Conditions for the Maintenance of Prezygotic and Zygotic Isolation in a Continent-Island Model

A continent-island model is studied in which differences are initially present at a gene locus with assortative mating (which causes prezygotic reproductive isolation) and at one or two unlinked selected loci, (which cause zygotic reproductive isolation). This model simulates secondary contact between two populations which have diverged allopatrically at loci which control isolating mechanisms. Two different models of prezygotic isolation and three different models of zygotic isolation are studied. The analysis is focused on those conditions under which differentiation is not lost through the swamping effect of gene now. In each case the critical migration rate (m_c) below which differences can be maintained is found. Results depend on the degree of assortative mating, on the level of selection on the genes involved, and on the particular models of reproductive isolation considered. However, in all the models, for high values of such parameters the two isolating mechanisms interact strongly, and consequently the stability of the difference at each locus (as measured by m_c) is noticeably influenced by the presence of the difference at the other locus (or loci). The nature and strength of the effects of this interaction differ according to whether or not there is selection on the assortative mating locus and whether selection against hybrids or directional selection is hypothesized.     

The reduction of gene exchange due to a prezygotic isolating mechanism with monogenic inheritance

The efficiency of an incomplete prezygotic reproductive isolating mechanism in one- and two-population models is studied. The isolating mechanism studied has a monogenic hereditary basis, and depends on the fact that the various genotypes "choose" different periods or sites to perform their reproductive activity. In the one-population models, the "neutral" gene exchange between the two morphs characterized by the alternative forms of the isolating mechanism decreases drastically only when there is an extremely low frequency of individuals with different genotypes reproducing in the same sites and during the same periods. Furthermore, the reduction in gene exchange caused by the prezygotic isolation is smaller with tight linkage between the gene-determining partial reproductive isolation and the neutral gene. In the two-population models the prezygotic isolation causes a reduction in gene exchange which is smaller with low migration rates, and is negligible for very low rates.     

Disentangling structural genomic and behavioural barriers in a sea of connectivity

Genetic divergence among populations arises through natural selection or drift and is counteracted by connectivity and gene flow. In sympatric populations, isolating mechanisms are thus needed to limit the homogenizing effects of gene flow to allow for adaptation and speciation. Chromosomal inversions act as an important mechanism maintaining isolating barriers, yet their role in sympatric populations and divergence with gene flow is not entirely understood. Here, we revisit the question of whether inversions play a role in the divergence of connected populations of the marine fish Atlantic cod (Gadus morhua), by exploring a unique data set combining whole‐genome sequencing data and behavioural data obtained with acoustic telemetry. Within a confined fjord environment, we find three genetically differentiated Atlantic cod types belonging to the oceanic North Sea population, the western Baltic population and a local fjord‐type cod. Continuous behavioural tracking over 4 year revealed temporally stable sympatry of these types within the fjord. Despite overall weak genetic differentiation consistent with high levels of gene flow, we detected significant frequency shifts of three previously identified inversions, indicating an adaptive barrier to gene flow. In addition, behavioural data indicated that North Sea cod and individuals homozygous for the LG12 inversion had lower fitness in the fjord environment. However, North Sea and fjord‐type cod also occupy different depths, possibly contributing to prezygotic reproductive isolation and representing a behavioural barrier to gene flow. Our results provide the first insights into a complex interplay of genomic and behavioural isolating barriers in Atlantic cod and establish a new model system towards an understanding of the role of genomic structural variants in adaptation and diversification.     

The effect on neutral gene flow of selection at a linked locus

The effect on gene flow at a neutral locus of a selective cline at a linked locus is investigated. A diffusion approximation for a two-locus island model is derived in which only one locus is subject to selection. The moments of the stationary distribution are obtained and compared to the corresponding moments from a one-locus, neutral island model. This comparison yields an effective migration rate. The effective migration rate is always less than the actual migration rate, but this effect is seen to be small for weak selection and loose linkage in the case of adult migration. The importance of selection at linked loci to the question of genetic differentiation in a subdivided population is discussed.     

Restricted gene flow within and between rapidly diverging Neotropical plant species

Speciation involves the evolution of traits and genetic differences that contribute to reproductive isolation and the cessation of gene flow, and studying closely related species and divergent populations gives insight into how these phenomena proceed. Here, we document patterns of gene flow within and between two members of a rapid Neotropical species radiation, Costus pulverulentus and Costus scaber (Costaceae). These species co‐occur in the tropical rainforest and share pollinators, but are reproductively isolated by a series of prezygotic barriers, some of which show evidence of reinforcement at sympatric sites. Here, we genotype microsatellite markers in plants from eight sites that span the geographical range of both species, including four sympatric sites. We also genotype putative hybrids found at two sympatric sites. We find high levels of genetic isolation among populations within each species and low but detectable levels of introgression between species at sympatric sites. Putative hybrids identified by morphology are consistent with F1 or more advanced hybrids. Our results highlight the effectiveness of prezygotic isolating mechanisms at maintaining species boundaries in young radiations and provide empirical data on levels of gene flow consistent with reinforcement.     

Evolution of Zygotic Linkage Disequilibrium in a Finite Local Population

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or between distinct zygotic LDs in a finite local population under constant immigration from a continent population. I derive the analytical theory under genetic hitchhiking effects or in a neutral process. Results indicate that zygotic LDs (diploid level) are more informative than gametic LD (haploid level) in indicating the effects of different evolutionary forces. Zygotic LDs may be greater than or comparable to gametic LD under the epistatic selection process, but smaller than gametic LD under the non epistatic selection process. The covariances between gametic and zygotic LDs are strongly affected by the mating system, linkage distance, and genetic drift effects, but weakly affected by seed and pollen flow and natural selection. The covariances between different zygotic LDs are generally robust to the effects of gene flow, selection, and linkage distance, but sensitive to the effects of genetic drift and mating system. Consistent patterns exist for the covariances between the zygotic LDs for the two-locus genotypes with one common genotype at one locus or without any common genotype at each locus. The results highlight that zygotic LDs can be applied to detecting natural population history.     

COMPONENTS OF REPRODUCTIVE ISOLATION BETWEEN ORCHIS MASCULA AND ORCHIS PAUCIFLORA

Studies of the strength and nature of reproductive isolation (RI) between species can greatly contribute to our understanding of speciation. Although the role of RI in speciation is well recognized, there is a dearth of information on the contributions of different barriers between related plant species. Here, we estimated multiple components of RI between two Mediterranean orchid sister species (Orchis mascula and Orchis pauciflora), disentangling the strength and absolute contributions of seven different isolating mechanisms. Our survey includes one prepollination, two postpollination prezygotic (pollen–stigma incompatibility, conspecific pollen precedence), two intrinsic postzygotic (embryo mortality and hybrid sterility) and two extrinsic postzygotic (hybrid habitat differentiation and hybrid pollination) isolating mechanisms. We found strong RI between the investigated species, although none of the barriers were able to completely impede gene flow. Five isolating mechanisms contributed positively to the maintenance of species boundaries. Contrary to most surveys of isolating mechanisms, our data speak against a clear predominance of prepollination or of prezygotic barriers but confirm the emerging pattern of multiple barriers contributing to the maintenance of species integrity. These findings suggest an allopatric condition during early phases of species divergence. We discuss our data in the wider context of previous studies carried out in this orchid group by using a comparative approach.     

Close clustering of anthers and stigma in Ipomoea hederacea enhances prezygotic isolation from Ipomoea purpurea

Theory predicts that, for taxa that are already substantially postzygotically isolated but for which hybrid mating is still costly, enhanced prezygotic isolation will be favored. Here, we tested this hypothesis by examining the potential contribution of one particular floral trait, herkogamy, to prezygotic isolation between two species of morning glory, Ipomoea hederacea and Ipomoea purpurea. This trait was experimentally manipulated to determine whether it is a likely prezygotic isolating barrier in naturally pollinated arrays in the field. Emasculated I. hederacea flowers set significantly fewer seeds than did control flowers, indicating that clustering of anthers and stigma in I. hederacea enhances prezygotic isolation from I. purpurea. We hypothesize that this occurs through some combination of mechanical protection and increased self-pollination, with the effect of mechanical protection estimated to be 30% greater than the effect of increased selfing. Our results identify stigma-anther proximity as a likely prezygotic isolating barrier and target of selection in the presence of heterospecific pollen flow, and provide motivation for further study of the role of floral morphology in reproductive isolation in this system.     

A formal assessment of gene flow and selection in the fire ant Solenopsis invicta

Abstract.— Recent studies of the introduced fire ant Solenopsis invicta suggest that introduced polygyne (with multiple queens per nest) populations are strongly influenced by male-mediated gene flow from neighboring monogyne (single queen per nest) populations and selection acting on a single locus, general protein-9 (Gp-9) . This investigation formally tests this hypothesis and determines if these processes can account for the genotypic structure of polygyne S. invicta . To increase the statistical power of this test, we considered the genotypes of polygyne queens and workers at both Gp-9 and the closely linked, selectively neutral locus Pgm-3 . We then constructed and analyzed a novel mathematical model to delimit the effects of monogyne male gene flow and selection on the joint genotypes at the Pgm-3/Gp-9 superlocus. Using this framework, a hierarchical maximum-likelihood method was developed to estimate the best-fitting gene flow and selection parameters based on the fit of our model to data from both the current study and an earlier one of the same population. In each case, selection on polygyne queens and workers alone, with no monogyne male gene flow, provides the most parsimonious explanation for the observed genotype frequencies. The apparent discrepancy between this result and the empirical evidence for monogyne male gene flow indicates that undocumented factors, such as other forms of selection in polygyne males or workers, are operating in introduced polygyne S. invicta .     

The Effect of Linkage on Establishment and Survival of Locally Beneficial Mutations

We study invasion and survival of weakly beneficial mutations arising in linkage to an established migration–selection polymorphism. Our focus is on a continent–island model of migration, with selection at two biallelic loci for adaptation to the island environment. Combining branching and diffusion processes, we provide the theoretical basis for understanding the evolution of islands of divergence, the genetic architecture of locally adaptive traits, and the importance of so-called “divergence hitchhiking” relative to other mechanisms, such as “genomic hitchhiking”, chromosomal inversions, or translocations. We derive approximations to the invasion probability and the extinction time of a de novo mutation. Interestingly, the invasion probability is maximized at a nonzero recombination rate if the focal mutation is sufficiently beneficial. If a proportion of migrants carries a beneficial background allele, the mutation is less likely to become established. Linked selection may increase the survival time by several orders of magnitude. By altering the timescale of stochastic loss, it can therefore affect the dynamics at the focal site to an extent that is of evolutionary importance, especially in small populations. We derive an effective migration rate experienced by the weakly beneficial mutation, which accounts for the reduction in gene flow imposed by linked selection. Using the concept of the effective migration rate, we also quantify the long-term effects on neutral variation embedded in a genome with arbitrarily many sites under selection. Patterns of neutral diversity change qualitatively and quantitatively as the position of the neutral locus is moved along the chromosome. This will be useful for population-genomic inference. Our results strengthen the emerging view that physically linked selection is biologically relevant if linkage is tight or if selection at the background locus is strong.     

Quantification of the zygotic barrier between interbreeding taxa using gene flow data

Hybridization and introgression via interspecific gene flow are common processes in the plant kingdom. The effectiveness of these processes is governed by the strengths of multiple zygotic barriers. These barriers have often been quantified in artificial settings using laborious and time‐consuming hand‐pollination experiments, but their quantification is nonexistent in the landscape. In this study, we utilized gene flow data within a spatially explicit simulation to assess the strengths of zygotic barriers. Our model system consisted of Populus nigra and its hybrid, P. × canadensis, which interbreed under natural conditions. The study population was located in the floodplain of the Eder River in central Germany. Pollen‐mediated introgression rates from hybrid males into the seeds of individual female trees were used as the target pattern using an inverse modeling approach. Simulations that treated pollen from both taxa equally revealed a large discrepancy between the observed and modeled rates of introgression for both taxa. The discrepancy was reduced by introducing a zygotic barrier against the pollen from the hybrid males. The best model outcome values indicated comparably strong zygotic barriers acting against pollen‐mediated introgressive gene flow into the two parental taxa, P. nigra and P. × canadensis. The sensitivity of our model was tested by applying different dispersal functions. Four common probability density functions were used along with a pollen dispersal function that had previously been fitted to gene flow data from the same dataset. The best barrier value was almost independent of the dispersal functions used here. Moreover, it was within the range previously determined in hand‐pollination‐based investigations, validating our model. These data indicate that the inverse modeling approach is a powerful method for quantifying hidden processes, and we discuss its use as a valuable tool for generating new insights into plant mating systems that are relevant to evolutionary biology and risk analyses in conservation efforts.     

Reduction of neutral gene flow due to the partial sterility of heterozygotes for a linked chromosome mutation

The effect of linkage between a chromosome mutation producing partially sterile heterozygotes and a neutral locus in reducing the gene flow at the neutral locus is studied using a two-population deterministic model. Chromosome mutations are more efficient in reducing gene flow with low migration rates than with high ones. The interaction between high values of partial heterozygote sterility and low recombination rates can produce, in the low migration pattern, a drastic reduction of gene flow. Nevertheless, since only chromosome mutations with low values of partial heterozygote sterility are likely to be involved in chromosomal speciation, a significant reduction of gene flow will probably occur only for a very limited part of the genome. Therefore, a single chromosome mutation is unlikely to play a primary role in speciation.     

Postmating barriers to hybridization between an island’s native eucalypts and an introduced congener

We evaluate postmating barriers to hybridization between an exotic eucalypt and a group of native congeners on the island of Tasmania. We aimed to better understand the basis of reproductive isolation between the species, glean insights into the evolution of isolating mechanisms, and inform genetic risk management. Compatibility between the exotic plantation species Eucalyptus nitens (pollen parent) and 18 native Tasmanian taxa was assayed using experimental crossing for 17 taxa (13,458 flowers pollinated to produce 1058 female × male cross combinations), and previous data for one species. Compatibility was assessed in terms of F₁ hybrid production, as well as F₁ hybrid survival and growth after 5 years. This data was combined with measurements of style length, and genetic distance from E. nitens to each maternal species, in order to determine the importance of a sequence of prezygotic and postzygotic barriers. We found that the early-acting barrier of style length (prezygotic) had the strongest isolating effect, while later-acting (postzygotic) barriers, affecting early-age growth and survival, contributed little to reproductive isolation. Style length alone explained 46 % of the variation in hybridization rate. Conversely, there was no significant relationship between genetic distance and prezygotic or postzygotic compatibility in these closely related species. This pattern is consistent with selection driving the rapid evolution of prezygotic barriers, while drift-like-processes lead to the more gradual evolution of intrinsic barriers. Although other premating and postmating barriers clearly contribute, our results highlight the important role of early-acting postmating barriers in preventing gene flow from exotic E. nitens plantations.     

Timing and tempo of primate speciation

Published molecular clocks for primates are used to estimate typical divergence times for phylogroups (1.6 Ma), species (3.3 Ma), sister species (2.7 Ma), genera (8.9 Ma) and sister genera (8.6 Ma). Significant median differences exist between major groups (infraorders and superfamilies) for various divergence times. These data are employed to estimate typical maximum duration of speciation. Typical primate values (1.1 Ma) suggest this process to be faster than is characteristic of many vertebrates. However, after considering divergence times for hybridizing congeneric and confamilial primates, this value is likely only to estimate the commencement of prezygotic isolating mechanisms, rather than the completion of reproductive isolation. Thus, speciation typically takes around 1.0 Ma to more than 4.0 Ma to occur, depending on whether prezygotic or post-zygotic isolating mechanisms are emphasized. Typical primate genus age is around 5.3 Ma, but we note differences among major groups. In light of these estimates, the classification of humans and chimpanzees is reconsidered using a molecular yardstick approach. Three taxonomic frameworks may flow from molecular analyses, all of them having major implications for understanding the evolution of humans and chimpanzees.     

The effects of linkage and gene flow on local adaptation: a two-locus continent-island model

Population subdivision and migration are generally considered to be important causes of linkage disequilibrium (LD). We explore the combined effects of recombination and gene flow on the amount of LD, the maintenance of polymorphism, and the degree of local adaptation in a subdivided population by analyzing a diploid, deterministic continent–island model with genic selection on two linked loci (i.e., no dominance or epistasis). For this simple model, we characterize explicitly all possible equilibrium configurations. Simple and intuitive approximations for many quantities of interest are obtained in limiting cases, such as weak migration, weak selection, weak or strong recombination. For instance, we derive explicit expressions for the measures and r² (the squared correlation in allelic state) of LD. They depend in qualitatively different ways on the migration rate. Remarkably high values of r² are maintained between weakly linked loci, especially if gene flow is low. We determine how the maximum amount of gene flow that admits preservation of the locally adapted haplotype, hence of polymorphism at both loci, depends on recombination rate and selection coefficients. We also investigate the evolution of differentiation by examining the invasion of beneficial mutants of small effect that are linked to an already present, locally adapted allele. Mutants of much smaller effect can invade successfully than predicted by naive single-locus theory provided they are at least weakly linked. Finally, the influence of linkage on the degree of local adaptation, the migration load, and the effective migration rate at a neutral locus is explored. We discuss possible consequences for the evolution of genetic architecture, in particular, for the emergence of clusters of tightly linked, slightly beneficial mutations and the evolution of recombination and chromosome inversions.     

A Theoretical Model for Estimating Linkage in F2 Populations with Distorted Single Gene Segregation

A model is presented which allows estimation of linkage from dihybrid F₂ populations with distorted single gene segregation by applying the maximum-likelihood method. For different selection processes operating on one locus at either the gametic or the zygotic level, it can be demonstrated that, if the deficit is previously taken into account, testing for free recombination can be carried out without prior knowledge of the causes of this deficit. In the presence of linkage, the expected frequencies of two phenotypic classes depend on whether gametic or zygotic selection is operating. The remaining two classes can be utilized for the estimation of linkage as their frequency ratio is independent of these selection types. The application of this procedure to situations with coupling, incomplete penetrance, gametic and zygotic selection is discussed.     

Strength and variability of postmating reproductive isolating barriers between four European white oak species

The identification and quantification of the relative importance of reproductive isolating barriers is of fundamental importance to understand species maintenance in the face of interspecific gene flow between hybridising species. Yet, such assessments require extensive experimental fertilisations that are particularly difficult when dealing with more than two hybridising and long-generation-time species such as oaks. Here, we quantify the relative contribution of four postmating reproductive isolating barriers consisting of two prezygotic barriers (gametic incompatibility, conspecific pollen precedence) and two postzygotic barriers (germination rate, early survival) from extensively controlled pollinations between four oak species (Quercus robur, Quercus petraea, Quercus pubescens and Quercus pyrenaica) that have been shown to frequently hybridise in natural populations. We found high variation in the strength of total reproductive isolation between species, ranging from total reproductive isolation to advantage toward hybrid formation. As previously found, Q. robur pollen was unable to fertilise Q. petraea due to a strong reproductive isolating mechanism. On the contrary, Q. pubescens pollen was more efficient at fertilising Q. petraea than conspecific pollen. Overall, prezygotic barriers contribute far more than postzygotic barriers to isolate species reproductively, suggesting a role for reinforcement in the development of prezygotic barriers. Conspecific pollen precedence reduced hybrid formation when pollen competition was allowed; however, presence of conspecific pollen did not totally prevent hybridization. Our results suggest that pollen competition depends on multiple ecological and environmental parameters, including species local abundance, and that it may be of uppermost importance to understand interspecific gene flow among natural multispecies populations.     

Divergence between the Courtship Songs of the Field Crickets Gryllus texensis and Gryllus rubens (Orthoptera, Gryllidae)

Acoustic mating signals are often important as both interspecific prezygotic isolating mechanisms and as sexually selected traits in intraspecific mate choice. Here, we investigate the potential for cricket courtship song to act as an isolating mechanism by assessing divergence between the courtship songs of Gryllus texensis and Gryllus rubens , two broadly sympatric cryptic sister species of field crickets with strong prezygotic isolation via the calling song and little or no postzygotic isolation. We found significant species-level differences in the courtship song, but the song has not diverged to the same extent as the calling song, and considerable overlap remains between these two species. Only two related courtship song characters are sufficiently distinct to play a possible role in prezygotic species isolation.     

The robustness of neutral models of geographical variation

The approximation of diploid migration by gametic dispersion is studied. The monoecious, diploid population is subdivided into panmictic colonies that exchange migrants. Generations are discrete and nonoverlapping; the analysis is restricted to a single locus in the absence of selection; every allele mutates to a new allele at the same rate u. Diploid-migration models without self-fertilization and with selfing at the “random” rate (equal to the reciprocal of the deme size in each deme) are investigated; in the gametic-dispersion models, selfing occurs at the random rate. It is shown for the unbounded stepping-stone model in one and two dimensions, the circular stepping-stone model, and the island model that the probabilitities of identity in state at equilibrium for diploid migration are close to those for gametic dispersion if the mutation rate is small or the deme size is large. Explicit error bounds are presented in all the above cases. It is also proved that if the number of demes is finite and the migration matrix is arbitrary but time independent and ergodic, then in the strong-migration approximation the equilibrium and the ultimate rate and pattern of convergence of both diploid-dispersion models are close to the corresponding gametic-dispersion formulae. For the strong-migration approximation at equilibrium, migration must dominate both mutation and random drift; for the convergence results, it suffices that migration dominate random drift. All the results apply to a dioecious population if the migration pattern and mutation rate are sex independent.