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Genetic determinants of metabolic syndrome components in the stroke-prone spontaneously hypertensive rat.

OBJECTIVE: The metabolic syndrome is a complex multifactorial disease, which results from interactions between genes on multiple chromosomes and environmental factors. Animal models may facilitate genetic analysis of complex phenotypes by allowing complete control of environmental conditions and the ability to produce designer strains. METHODS: Stroke-prone spontaneously hypertensive (SHRSP) and Wistar-Kyoto (WKY) rat strains were used to construct congenic (SP.WKYGla2a), consomic (SP.WKYGlaYw, WKY.SPGlaYs) and double-introgressed (SP.WKYGla2aYw) strains, which were characterized for metabolic syndrome phenotypes (systolic blood pressure, glucose tolerance and lipid profile) after feeding a 60% fructose diet for 14 days. RESULTS: The Y consomic strain (SP.WKYGlaYw) demonstrated that the WKY Y chromosome significantly lowered triglyceride levels (3.77 +/- 0.60 versus 9.09 +/- 1.47 mmol/l; P < 0.001) and improved glucose tolerance [area under the curve (AUC): 26.93 +/- 0.81 versus 31.47 +/- 0.89; P < 0.05] compared with SHRSP. The chromosome 2 congenic strain (SP.WKYGla2a) exhibited significantly improved glucose tolerance (AUC: 28.19 +/- 1.17 versus 31.47 +/- 0.89; P < 0.05) and lower systolic blood pressure (161.2 +/- 6.2 versus 179.7 +/- 3.9 mmHg; P < 0.05) compared with SHRSP. 2 x 2 factorial ANOVA identified a significant interaction for glucose metabolism (P = 0.004) in the double-introgressed strain (SP.WKYGla2aYw) between chromosome 2 and Y. CONCLUSIONS: These results identify novel interacting regions on chromosome 2 and the Y chromosome influencing a cluster of metabolic and cardiovascular phenotypes. Translation to clinical studies will facilitate genetic dissection of human metabolic syndrome.

Animals↗

Reinforcement and divergence under assortative mating.

Traits that cause assortative mating such as the flowering time in plants and body size in animals can produce reproductive isolation between hybridizing populations. Can selection against unfit hybrids cause two populations to diverge in their mean values for these kinds of traits? Here I present a haploid analytical model of one population that receives gene flow from another. The partial pre-zygotic isolation between the two populations is caused by assortative mating for a trait that is influenced by any number of genes with additive effects. The post-zygotic isolation is caused by selection against genetic incompatibilities that can involve any form of selection on individual genes and gene combinations (epistasis). The analysis assumes that the introgression rate and selection coefficients are small. The results show that the assortment trait mean will not diverge from the immigrants unless there is direct selection on the trait favouring it to do so or there are genes of very large effect. The amount of divergence at equilibrium is determined by a balance between direct selection on the assortment trait and introgression from the other population. Additional selection against hybrid genetic incompatibilities reduces the effective migration rate and allows greater divergence. The role of assortment in speciation is discussed in the light of these results.

Animals↗

Phylogeography of Lake Malawi cichlids of the genus Pseudotropheus: significance of allopatric colour variation.

One of the most compelling features of the cichlid fishes of the African Great Lakes is the seemingly endless diversity of male coloration. Colour diversification has been implicated as an important factor driving cichlid speciation. Colour has also been central to cichlid taxonomy and, thus, to our concept of species diversity. We undertook a phylogeographical examination of several allopatric populations of the Lake Malawi cichlid Pseudotropheus zebra in order to reconstruct the evolutionary history of the populations, which exhibit one of two dorsal fin colours. We present evidence that populations with red dorsal fins (RT) are not monophyletic. The RT population defining the northern limit of the distribution has evidently originated independently of the southern RT populations, which share a common ancestry. This evidence of species-level colour convergence is an important discovery in our understanding of cichlid evolution. It implies that divergence in coloration may accompany speciation, and that allopatric populations with similar coloration cannot be assumed to be conspecific. In addition to this finding, we have observed evidence for introgression, contributing to current evidence that this phenomenon may be extremely widespread. Thus, in species-level phylogenetic reconstructions, including our own, consideration must be given to the potential effects of introgression.

Alleles↗

Sex chromosome evolution and speciation in Ficedula flycatchers.

Speciation is the combination of evolutionary processes that leads to the reproductive isolation of different populations. We investigate the significance of sex-chromosome evolution on the development of post- and prezygotic isolation in two naturally hybridizing Ficedula flycatcher species. Applying a tag-array-based mini-sequencing assay to genotype single nucleotide polymorphisms (SNPs) and interspecific substitutions, we demonstrate rather extensive hybridization and backcrossing in sympatry. However, gene flow across the partial postzygotic barrier (introgression) is almost exclusively restricted to autosomal loci, suggesting strong selection against introgression of sex-linked genes. In addition to this partial postzygotic barrier, character displacement of male plumage characteristics has previously been shown to reinforce prezygotic isolation in these birds. We show that male plumage traits involved in reinforcing prezygotic isolation are sex linked. These results suggest a major role of sex-chromosome evolution in mediating post- and prezygotic barriers to gene flow and point to a causal link in the development of the two forms of reproductive isolation.

Animals↗

Patterns of male sterility in a grasshopper hybrid zone imply accumulation of hybrid incompatibilities without selection.

It is now widely accepted that post-zygotic reproductive isolation is the result of negative epistatic interactions between derived alleles fixed independently at different loci in diverging populations (the Dobzhansky-Muller model). What is less clear is the nature of the loci involved and whether the derived alleles increase in frequency through genetic drift, or as a result of natural or sexual selection. If incompatible alleles are fixed by selection, transient polymorphisms will be rare and clines for these alleles will be steep where divergent populations meet. If they evolve by drift, populations are expected to harbour substantial genetic variation in compatibility and alleles will introgress across hybrid zones once they recombine onto a genetic background with which they are compatible. Here we show that variation in male sterility in a naturally occurring Chorthippus parallelus grasshopper hybrid zone conforms to the neutral expectations. Asymmetrical clines for male sterility have long tails of introgression and populations distant from the zone centre show significant genetic variation for compatibility. Our data contrast with recent observations on 'speciation genes' that have diverged as a result of strong natural selection.

Animals↗

Evolutionary history of a mosquito endosymbiont revealed through mitochondrial hitchhiking.

Due to cytoplasmic inheritance, spread of maternally inherited Wolbachia symbionts can result in reduction of mitochondrial variation in populations. We examined sequence diversity of the mitochondrial NADH dehydrogenase subunit 4 (ND4) gene in Wolbachia-infected (South Africa (SA), California and Thailand) and uninfected (SA) Culex pipiens complex populations. In total, we identified 12 haplotypes (A-L). In infected populations, 99% of individuals had haplotype K. In the uninfected SA population, 11 haplotypes were present, including K. Nuclear allozyme diversity was similar between infected and uninfected SA populations. Analysis of nuclear DNA sequences suggested that haplotype K presence in uninfected SA Cx. pipiens was probably due to a shared ancestral polymorphism rather than hybrid introgression. These data indicate that Wolbachia spread has resulted in drastic reduction of mitochondrial variability in widely separated Cx. pipiens complex populations. In contrast, the uninfected SA population is probably a cryptic species where Wolbachia introgression has been prevented by reproductive isolation, maintaining ancestral levels of mitochondrial diversity. Molecular clock analyses suggest that the Wolbachia sweep occurred within the last 47000 years. The effect of Wolbachia on mitochondrial dynamics can provide insight on the potential for Wolbachia to spread transgenes into mosquito populations to control vector-borne diseases.

Animals↗

Adaptive radiation and hybridization in Wallace's Dreamponds: evidence from sailfin silversides in the Malili Lakes of Sulawesi.

Adaptive radiations are extremely useful to understand factors driving speciation. A challenge in speciation research is to distinguish forces creating novelties and those relevant to divergence and adaptation. Recently, hybridization has regained major interest as a potential force leading to functional novelty and to the genesis of new species. Here, we show that introgressive hybridization is a prominent phenomenon in the radiation of sailfin silversides (Teleostei: Atheriniformes: Telmatherinidae) inhabiting the ancient Malili Lakes of Sulawesi, correlating conspicuously with patterns of increased diversity. We found the most diverse lacustrine species-group of the radiation to be heavily introgressed by genotypes originating from streams of the lake system, an effect that has masked the primary phylogenetic pattern of the flock. We conclude that hybridization could have acted as a key factor in the generation of the flock's spectacular diversity. To our knowledge, this is the first empirical evidence for massive reticulate evolution within a complex animal radiation.

Adaptation, Biological↗

Recurrent replacement of mtDNA and cryptic hybridization between two sibling bat species Myotis myotis and Myotis blythii.

The two sibling bat species Myotis myotis and Myotis blythii occur in sympatry over wide areas of Southern and Central Europe. Morphological, ecological and previous genetic evidence supported the view that the two species constitute two well-differentiated groups, but recent phylogenetic analyses have shown that the two species share some mtDNA haplotypes when they occur in sympatry. In order to see whether some genetic exchange has occurred between the two species, we sequenced a highly variable segment of the mitochondrial control region in both species living in sympatry and in allopatry. We also analysed the nuclear diversity of 160 individuals of both species found in two mixed nursery colonies located north and south of the Alps. MtDNA analysis confirmed that European M. blythii share multiple, identical or very similar haplotypes with M. myotis. Since allopatric Asian M. blythii presents mtDNA sequences that are very divergent from those of the two species found in Europe, we postulate that the mitochondrial genome of the European M. blythii has been replaced by that of M. myotis. The analysis of nuclear diversity shows a strikingly different pattern, as both species are well differentiated within mixed nursery colonies (F(ST) = 0.18). However, a Bayesian analysis of admixture reveals that the hybrids can be frequently observed, as about 25% of sampled M. blythii show introgressed genes of M. myotis origin. In contrast, less than 4% of the M. myotis analysed were classified as non-parental genotypes, revealing an asymmetry in the pattern of hybridization between the two species. These results show that the two species can interbreed and that the hybridization is still ongoing in the areas of sympatry. The persistence of well-differentiated nuclear gene pools, in spite of an apparent replacement of mitochondrial genome in European M. blythii by that of M. myotis, is best explained by a series of introgression events having occurred repeatedly during the recent colonization of Europe by M. blythii from Asia. The sharp contrast obtained from the analysis of mitochondrial and nuclear markers further points to the need to cautiously interpret results based on a single class of genetic markers.

Animals↗

Spontaneous gene flow from rapeseed (Brassica napus) to wild Brassica oleracea.

Research on the environmental risks of gene flow from genetically modified (GM) crops to wild relatives has traditionally emphasized recipients yielding most hybrids. For GM rapeseed (Brassica napus), interest has centred on the 'frequently hybridizing' Brassica rapa over relatives such as Brassica oleracea, where spontaneous hybrids are unreported in the wild. In two sites, where rapeseed and wild B. oleracea grow together, we used flow cytometry and crop-specific microsatellite markers to identify one triploid F1 hybrid, together with nine diploid and two near triploid introgressants. Given the newly discovered capacity for spontaneous introgression into B. oleracea, we then surveyed associated flora and fauna to evaluate the capacity of both recipients to harm cohabitant species with acknowledged conservational importance. Only B. oleracea occupies rich communities containing species afforded legislative protection; these include one rare micromoth species that feeds on B. oleracea and warrants further assessment. We conclude that increased attention should now focus on B. oleracea and similar species that yield few crop-hybrids, but possess scope to affect rare or endangered associates.

Brassica↗

Reconstructing the 3D genome organization of Neanderthals reveals that chromatin folding shaped phenotypic and sequence divergence.

Changes in gene regulation were a major driver of the divergence of archaic hominins (AHs)-Neanderthals and Denisovans-and modern humans (MHs). The three-dimensional (3D) folding of the genome is critical for regulating gene expression; however, its role in recent human evolution has not been explored because the degradation of ancient samples does not permit experimental determination of AH 3D genome folding. To fill this gap, we apply novel deep learning methods for inferring 3D genome organization from DNA sequence to Neanderthal, Denisovan, and diverse MH genomes. Using the resulting 3D contact maps across the genome, we identify 167 distinct regions with diverged 3D genome organization between AHs and MHs. We show that these 3D-diverged loci are enriched for genes related to the function and morphology of the eye, supra-orbital ridges, hair, lungs, immune response, and cognition. Despite these specific diverged loci, the 3D genome of AHs and MHs is more similar than expected based on sequence divergence, suggesting that the pressure to maintain 3D genome organization constrained hominin sequence evolution. We also find that 3D genome organization constrained the landscape of AH ancestry in MHs today: regions more tolerant of 3D variation are enriched for introgression in modern Eurasians. Finally, we identify loci where modern Eurasians have inherited novel 3D genome folding patterns from AH ancestors and validate folding differences in a high-frequency locus using Hi-C, revealing a putative molecular mechanism for phenotypes associated with archaic introgression. In summary, our application of deep learning to predict archaic 3D genome organization illustrates the potential of inferring molecular phenotypes from ancient DNA to reveal previously unobservable biological differences.

Journal Article↗

Genomic islands of differentiation between house mouse subspecies.

Understanding the genes that contribute to reproductive isolation is essential to understanding speciation, but isolating such genes has proven very difficult. In this study I apply a multilocus test statistic to >10,000 SNP markers assayed in wild-derived inbred strains of house mice to identify genomic regions of elevated differentiation between two subspecies of house mice, Mus musculus musculus and M. m. domesticus. Differentiation was high through approximately 90% of the X chromosome. In addition, eight regions of high differentiation were identified on the autosomes, totaling 7.5% of the autosomal genome. Regions of high differentiation were confirmed by direct sequencing of samples collected from the wild. Some regions of elevated differentiation have an overrepresentation of genes with host-pathogen interactions and olfaction. The most strongly differentiated region on the X has previously been shown to fail to introgress across a hybrid zone between the two subspecies. This survey indicates autosomal regions that should also be examined for differential introgression across the hybrid zone, as containing potential genes causing hybrid unfitness.

Animals↗

Effect of Vernalization, Photoperiod, and Light Quality on the Flowering Phenotype of Arabidopsis Plants Containing the FRIGIDA Gene.

We have compared the flowering response to vernalization, photoperiod, and far-red (FR) light of the Columbia (Col) and Landsberg erecta (Ler) ecotypes of Arabidopsis into which the flowering-time locus FRIGIDA (FRI) has been introgressed with that of the wild types Col, Ler, and San Feliu-2 (Sf-2). In the early-flowering parental ecotypes, Col and Ler, a large decrease in flowering time in response to vernalization was observed only under short-day conditions. However, Sf-2 and the Ler and Col genotypes containing FRI showed a strong response to vernalization when grown in either long days or short days. Although vernalization reduced the responsiveness to photoperiod, plants vernalized for more than 80 d still showed a slight photoperiod response. The effect of FRI on flowering was eliminated by 30 to 40 d of vernalization; subsequently, the response to vernalization in both long days and short days was the same in Col and Ler with or without FRI. FR-light enrichment accelerated flowering in all ecotypes and introgressed lines. However, the FR-light effect was most conspicuous in the FRI-containing plants. Saturation of the vernalization effect eliminated the effect of FR light on flowering, although vernalization did not eliminate the increase of petiole length in FR light.

Journal Article↗

Speciation on the coasts of the new world: phylogeography and the evolution of bindin in the sea urchin genus Lytechinus.

Beginning with E. Mayr's study in 1954, tropical sea urchins have played an important role in studies of speciation in the sea, but what are the processes of cladogenesis and divergence that give rise to new species in this group? We attempt to answer this question in the genus Lytechinus. Unlike the majority of other tropical sea urchin genera, which have circumtropical distributions, Lytechinus is mostly confined to the tropics and subtropics of the New World. We sequenced a region of mitochondrial cytochrome oxidase I and the entire molecule of nuclear bindin (a sperm gamete recognition protein) of nearly all species in the genus, and we assayed isozymes of three partially sympatric closely related species and subspecies. We found that in both mitochondrial DNA (mtDNA) and in bindin the genus Lytechinus is paraphyletic, encompassing Sphaerechinus granularis as the sister species of L. euerces. The rest of the species are arranged in an Atlantic clade composed of L. williamsi and L. variegatus, and a Pacific clade containing L. anamesus, L. pictus, L. semituberculatus, and L. panamensis. Divergence between these clades suggests that they were separated no later than the closure of the Isthmus of Panama, and possibly before this time. Our data confirm that L. anamesus and L. pictus from California are a single species, and provide no evidence of differentiation between L. variegatus variegatus from the Caribbean and L. variegatus atlanticus from Bermuda. Lytechinus variegatus variegatus mtDNA is distinct from that of L. variegatus carolinus from the North American seaboard and the Gulf of Mexico, whereas their bindins are very similar. However, there is clear evidence of introgression of mtDNA between the two subspecies and they share alleles in all sampled isozyme loci. Lytechinus williamsi from the Caribbean shares mtDNA haplotypes with L. variegatus variegatus, and they also share isozymes in all assayed loci. Their bindin, however, is distinct and coalesces within each morphospecies. A private clade of mtDNA in L. williamsi may be indicative of former differentiation in the process of being swamped by introgression, or of recent speciation. Recent sudden expansions in effective population size may explain the predominance of a few mitochondrial haplotypes common to the two species. Despite the high divergence of bindin (relative to differentiation of mtDNA) between L. variegatus and L. williamsi, comparison of amino acid replacement to silent substitutions by various methods uncovered no evidence for positive selection on the bindin of any clade of Lytechinus. With the possible exception of L. williamsi and L. variegatus, our results are consistent with a history of allopatric speciation in Lytechinus. The molecular results from Lytechinus, along with those of other similar studies of sea urchins, suggest that the general speciation patterns deduced in the middle of last century by Mayr from morphology and geography have held up, but also have uncovered peculiarities in the evolution of each genus.

Americas↗

A polymorphism in randomly amplified DNA that differentiates the Y chromosomes of Bos indicus and Bos taurus.

A small number of west African Bos taurus cattle breeds, including the N'Dama, constitute a valuable genetic resource by virtue of their ability to remain productive under trypanosomiasis challenge. However, introgression of Bos indicus genes into the trypanotolerant breeds, particularly by introduction of zebu bulls, is a threat to this resource. This work describes the characterization and cloning of a bovine randomly amplified polymorphic DNA (RAPD) that is generated in polymorphic DNA (RAPD) that is generated in polymerase chain reaction (PCR) with the 10 base primer ILO1065 from Bos indicus male templates, but not from B. taurus male templates or female templates of either type. Male-specific sequences with homology to the RAPD also occur in B. taurus breeds. This suggests that the polymorphism may be due to base substitution(s) in an ILO1065 priming site, or insertion/deletion events either affecting priming sites or occurring between sites on the cattle Y chromosome. We have shown that cattle, whether of B. indicus or B. taurus phenotype, which possess a typically B. indicus metaphase Y chromosome on the basis of QFQ banding, have a B. indicus ILO1065-generated genotype. The ILO1065-primed RAPD can be used in a simple dot blot assay as a probe of RAPD-PCR products, to provide a convenient, reliable and effective means of detecting introgression of zebu genes in B. taurus cattle populations.

Africa, Western↗

Genetic variation within and among domesticated Atlantic salmon broodstocks in British Columbia, Canada.

Atlantic salmon have been reared in the British Columbia, Canada aquaculture industry since the early 1980s. No breeding programmes spanned the entire production period and pedigree records were not kept for broodstocks prior to or since importation. Of the three recognized industry strains, two are of European ancestry ('Mowi' from Norway and 'McConnell' from Scotland) and one is of North American heritage ('Cascade' from Gaspe, Quebec). We evaluated the amount and distribution of genetic variation within industry broodstocks by surveying microsatellite variation at 11 loci in 20 broodstock groups sampled from major production facilities. Allelic richness averaged 10.9 (range 5.8-13.8), compared with a value of 20.3 obtained for a North American wild population. Pairwise genetic distances (D(S)) between samples within strains were generally less than those between strains, with samples attributed to the same strain clustering together in a neighbour-joining dendrogram. Nevertheless, average distances between samples within the European strains were high (0.41 for Mowi; 0.71 for McConnell) but lower (0.06) for the Cascade strain. The reduced intra-sample and increased intra-strain genetic variation observed for the BC domesticated samples compared with wild populations was similar to observations for European domesticated Atlantic salmon. Evidence of introgression of the Cascade strain into European broodstocks was provided by the presence of large Ssa202 alleles (confined to North America in wild populations) in some Mowi and McConnell samples. Introgression likely also contributed to the decreased intercontinental genetic distance for the domesticated samples of this study compared with that observed for wild populations.

Alleles↗

Genetic diversity among horse populations with a special focus on the Franches-Montagnes breed.

Genetic characterization helps to assure breed integrity and to assign individuals to defined populations. The objective of this study was to characterize genetic diversity in six horse breeds and to analyse the population structure of the Franches-Montagnes breed, especially with regard to the degree of introgression with Warmblood. A total of 402 alleles from 50 microsatellite loci were used. The average number of alleles per locus was significantly lower in Thoroughbreds and Arabians. Average heterozygosities between breeds ranged from 0.61 to 0.72. The overall average of the coefficient of gene differentiation because of breed differences was 0.100, with a range of 0.036-0.263. No significant correlation was found between this parameter and the number of alleles per locus. An increase in the number of homozygous loci with increasing inbreeding could not be shown for the Franches-Montagnes horses. The proportion of shared alleles, combined with the neighbour-joining method, defined clusters for Icelandic Horse, Comtois, Arabians and Franches-Montagnes. A more disparate clustering could be seen for European Warmbloods and Thoroughbreds, presumably from frequent grading-up of Warmbloods with Thoroughbreds. Grading-up effects were also observed when Bayesian and Monte Carlo resampling approaches were used for individual assignment to a given population. Individual breed assignments to defined reference populations will be very difficult when introgression has occurred. The Bayesian approach within the Franches-Montagnes breed differentiated individuals with varied proportions of Warmblood.

Animals↗

Low level of gene flow from cultivated beets (Beta vulgaris L. ssp. vulgaris) into Danish populations of sea beet (Beta vulgaris L. ssp. maritima (L.) Arcangeli).

Gene flow from sugar beets to sea beets occurs in the seed propagation areas in southern Europe. Some seed propagation also takes place in Denmark, but here the crop-wild gene flow has not been investigated. Hence, we studied gene flow to sea beet populations from sugar beet lines used in Danish seed propagation areas. A set of 12 Danish, two Swedish, one French, one Italian, one Dutch, and one Irish populations of sea beets, and four lines of sugar beet were analysed. To evaluate the genetic variation and gene flow, eight microsatellite loci were screened. This analysis revealed hybridization with cultivated beet in one of the sea beet populations from the centre of the Danish seed propagation area. Triploid hybrids found in this population were verified with flow cytometry. Possible hybrids or introgressed plants were also found in the French and Italian populations. However, individual assignment test using a Bayesian method provided 100% assignment success of diploid individuals into their correct subspecies of origin, and a Bayesian Markov chain Monte Carlo (MC MC) approach revealed clear distinction of individuals into groups according to their subspecies of origin, with a zero level of genetic admixture among subspecies. This underlines that introgression beyond the first hybridization is not extensive. The overall pattern of genetic distance and structure showed that Danish and Swedish sea beet populations were closely related to each other, and they are both more closely related to the population from Ireland than to the populations from France, the Netherlands, and Italy.

Bayes Theorem↗

Genetic entities and mating system in hermaphroditic Fucus spiralis and its close dioecious relative F. vesiculosus (Fucaceae, Phaeophyceae).

To date, molecular markers have not settled the question of the specific status of the closely related, but phylogenetically unresolved, brown seaweeds, hermaphroditic Fucus spiralis and dioecious Fucus vesiculosus, nor their propensity for natural hybridization. To test the degree of species integrity and to assess effect of the mating system on the population genetic structure, 288 individuals coming from parapatric (discontinuous) and sympatric (contiguous) spatial configurations at two sites were genotyped with five microsatellite loci. Using a Bayesian admixture analysis, our results show that F. spiralis and F. vesiculosus comprise clearly distinct genetic entities (clusters) generally characterized by cosexual and unisexual individuals, respectively. Genetic diversity within each entity suggests that F. spiralis reproduces primarily through selfing while F. vesiculosus is characterized by an endogamous breeding regime. Nevertheless, aberrant sexual phenotypes were observed in each cluster, no diagnostic alleles were revealed and 10% of study individuals were intermediate between the two genetic entities. This pattern can be explained by recent divergence of two taxa with retention of ancestral polymorphism or asymmetrical, introgressive hybridization. However, given (i) coincident monomorphism at three loci in spiralis clusters and (ii) that significantly more intermediates were observed in sympatric stations than in parapatric stations, we argue that interspecific gene flow has occurred after divergence of the two taxa. Finally, we show that whether recently separated or recently introgressive, the divergent breeding systems probably contribute to species integrity in these two taxa.

Bayes Theorem↗