Haldane's rule and somatic mutations]

Haldane's rule stating that viability and fertility in the heterogametic sex of hybrids are lower than in the homogametic sex is explained on the basis of the assumption that diploidy is aimed at protecting individuals having large body size and large genomes from somatic mutations. The presence of hemizygous sex chromosomes, which are effectively haploid in the heterogametic sex, results in the phenotypic expression of all deleterious somatic mutations arising in them. In the homogametic sex, somatic mutations that affect one out of two identical sex chromosomes are not expressed because the unaffected chromosome functions normally. Thus, the heterogametic sex is more sensitive to the harmful effect of somatic mutations. In hybrids, this difference may be critical. Consequently, when genetic distance between hybridizing species increases, the heterogametic sex of hybrids loses viability and fertility earlier than the homogametic sex, which agrees with Haldane's rule. On the basis of Haldane's rule and data on the small size of natural hybrid zones, restrictions on maximum heterozygosity compatible with viability were established.     

Haldane's rule by sexual transformation in Caenorhabditis

Haldane's rule in C. briggsae x C. remanei broods was caused by sexual transformation; XX and XO hybrids were female. C. briggsae and C. remanei variants that partially suppress hybrid sexual transformation were identified. Effects of variant strains were cumulative. Hence, aberrant sex determination is a reproductive isolation mechanism in Caenorhabditis.     

100 years of Haldane's rule

Haldane's rule is one of the ‘two rules of speciation’. It states that if one sex is ‘absent, rare or sterile’ in a hybrid population, then that sex will be heterogametic. Since Haldane first made this observation, 100 years have passed and still questions arise over how many independent examples exist and what the underlying causes of Haldane's rule are. This review aims to examine research that has occurred over the last century. It seeks to do so by discussing possible causes of Haldane's rule, as well as gaps in the research of these causes that could be readily addressed today. After 100 years of research, it can be concluded that Haldane's rule is a complicated one, and much current knowledge has been accrued by studying the model organisms of speciation. This has led to the primacy of dominance theory and faster-male theory as explanations for Haldane's rule. However, some of the most interesting findings of the 21st century with regard to Haldane's rule have involved investigating a wider range of taxa emphasizing the need to continue using comparative methods, including ever more taxa as new cases are discovered.     

Haldane's rule in the 21st century

Haldane's Rule (HR), which states that 'when in the offspring of two different animal races one sex is absent, rare, or sterile, that sex is the heterozygous (heterogametic) sex', is one of the most general patterns in speciation biology. We review the literature of the past 15 years and find that among the ～85 new studies, many consider taxa that traditionally have not been the focus for HR investigations. The new studies increased to nine, the number of 'phylogenetically independent' groups that comply with HR. They continue to support the dominance and faster-male theories as explanations for HR, although due to increased reliance on indirect data (from, for example, differential introgression of cytoplasmic versus chromosomal loci in natural hybrid zones) unambiguous novel results are rare. We further highlight how research on organisms with sex determination systems different from those traditionally considered may lead to more insight in the underlying causes of HR. In particular, haplodiploid organisms provide opportunities for testing specific predictions of the dominance and faster X chromosome theory, and we present new data that show that the faster-male component of HR is supported in hermaphrodites, suggesting that genes involved in male function may evolve faster than those expressed in the female function.     

The role of Haldane's rule in sex allocation

Sex allocation theory predicts that parents should bias their reproductive investments toward the offspring sex generating the greatest fitness return. When females are the heterogametic sex (e.g., ZW in butterflies, some lizards, and birds), production of daughters is associated with an increased risk of offspring inviability due to the expression of paternal, detrimental recessives on the Z chromosome. Thus, daughters should primarily be produced when mating with partners of high genetic quality. When female sand lizards (Lacerta agilis) mate with genetically superior males, exhibiting high MHC Class I polymorphism, offspring sex ratios are biased towards daughters, possibly due to recruitment of more Z-carrying oocytes when females have assessed the genetic quality of their partners. If our study has general applicability across taxa, it predicts taxon-specific sex allocation effects depending on which sex is the heterogametic one.     

Genetics of postzygotic isolation and Haldane's rule in haplodiploids

The process of speciation has puzzled scientists for decades, but only recently they have they been able to reveal the genetic basis of reproductive isolation. Much emphasis has been on Haldane's rule, the observation that the heterogametic sex often suffers more from hybridization than the homogametic sex. Most research on Haldane's rule has focused on diploid organisms with chromosomal sex determination. We argue that species lacking chromosomal sex determination, such as haplodiploids, also follow Haldane's rule and thus should be included in the definition of this rule. We provide evidence for Haldane's rule in Nasonia wasps and describe how haplodiploids can be used to test the different theories that have been proposed to explain Haldane's rule. We discuss how the faster-male and faster-X theories can shape speciation differently in haplodiploids compared to diploids.     

Asymmetric postmating isolation: Darwin's corollary to Haldane's rule

Asymmetric postmating isolation, where reciprocal interspecific crosses produce different levels of fertilization success or hybrid sterility/inviability, is very common. Darwin emphasized its pervasiveness in plants, but it occurs in all taxa assayed. This asymmetry often results from Dobzhansky-Muller incompatibilities (DMIs) involving uniparentally inherited genetic factors (e.g., gametophyte-sporophyte interactions in plants or cytoplasmic-nuclear interactions). Typically, unidirectional (U) DMIs act simultaneously with bidirectional (B) DMIs between autosomal loci that affect reciprocal crosses equally. We model both classes of two-locus DMIs to make quantitative and qualitative predictions concerning patterns of isolation asymmetry in parental species crosses and in the hybrid F(1) generation. First, we find conditions that produce expected differences. Second, we present a stochastic analysis of DMI accumulation to predict probable levels of asymmetry as divergence time increases. We find that systematic interspecific differences in relative rates of evolution for autosomal vs. nonautosomal loci can lead to different expected F(1) fitnesses from reciprocal crosses, but asymmetries are more simply explained by stochastic differences in the accumulation of U DMIs. The magnitude of asymmetry depends primarily on the cumulative effects of U vs. B DMIs (which depend on heterozygous effects of DMIs), the average number of DMIs required to produce complete reproductive isolation (more asymmetry occurs when fewer DMIs are required), and the shape of the function describing how fitness declines as DMIs accumulate. Comparing our predictions to data from diverse taxa indicates that unidirectional DMIs, specifically involving sex chromosomes, cytoplasmic elements, and maternal effects, are likely to play an important role in postmating isolation.     

Speciation in two neotropical butterflies: extending Haldane's rule

Anartia fatima and A. amathea form a hybrid zone in Panama where F1 and back-cross hybrids are found. Crosses were carried out to determine the nature of any reproductive isolation between these two butterflies. A novel analysis demonstrated both strong assortative mating among the pure forms and an unusual example of Haldane''s rule: F1 hybrid females (the heterogametic sex) from the cross A. amathea (female) multiplied by A. fatima (male) have a reduced tendency to mate. Historically, Haldane''s rule has been restricted to hybrid mortality or sterility and most studies have concentrated on taxa (predominantly Drosophila) between which strong barriers to gene flow already exist. Our data suggest that Haldane''s rule might be extended to cover any decrease in hybrid fitness and that mating propensity may provide a sensitive and comparable means of assessing such decreases. Other barriers to gene flow were also evident in Anartia: F1 hybrid females have reduced fertility (also a Haldane effect) and larval survivorship was greatly reduced in F2 hybrids of both sexes. These examples of hybrid disruption are expected under the dominance theory of Haldane''s rule but do not exclude other explanations.     

Gametic selection,developmental trajectories,and extrinsic heterogeneity in Haldane's rule

Deciphering the genetic and developmental causes of the disproportionate rarity, inviability, and sterility of hybrid males, Haldane's rule, is important for understanding the evolution of reproductive isolation between species. Moreover, extrinsic and prezygotic factors can contribute to the magnitude of intrinsic isolation experienced between species with partial reproductive compatibility. Here, we use the nematodes Caenorhabditis briggsae and C. nigoni to quantify the sensitivity of hybrid male viability to extrinsic temperature and developmental timing, and test for a role of mito‐nuclear incompatibility as a genetic cause. We demonstrate that hybrid male inviability manifests almost entirely as embryonic, not larval, arrest and is maximal at the lowest rearing temperatures, indicating an intrinsic‐by‐extrinsic interaction to hybrid inviability. Crosses using mitochondrial substitution strains that have reciprocally introgressed mitochondrial and nuclear genomes show that mito‐nuclear incompatibility is not a dominant contributor to postzygotic isolation and does not drive Haldane's rule in this system. Crosses also reveal that competitive superiority of X‐bearing sperm provides a novel means by which postmating prezygotic factors exacerbate the rarity of hybrid males. These findings highlight the important roles of gametic, developmental, and extrinsic factors in modulating the manifestation of Haldane's rule.     

Hybrid sterility,Haldane's rule and speciation in Heliconius cydno and H. melpomene

Most genetic studies of Haldane's rule, in which hybrid sterility or inviability affects the heterogametic sex preferentially, have focused on Drosophila. It therefore remains unclear to what extent the conclusions of that work apply more generally, particularly in female-heterogametic taxa such as birds and Lepidoptera. Here we present a genetic analysis of Haldane's rule in Heliconius butterflies. Female F(1) hybrids between Heliconius melpomene and H. cydno are completely sterile, while males have normal to mildly reduced fertility. In backcrosses of male F(1) hybrids, female offspring range from completely sterile to fully fertile. Linkage analysis using the Z-linked triose-phosphate isomerase locus demonstrates a "large X" (Z) effect on sterility. Expression of female sterility varies among crosses in this and a previous study of Heliconius. Sterility may result from the production of normal but infertile eggs, production of small infertile eggs, or from a complete failure to develop ovarioles, which suggests multiple routes to the evolution of hybrid sterility in these Heliconius species. These results conform to the expectations of the "dominance" rather than "faster male" theories of Haldane's rule and suggest that relatively few loci are responsible. The two species are broadly sympatric and hybridize in the wild, so that female hybrid sterility forms one of several strong but incomplete barriers to gene flow in nature. The effect of female sterility is comparable to that of selection against non-mimetic hybrids, while mate choice forms a much stronger barrier to gene transfer.     

Sex, bugs and Haldane's rule: the nematode genus Pristionchus in the United States

The haplodiploid sex determining mechanism in Hymenoptera (males are haploid, females are diploid) has played an important role in the evolution of this insect order. In Hymenoptera sex is usually determined by a single locus, heterozygotes are female and hemizygotes are male. Under inbreeding, homozygous diploid and sterile males occur which form a genetic burden for a population. We review life history and genetical traits that may overcome the disadvantages of single locus complementary sex determination (sl-CSD). Behavioural adaptations to avoid matings between relatives include active dispersal from natal patches and mating preferences for non-relatives. In non-social species, temporal and spatial segregation of male and female offspring reduces the burden of sl-CSD. In social species, diploid males are produced at the expense of workers and female reproductives. In some social species, diploid males and diploid male producing queens are killed by workers. Diploid male production may have played a role in the evolution or maintenance of polygyny (multiple queens) and polyandry (multiple mating). Some forms of thelytoky (parthenogenetic female production) increase homozygosity and are therefore incompatible with sl-CSD. We discuss a number of hypothetical adaptations to sl-CSD which should be considered in future studies of this insect order.     

Differential strength of sex-biased hybrid inferiority in impeding gene flow may be a cause of Haldane's rule

Abstract In animals, if one sex of the F₁ hybrid between two species is sterile or inviable, it is usually the heterogametic (XY or WZ) sex. This phenomenon, known as Haldane's rule, is currently thought to be coincidentally caused by different mechanisms in separate entities. The following questions have never been asked: Are heterogametic and homogametic inferiority (sterility or inviability) equivalent as isolating mechanisms? Could discrepancies between them, if existing, produce Haldane's rule? Here I consider sex‐biased hybrid inferiority strictly as an isolating mechanism, and quantitatively evaluate its strength in impeding gene flow. The comparison reveals that the ability of sex‐biased inferiority to impede gene flow varies according to the sex and chromosome involved. Heterogametic inferiority is a weaker barrier when unidirectional and a much stronger one when in compound reciprocal directions, compared with homogametic inferiority. Such differential strength may affect divergence in speciation and produce Haldane's rule.     

Female sterility in hybrids between Anopheles gambiae and A. arabiensis, and the causes of Haldane's rule

Although F1 female hybrids between Anopheles gambiae and A. arabiensis are fully fertile, sterility is present in backcross females. Here we report the results of a study into the genetic basis of backcross female sterility. Using 23 markers, we performed quantitative trait loci (QTL) mapping analyses to identify chromosomal regions involved in hybrid female sterility. We found that female sterility in backcrosses in both directions is primarily caused by interspecific interactions between a heterozygous X chromosome and recessive autosomal factors. In addition, our data provide support for two theories implicated in Haldane's rule in a single taxon. A comparison with data from a previous study shows that male hybrid sterility QTL are present in higher numbers than female hybrid sterility QTL. Furthermore, autosomal female sterility factors tend to be recessive, supporting the dominance theory for female sterility. Finally, our data indicate a very large effect of the X chromosome from both species on hybrid female sterility, despite the fact that the X chromosome represents less than 9% of the genome. However, this could be the result of a lack of introgression of the X chromosome between A. gambiae and A. arabiensis, rather than a faster evolution of sterility factors on the X chromosome.     

Fisher's microscope and Haldane's ellipse

Fisher's geometrical model was introduced to study the phenotypic size of mutations contributing to adaptation. However, as pointed out by Haldane, the model involves a simplified picture of the action of natural selection, and this calls into question its generality. In particular, Fisher's model assumes that each trait contributes independently to fitness. Here, we show that Haldane's concerns may be incorporated into Fisher's model solely by allowing the intensity of selection to vary between traits. We further show that this generalization may be achieved by introducing a single, intuitively defined quantity that describes the phenotype prior to adaptation. Comparing the process of adaptation under the original and generalized models, we show that the generalization may bias results toward either larger or smaller mutations. The applicability of Fisher's model is then discussed.     

Haldane's rule in Carabus: interspecific mating between Carabus punctatoauratus and Carabus splendens using experimental tests and molecular markers

Carabus splendens Olivier and Carabus punctatoauratus Germar (Coleoptera: Carabidae: Carabini) are ground beetles found in sympatry in forests in the eastern Pyrénées. We investigated potential interspecific mating using crossing experiments under controlled laboratory conditions and paternity analyses based on microsatellite markers. We show that under laboratory conditions, interspecific mating produces viable and fertile offspring. Although hybrid males were sterile, females were fertile and thus reproductive isolation between the two species is far from complete. We discuss the results in relation to species integrity due to pre- or post-zygotic barriers, and compare them to a previous study quantifying hybridization between the two species in natural populations.