-heterozygous mothers has been made for six mutations in the zeste-white region of the Drosophila X chromosome. Four of the mutations are defective in single cistrons and two are deficiencies that between them remove thirteen essential loci. All of these mutations had previously been shown to have both maternal and zygotic effects, and all of them had been tested, using homozygous germ-line clones, for the effects of complete maternal defects. For several of them, homozygous germ-line clones cause embryonic defects. Of the six, only one, Df(l)K95, shows a shift from larval to embryonic lethality when the mothers are heterozygous, and even in that case lethality occurs at the very end of embryogenesis. These results have two implications: (1) maternally-derived transcripts do not always serve a solely embryonic role; and (2) an embryonic effect of a complete maternal deficit does not by itself demonstrate an embryo-restricted function for the maternal transcript.

Superstructure of the Drosophila ribosomal gene family

Determining the spatial organization of middle repetitive DNA has proven difficult for several reasons. Repeated arrays are often so large that molecular methods alone cannot resolve their organization, and the lack of phenotypic markers within arrays limits the value of classical genetic analysis. We have characterized the superstructure of one repeated gene family, the ribosomal gene family of Drosophila melanogaster, by a combination of recombinational and molecular analyses of spacer-length variants. The resulting genetic maps demonstrate that some spacer variants are widely dispersed, while others are limited in their distribution. Moreover, exchange among ribosomal DNA (DNA encoding rRNA) arrays was often unequal, leading to a prediction of little or no relationship between physical location in an array and relatedness of gene family members. Extensions of our procedure may be generally useful for mapping the superstructure of repetitive DNA.

Reciprocal recombination and the evolution of the ribosomal gene family of Drosophila melanogaster

The role of reciprocal recombination in the coevolution of the ribosomal RNA gene family on the X and Y chromosomes of Drosophila melanogaster was assessed by determining the frequency and nature of such exchange. In order to detect exchange events within the ribosomal RNA gene family, both flanking markers and restriction fragment length polymorphisms within the tandemly repeated gene family were used. The vast majority of crossovers between flanking markers were within the ribosomal RNA gene region, indicating that this region is a hotspot for heterochromatic recombination. The frequency of crossovers within the ribosomal RNA gene region was approximately 10(-4) in both X/X and X/Y individuals. In conjunction with published X chromosome-specific and Y chromosome-specific sequences and restriction patterns, the data indicate that reciprocal recombination alone cannot be responsible for the observed variation in natural populations.

Rex-induced recombination implies bipolar organization of the ribosomal RNA genes of Drosophila melanogaster

Rex-induced mitotic recombination was used to determine whether nucleolus organizers can pair in both inverted and noninverted orientations. Two target chromosomes, each duplicated for the rDNA region, were exposed to maternal Rex activity. Recombination in one orientation should yield deletion of the material between the two nucleolus organizers, recombination in the other orientation should yield inversion of the same material. Both products were recovered from both target chromosomes. The generality of using Rex-mediated recombination for analysis of the rDNA is considered.

Identification and characterization of mutations affecting sporulation in Saccharomyces cerevisiae

Mutations affecting the synthesis of the sporulation amyloglucosidase were isolated in a homothallic strain of Saccharomyces cerevisiae, SCMS7-1. Two were found, both of which were deficient in sporulation at 34 degrees. One, SL484, sporulated to 50% normal levels at 30 degrees but less than 5% at 34 degrees or 22 degrees. The other, SL641, failed to sporulate at any temperature. Both mutants were blocked before premeiotic DNA synthesis, and both complemented spo1, spo3, and spo7. Genetic analysis of the mutation in SL484 indicated linkage to TRP5 and placed the gene 10 map units from TRP5 on chromosome VII. A plasmid containing an insert which complements the mutation in SL484 fails to complement SL641. We therefore conclude that these two mutations are in separate genes and we propose to call these genes SPO17 and SPO18. These two genes are (with SPO7, SPO8, and SPO9) among the earliest identified in the sporulation pathway and may interact directly with the positive and negative regulators RME and IME.

Developmental use of gene products in Drosophila: the maternal-zygotic transition

Recent results suggest that activity of a large fraction of the Drosophila genome is needed at multiple developmental stages. The timing of the transition from dependence on maternally stored gene products to reliance on zygotically coded products has been examined for several zygotic-lethal mutations in the z-w region of the X chromosome. The mutants differ in zygotic sensitivity to reduced maternal activity, and they have a wide range of times of lethality. Nevertheless, both temperature shift experiments and clonal analysis indicate that all of the maternal-zygotic transitions occur around the time of blastoderm formation.

MATERNAL-ZYGOTIC LETHAL INTERACTIONS IN DROSOPHILA MELANOGASTER: ZESTE-WHITE REGION SINGLE-CISTRON MUTATIONS

Thirty-eight mutations in 13 essential loci in the zeste-white region were tested for interacting maternal and zygotic gene activity. Maternal mutant heterozygosity provided a partial maternal defect and position-effect variegation was used to alter the level of zygotic gene activity. This method yields a minimum estimate of the number of genes for which zygotic development depends upon both gene products stored in the egg and gene products synthesized in the zygote. Lethal interactions were found for one or more alleles at 10 of the 13 loci. The implications of these observations with respect to gene regulation and developmental sequence are considered.

VIABILITY OF FEMALE GERM-LINE CELLS HOMOZYGOUS FOR ZYGOTIC LETHALS IN DROSOPHILA MELANOGASTER

We have analyzed the viability of different types of X chromosomes in homozygous clones of female germ cells. The chromosomes carried viable mutations, single-cistron zygotic-lethal and semi-lethal mutations, or small (about six chromosome band) deletions. Homozygous germ-line clones were produced by recombination in females heterozygous for an X-linked, dominant, agametic female sterile.

All the zygotic-viable mutants are also viable in germ cells. Of 16 deletions tested (uncovering a total of 93 bands) only 2 (of 4 and 5 bands) are germ-cell viable. Mutations in 15 lethal complementation groups in the zeste-white region were tested. When known, the most extreme alleles at each locus were tested. Only in five loci (33%) were the mutants viable in the germ line. Similar studies of the same deletions and point-mutant lethals in epidermal cells show that 42% of the bands and 77% of the lethal alleles are viable. Thus, germ-line cells have more stringent cell-autonomous genetic requirements than do epidermal cells.

The eggs recovered from clones of three of the germ-cell viable zw mutations gave embryos arrested early in embryogenesis, although genotypically identical embryos derived from heterozygous oogonia die as larvae or even hatch as adult escapers. For two genes, homozygosis of the mutations tested also caused embryonic arrest of heterozygous female embryos, and in one case, the eggs did not develop at all. Germ-line clones of one quite leaky mutation gave eggs that were indistinguishable from normal. The abundance of genes whose products are required for oogenesis, whose products are required in the oocyte, and whose activity is required during zygotic development is discussed.

Genetically induced mitotic exchange in the heterochromatin of Drosophila melanogaster

Multiple copies of the 18S and 28S ribosomal RNA cistrons are present in both the X and Y chromosomes of Drosophila melanogaster. Data are presented here that identify a locus, Rex, that causes exchange-like events between duplicated ribosomal complexes at the ends of an attached-XY chromosome. Rex: (1) is close to or in the basal heterochromatin of the X chromosome; (2) is semidominant and (its effect) is temperature sensitive; (3) acts maternally; and (4) affects behavior of paternally derived attached-XY chromosomes shortly after fertilization. Though, at this point, the existence of Rex is known only from its effects on behavior of a particular compound chromosome, it presents intriguing possibilities for understanding regulation of chromosome behavior and organization of the ribosomal cistrons.

The meiotic behavior of some single-cistron mutants in the zeste-white region of the Drosophila melanogaster X chromosome

There are two dosage sensitive sites in the zeste-white region of the Drosophila melanogaster X chromosome that affect meiotic chromosome behavior. Single-cistron mutants at essential and female fertility loci in the two segments have been tested for meiotic effects similar to those of deficiencies. None of the mutants have detectable meiotic effects. A de novo search for meiotic mutants in the region has not uncovered any, but the results suggest that a deficiency for the zeste-white region would be useful for detecting meiotic mutants elsewhere in the genome. Tests for interactions between the deficiency and known meiotic mutants support this. Though tentative, these results suggest that non-essential regions need not be devoid of function.

Maternal-zygotic lethal interactions in Drosophila melanogaster: the effects of deficiencies in the zeste-white region of the X chromosome

The possibility that essential loci in the zeste-white region of the Drosophila melanogaster X chromosome are expressed both maternally and zygotically has been tested. Maternal gene activity was varied by altering gene dose, and zygotic gene activity was manipulated by use of position-effect variegation of a duplication. Viability is affected when both maternal and zygotic gene activity are reduced, but not when either maternal or zygotic gene activity is normal. Tests of a set of overlapping deficiencies demonstrate that at least three sections of the zeste-white region yield maternal zygotic lethal interactions. Single-cistron mutations at two loci in one of these segments have been tested, and maternal heterozygosity for mutations at both loci give lethal responses of mutant-duplication zygotes. Thus, at least four of the 13 essential functions coded in the zeste-white region are active both maternally and zygotically, suggesting that a substantial fraction of the genome may function at both stages. The normal survival of zygotes when either maternal gene expression or zygotic gene expression is normal, and their inviability when both are depressed, suggests that a developmental stage exists when maternally determined functions and zygotically coded functions are both in use.

The Meiotic Effects of a Deficiency in DROSOPHILA MELANOGASTER: Identification of Two Dosage-Sensitive Sites

Heterozygosity for a deficiency for the entire zeste-white region of the X chromosome of Drosophila melanogaster females causes both reduced recombination and increased nondisjunction. The location of the dosage-sensitive sites responsible for these two meiotic defects has been studied by use of a set of deficiencies that subdivide the region. Recombination is reduced when the zw7-zw11 region is present in one dose, while nondisjunction is increased only if the doses of both the zw8-zw10 and zw6-zw11 segments are reduced. Examination of trans heterozygotes of two deficiencies explicitly demonstrates the compound nature of the meiotic dose effect and further delimits the location of the proximal disjunctional site to the zw12-zw11 interval. In inversion/deficiency heterozygotes, reduced dose of the zw8-zw10 region alone, without reduced dose of the proximal site, yields increased nondisjunction, suggesting that the proximal element that affects disjunction is the same as that which affects recombination. Thus, the zeste-white region contains at least two dosagesensitive loci that affect meiosis: reduced dosage of one locus, in the zw7-zw11 interval, causes reduced recombination; reduced dose of another, in the zw8-zw10 region, increases the probability that nonexchange chromosomes will nondisjoin. A slight effect on the regional distribution of exchange may also be a property of the zw8-zw10 region locus, but could be an effect of yet another locus or of structural heterozygosity. The implications of these results for understanding meiotic control and the prospects for further analysis of the structure of the zeste-white interval are considered.

The meiotic effect of a deficiency in Drosophila melanogaster with a model for the effects of enzyme deficiency on recombination

The meiotic effects of heterozygosity for a deficiency of the zeste-white region of the X chromosome include reduced recombination and increased non-disjunction of the entire chromosome complement. Reduced dosage of a gene or genes in the zeste-white interval, rather than structural heterozygosity, is responsible for the meiotic effect. A model for the recombination effects of reduced enzyme concentration has been developed, and its consequences are comparable with the results obtained for deficiency heterozygosity. Thus, all of the observations can be accounted for by imagining a dosage-sensitive locus in the zeste-white region that codes for an enzyme involved in the recombination process. The interaction of the interchromosomal effect of heterozygous inversions with the deficiency has been examined, and the possibility of using the model for the analysis of other meiotic phenomena is considered.

Exchange within heterozygous inversions in Drosophila melanogaster

The exchange behavior of non-attached, whole arm, X chromosome inversions was reexamined using nondisjunction in XXY females as an indirect measure of the frequency of nonexchange tetrads. Crossing over is quite normal in these inversion heterozygotes and is independent of the arrangement of the basal heterochromatin.