The effects of admixture and population subdivision on cytonuclear disequilibria

Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa

Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of Neurospora crassa. The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit [Formula: see text] was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting [Formula: see text] per data point was only [Formula: see text] = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for "cell size". The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the light-driven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 10⁷ cells.

Spatial genetic structure in wild cardoon, the ancestor of cultivated globe artichoke: Limited gene flow, fragmentation and population history

Nuclear and chloroplast markers and phenotypic characters were integrated to analyse the population genetic structure of wild cardoon, Cynara cardunculus var. sylvestris, the ancestor of cultivated globe artichoke, Cynara cardunculus var. scolymus on the island of Sardinia, Italy. The spatial scale ranged from a few metres to ∼200km. Wild cardoon appears to be genetically fragmented, with significant genetic divergence at various scales, indicating that gene flow is insufficient to counterbalance the effects of genetic drift or founder effects. Divergence between populations was higher for chloroplast (40%) than for nuclear markers (15%), suggesting that gene flow via seed was lower than via pollen. Two main genetic groups were detected; these correlated with differences in flowering time, capitula size, glossiness, and anthocyanin pigmentation. A complex population structure of wild cardoon emerged over small spatial scales, likely resulting from the interplay between gene dispersal, colonisation history and selective forces. Indeed, Sardinia appears to be a 'hybrid zone' of different gene pools. The island has unique diverse germplasm that has originated from hybridisation among different gene pools. The sampling of seeds from a few plants but from many sites is suggested as the best strategy to harvest the genetic diversity of wild cardoon.

Mitonuclear linkage disequilibrium in human populations

There is extensive evidence from model systems that disrupting associations between co-adapted mitochondrial and nuclear genotypes can lead to deleterious and even lethal consequences. While it is tempting to extrapolate from these observations and make inferences about the human-health effects of altering mitonuclear associations, the importance of such associations may vary greatly among species, depending on population genetics, demographic history and other factors. Remarkably, despite the extensive study of human population genetics, the statistical associations between nuclear and mitochondrial alleles remain largely uninvestigated. We analysed published population genomic data to test for signatures of historical selection to maintain mitonuclear associations, particularly those involving nuclear genes that encode mitochondrial-localized proteins (N-mt genes). We found that significant mitonuclear linkage disequilibrium (LD) exists throughout the human genome, but these associations were generally weak, which is consistent with the paucity of population genetic structure in humans. Although mitonuclear LD varied among genomic regions (with especially high levels on the X chromosome), N-mt genes were statistically indistinguishable from background levels, suggesting that selection on mitonuclear epistasis has not preferentially maintained associations involving this set of loci at a species-wide level. We discuss these findings in the context of the ongoing debate over mitochondrial replacement therapy.

Sex-specific effects of sympatric mitonuclear variation on fitness in Drosophila subobscura

Background

A number of recent studies have shown that the pattern of mitochondrial DNA variation and evolution is at odds with a neutral equilibrium model. Theory has suggested that selection on mitonuclear genotypes can act to maintain stable mitonuclear polymorphism within populations. However, this effect largely relies upon selection being either sex-specific or frequency dependent. Here, we use mitonuclear introgression lines to assess differences in a series of key life-history traits (egg-to-adult developmental time, viability, offspring sex-ratio, adult longevity and resistance to desiccation) in Drosophila subobscura fruit flies carrying one of three different sympatric mtDNA haplotypes.

Results

We found functional differences between these sympatric mtDNA haplotypes, but these effects were contingent upon the nuclear genome with which they were co-expressed. Further, we demonstrate a significant mitonuclear genetic effect on adult sex ratio, as well as a sex × mtDNA × nuDNA interaction for adult longevity.

Conclusions

The observed effects suggest that sex specific mitonuclear selection contributes to the maintenance of mtDNA polymorphism and to mitonuclear linkage disequilibrium in this model system.

Electronic supplementary material

The online version of this article (doi:10.1186/s12862-015-0421-2) contains supplementary material, which is available to authorized users.

Introgressive hybridization and latitudinal admixture clines in North Atlantic eels

BACKGROUND

Hybridization, the interbreeding of diagnosably divergent species, is a major focus in evolutionary studies. Eels, both from North America and Europe migrate through the Atlantic to mate in a vast, overlapping area in the Sargasso Sea. Due to the lack of direct observation, it is unknown how these species remain reproductively isolated. The detection of inter-species hybrids in Iceland suggests on-going gene flow, but few studies to date have addressed the influence of introgression on genetic differentiation in North Atlantic eels.

RESULTS

Here, we show that while mitochondrial lineages remain completely distinct on both sides of the Atlantic, limited hybridization is detectable with nuclear DNA markers. The nuclear hybridization signal peaks in the northern areas and decreases towards the southern range limits on both continents according to Bayesian assignment analyses. By simulating increasing proportions of both F1 hybrids and admixed individuals from the southern to the northern-most locations, we were able to generate highly significant isolation-by-distance patterns in both cases, reminiscent of previously published data for the European eel. Finally, fitting an isolation-with-migration model to our data supports the hypothesis of recent asymmetric introgression and refutes the alternative hypothesis of ancient polymorphism.

CONCLUSIONS

Fluctuating degrees of introgressive hybridization between Atlantic eel species are sufficient to explain temporally varying correlations of geographic and genetic distances reported for populations of the European eel.

Symbiote transmission and maintenance of extra-genomic associations

Symbiotes can be transmitted from parents to offspring or horizontally from unrelated hosts or the environment. A key question is whether symbiote transmission is similar enough to Mendelian gene transmission to generate and maintain coevolutionary associations between host and symbiote genes. Recent papers come to opposite conclusions, with some suggesting that any horizontal transmission eliminates genetic association. These studies are hard to compare owing to arbitrary differences in modeling approach, parameter values, and assumptions about selection. I show that associations between host and symbiote genes (extra-genomic associations) can be described by the same dynamic model as conventional linkage disequilibria between genes in the same genome. Thus, covariance between host and symbiote genomes depends on population history, geographic structure, selection, and co-transmission rate, just as covariance between genes within a genome. The conclusion that horizontal transmission rapidly erodes extra-genomic associations is equivalent to the conclusion that recombination rapidly erodes associations between genes within a genome. The conclusion is correct in the absence of population structure or selection. However, population structure can maintain spatial associations between host and symbiote traits, and non-additive selection (interspecific epistasis) can generate covariances between host and symbiote genotypes. These results can also be applied to cultural or other non-genetic traits. This work contributes to a growing consensus that genomic, symbiotic, and gene-culture evolution can be analyzed under a common theoretical framework. In terms of coevolutionary potential, symbiotes can be viewed as lying on a continuum between the intimacy of genes and the indifference of casually co-occurring species.

F(ST) in the cytonuclear system

Selection on nuclear (or organelle) sites inevitably affects the spatial distribution of a neutral organelle (or nuclear) allele via transient cytonuclear disequilibrium. Here I examine this effect in terms of F(st) for a neutral allele by bringing together cytonuclear genomes with contrasting modes of inheritance. The relationships between cytonuclear disequilibrium and increment in F(st) are explored and confirmed through Monte Carlo simulations. Results show that the transient increment in F(st) for a neutral allele is not only related to the vectors of seed and pollen dispersal but also to the mode of its inheritance. Such increments can be substantial under certain conditions. Seed dispersal is more effective than pollen dispersal in changing the transient increment. The cumulative effects from multiple selective nuclear sites can amplify the transient increment in F(st) for a neutral paternal or maternal organelle allele. Selection on selective organelle sites facilitates the transient increment in F(st) for a neutral nuclear allele. Partial selfing can significantly reinforce the transient increment in F(st). These theoretical insights highlight the roles of transient cytonuclear disequilibrium as a biological factor in evolving population differentiation and refine our practical interpretations of F(st) with cytonuclear markers.

Cytonuclear disequilibria in a spatially structured hybrid zone

A hybrid zone model was developed that uses a stepping-stone model of population structure along with both nuclear and cytoplasmic genotypes to evaluate the effect that migration has on random mating organisms when no selection is present. Numerical simulations indicate that a number of different allele frequency and cytonuclear disequilibrium patterns can be found across the hybrid zone when it has reached equilibrium, and these results are discussed in the context of relative migration rates of the two sexes and the two source populations. The importance of numbers of subpopulations sampled, census time, and the persistence of pure species individuals into the hybrid zone are also discussed. Although this model does not consider selection or assortative mating in the hybrid zone, it should provide a useful baseline for evaluating joint cytonuclear genetic data from a structurally complex hybrid zone.

Tension versus ecological zones in a two-locus system

Previous theories show that tension and ecological zones are indistinguishable in terms of gene frequency clines. Here I analytically show that these two types of zones can be distinguished in terms of genetic statistics other than gene frequency. A two-locus cline model is examined with the assumptions of random mating, weak selection, no drift, no mutation, and multiplicative viabilities. The genetic statistics for distinguishing the two types of zones are the deviations of one- or two-locus genotypic frequencies from Hardy-Weinberg equilibrium (HWE) or from random association of gametes (RAG), and the deviations of additive and dominance variances from the values at HWE. These deviations have a discontinuous distribution in space and different extents of interruptions in the ecological zone with a sharp boundary, but exhibit a continuous distribution in the tension zone. Linkage disequilibrium enhances the difference between the deviations from HWE and from RAG for any two-locus genotypic frequency.

Allelic Variation at the VHa Locus in Natural Populations of Rabbit (Oryctolagus cuniculus, L.)

The large interallelic distances between the three rabbit Ig V(H)a lineages, a1, a2 and a3, suggest that the persistence time of the V(H)a polymorphism could amount to 50 million years, which is much longer than that of MHC polymorphisms. Rabbit originated in the Iberian Peninsula where two subspecies coexist, one of which is confined to Southwestern Iberia (Oryctolagus cuniculus algirus). We studied the V(H) loci in the original species range to obtain a better understanding of the evolutionary history of this unusual polymorphism. Serological surveys revealed that sera from the subspecies algirus, when tested with V(H)a locus-specific alloantisera, showed either cross-reactivity ("a-positive" variants) or no reaction at all ("a-blank"). Using RT-PCR, we determined 120 sequences of rearranged V(H) genes expressed in seven algirus rabbits that were typed as either a-positive or a-blank. The data show that the V(H) genes transcribed in a-positive rabbits are closely related to the V(H)1 alleles of domestic rabbits. In contrast, a-blank rabbits were found to preferentially use V(H) genes that, although clearly related to the known V(H)a genes, define a new major allotypic lineage, designated a4. The a4 sequences have hallmark rabbit V(H)a residues together with a number of unprecedented amino acid changes in framework region 2 and 3. The net protein distances between the V(H)a4 and the V(H)a1, a2, and a3 lineages were 20, 29, and 21% respectively. We conclude that at least four distantly related lineages of the rabbit V(H)a locus exist, one of which seems to be endemic in the Iberian range.

Associations among cytoplasmic molecular markers, gender, and components of fitness in Silene vulgaris, a gynodioecious plant

It has been suggested that the dynamics of chloroplast DNA (cpDNA) or mitochondrial DNA (mtDNA) genetic markers used in studies of plant populations could be influenced by natural selection acting elsewhere in the genome. This could be particularly true in gynodioecious plants if cpDNA or mtDNA genetic markers are in gametic disequilibrium with genes responsible for sex expression. In order to investigate this possibility, a natural population of the gynodioecious plant Silene vulgaris was used to study associations among mtDNA haplotype, cpDNA haplotype, sex and some components of fitness through seed. Individuals were sampled for mtDNA and cpDNA haplotype as determined using restriction fragment length polymorphism (RFLP) methods, sex (female or hermaphrodite), fruit number, fruit set, seeds/fruit and seed germination. The sex of surviving germinating seeds was also noted. All individuals in the population fell into one of two cytoplasmic categories, designated haplotypes f and g by a unique electrophoretic signature in both the mtDNA and cpDNA. The subset of the population carrying haplotype g included a significantly higher proportion of females when compared with the sex ratio of the subset carrying the f haplotype. Haplotype g had a significantly higher fitness when measured by fruit number, fruit set and seeds/fruit, whereas haplotype f had significantly higher fitness when measured by seed germination. Offspring of individuals carrying haplotype g included a significantly greater proportion of females when compared with offspring of individuals carrying the f haplotype. Other studies of gynodioecious plants have shown that females generally have higher fitness through seed than hermaphrodites, but in this study not all fitness differences between haplotypes could be predicted from differences in haplotype-specific sex ratio alone. Rather, some differences in haplotype-specific fitness were due to differences in fitness between individuals of the same sex, but carrying different haplotypes. The results are discussed with regard to the potential for hitchhiking selection to influence the dynamics of the noncoding regions used to designate the cpDNA and mtDNA haplotypes.

Associations between cytoplasmic and nuclear Loci in hybridizing populations

We extend current multilocus models to describe the effects of migration, recombination, selection, and nonrandom mating on sets of genes in diploids with varied modes of inheritance, allowing us to consider the patterns of nuclear and cytonuclear associations (disequilibria) under various models of migration. We show the relationship between the multilocus notation recently presented by Kirkpatrick, Johnson, and Barton (developed from previous work by Barton and Turelli) and the cytonuclear parameterization of Asmussen, Arnold, and Avise and extend this notation to describe associations between cytoplasmic elements and multiple nuclear genes. Under models with sexual symmetry, both nuclear-nuclear and cytonuclear disequilibria are equivalent. They differ, however, in cases involving some type of sexual asymmetry, which is then reflected in the asymmetric inheritance of cytoplasmic markers. An example given is the case of different migration rates in males and females; simulations using 2, 3, 4, or 5 unlinked autosomal markers with a maternally inherited cytoplasmic marker illustrate how nuclear-nuclear and cytonuclear associations can be used to separately estimate female and male migration rates. The general framework developed here allows us to investigate conditions where associations between loci with different modes of inheritance are not equivalent and to use this nonequivalence to test for deviations from simple models of admixture.

Sexually antagonistic cytonuclear fitness interactions in Drosophila melanogaster

Theoretical and empirical studies have shown that selection cannot maintain a joint nuclear-cytoplasmic polymorphism within a population except under restrictive conditions of frequency-dependent or sex-specific selection. These conclusions are based on fitness interactions between a diploid autosomal locus and a haploid cytoplasmic locus. We develop a model of joint transmission of X chromosomes and cytoplasms and through simulation show that nuclear-cytoplasmic polymorphisms can be maintained by selection on X-cytoplasm interactions. We test aspects of the model with a "diallel" experiment analyzing fitness interactions between pairwise combinations of X chromosomes and cytoplasms from wild strains of Drosophila melanogaster. Contrary to earlier autosomal studies, significant fitness interactions between X chromosomes and cytoplasms are detected among strains from within populations. The experiment further demonstrates significant sex-by-genotype interactions for mtDNA haplotype, cytoplasms, and X chromosomes. These interactions are sexually antagonistic--i.e., the "good" cytoplasms in females are "bad" in males--analogous to crossing reaction norms. The presence or absence of Wolbachia did not alter the significance of the fitness effects involving X chromosomes and cytoplasms but tended to reduce the significance of mtDNA fitness effects. The negative fitness correlations between the sexes demonstrated in our empirical study are consistent with the conditions that maintain cytoplasmic polymorphism in simulations. Our results suggest that fitness interactions with the sex chromosomes may account for some proportion of cytoplasmic variation in natural populations. Sexually antagonistic selection or reciprocally matched fitness effects of nuclear-cytoplasmic genotypes may be important components of cytonuclear fitness variation and have implications for mitochondrial disease phenotypes that differ between the sexes.

Cytonuclear disequilibrium and genetic drift in a natural population of ponderosa pine

We measured the cytonuclear disequilibrium between 11 nuclear allozyme loci and both mitochondrial and chloroplast DNA haplotypes in a natural population of ponderosa pine (Pinus ponderosa, Laws). Three allozyme loci showed significant associations with mtDNA variation, while two other loci showed significant association with cpDNA. However, the absolute number of individuals involved in any of the associations was small, such that in none of the nuclear-organellar combinations was the difference between observed and expected numbers >11 individuals. Patterns of association were not consistent across loci or organellar genomes, suggesting that they are not the result of mating patterns, which would act uniformly on all loci. This pattern of disequilibria is consistent with the action of genetic drift and with existing knowledge of the structure of this population and thus does not imply the action of other evolutionary processes. The overall magnitude (normalized disequilibrium) of associations was greater for maternally inherited mtDNA than for paternally inherited cpDNA, though this difference was neither large nor significant. Such significant disequilibria involving the paternally inherited organelle indicate that not only are there a limited number of seed parents, but the effective number of pollen parents is also limited.

The cytonuclear effects of facultative apomixis. II. Definitions and dynamics of disequilibria in tetraploid populations

We develop a cytonuclear framework for tetraploid populations in which a diallelic nuclear marker exhibits tetrasomic inheritance. This system requires two separate parameterizations, with six cytonuclear disequilibria (nonrandom associations) in tetraploid individuals and four in their diploid gametes. Double reduction during meiosis adds further complexity by causing gametic output to vary with the distance of the nuclear locus from the centromere. We derive and analyze dynamical solutions for the disequilibria under generalized mixed mating, with any combination of apomixis, selfing, and outcrossing, with and without double reduction. As in comparable diploid systems, all disequilibria ultimately decay to zero, unless nuclear and cytoplasmic alleles are nonrandomly associated and outcrossing is absent, in which case permanent associations result. Selfing and apomixis retard the decay of disequilibria (or approach to equilibrium), and often to the same extent. In contrast, double reduction can accelerate the loss of tetraploid cytonuclear associations, but only negligibly in hybrid zones, and this loss is never faster than in diploids. Only in the absence of allelic associations or outcrossing is the asymptotic approach to equilibrium differentially affected by apomixis and selfing or slower under tetrasomic than disomic inheritance. To facilitate empirical applications, we also examine tetraploid hybrid zone dynamics and offer practical guidelines for experimental design and data analysis, showing how the consequences of the mating system alone provide a valuable baseline for drawing evolutionary inferences from the observed patterns of cytonuclear associations.

The cytonuclear effects of facultative apomixis. I. Disequilibrium dynamics in diploid populations

We comprehensively analyze the cytonuclear effects of generalized mixed mating, including all combinations of selfing, outcrossing, and apomixis, the asexual production of seeds. After first deriving the time-dependent solutions for nonrandom associations (disequilibria) between a diallelic cytoplasmic marker and the alleles and genotypes at a diploid nuclear locus, we delimit all possible dynamical behaviors and the conditions under which each occurs. As in standard mixed mating systems, all disequilibria ultimately decay to zero except when outcrossing is absent, in which case permanent disequilibria result if the allelic association is initially nonzero. When at least some outcrossing is present, any initial allelic association decays at a constant geometric rate, whereas genotypic disequilibria may first increase in magnitude or change sign. Although selfing and apomixis tend to retard the decay of disequilibria (or approach to equilibrium) and often to the same extent, apomixis can have a stronger effect under some conditions. We also determine the dynamics of cytonuclear disequilibria in specific examples that may be of particular interest for empirical studies of hybrid zones. The results suggest several practical guidelines for experimental design and data analysis and show how the cytonuclear disequilibrium dynamics under mating system alone furnish a quantitative baseline for null hypotheses against which to test for the presence of other evolutionary forces.

The effects of pollen and seed migration on nuclear-dicytoplasmic systems. I. Nonrandom associations and equilibrium structure with both maternal and paternal cytoplasmic inheritance

We determine the nuclear-dicytoplasmic effects of unidirectional gene flow via pollen and seeds upon a mixed-mating plant population, focusing on nuclear-mitochondrial-chloroplast systems where mitochondria are inherited maternally and chloroplasts paternally, as in many conifers. After first delineating the general effects of admixture (via seeds or individuals) on the nonrandom associations in such systems, we derive the full dicytonuclear equilibrium structure, including when disequilibria may be indicators of gene flow. Substantial levels of permanent two- and three-locus disequilibria can be generated in adults by (i) nonzero disequilibria in the migrant pools or (ii) intermigrant admixture effects via different chloroplast frequencies in migrant pollen and seeds. Additionally, three-locus disequilibria can be generated by higher-order intermigrant effects such as different chloroplast frequencies in migrant pollen and seeds coupled with nuclear-mitochondrial disequilibria in migrant seeds, or different nuclear frequencies in migrant pollen and seeds coupled with mitochondrial-chloroplast disequilibria in migrant seeds. Further insight is provided by considering special cases with seed or pollen migration alone, complete random mating or selfing, or migrant pollen and seeds lacking disequilibria or intermigrant admixture effects. The results complete the theoretical foundation for a new method for estimating pollen and seed migration using joint cytonuclear or dicytonuclear data.

Extensive gene flow within sibling species in the deep-sea fish Beryx splendens

Molecular markers allow insights into the population biology and ecology of deep-sea organisms, which are usually hardly accessible to direct observation and poorly known. Such a study was undertaken here for the deep-sea fish Beryx splendens, a species of growing interest to fisheries. B. splendens populations were sampled on seamounts and continental margins in the southwestern Pacific (New Caledonia, New Zealand, southeastern Australia) and in the northeastern Atlantic. Two hundred and fifty individuals were characterised by their single-strand DNA conformation (SSCP) of a approximately 360-base-pair (bp) fragment of the mitochondrial cytochrome b gene, amplified by the polymerase chain reaction (PCR). Two major SSCP haplotypes were observed in New Caledonia, a and w, whose frequencies were negatively correlated along a north-to-south cline. All SSCP haplotypes in the total sample were sequenced on 273 bp. The phylogenetic tree of B. splendens haplotype sequences, rooted by two B. decadactylus sequences, showed that a and w belong to distinct mitochondrial clades, A and W, which are separated by approximately 4-6% nucleotide divergence. Thirty individuals from New Caledonia were characterised by their DNA fingerprint from arbitrary-primed PCR. The distribution of individual-pairwise similarity indices was strongly bimodal. The larger similarity values all corresponded to comparisons within a clade (A or W) while the lower values were all between clades. Therefore, there was a strict association between the mitochondrial type and the DNA (presumably, nuclear DNA) fingerprint of an individual. Altogether, these results point to the existence of two biological species (sp. A and sp. W) within the current taxon B. splendens. No within-species differentiation was detected at the regional scale (New Caledonia). A remarkable result is that the three cytochrome b haplotypes of northeastern Atlantic B. cf. splendens sp. A were also the three commonest in the southwestern Pacific populations of this species. Such a level of homogeneity in the distribution of haplotypes suggests there is, or recently has been, gene flow at the inter-oceanic scale.

A comparison of multilocus clines maintained by environmental adaptation or by selection against hybrids

There has recently been considerable debate over the relative importance of selection against hybrids ("endogenous" selection) vs. adaptation to different environments ("exogenous") in maintaining stable hybrid zones and hence in speciation. Single-locus models of endogenous and exogenous viability selection generate clines of similar shape, but the comparison has not been extended to multilocus systems, which are both quantitatively and qualitatively very different from the single-locus case. Here we develop an analytical multilocus model of differential adaptation across an environmental transition and compare it to previous heterozygote disadvantage models. We show that the shape of clines generated by exogenous selection is indistinguishable from that generated by endogenous selection. A stochastic simulation model is used to test the robustness of the analytical description to the effects of drift and strong selection, and confirms the prediction that pairwise linkage disequilibria are predominantly generated by migration. However, although analytical predictions for the width of clines maintained by heterozygote disadvantage fit well with the simulation results, those for environmental adaptation are consistently too narrow; reasons for the discrepancy are discussed. There is a smooth transition between a system in which a set of loci effectively act independently of each other and one in which they act as a single nonrecombining unit.

Introgression through rare hybridization: A genetic study of a hybrid zone between red and sika deer (genus Cervus) in Argyll, Scotland

In this article we describe the structure of a hybrid zone in Argyll, Scotland, between native red deer (Cervus elaphus) and introduced Japanese sika deer (Cervus nippon), on the basis of a genetic analysis using 11 microsatellite markers and mitochondrial DNA. In contrast to the findings of a previous study of the same population, we conclude that the deer fall into two distinct genetic classes, corresponding to either a sika-like or red-like phenotype. Introgression is rare at any one locus, but where the taxa overlap up to 40% of deer carry apparently introgressed alleles. While most putative hybrids are heterozygous at only one locus, there are rare multiple heterozygotes, reflecting significant linkage disequilibrium within both sika- and red-like populations. The rate of backcrossing into the sika population is estimated as H = 0.002 per generation and into red, H = 0.001 per generation. On the basis of historical evidence that red deer entered Kintyre only recently, a diffusion model evaluated by maximum likelihood shows that sika have increased at approximately 9.2% yr-1 from low frequency and disperse at a rate of approximately 3.7 km yr-1. Introgression into the red-like population is greater in the south, while introgression into sika varies little along the transect. For both sika- and red-like populations, the degree of introgression is 30-40% of that predicted from the rates of current hybridization inferred from linkage disequilibria; however, in neither case is this statistically significant evidence for selection against introgression.

Effects of differential selection in the sexes on cytonuclear dynamics. Life stages with sex differences

We extend our investigation of cytonuclear selection by determining when differential selection between the sexes will generate allele frequency changes or cytonuclear disequilibria in populations with constant viability selection and an adult census. We demonstrate analytically that there can be a cytonuclear hitchhiking effect upon a selectively neutral marker in either sex provided the other marker is selected in that sex and there is allelic disequilibrium between the loci in females. Cytonuclear disequilibria are generated de novo in both sexes when both loci affect fitness in females and there is a nonmultiplicative fitness interaction between them. Similar fitness interactions in males generate male disequilibria only. Through numerical analyses, we investigate the potential magnitude of such disequilibria, their qualitative dynamics, the expected frequency of detectable disequilibria under particular patterns or strengths of selection, and the possible disequilibrium sign patterns resulting from selection. These adult/viability results subsume those for populations with a gamete census and either constant fertility or viability selection. Although previous work suggests that the disequilibria generated by cytonuclear selection may be difficult to detect experimentally, this study shows that cytonuclear disequilibria at life stages with sex differences can be useful markers of the presence and strength of selection.

Constraints and normalized measures for cytonuclear disequilibria

The full bounds are derived for cytonuclear disequilibria in two-locus systems with an arbitrary number of alleles at the cytoplasmic and nuclear markers. The associated marginal frequencies constrain the nonrandom associations between cytoplasmic alleles and nuclear genotypes in the same way that the allele frequencies constrain the linkage disequilibrium between two nuclear loci. Additional constraints are imposed on the nonrandom associations between cytoplasmic and nuclear alleles, however, by the marginal frequencies of nuclear genotypes carrying either two or no copies of the associated nuclear allele. These bounds are analysed and used to define normalized measures of cytonuclear disequilibria, whose practical utility is illustrated through applications to two sets of recent nuclear-mitochondrial data.

Dynamics of cytonuclear disequilibria in finite populations and comparison with a two-locus nuclear system

We study the behavior of cytonuclear disequilibria in a finite monoecious population due to (1) random drift alone, (2) random drift and mutation, and (3) random drift and migration, using exact results on the RUZ (Random Union of Zygotes) model and diffusion approximations. We also show that the RUG (Random Union of Gametes) model is not suitable for a cytonuclear system. The study is also accompanied by a comparison with a two-locus nuclear system. We show that in a finite population of size N without mutation, the rate of decrease of the cytonuclear allelic disequilibrium is the same as that in the corresponding unlinked two-locus nuclear system. The principal rate of decrease of variance in allelic disequilibrium in a cytonuclear system is slightly faster than that in the corresponding nuclear system. However, the expected value of the variance in cytonuclear disequilibria is larger than that in a two-locus nuclear system for at least the first N generations. With mutation, the expected value of steady state variances of both systems are about the same; however, the normalized variance in linkage disequilibrium sigma 2d of the cytonuclear system is about twice as large as that for the corresponding nuclear system. For the migration process, two sets of steady state solutions are provided, one for the variables before migration and the other for the variables after migration. Diffusion approximations for both the principal rate of decay and steady state solutions in both systems are found to be satisfactory. A more accurate backward diffusion equation for a two-locus nuclear system is provided when the recombination fraction R is large.