ORIGINAL ARTICLE

doi:10.1111/evo.12725

The genetic architecture of hybridincompatibilities and their effect on barriersto introgression in secondary contactDorothea Lindtke1,2,3 and C. Alex Buerkle1

1Department of Botany and Program in Ecology, University of Wyoming, Laramie, Wyoming 820712Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, United Kingdom

3E-mail: d.lindtke@sheffield.ac.uk

Received March 14, 2015

Accepted July 8, 2015

Genetic incompatibilities are an important component of reproductive isolation. Although theoretical studies have addressed their

evolution, little is known about their maintenance when challenged by potentially high migration rates in secondary contact. Al-

though theory predicts that recombination can erode barriers, many empirical systems have been found to retain species-specific

differences despite substantial gene flow. By simulating whole genomes in individuals of hybridizing species, we find that the ge-

netic architecture of two contrasting models of epistatic hybrid incompatibilities and the context of hybridization can substantially

affect species integrity and genomic heterogeneity. In line with theory, our results show that intergenomic incompatibilities break

down rapidly by recombination, but can maintain genome-wide differentiation under very limited conditions. By contrast, intrage-

nomic interactions that arise from genetic pathways can maintain species-specific differences even with high migration rates and

gene flow, whereas introgression at large parts of the genome can simultaneously remain extensive, consistent with empirical

observations. We discuss the importance of intragenomic interactions in speciation and consider how this form of epistatic fitness

variation is implicated and supported by other theoretical and empirical studies. We further address the relevance of replicates

and knowledge of context when investigating the genomics of speciation.

KEY WORDS: Coadaptation, Dobzhansky–Muller incompatibilities, gene flow, genetic pathways, simulation, speciation.

Speciation involves the accumulation of genetic changes that

contribute to reproductive isolation and the maintenance of

species-specific traits in primary or secondary contact. Thus,

understanding the process of speciation includes uncovering the

genetic architecture of fitness variation in hybridizing species

and how it is affected by migration and gene flow (Endler 1973;

Butlin et al. 2012; Seehausen et al. 2014). Advances in this field

involve theoretical questions (e.g., which genetic architectures

are effective in reducing gene flow), as well as methodological

questions (e.g., how to detect genetic changes important for

speciation in empirical systems). Progress in speciation research

resulted in revised or complementary evolutionary concepts, such

as the “genic view” of speciation (Wu 2001), sympatric speciation

(Bolnick and Fitzpatrick 2007), and the impact of hybridization

on speciation (Arnold and Hodges 1995; Seehausen 2004; Abbott

et al. 2013). Some of the evolutionary theory that predates these

advances, however, has only begun to be reconsidered in the light

of new data. For example, the “classic” Dobzhansky–Muller

model (following the formulation by Dobzhansky 1937; Muller

1942) for the evolution of hybrid incompatibilities, often con-

sidered a “standard” model for reproductive isolation (Gavrilets

2003; Coyne and Orr 2004), has limited efficacy in the face of

gene flow (Barton and Bengtsson 1986; Gavrilets 1997; Bank

et al. 2012). If some hybrids produce fertile recombinant progeny,

Dobzhansky–Muller incompatibilities (DMIs) can be eroded.

Thus, DMIs are unlikely to be the primary cause of reproductive

isolation under conditions that constitute high probabilities for

interspecific recombination, for example, arising from overlap-

ping species distributions and the presence of at least partially fit

hybrids.

1 9 8 7C© 2015 The Author(s). Evolution C© 2015 The Society for the Study of Evolution.Evolution 69-8: 1987–2004

D. LINDTKE AND C. A. BUERKLE

Despite the limitations of classic DMIs and although several

alternative concepts for the evolution of genetic hybrid incom-

patibilities exist in the speciation literature (e.g., Johnson 2010;

Presgraves 2010; Nei and Nozawa 2011), the respective theory

has received little formal exploration. One potentially important

alternative model states that allele combinations within species

become coadapted and recombination disrupts epistatic interac-

tions in coadapted genomes, resulting in reduced hybrid fitness.

For example, intragenomic coadaptation can result from protein–

protein interactions or regulatory genetic pathways (Johnson and

Porter 2000; Edmands and Timmerman 2003; Ortiz-Barrientos

et al. 2007; Livingstone et al. 2012). For simplicity, we re-

fer to such intragenomic epistatic interactions as the “pathway”

model in the following. Divergent genetic pathways can evolve

easily and might have high relevance for the maintenance of

species differences in conditions with high gene flow (see be-

low), thus representing a potentially important alternative to clas-

sic DMIs. Given the known limited efficacy of DMIs and the

need for more detailed theoretical investigations of alternatives,

we focus on comparing the DMI and pathway models of epistatic

hybrid incompatibilities, but do not study selection acting inde-

pendently on multiple loci without epistasis (e.g., as in Barton

1983; Flaxman et al. 2014). Our particular goal is to investigate

the maintenance of species barriers in conditions that include high

migration, in contrast to previous work that addressed the evolu-

tionary origin (but not maintenance) of barriers mainly under low

migration conditions (including allopatry). We evaluated the ef-

ficacy of different genetic architectures in terms of maintenance

of differentiation at directly selected loci, but (and unlike the ma-

jority of previous studies) also in terms of effects on linked and

unlinked variants across the whole genome, as stronger isolation

between species should result in a greater fraction of the genome

that is protected from recombination and introgression (Barton

and De Cara 2009).

In addition to building our understanding of the efficacy of

different genetic architectures of hybrid fitness, additional theo-

retical modeling is needed to build expectations for observable

genomic variation in empirical studies of natural species’ bound-

aries. Although searching genomes for statistical extreme or dis-

tinctive patterns is increasingly feasible, it remains unclear how

heterogeneous genomic differentiation can be linked to underly-

ing processes (Seehausen et al. 2014). In this article, we therefore

extend previous attempts (e.g., Gompert et al. 2012) and investi-

gate the genomic outcomes of different genetic architectures of

hybrid incompatibilities and how they are affected by the context

of hybridization (e.g., time since contact and population demog-

raphy). To address these questions, we use computer simulation

to model whole diploid genomes subjected to selection and ad-

mixture in secondary contact zones. In the next section, we briefly

review the concepts of our focal models of hybrid incompatibili-

ties: DMIs and pathways. We then outline their differences, and

provide an overview of our main goals and findings of this study.

TWO MODELS OF EPISTATIC HYBRID

INCOMPATIBILITIES

To solve the problem of how hybrid sterility or unfitness can

evolve without populations having to cross a maladaptive fitness

valley, Dobzhansky (1937) and Muller (1942) recognized that at

least two interacting loci are necessary. That is, given the ancestral,

diploid two-locus genotype aabb and the innocuous substitutions

to genotype aaB B in one allopatric population and to AAbb in

another, hybrids a AbB that simultaneously carry derived, dom-

inant alleles A and B will experience at least partially reduced

fitness (Dobzhansky 1937; Muller 1942). The simplicity of the

model made DMIs a very popular explanation for the evolution

of reproductive isolation, although empirical studies supporting

their importance for speciation remain rare (Brideau et al. 2006;

Rieseberg and Willis 2007; Nei and Nozawa 2011). The analytical

tractability of DMIs resulted in various theoretical studies of their

origin, barrier strength and maintenance (e.g., Orr 1995; Gavrilets

1997; Turelli and Orr 2000). However, the classic DMI model re-

quired modifications to prevent the collapse of the barrier if F1 hy-

brids were not always sterile. Particularly, if compatible ancestral

genotypes reemerge through recombination, compatible variants

can rapidly increase in frequency and the barrier is lost (Fig. 1A;

Barton and Bengtsson 1986; Gavrilets 1997; Gompert et al. 2012).

Accordingly, most theoretical work on DMIs includes adaptive

(and often divergent) selection on derived variants, or recessiv-

ity of incompatible alleles (Fierst and Hansen 2010; Nosil and

Flaxman 2011; Bank et al. 2012). This indicates that classic DMIs

on their own are ineffective at maintaining a species barrier un-

der conditions that allow recombination and gene flow. Although

various interpretations of DMIs and corresponding epistatic fit-

ness matrices exist in the literature (e.g., Agrawal et al. 2011;

Maheshwari and Barbash 2011; Nei and Nozawa 2011; Nosil and

Flaxman 2011; Bank et al. 2012), here we consider “classic” DMIs

(as described by Dobzhansky 1937; Muller 1942) as a special case

within other forms of epistatic fitness variation that gives rise to

hybrid incompatibilities. We emphasize this distinction because

of the variety of possible epistatic interactions in hybrids and the

substantial differences in their expected outcomes (see below).

An alternative model of epistatic hybrid incompatibilities

that might have high biological significance arises from knowl-

edge of coadaptation within genomes (Edmands and Timmerman

2003) and regulatory genetic pathways (Johnson and Porter 2000;

Ortiz-Barrientos et al. 2007). The common principle of these in-

tragenomic interactions is that a trait is expressed normally if all its

genetic components interact properly (e.g., transcription factors,

1 9 8 8 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

A B

Figure 1. Schematic illustration of two contrasting models of epistatic hybrid incompatibilities. Species 1 and species 2 evolve from a

common ancestor and establish new mutations at two different loci. The derived genotypes can be recombined in secondary contact.

Fitnesses of F1 and recombinant hybrids differ between the two models, from full fitness (white circles) to reduced fitness (gray circles;

Tables 1 and 2). (A) With DMI-type incompatibilities, F1 hybrids have reduced fitness as they carry independently derived, incompatible

alleles A and B at the two loci. Recombinant hybrids that do not carry the incompatible allele combinations can be fit. (B) With pathway-

type incompatibilities, fitness depends on the presence of compatible haplotypes A1 B1 or A2 B2 at coadapted loci. F1 hybrids with

balanced genotypes can be fit, whereas disrupted, unbalanced genotypes result in reduced fitness in recombinants.

biosynthetic steps or protein substructures; Fig. 1B). Disruption of

the interacting genetic components through interspecific recom-

bination can result in low hybrid fitness, known as outbreeding

depression (Lynch 1991). The potential importance of pathways

in speciation is supported by various studies showing that: (1)

regulatory genetic pathways are a widespread mechanism to gen-

erate phenotypic variation (Romero et al. 2012; Boyle et al. 2014),

(2) divergent evolution of pathways can be induced by adaptation

(Johnson and Porter 2000, 2007; Porter and Johnson 2002; Palmer

and Feldman 2009; Chevin et al. 2014; Tulchinsky et al. 2014)

or random genetic drift (Lynch and Hagner 2015), and (3) low

hybrid fitness can result from incompatibilities between regula-

tory elements (True and Haag 2001; Landry et al. 2007; Hegarty

et al. 2009; Renaut and Bernatchez 2011). Pathways might thus

constitute an important alternative mechanism to DMIs for the

maintenance of species differences in conditions with high gene

flow. However, this hypothesis has not yet received much atten-

tion in theoretical work, a gap that we want to address with the

current study.

A critical difference between DMIs and pathways are the ex-

pected fitnesses of recombinant hybrids, which can be described

by parameters in a fitness matrix or an adaptive landscape (e.g.,

Gavrilets 1997). With DMIs, recombinants with high fitness can

emerge and thus negatively interacting (derived) alleles from dif-

ferent species will be purged from a hybrid population (Table 1,

Fig. 1A). With the pathway model, recombinants with

Table 1. Genotype fitnesses for the DMI model.

B B bB bb

aa 1 1 1a A 1 − s 1 − s 1AA 1 − s 1 − s 1

Notes Genotype aabb is ancestral, and allele A is derived in one species

at the first locus, allele B is derived in the other species at the second

locus. Genotypes aaB B and AAbb are fixed in species 1 and species 2.

Combinations of alleles A and B result in fitness reduction by s.

Table 2. Genotype fitnesses for the pathway model.

B1 B1 B1 B2 B2 B2

A1 A1 1 1 − s/2 1 − sA1 A2 1 − s/2 1 1 − s/2A2 A2 1 − s 1 − s/2 1

Notes Genotypes A1 A1 B1 B1 and A2 A2 B2 B2 are fixed in species 1 and

species 2. The presence of compatible alleles at interacting loci (A1 B1 or

A2 B2) is required for full fitness. Missing compatible combinations result in

fitness reduction by s/2.

disrupted intragenomic interactions will have low fitness (Table 2,

Fig. 1B). Thus, in contrast to DMIs, interspecific recombination

and gene flow will not erode the species barrier at epistatic loci in

pathways. This makes alternative pathways with coevolved allelic

EVOLUTION AUGUST 2015 1 9 8 9

D. LINDTKE AND C. A. BUERKLE

differences a potentially effective mechanism for the maintenance

of species differences in conditions with high gene flow, the set-

ting where DMIs typically fail.

The majority of previous theoretical work on epistatic hy-

brid incompatibilities investigated simple genetic architectures

and the maintenance of incompatibilities in parapatric contact

(e.g., Gavrilets 1997; Bank et al. 2012), or the build-up of re-

productive isolation during adaptation (e.g., Johnson and Porter

2000; Agrawal et al. 2011; Nosil and Flaxman 2011). Further,

many studies did not address recombination (e.g., Palmer and

Feldman 2009) or used haploid models (e.g., Agrawal et al.

2011), although the barrier to gene flow is expected to be substan-

tially affected by recombination in diploid organisms (Gavrilets

1997; Barton 2001). With few exceptions (e.g., Gompert et al.

2012), only directly selected loci and limited sets of linked or

unlinked variants were studied, thus it remains uncertain to what

extent different genetic architectures of selection cause heteroge-

neous genomic introgression in hybrids and affect species barriers.

The goal of this study was therefore twofold: assessing two

contrasting genetic architectures of hybrid incompatibilities in

diploids to investigate (1) their efficacy as species barriers in spa-

tially explicit hybrid zones with high migration rates, and (2) their

genomic outcomes of selection.

Our model differs from other studies in that we modeled

a large, spatially explicit and ecologically homogeneous con-

tact zone between previously diverged species that allowed for

source-sink dynamics and substantial migration rates between

pure species and hybrids (but see Gavrilets 1997), and that we in-

vestigated simple and complex architectures of epistasis and their

effects on admixture by modeling whole diploid genomes rather

than a limited set of loci (but see Gompert et al. 2012).

We modeled intrinsic postzygotic isolation arising from

DMIs and pathways with different selection strengths and mi-

gration rates, and monitored how genetic differentiation, intro-

gression, and admixture were affected across time and space and

along the genome. We emphasize two main findings. First, path-

ways constitute a promising model for the maintenance of species

differences, particularly in the problematic conditions of high

gene flow in sympatry and high hybrid fitness. We further con-

firm that these are the conditions when classic DMIs break down.

Thus, pathways or analogous forms of intragenomic interactions

require more attention as an important mechanism involved in

speciation. Second, selection on hybrid incompatibilities resulted

in heterogeneous genomic introgression and admixture that could

differ among genetic architectures of epistasis. However, genomic

patterns of variation also strongly depended on the spatial, tem-

poral, and demographic context of hybridization, highlighting

that empirical observations need to be interpreted cautiously. We

discuss our main findings in relation to empirical studies and other

theoretical work.

Model and MethodsTo investigate the genetic architecture of hybrid incompatibil-

ities and their effects on the maintenance of genome differ-

entiation, we simulated whole genomes of individuals in sec-

ondary contact between previously diverged species. As our aim

was to address barrier maintenance, we assumed that incompat-

ibilities already evolved and started with fixed genomic differ-

ences between species and recorded admixture and introgression

through time. We modeled a chain of demes with finite population

sizes that were connected by migration using a stepping-stone

model (similar to Gavrilets 1997). Infinitely sized populations

of different species at each end of the chain acted as continuous

sources of unadmixed individuals. We thus modeled the metapop-

ulation (the chain of demes) as only receiving immigrants (a sink)

without any emigration to the core of species’ ranges (the source),

in line with hybridization often occurring at range margins (Bridle

and Vines 2007; Abbott et al. 2013). We assessed the maintenance

of species differences in a homogeneous environment using two

models of intrinsic epistatic selection: intergenomic incompatibil-

ities (DMIs) and intragenomic interactions (pathways). We chose

these architectures to investigate two extremes of many other con-

ceivable forms of epistasis that might contribute to speciation. In

both models, some hybrid genotypes were assigned full fitness,

thus pure species’ epistatic genotypes were not separated by fit-

ness valleys (Tables 1 and 2). We note that the two fitness matrices

can converge under less strict definitions that allow for separated

fitness peaks. For example, by modifying our specification for

classic DMIs of Table 1 to simultaneously allow for nondomi-

nant incompatibilities and fitness disadvantage of ancestral alleles

(Table S1), the resulting fitness matrix can become very similar

(and even identical) to our specification for the pathway model

(Tables 2 and S2). In the following, we describe the basic sim-

ulation setup, selection models, and summary statistics on the

simulation runs. Further details are in the Supporting Informa-

tion. Simulation C code together with a brief description of the

software (which we named dfuse) is available from the second

author’s website.

SIMULATION SETUP

We describe the basic simulation setup used for the majority

of our simulation runs below. We subsequently modified this

basic model and tested the robustness of our results (Support-

ing Information). We simulated secondary contact with source-

sink dynamics by connecting two species’ source populations (of

infinite size) by three finite demes with adult carrying capac-

ity of Nc = 500. Neighboring demes were connected by migra-

tion of rate m/2, and we chose high m = {0.01, 0.2} for most

runs to emulate hybrid zone dynamics. Every generation, un-

admixed individuals from species sources immigrated into the

1 9 9 0 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

peripheral demes (i.e., deme 1 or deme 3), whereas individuals that

emigrated from the peripheral demes outward were eliminated.

We initialized demes with unadmixed individuals, with the cen-

tral deme receiving an equal mixture from both species, consistent

with sympatric contact between previously isolated species. We

assumed a homogeneous environment (i.e., no ecological differ-

ences among demes). We modeled genomes of diploid individuals

with 2N = 20 autosomal chromosomes, each of 1 Morgan length.

The average number of crossovers per chromosome per meiosis

was one (Poisson distributed). We stored ancestry of chromosome

blocks and the history of interspecific recombination events as in

previous simulations (Buerkle and Rieseberg 2008; Gompert and

Buerkle 2011; Gompert et al. 2012), and placed markers every 2

cM to sample 510 loci (51 per chromosome; including directly

selected sites) for locus-specific statistics every 10 generations.

We modeled hermaphroditic, nonselfing individuals with discrete

generations. Mating was random within a deme and viability

selection (see section below) acted on progeny. The reproduc-

tive phase continued until surviving offspring filled the deme to

progeny carrying capacity Np = 1000 or available maternal ga-

metes (mean of five per individual) were depleted, whichever oc-

curred first. Beyond reproduction, the life cycle was completed by

progeny dispersal, adult mortality, and random survivorship dur-

ing aging of progeny to cap the new generation at adult carrying

capacity. We describe model modifications, including different

carrying capacities Nc = {50, 5000} and Np = {100, 10 000}, or

parapatric contact, in the Supporting Information.

SELECTION

As outlined in the Introduction, our goal with this study was to

investigate two contrasting genetic architectures of epistatic hy-

brid incompatibilities. The two models, DMIs and pathways, were

intended to simulate alternative genetic architectures resulting in

unfit or fit F1 and recombinant hybrids (corresponding to the wide

range of hybrid fitnesses in empirical systems; Arnold and Hodges

1995; Barton 2001; Burke and Arnold 2001; Presgraves 2010).

We focused on intrinsic postzygotic selection in a homogeneous

environment, as this is a condition that can result in a largely sta-

ble barrier to gene flow (i.e., independent on changes in environ-

ment or mating preferences). Epistatic selection against incom-

patible two-locus interactions reduced the survival probability of

progeny before dispersal (Tables 1 and 2), where survival prob-

abilities of multiple two-locus epistatic interactions were com-

bined multiplicatively (i.e., for more than two loci under selection;

Tables S3 and S4). Because strong selection was required to result

in observable effects, we chose selection strength s = {0.2, 0.9}for most runs. As our goal was to model the characteristics of

DMIs and pathways and to compare them, we chose appropriate

numbers of interacting loci and their recombination distance for

our basic settings, and then investigated modifications of these

architectures (Supporting Information).

We modeled intergenomic incompatibilities (DMIs) follow-

ing Dobzhansky (1937) and Muller (1942) strictly. In particular,

we modeled incompatible interactions between dominant alle-

les that derived independently between species at two different

loci (Table 1, Fig. 1A). Incompatibilities were thus manifested

in interspecific heterozygotes (i.e., F1s were unfit). In our basic

setting, we assumed that derived alleles within a species were

selectively neutral (which is not explicit in the original descrip-

tion). We modeled interactions between two loci at recombination

distance of 20 cM. We then extended this model and investigated

complex multilocus interactions (up to 10 loci) and their genomic

consequences (Supporting Information; Figs. S1 and S2).

We modeled intragenomic interactions (pathways) follow-

ing ideas from simulation studies on intrinsic coadaptation

(Edmands and Timmerman 2003) or linear regulatory genetic

pathways (Johnson and Porter 2000). We modeled p linearly in-

teracting loci, and fitness varied according to epistatic interactions

between all p − 1 consecutive pairs of loci and their multiplicative

effects. The model corresponds, for example, to a genetic pathway

where a promoter at the first locus is necessary to regulate a gene

at the second locus, whose product then interacts with the next

locus, and so on. Interacting sites that diverged between species

can lose compatibility, resulting in aberrant traits in recombinants

(Fig. 1B). Fitness was reduced by s/2 or s if one or two alleles at

interacting loci were incompatible (Table 2). With this model, we

explicitly allowed for full fitness of individuals with functional

genetic pathways, independent on the origin of that pathway (i.e.,

pure species, F1 hybrids, and the subset of recombinant hybrids

with complete sets of interacting loci could be fully fit). Our

basic setting involved four loci, each separated by 20 cM. We

investigated additional genetic architectures involving two to 36

interacting loci (Supporting Information; Figs. S1 and S2).

SIMULATION OUTPUT AND STATISTICS

We ran 20 replicates of each of our settings for 100 genera-

tions, which appeared to be sufficient to investigate the most

determining parameters of barrier efficacy and the genomic

outcomes of selection. We included simulations where we set

selection strength to zero to obtain base levels of admixture

and introgression from purely demographic processes. For each

generation, replicate, and deme, we recorded genome-wide

admixture proportion (proportion of species 1 ancestry) and

genome-wide intersource ancestry (interspecific heterozygosity),

and locus-specific ancestry (0, 1, or 2 alleles from species 1)

for all 500 adult individuals per deme. Locus-specific admixture

proportion and locus-specific intersource ancestry were computed

as averages from individual locus-specific ancestries within each

deme or for the metapopulation. We calculated genome-wide and

EVOLUTION AUGUST 2015 1 9 9 1

D. LINDTKE AND C. A. BUERKLE

locus-specific FST = (HT − HS)/HT (Nei 1977) by obtaining

the expected heterozygosity in the metapopulation (HT) and

the average expected heterozygosity within demes (HS) directly

from the genome-wide or locus-specific admixture proportions.

We further calculated linkage disequilibrium from haplotype

frequencies, adjusted by allele frequencies (D′; Lewontin 1964),

from 50 randomly sampled individuals from the central deme.

We simplified D′ to one dimension by reporting values only for

locus pairs separated by 10 cM distance on the genetic map.

Further details are in the Supporting Information.

ResultsWe modeled classic intergenomic incompatibilities (DMIs) and

intragenomic interactions resulting from genetic pathways as

two extreme forms of epistatic hybrid incompatibilities out of

many other possible architectures, and investigated their poten-

tial efficacy in maintaining genetic differences between species

in secondary contact. We describe the resulting genome-wide and

locus-specific processes and patterns of admixture and introgres-

sion and how they were affected by the demographic and spatial

context of hybridization and our model specifics. In particular,

consistent with previous studies (Barton and Bengtsson 1986;

Gavrilets 1997; Gompert et al. 2012), we show that DMIs typically

broke down rapidly when interspecific recombination occurred,

but constituted very efficient species barriers that protected whole

genomes from introgression under some limited conditions. By

contrast, barriers to gene flow resulting from genetic pathways

were less affected by model specifics or temporal dynamics, but

reduced introgression only for parts of the genome.

THE GENETIC ARCHITECTURE OF HYBRID

INCOMPATIBILITIES AND GENOME-WIDE PROCESSES

OF ADMIXTURE

Classic DMIsWe illustrate the outcomes of genome-wide admixture after sec-

ondary contact with classic DMIs under different strengths of

selection and different migration rates in Figure 2 (top row of

A and B). As expected, the rate of reduction of FST over 100

generations was strongly affected by migration rate. Compared

to purely demographic processes (s = 0.0, black lines in Fig. 2),

only strongly selected DMIs (s = 0.9, orange lines) and low mi-

gration rates (m = 0.01) impeded the reduction of genome-wide

FST considerably (Fig. 2A). Weaker selection (s = 0.2, green

lines) or high migration rates (m = 0.2; Fig. 2B) resulted in dis-

ruption of DMIs because the formation and survival of F1 hybrids

was more likely, enabling interspecific recombination (see below).

The consequent rapid breakdown of the species barrier resulted in

converging levels of genome-wide FST among models with and

without selection. With low migration rates, the timing of break-

down reflected chance variation (wide SDs among replicates in

Fig. 2A for s = 0.9), but occurred after only few generations with

high migration rates (Fig. 2B).

Genetic pathwaysBy contrast, with the pathway model, we explicitly allowed full

fitness for F1 hybrids, but selection acted against interspecific re-

combinants with unbalanced epistatic genotypes: species-specific

alleles at epistatically interacting loci needed to segregate jointly

for full fitness. As F1s were fully fit, genomic admixture was

largely unrestricted and genome-wide FST was reduced immedi-

ately and at a rate inversely proportional to selection (Fig. 2, top

row of C and D). The reduction of FST varied less stochastically

among replicates and instead declined linearly with little variance

among replicates, as parts of the genome unlinked to selected

loci introgressed freely (see below). Genome-wide FST stabilized

after few generations and was not subjected to further reduction

even with high migration rates (Fig. 2D).

THE GENETIC ARCHITECTURE OF HYBRID

INCOMPATIBILITIES AND LOCUS-SPECIFIC

CONSEQUENCES OF INTROGRESSION

Classic DMIsWe also monitored the genomic outcomes of hybridization at indi-

vidual loci by calculating FST, admixture proportion, intersource

ancestry, and D′ after several generations since contact (Fig. 2,

second and third row of A and B; Figs. 3 and 4A, B). The observed

dynamics were dependent on selection strength, migration rate,

and time since contact. Within the first few generations, DMIs

could remain intact and thus reduced gene flow genome-wide as

hybrid fitness was low (Fig. 2, second and third row of A and B;

thick, light-colored lines; Fig. S30A, B). However, DMIs were

rapidly disrupted in the hybrid deme through interspecific re-

combination (Fig. 5). Consequently, incompatible derived alleles

were quickly purged and compatible ancestral alleles increased

in frequency (Figs. 3 and 4, top rows of A and B), whereas re-

combinant hybrids with compatible ancestral alleles recovered

full fitness (Fig. S30A, B). This then allowed largely unrestricted

introgression and reduction of FST across the genome (Fig. 2,

second and third row of A and B; thin, dark-colored lines). In-

tact DMIs and derived variants from the infinite parental source

populations continued to enter the hybrid deme, but did not cross

it (Figs. 5 and S3). As unselected parts of the genome could

introgress freely among demes after barrier breakdown, FST re-

mained elevated relative to the remainder of the genome only at

or closely linked to selected sites (Fig. 2A, B; these FST peaks

disappeared through time when modeling finite source popula-

tions with high migration, Fig. S7B).

1 9 9 2 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

0 20 40 60 80 100

0.0

00

.25

0.5

00

.75

1.0

0

FS

T

Generation

DMIs, m=0.01A

0.0

0.5

1.0

FS

T

s=0.2

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

0 20 40 60 80 100

0.0

00

.25

0.5

00

.75

1.0

0

FS

T

Generation

DMIs, m=0.2B

mean+/− SD

s=0.0s=0.2s=0.9

0.0

0.5

1.0

FS

T

s=0.2

g=10g=20

g=40g=60

g=80

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

0 20 40 60 80 100

0.0

00

.25

0.5

00

.75

1.0

0

FS

T

Generation

Pathways, m=0.01C

0.0

0.5

1.0

FS

T

s=0.2

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

0 20 40 60 80 100

0.0

00

.25

0.5

00

.75

1.0

0

FS

T

Generation

Pathways, m=0.2D

0.0

0.5

1.0

FS

T

s=0.2

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

Figure 2. Reduction of genome FST and locus-specific patterns of FST for two models of epistasis (DMIs and pathways) and different

migration rates (m = 0.01 and 0.2). Depicted are results for the basic model (infinite source populations, three demes, each with capacity

Nc = 500). Top row shows reduction of genome FST over generations for different strengths of selection (black, no selection; green,

s = 0.2; orange, s = 0.9). Thick and thin lines show mean and ± SD over 20 replicates. Other rows show locus-specific patterns of FST

along the genome (x-axis, truncated within chromosome V; dotted vertical lines indicate chromosome boundaries). Shades of blue

indicate generations since contact when samples were taken. Triangles show genome position of selected loci. The second and third row

show mean values over 20 replicates for s = 0.2 and 0.9, the fourth row shows results for a single replicate with s = 0.9.

Genetic pathwaysWith pathways, genome-wide gene flow was not delayed and in-

stead started immediately after contact (Fig. 2C, D). However,

gene flow at selected loci and linked sites remained low, resulting

in elevated and even increasing FST with low migration rates over

time (Fig. 2C; FST peaks did not disappear when modeling finite

source populations, Fig. S7C, D). We did not observe an increase

of particular species-specific alleles for pathway loci when aver-

aging over replicates (Figs. 3 and 4, top row of C and D). However,

the decrease in intersource ancestry with low migration (Fig. 4,

middle row of C) suggests that one of the pathways became fixed

in the hybrid deme, which we could confirm with our results for

single replicates (Fig. S3, middle row of C). Fixation of one of the

pathways will amplify population structure and probably caused

the observed increase in FST. Allele combinations at pathway loci

remained largely intact through time (Fig. 6), although popula-

tion fitness was reduced by hybrids with unbalanced genotypes

(Fig. S30C, D), consistent with outbreeding depression. With

strong selection and high migration rates, alleles at pathway loci

remained associated within large chromosomal blocks, as evi-

denced by highly elevated D′ across large parts of the selected

chromosome (Fig. 4, bottom row of D; Fig. S32D).

THE CONTEXT OF HYBRIDIZATION AFFECTS

GENOMIC OUTCOMES

Our results indicate that the demographic, spatial, and temporal

context of hybridization strongly influenced outcomes, even for

a single model of epistasis. Population demography, particularly

migration rate, had a strong effect on the genomic outcomes of

hybridization by altering the probability of interspecific recom-

bination and by affecting the rate of genetic drift within a deme.

For example, DMIs constituted strong barriers to gene flow but

required very high selection coefficients and low migration rates

(m � s) to maintain species integrity over several tens of gen-

erations, but broke down otherwise (Fig. 7, orange symbols).

EVOLUTION AUGUST 2015 1 9 9 3

D. LINDTKE AND C. A. BUERKLE

0.0

0.5

1.0

Adm

. pro

p.

DMIs, m=0.01, s=0.2A0.0

0.5

1.0

Inte

r−sourc

e a

nc.

I II III IV V

0.0

0.5

1.0

Chromosome

D'

0.0

0.5

1.0

Adm

. pro

p.

DMIs, m=0.2, s=0.2Bg=10g=20

g=40g=60

g=80

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

g=10g=20

g=40g=60

g=80

I II III IV V

0.0

0.5

1.0

Chromosome

D'

g=10g=20

g=40g=60

g=80

0.0

0.5

1.0

Adm

. pro

p.

Pathways, m=0.01, s=0.2C

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

I II III IV V

0.0

0.5

1.0

Chromosome

D'

0.0

0.5

1.0

Adm

. pro

p.

Pathways, m=0.2, s=0.2D

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

I II III IV V

0.0

0.5

1.0

Chromosome

D'

Figure 3. Locus-specific patterns of admixture for two models of epistasis (DMIs and pathways) and different migration rates (m = 0.01

and 0.2) with selection strength s = 0.2. Depicted are results for the hybrid deme (deme 2) for the basic model (infinite source populations,

three demes, each with capacity Nc = 500), mean over 20 replicates. Top, admixture proportion; middle, intersource ancestry; bottom,

linkage disequilibrium (D′) between loci each 10 cM apart. Shades of color indicate generations since contact when samples were taken.

Triangles show genome position of selected loci. Dotted vertical lines indicate chromosome boundaries, and the genome is truncated

within chromosome V.

0.0

0.5

1.0

Adm

. pro

p.

DMIs, m=0.01, s=0.9A

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

I II III IV V

0.0

0.5

1.0

Chromosome

D'

0.0

0.5

1.0

Adm

. pro

p.

DMIs, m=0.2, s=0.9Bg=10g=20

g=40g=60

g=80

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

g=10g=20

g=40g=60

g=80

I II III IV V

0.0

0.5

1.0

Chromosome

D'

g=10g=20

g=40g=60

g=80

0.0

0.5

1.0

Adm

. pro

p.

Pathways, m=0.01, s=0.9C

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

I II III IV V

0.0

0.5

1.0

Chromosome

D'

0.0

0.5

1.0

Adm

. pro

p.

Pathways, m=0.2, s=0.9D

0.0

0.5

1.0

Inte

r−sourc

e a

nc.

I II III IV V

0.0

0.5

1.0

Chromosome

D'

Figure 4. As in Figure 3, but selection strength s = 0.9.

In strong contrast, we did not observe this high dependency on

selection strength and migration rate for pathways (Fig. 7, red

symbols). Low migration rates intensified genetic drift for both

architectures, for example, when one of the variants in pathways

was lost from a deme (Fig. 4, middle row of C; Fig. S3C). The

spatial context of hybridization, particularly the position of the

sampled deme (e.g., middle or peripheral position) had a strong

effect on the observable outcomes of hybridization for that deme

(Figs. 5, 6, S3, S4, and S28–S31). The temporal context of hy-

bridization (i.e., time since contact) substantially affected admix-

ture and gene flow, particularly within the first 20–40 genera-

tions (Figs. 2–6). Our findings thus illustrate that samples taken

from different replicate hybrid zones can potentially show very

different outcomes of hybridization even if the underlying genetic

architecture of epistasis is identical. This context of hybridiza-

tion also affected the genomic consequences of selection that we

address below.

HETEROGENEOUS GENOMIC OUTCOMES OF

SELECTION

Summary statistics at and near selected loci were often more ex-

treme than statistics for the remainder of the genome. The extent

of this heterogeneity in locus-specific statistics was in some cases

affected by the specific genetic architecture of hybrid incompati-

bilities (Figs. 2–4). For example, FST was highly elevated across

a large part of the selected chromosome with pathways, but was

1 9 9 4 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Fre

quency

DMIs, m=0.01, s=0.9

mean q+/− SD for mean qspecies 1 DMI intactspecies 2 DMI intacttotal intact

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Fre

quency

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Fre

quency

Generation

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Dem

e 1

DMIs, m=0.2, s=0.9

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Dem

e 2

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Dem

e 3

Generation

Figure 5. Disruption of DMIs over time (x-axis) and space (rows) for different migration rates (m = 0.01 and 0.2) and selection strength

s = 0.9. Shown is the frequency of intact DMI loci with ancestry in species 1 (blue), species 2 (red), and the total frequency of intact

complexes (white) in the hybrid deme (middle row; deme 2), and the peripheral demes (top and bottom row; deme 1 and deme 3).

Boxplots summarize results for 20 replicates of the basic model. Thick and thin gray lines show mean deme admixture proportion q and

± SD of mean q over 20 replicates.

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Fre

quency

Pathways, m=0.01, s=0.9

mean q+/− SD for mean qspecies 1 pathway intactspecies 2 pathway intacttotal intact

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Fre

quency

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Fre

quency

Generation

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Dem

e 1

Pathways, m=0.2, s=0.9

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Dem

e 2

0.0

0.5

1.0

10 20 30 40 50 60 70 80 90 100

Dem

e 3

Generation

Figure 6. Disruption of pathways over time (x-axis) and space (rows). Shown is the frequency of fully intact pathways with ancestry in

species 1 (blue), species 2 (red), and the total frequency of fully intact pathways (white). Otherwise as in Figure 5.

less extremely elevated and this only closely linked to selected

sites with DMIs (Fig. 2). In contrast, admixture proportions did

not reveal any extreme statistics at or near selected loci for path-

ways when averaging replicates, but showed a very conspicuous

outcome for DMIs (Figs. 3 and 4, top row). These extreme ad-

mixture proportions only emerged after DMIs broke down due to

the rapid increase of compatible ancestral alleles. Averaging over

replicates erased some consequences of admixture that are evident

in individual simulations (i.e., random fixation of different path-

way variants, Fig. 4C, top row, and Fig. S3C), but in most instances

replicates were essential for detecting any genomic consequence

of selection (particularly when drift obscured outcomes; Fig. 2,

bottom row; Figs. S3 and S4). Low migration rates often, but not

always, increased genomic heterogeneity, and several generations

since contact typically amplified average statistical parameters for

selected loci across replicates.

EVOLUTION AUGUST 2015 1 9 9 5

D. LINDTKE AND C. A. BUERKLE

Figure 7. Reduction of genome FST for DMIs (orange), pathways (red), and purely demographic processes (black) dependent on migration

rate (m, x-axis) for different generations since admixture (g, columns) and selection strengths (s, rows). Circles show mean over 20

replicates, vertical lines indicate ± SD. Simulations were run using the basic model.

MODEL MODIFICATIONS

We investigated how the above results were affected by several

of the specifics of our basic model. In particular, we studied

more complex genetic architectures of epistasis, which could have

evolved after long allopatric divergence. We further investigated

the effects of recombination distance between interacting loci,

and of population demography and spatial arrangement of demes.

Complexity of epistasisWe constructed complex epistatic interactions for DMIs (involv-

ing two complexes, each with five interacting linked loci), and

pathways (nine complexes, each with three linked loci and one

unlinked locus; Supporting Information). Selection of strength

s = 0.2 or 0.9 acted on each pairwise epistatic interaction and

was combined multiplicatively for all interaction pairs, resulting

1 9 9 6 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

0 20 40 60 80 100

0.0

00.2

50.5

00.7

51.0

0

FS

T

Generation

Complex DMIs, m=0.01A

0.0

0.5

1.0

FS

T

s=0.2

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

0 20 40 60 80 100

0.0

00.2

50.5

00.7

51.0

0

FS

TGeneration

Complex DMIs, m=0.2B

mean+/− SD

s=0.0s=0.2s=0.9

0.0

0.5

1.0

FS

T

s=0.2

g=10g=20

g=40g=60

g=80

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

0 20 40 60 80 100

0.0

00.2

50.5

00.7

51.0

0

FS

T

Generation

Complex pathways, m=0.01C

0.0

0.5

1.0

FS

T

s=0.2

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

Ts=0.9, single replicate

0 20 40 60 80 100

0.0

00.2

50.5

00.7

51.0

0

FS

T

Generation

Complex pathways, m=0.2D

0.0

0.5

1.0

FS

T

s=0.2

0.0

0.5

1.0

FS

T

s=0.9

I II III IV V

0.0

0.5

1.0

Chromosome

FS

T

s=0.9, single replicate

Figure 8. As in Figure 2, but for complex genetic architectures of epistasis.

in very strong selection against F1s with DMIs and potentially

very strong selection against recombinants with pathways. With

these settings, species barriers became absolute for both DMIs

and pathways even with high migration rates, and remained stable

through time (Fig. 8). Nevertheless, some genetic introgression

still occurred for s = 0.2 (Fig. 8, second row; Fig. S5), but not

with s = 0.9 (Fig. 8, third row; Fig. S6). We describe additional

modifications of the genetic architectures of epistasis including

various numbers of interacting loci with different recombination

distances, and selection against ancestral variants or recessive

incompatibilities, in the Supporting Information.

Recombination distance between interacting lociModifying linkage between epistatic loci had differing effects

for DMIs and pathways (Supporting Information; Figs. S11 and

S12). Tightly linked loci (2 cM) delayed barrier breakdown for

DMIs (Fig. S11A), but did not reduce gene flow for pathways

(Fig. S11C). Correspondingly, unlinked loci decreased barrier

strength for DMIs (Fig. S11B; both loci unlinked), but increased

barrier strength for pathways (Fig. S11D; second interaction

unlinked). These results should be expected because reduced re-

combination distance between DMIs will delay their breakdown

(with complete linkage being equivalent to single-locus under-

dominance), whereas tight linkage within pathways will make

them effectively behave like a single locus if their recombination

is sufficiently rare. We note that the effects of linkage can differ

for more complex architectures of DMIs, which is addressed in

the Supporting Information.

Population demography and spatial settingsIn our basic model, we simulated the hybrid zone as a metapop-

ulation with three demes connected by bidirectional migration,

but with unidirectional migration from infinite-sized unadmixed

species sources, corresponding to secondary contact at range mar-

gins. We modeled sympatric contact and set the carrying capacity

of each deme to Nc = 500. In additional simulations, we modified

these three assumptions and simulated finite species source popu-

lations that could receive admixed immigrants, parapatric contact,

or carrying capacities Nc = {50, 5000} (Supporting Information).

Briefly, finite source populations affected the results significantly

after several generations since contact for high migration rates

(Fig. S7). Here, genome-wide FST decreased close to zero for both

models of epistasis, as no new unadmixed individuals entered

the metapopulation. DMIs inevitably broke down, and FST at

selected sites remained high only for pathways. Parapatric contact

increased the efficacy of DMIs as species barriers, particularly

for low migration rates, but only had a minor effect on pathways

(Fig. S8). High carrying capacities of Nc = 5000 resulted in less

EVOLUTION AUGUST 2015 1 9 9 7

D. LINDTKE AND C. A. BUERKLE

effective species barriers for DMIs (Fig. S9), whereas pathways

remained largely unaffected (Fig. S10). In summary, species

barriers and genomic patterns of admixture for pathways showed

little dependency on model specifics. The effects for DMIs were

more substantial, congruent with their breakdown depending on

recombination opportunity, which increased with finite source

populations, sympatric contact, and large hybrid zones. We

address these dynamics and other model modifications (e.g., the

effects resulting from ecologically based divergent selection on

epistatic loci) in more detail in the Supporting Information.

DiscussionVarious mechanisms for the evolution of hybrid incompatibil-

ities have been suggested by theoretical studies, but little is

known about their efficacy in maintaining species barriers in sec-

ondary contact and how empirical observations might be infor-

mative about different processes that shape genomic outcomes

of hybridization. DMIs are sometimes treated as synonymous

with epistatic hybrid incompatibilities, despite fundamental dif-

ferences between the classic model of DMIs and other forms of

epistatic interactions, including genetic pathways. Using simula-

tions to study classic DMIs and genetic pathways and their effi-

cacy as species barriers, we found that both models were unable

to prevent extensive genomic introgression in secondary contact

zones unless particular conditions were met. However, the mod-

els differed strongly in their consequences for species barriers and

patterns of admixture. Although DMIs cause low F1 hybrid fitness

and thus could prevent whole genomes from introgression, even

rare reproduction from F1 hybrids and fit recombinant progeny

resulted in barrier breakdown and subsequent unrestricted gene

flow between species (consistent with previous work; Barton

and Bengtsson 1986; Gavrilets 1997; Gompert et al. 2012). In

contrast, with genetic pathways, F1 hybrids were fully fit, and

thus gene flow occurred immediately across the genome except

at sometimes large chromosomal blocks linked to epistatic loci,

where recombinant genotypes were selected against. Integrity of

species-specific interactions could thus be maintained through

time. Consequently, the two models of epistasis differ strongly in

their genomic outcomes, temporal dynamics, and their efficacy as

species barriers depending on the extent of migration in secondary

contact. Our results indicate that heterogeneous patterns of intro-

gression and substantial gene flow in empirical hybrid zones are

unlikely to result from intact DMIs, but are consistent with the

outcomes of intragenomic epistasis in genetic pathways.

CLASSIC DMIS AND THE MAINTENANCE OF SPECIES

BARRIERS IN SECONDARY CONTACT ZONES

Our results show that barriers to gene flow are unlikely to be

maintained by classic DMIs unless certain conditions are met.

Specifically, DMIs only constituted effective barriers if recom-

bination between interacting loci was prevented. This could be

achieved by very strong and invariant selection against F1 hybrids

(s ≈ 1 or high complexity of epistatic interactions), very low mi-

gration rates between species so that the formation of F1 hybrids

was unlikely, or a combination of these factors (Fig. 2A, B; Figs.

7, 8A, B, and S8A). In these cases, parental allele combinations

at DMIs remained associated and resulted in very strong species

barriers as no F1 hybrids reproduced and no fit interspecific re-

combinants could be formed, protecting the whole genome from

introgression (panels A and B in Figs. 8, S6, S13, and S14). The

efficacy of complex DMIs can be attributed to our model specifics

where each pairwise epistatic interaction contributed multiplica-

tively to fitness. The probability of survival and reproduction of

F1 hybrids was thus near zero and even with rare recombination

events, epistatic interactions among additional locus pairs reduced

fitness of recombinants severely. Multiple pairwise DMIs versus

complex multilocus interactions had very similar effects on the

species barrier (Figs. S13 and S14; see Supporting Information for

further discussion). Our results thus confirm that complex hybrid

incompatibilities can constitute very strong species barriers (Orr

1995; Gavrilets 2003), and can be maintained even with “neu-

tral” DMIs (i.e., without selection against ancestral variants). The

latter finding differs from previous studies that showed instabil-

ity of nearly neutral two-locus DMIs in two-deme setups (Nosil

and Flaxman 2011; Bank et al. 2012), suggesting that our model

specifics with multiple demes and complex genetic architectures

under very strong selection were critical for barrier maintenance.

Importantly, intact parental allele combinations at DMIs that pro-

hibit hybrid survival provide genome-wide barriers to gene flow.

Our finding that DMIs require very particular conditions to

constitute persistent species barriers is congruent with analytical

theory and previous simulation studies (Gavrilets 1997; Bank

et al. 2012). The classic two-locus model of DMIs might thus

be viewed as a simplified model of how complete speciation in

allopatry could arise (see Porter and Johnson 2002). However, this

model for the origin of intergenomic incompatibilities is limited in

explaining the maintenance of species barriers that are incomplete

and permeable to gene flow.

Consistent with our results, few empirical studies have pro-

vided direct evidence for the significance of DMIs as species

barriers (Brideau et al. 2006; Sweigart et al. 2006), although

the suggested support has also been questioned by some authors

and remains controversial (Rieseberg and Willis 2007; Presgraves

2010; Nei and Nozawa 2011). Experiments were rarely run for

many generations and might thus have missed delayed barrier

breakdown, whereas DMIs that fully preclude hybrid survival,

or those that are located in nonrecombining chromosome inver-

sions, will be particularly difficult to detect. By contrast, DMI-like

epistatic polymorphisms exist within species (Corbett-Detig et al.

1 9 9 8 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

2013; Chae et al. 2014), although their importance for specia-

tion remains questionable because they are not associated with

species boundaries (Rieseberg and Willis 2007). Such intraspe-

cific incompatibilities can potentially be maintained as a stable

polymorphism under pleiotropic selection, for example, when de-

rived alleles cause a considerable increase in fitness (see Nosil

and Flaxman 2011; Bank et al. 2012). Indeed, we also found

that strong epistatic selection combined with strong selection

against ancestral variants resulted in efficient species barriers even

with high migration rates (Fig. S20), which should be expected

as fitness peaks of pure species’ epistatic genotypes became

separated. Ecologically based divergent selection can facilitate

the evolution and maintenance of DMIs because differential fix-

ation of derived variants and selection against ancestral alleles is

more likely (Gavrilets 2003; Schluter 2009; Bank et al. 2012; Ab-

bott et al. 2013), and weak DMIs resulting in reduced F1 fitness

might amplify divergent selection or enhance coupling (Abbott

et al. 2013). However, incompatibilities that critically rely on

ecologically based divergent selection will not on their own act

as effective species barriers when ecological conditions change.

GENETIC PATHWAYS AND THE MAINTENANCE OF

SPECIES BARRIERS IN SECONDARY CONTACT ZONES

We have modeled intragenomic interactions as an alternative ar-

chitecture of epistatic hybrid incompatibilities. Pathways resulted

in poor genome-wide barriers to gene flow, but could effectively

prevent introgression for some parts of the genome, whereas ad-

mixture was largely unrestricted and rapid across the remainder

of the genome (Fig. 2C, D; Fig. 6). Our results show that these

dynamics were mostly independent of migration rate and other

population demographic or spatial settings, and remained stable

through time (Figs. 7, S7, S8, S10, and S27). This insensitivity of

simulation results to particular settings and their primarily linear

response to selection strength (Fig. 2C, D; Fig. 7) makes pathway

models more likely to persist long enough, even when external

conditions change, to allow stronger isolation to arise through ad-

ditional mutations and further evolution. These results differ from

those for DMI models that were highly susceptible to parame-

ter settings and thus DMIs might persist only temporarily. If an

initial barrier is eroded faster than additional evolution enhances

isolation, several pairwise or complex DMIs that can build effec-

tive species barriers are less likely to arise. Thus, when intense

secondary contact and hybridization between diverging taxa are

common, differential genetic pathways have greater potential to

lead to speciation. We further discuss this topic below.

The potential importance of intragenomic epistatic interac-

tions for speciation through genetic pathways or intrinsic coad-

aptation has been emphasized by many previous studies (Johnson

and Porter 2000, 2007; Porter and Johnson 2002; Edmands and

Timmerman 2003; Landry et al. 2007; Ortiz-Barrientos et al.

2007; Johnson 2010; Presgraves 2010; Nei and Nozawa 2011;

Schumer et al. 2015). Empirical investigations of gene expres-

sion support that gene regulation is important for species integrity

and can be distorted in hybrids (Landry et al. 2005; Hegarty

et al. 2009; McManus et al. 2010; Renaut and Bernatchez 2011).

Both cis- and trans-regulatory changes that can coevolve during

species divergence can contribute to misexpression in hybrids

when regulatory interactions are impaired (Landry et al. 2005;

McManus et al. 2010). Further, evolutionary divergence between

gene regulatory pathways is feasible, as shown by previous the-

oretical studies (reviewed in the Introduction; e.g., Johnson and

Porter 2000; Porter and Johnson 2002; Palmer and Feldman 2009;

Lynch and Hagner 2015). Yet, the maintenance of differentially

evolved pathways in secondary contact zones and their effects on

genomic introgression has not been investigated in previous work.

Our study shows that pathways, once established, did not depend

on ecologically based divergent selection and can therefore be

maintained when environments change. They can thus provide

a persistent barrier to gene flow, although only for parts of the

genome.

In our model, we assigned full fitness to F1 hybrids. This is

unlikely for many systems where misregulation already affects

F1s (e.g., Landry et al. 2005; Hegarty et al. 2009; McManus et al.

2010; Renaut and Bernatchez 2011), which should additionally

increase barrier strength as fitness peaks of pure species will

become separated. In contrast, heterosis can increase F1 fitness

relative to their parents (e.g., Edmands 1999; Barton 2001;

Charlesworth and Willis 2009), and might thus decrease barrier

strength (Ingvarsson and Whitlock 2000).

DIFFERENT CONSEQUENCES OF INTERSPECIFIC

RECOMBINATION AND IMPLICATIONS FOR

SPECIATION

The strong differences in the outcomes of the two models of

epistatic hybrid incompatibilities can be explained by their con-

trasting response to interspecific recombination. Although recom-

bination can separate intergenomic incompatibilities in DMIs, re-

sulting in fit hybrids and barrier breakdown, recombination in

pathways can disrupt coadapted alleles, resulting in unfit hy-

brids and barrier maintenance. This shows that high migration

rates and gene flow in hybrid zones do not necessarily threaten

species integrity.

As noted previously, fitness variation according to the DMI

model can take several forms and has not always been defined as

we did in this study. For example, Dobzhansky (1937) and Muller

(1942) introduced the idea that the origin of hybrid incompatibil-

ities requires at least two interacting loci with alternative alleles

fixed in allopatric populations. When interpreted as any pair-

wise interactions, various forms of epistasis can be referred to as

DMI. Accordingly, some theoretical studies of haploid models or

EVOLUTION AUGUST 2015 1 9 9 9

D. LINDTKE AND C. A. BUERKLE

recessive incompatibilities and that were presented in the context

of DMIs (e.g., Agrawal et al. 2011; Bank et al. 2012) more closely

match our pathway model. More precisely, haploid models or re-

cessive incompatibilities can only assign low fitness to recombi-

nants and cannot address dynamics that will arise with interactions

in diploids (as in our DMI model), where allelic incompatibilities

are expressed prior to recombination in F1s. Thus, haploid mod-

els differ from our DMI model and are more comparable to our

pathway model, where only recombinant haplotypes can show in-

compatibilities. In accordance with our results, haploid models of

epistatic hybrid incompatibilities identified an increase in barrier

strength with recombination rate in a homogeneous environment,

but a decrease in strength in diploid models (Bank et al. 2012).

Our results indicate that the characteristics of the genetic

architecture of epistasis can be crucial for the maintenance of

species integrity in secondary contact. DMIs can constitute very

efficient barriers if migration rates are low and selection coeffi-

cients are very high, but with high migration rates or moderate

selection coefficients, pathways can be more effective for species

maintenance. Without sufficiently long periods of strict allopa-

try between species, DMIs that possess characteristics required

for their persistence when challenged in secondary contact might

evolve only rarely (e.g., given the waiting time for the neces-

sary mutations and required high selection coefficients; Gavrilets

2003). If secondary contact occurs before reproductive barriers are

completed, previous divergence can easily be erased. In contrast,

pathways might only require short periods of allopatry to evolve,

as the resulting barrier to gene flow does not need to be absolute

to maintain differentiation for parts of the genome. Additional

pathways might differentiate (perhaps during intermittent periods

of reduced migration) and several divergent pathways distributed

across the genome might accumulate through time. This process

can potentially build up and strengthen barriers to introgression

continuously, resulting in a gradual increase in genome differen-

tiation and reproductive isolation. This expectation accords with

empirical evidence that reproductive barriers and differentiation

accumulate through time (Coyne and Orr 1998; Feder et al. 2012;

Seehausen et al. 2014). In contrast, our results indicate that a

gradual increase in barrier strength is less likely to be achieved

with DMIs; instead, they will constitute a very strong barrier or

they will break down. Further theoretical and empirical work is

required to test the validity of these hypotheses.

RELATION TO EMPIRICAL STUDIES

Our results are consistent with several empirical findings on (1)

hybrid fitness, (2) variable outcomes of hybridization among repli-

cates, and (3) heterogeneous patterns of introgression in hybrid

zones. These findings are commonly attributed to processes in-

volving some sort of ecological adaptation, divergent selection,

or hybrid speciation. Our simulations suggest that alternative

explanations might exist that do not require exogenous mech-

anisms. First, the fitness of different hybrid classes can differ

among systems (Arnold and Hodges 1995; Burke and Arnold

2001). Loci involved in epistatic coadaptation or regulatory ge-

netic pathways that are distributed across the genome can ex-

plain hybrid zones with fit F1s and selection against recombinants

(Edmands 1999; Lindtke et al. 2014), together with reduced aver-

age fitness in the hybrid population. By contrast, unstable DMIs

might exist in systems with low F1 fitness but recovery in recom-

binant hybrids (Rieseberg et al. 1999b), although this combina-

tion of hybrid fitnesses can also arise by transgressive segregation

(Rieseberg et al. 1999a). Second, variability in the genetic compo-

sition among replicate hybrid zones is common (e.g., Nolte et al.

2009; Teeter et al. 2010; Mandeville et al. 2015). Our study high-

lights that such variation can result from the demographic, spatial,

and temporal context of hybridization, as well as purely stochastic

processes. Finally, pathways can protect parts of the genome from

introgression, whereas the genome-wide barrier to gene flow re-

mains poor (Fig. 2C, D), consistent with heterogeneous genomic

differentiation and introgression (Wu 2001; Payseur 2010; Teeter

et al. 2010; Abbott et al. 2013). If the underlying loci contribute to

expression of species-specific traits, genetic pathways can explain

the genomic outcomes of hybridization in systems that show ex-

tensive gene flow but nevertheless remain phenotypically distinct

(Hohenlohe et al. 2012; Nadeau et al. 2012; Gompert et al. 2013;

Poelstra et al. 2014). On the other hand, this heterogeneity cannot

easily be explained with classic DMIs that will either maintain

genome-wide differentiation or break down.

THE CONTEXT OF HYBRIDIZATION AND PRACTICAL

IMPLICATIONS FOR DETECTING GENOMIC

CONSEQUENCES OF SELECTION

Our results highlight that detecting genomic consequences of se-

lection in empirical hybrid zones can be difficult in many cases,

although possible and even straightforward in others. As the con-

text of hybridization will have pronounced effects on variation in

genome differentiation, knowledge of this context will be essential

when attempting to identify the genetic architecture of fitness from

empirical data. In particular, information on migration rate, pop-

ulation size, and time since contact, as well as the spatial position

of the sampling site within the hybrid zone and the type of contact

will be beneficial; stochasticity in the outcomes of hybridization

can be addressed by investigating replicates. In our simulations,

genomic outcomes for single runs were often strongly affected by

random processes (e.g., Fig. 2, bottom row; Figs. S3 and S4), and

we found that very different processes (based on the genetic archi-

tecture of fitness or population demography) could lead to similar

genomic outcomes, which are likely to be further obscured in

empirical data that are subjected to confounding factors (Buerkle

et al. 2011; Gompert et al. 2012; Bierne et al. 2013). For example,

2 0 0 0 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

locus-specific consequences of fitness variation can be indistin-

guishable between pathways and ecologically based, multilocus

selection, as the underlying genomic processes are very similar.

Nevertheless, careful analysis of data from replicate populations

and different spatial localities can potentially identify candidate

genetic regions involved in speciation and that can be subjected

to additional investigation.

LIMITATIONS OF THE STUDY

Our results are based on model simplifications and particular

assumptions about hybrid zone dynamics. In particular, we in-

vestigated postzygotic selection in secondary contact zones in a

homogeneous environment for a limited range of population de-

mographic settings and assumed a particular life cycle and no

mutations, and modeled purely intrinsic architectures of epistasis

as a “null model” for hybrid incompatibilities. These assumptions

are unlikely for real organisms; for example, truly neutral genetic

variation will be an exception (e.g., Ohta 1992; Hahn 2008),

but nonneutral variation will presumably affect introgression and

gene flow. We also studied only a small and extreme fraction of

possible genetic architectures of epistasis and did not investigate

effects of structural genome organization. For example, chromo-

some inversions are likely to play a role in speciation because

they suppress recombination (e.g., Rieseberg 2001; Kirkpatrick

and Barton 2006), which can result in heterogeneous introgres-

sion across the genome (Butlin 2005) or strong underdominance

when interspecific incompatibilities accumulate within inversions

(Rieseberg 2001; Navarro and Barton 2003).

Our study is also limited by being primarily descriptive as

we did not quantify the extent of species differentiation more for-

mally to compare results among different genetic architectures

of epistasis and population demographic settings. Previously uti-

lized statistics to quantify the barrier to gene flow (e.g., Barton

and Bengtsson 1986; Gavrilets 1997; Vuilleumier et al. 2010) will

not be sensible to measure barrier strength in the context of our

simulation setup, where we explicitly allowed fit hybrids and gene

flow, and considered species barriers that can be heterogeneous

across the genome, consistent with empirical observations (e.g.,

Wu 2001). The difficulty in directly comparing among our models

was further amplified by their particular genetic architectures and

contrasting responses to parameter combinations. Future work

will require modified approaches to quantify barrier strength that

better correspond to the parameters of relevance for species iso-

lation in nature.

CONCLUSIONS

Population demography, the spatial context of admixture, organ-

ismal life histories, and additional factors affect the genomic

outcomes of hybridization. Accordingly, different genetic archi-

tectures of fitness variation might be more effective as species

barriers than others depending on the context of secondary con-

tact and features of the organisms. We have shown that intraspe-

cific epistatic interactions that arise from genetic pathways can

maintain species-specific differentiation in homogeneous envi-

ronments with high migration rates between species. Reproduc-

tive isolation might build up gradually when genetic pathways

evolve during periods of reduced migration, whereas interspe-

cific gene flow will remain possible during phases of secondary

contact. This highlights the potential contribution of intragenomic

interactions to speciation with gene flow and suggests the value

of a broader set of epistatic models in speciation research. Fu-

ture progress may come from additional modeling studies that

continue to test verbal theory on the genetic architecture of re-

productive isolation, and from comprehensive experiments that

explicitly address the molecular basis of hybrid incompatibilities

in simple empirical systems.

ACKNOWLEDGMENTSWe thank C. Bank for insightful discussion, and P. Nosil, Associate Ed-itor R. Azevedo, and two reviewers for helpful comments on an ear-lier version of this manuscript. This work was supported by a mobilityfellowship of the Swiss National Science Foundation to DL (grant no.PBFRP3 145869) and by a U.S. National Science Foundation grant toCAB (DEB–1050149). The authors declare no conflict of interest.

DATA ARCHIVINGSimulation C code together with a brief description of the softwareis available from the second author’s website: http://www.uwyo.edu/buerkle/software/dfuse/, and from the Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.0506g (including scripts to recreate simulationresults).

LITERATURE CITEDAbbott, R., D. Albach, S. Ansell, J. W. Arntzen, S. J. E. Baird, N. Bierne,

J. Boughman, A. Brelsford, C. A. Buerkle, R. Buggs, et al. 2013. Hy-bridization and speciation. J. Evol. Biol. 26:229–246.

Agrawal, A. F., J. L. Feder, and P. Nosil. 2011. Ecological divergence andthe origins of intrinsic postmating isolation with gene flow. Int. J. Ecol.2011:1–15. doi:10.1155/2011/435357

Arnold, L. M., and S. A. Hodges. 1995. Are natural hybrids fit or unfit relativeto their parents? Trends Ecol. Evol. 10:67–71.

Bank, C., R. Buerger, and J. Hermisson. 2012. The limits to parapatric specia-tion: Dobzhansky–Muller incompatibilities in a continent-island model.Genetics 191:845–U345.

Barton, N., and B. Bengtsson. 1986. The barrier to genetic exchange betweenhybridizing populations. Heredity 57:357–376.

Barton, N. H. 1983. Multilocus clines. Evolution 37:454–471.———. 2001. The role of hybridization in evolution. Mol. Ecol. 10:551–568.Barton, N. H., and M. A. R. De Cara. 2009. The evolution of strong reproduc-

tive isolation. Evolution 63:1171–1190.Bierne, N., P.-A. Gagnaire, and P. David. 2013. The geography of introgression

in a patchy environment and the thorn in the side of ecological speciation.Curr. Zool. 59:72–86.

Bolnick, D. I., and B. M. Fitzpatrick. 2007. Sympatric speciation: models andempirical evidence. Ann. Rev. Ecol. Evol. Syst. 38:459–487.

EVOLUTION AUGUST 2015 2 0 0 1

D. LINDTKE AND C. A. BUERKLE

Boyle, A. P., C. L. Araya, C. Brdlik, P. Cayting, C. Cheng, Y. Cheng, K.Gardner, L. W. Hillier, J. Janette, L. Jiang, et al. 2014. Comparativeanalysis of regulatory information and circuits across distant species.Nature 512:453–456.

Brideau, N. J., H. A. Flores, J. Wang, S. Maheshwari, X. Wang, and D. A.Barbash. 2006. Two Dobzhansky-Muller genes interact to cause hybridlethality in Drosophila. Science 314:1292–1295.

Bridle, J. R., and T. H. Vines. 2007. Limits to evolution at range mar-gins: when and why does adaptation fail? Trends Ecol. Evol. 22:140–147.

Buerkle, C. A., and L. H. Rieseberg. 2008. The rate of genome stabilizationin homoploid hybrid species. Evolution 62:266–275.

Buerkle, C. A., Z. Gompert, and T. L. Parchman. 2011. The n=1 constraint inpopulation genomics. Mol. Ecol. 20:1575–1581.

Burke, J. M., and M. L. Arnold. 2001. Genetics and the fitness of hybrids.Ann. Rev. Genet. 35:31–52.

Butlin, R. 2005. Recombination and speciation. Mol. Ecol. 14:2621–2635.Butlin, R., A. Debelle, C. Kerth, R. R. Snook, L. W. Beukeboom, R. F. C.

Cajas, W. Diao, M. E. Maan, S. Paolucci, F. J. Weissing, et al. 2012. Whatdo we need to know about speciation? Trends Ecol. Evol. 27:27–39.

Chae, E., K. Bomblies, S.-T. Kim, D. Karelina, M. Zaidem, S. Ossowski, C.Martin-Pizarro, R. A. E. Laitinen, B. A. Rowan, H. Tenenboim, et al.2014. Species-wide genetic incompatibility analysis identifies immunegenes as hot spots of deleterious epistasis. Cell 159:1341–1351.

Charlesworth, D., and J. H. Willis. 2009. The genetics of inbreeding depres-sion. Nat. Rev. Genet. 10:783–796.

Chevin, L.-M., G. Decorzent, and T. Lenormand. 2014. Niche dimensionalityand the genetics of ecological speciation. Evolution 68:1244–1256.

Corbett-Detig, R. B., J. Zhou, A. G. Clark, D. L. Hartl, and J. F. Ayroles.2013. Genetic incompatibilities are widespread within species. Nature504:135–137.

Coyne, J. A., and H. A. Orr. 1998. The evolutionary genetics of speciation.Philos. Trans. R. Soc. Lond. B Biol. Sci. 353:287–305.

———. 2004. Speciation. Sinauer Associates, Sunderland, MA.Dobzhansky, T. H. 1937. Genetics and the origin of species. Columbia Univ.

Press, New York.Edmands, S. 1999. Heterosis and outbreeding depression in interpopulation

crosses spanning a wide range of divergence. Evolution 53:1757–1768.Edmands, S., and C. Timmerman. 2003. Modeling factors affecting the sever-

ity of outbreeding depression. Conserv. Biol. 17:883–892.Endler, J. 1973. Gene flow and population differentiation. Science 179:243–

250.Feder, J. L., S. P. Egan, and P. Nosil. 2012. The genomics of speciation-with-

gene-flow. Trends Genet. 28:342–350.Fierst, J. L., and T. F. Hansen. 2010. Genetic architecture and postzygotic re-

productive isolation: evolution of Bateson-Dobzhansky-Muller incom-patibilities in a polygenic model. Evolution 64:675–693.

Flaxman, S. M., A. C. Wacholder, J. L. Feder, and P. Nosil. 2014. Theoreticalmodels of the influence of genomic architecture on the dynamics ofspeciation. Mol. Ecol. 23:4074–4088.

Gavrilets, S. 1997. Hybrid zones with Dobzhansky-type epistatic selection.Evolution 51:1027–1035.

———. 2003. Perspective: models of speciation—what have we learned in40 years? Evolution 57:2197–2215.

Gompert, Z., and C. A. Buerkle. 2011. Bayesian estimation of genomic clines.Mol. Ecol. 20:2111–2127.

Gompert, Z., T. L. Parchman, and C. A. Buerkle. 2012. Genomics of isolationin hybrids. Philos. Trans. R. Soc. B Biol. Sci. 367:439–450.

Gompert, Z., L. K. Lucas, C. C. Nice, and C. A. Buerkle. 2013. Genomedivergence and the genetic architecture of barriers to gene flow betweenLycaeides idas and L. melissa. Evolution 67:2498–2514.

Hahn, M. W. 2008. Toward a selection theory of molecular evolution. Evolu-tion 62:255–265.

Hegarty, M. J., G. L. Barker, A. C. Brennan, K. J. Edwards, R. J. Abbott,and S. J. Hiscock. 2009. Extreme changes to gene expression associatedwith homoploid hybrid speciation. Mol. Ecol. 18:877–889.

Hohenlohe, P. A., S. Bassham, M. Currey, and W. A. Cresko. 2012. Ex-tensive linkage disequilibrium and parallel adaptive divergence acrossthreespine stickleback genomes. Philos. Trans. R. Soc. B Biol. Sci.367:395–408.

Ingvarsson, P., and M. Whitlock. 2000. Heterosis increases the effective mi-gration rate. Proc. R. Soc. B Biol. Sci. 267:1321–1326.

Johnson, N. A. 2010. Hybrid incompatibility genes: remnants of a genomicbattlefield? Trends Genet. 26:317–325.

Johnson, N. A., and A. H. Porter. 2000. Rapid speciation via parallel, direc-tional selection on regulatory genetic pathways. J. Theor. Biol. 205:527–542.

———. 2007. Evolution of branched regulatory genetic pathways: directionalselection on pleiotropic loci accelerates developmental system drift.Genetica 129:57–70.

Kirkpatrick, M., and N. Barton. 2006. Chromosome inversions, local adapta-tion and speciation. Genetics 173:419–434.

Landry, C. R., P. J. Wittkopp, C. H. Taubes, J. M. Ranz, A. G. Clark, andD. L. Hartl. 2005. Compensatory cis-trans evolution and the dysregula-tion of gene expression in interspecific hybrids of Drosophila. Genetics171:1813–1822.

Landry, C. R., D. L. Hartl, and J. M. Ranz. 2007. Genome clashes in hybrids:insights from gene expression. Heredity 99:483–493.

Lewontin, R. C. 1964. The interaction of selection and linkage. i. generalconsiderations; heterotic models. Genetics 49:49–67.

Lindtke, D., Z. Gompert, C. Lexer, and C. A. Buerkle. 2014. Unex-pected ancestry of populus seedlings from a hybrid zone implies alarge role for postzygotic selection in the maintenance of species.Mol. Ecol 23:4316–4330.

Livingstone, K., P. Olofsson, G. Cochran, A. Dagilis, K. MacPherson, and K.A. Seitz, Jr. 2012. A stochastic model for the development of Bateson-Dobzhansky-Muller incompatibilities that incorporates protein interac-tion networks. Math. Biosci. 238:49–53.

Lynch, M. 1991. The genetic interpretation of inbreeding depression andoutbreeding depression. Evolution 45:622–629.

Lynch, M., and K. Hagner. 2015. Evolutionary meandering of intermolecularinteractions along the drift barrier. Proc. Natl. Acad. Sci. 112:E30–E38.

Maheshwari, S., and D. A. Barbash. 2011. The genetics of hybrid incompati-bilities. Ann. Rev. Genet. 45:331–355.

Mandeville, E. G., T. L. Parchman, D. B. McDonald, and C. A. Buerkle.2015. Highly variable reproductive isolation among pairs of Catostomus

species. Mol. Ecol. 24:1856–1872.McManus, C. J., J. D. Coolon, M. O. Duff, J. Eipper-Mains, B. R. Graveley,

and P. J. Wittkopp. 2010. Regulatory divergence in Drosophila revealedby mRNA-seq. Genome Res. 20:816–825.

Muller, H. J. 1942. Isolating mechanisms, evolution, and temperature. Biol.Symp. 6:71–125.

Nadeau, N. J., A. Whibley, R. T. Jones, J. Davey, K. K. Dasmahapa-tra, S. W. Baxter, M. A. Quail, M. Joron, R. H. ffrench-Constant,M. Blaxter, J. Mallet, and C. D. Jiggns. 2012. Genomic islands ofdivergence in hybridizing Heliconius butterflies identified by large-scale targeted sequencing. Philos. Trans. R. Soc. B Biol. Sci. 367:343–353.

Navarro, A., and N. H. Barton. 2003. Accumulating postzygotic isolationgenes in parapatry: a new twist on chromosomal speciation. Evolution57:447–459.

2 0 0 2 EVOLUTION AUGUST 2015

THE GENETIC ARCHITECTURE OF HYBRID INCOMPATIBILITIES

Nei, M. 1977. F-statistics and analysis of gene diversity in subdivided popu-lations. Ann. Hum Genet. 41:225–233.

Nei, M., and M. Nozawa. 2011. Roles of mutation and selection in speciation:From Hugo de Vries to the modern genomic era. Genome Biol. Evol.3:812–829.

Nolte, A. W., Z. Gompert, and C. A. Buerkle. 2009. Variable patterns ofintrogression in two sculpin hybrid zones suggest that genomic isolationdiffers among populations. Mol. Ecol. 18:2615–2627.

Nosil, P., and S. M. Flaxman. 2011. Conditions for mutation-order speciation.Proc. R. Soc. B Biol. Sci. 278:399–407.

Ohta, T. 1992. The nearly neutral theory of molecular evolution. Ann. Rev.Ecol. Syst. 23:263–286.

Orr, H. 1995. The population-genetics of speciation—the evolution of hybridincompatibilities. Genetics 139:1805–1813.

Ortiz-Barrientos, D., B. A. Counterman, and M. A. F. Noor. 2007. Geneexpression divergence and the origin of hybrid dysfunctions. Genetica129:71–81.

Palmer, M. E., and M. W. Feldman. 2009. Dynamics of hybrid incompati-bility in gene networks in a constant environment. Evolution 63:418–431.

Payseur, B. A. 2010. Using differential introgression in hybrid zones to iden-tify genomic regions involved in speciation. Mol. Ecol. Resour. 10:806–820.

Poelstra, J. W., N. Vijay, C. M. Bossu, H. Lantz, B. Ryll, I. Mueller, V.Baglione, P. Unneberg, M. Wikelski, M. G. Grabherr, et al. 2014. Thegenomic landscape underlying phenotypic integrity in the face of geneflow in crows. Science 344:1410–1414.

Porter, A., and N. Johnson. 2002. Speciation despite gene flow when devel-opmental pathways evolve. Evolution 56:2103–2111.

Presgraves, D. C. 2010. The molecular evolutionary basis of species formation.Nat. Rev. Genet. 11:175–180.

Renaut, S., and L. Bernatchez. 2011. Transcriptome-wide signature of hybridbreakdown associated with intrinsic reproductive isolation in lake white-fish species pairs (Coregonus spp. Salmonidae). Heredity 106:1003–1011.

Rieseberg, L. 2001. Chromosomal rearrangements and speciation. TrendsEcol. Evol. 16:351–358.

Rieseberg, L. H., and J. H. Willis. 2007. Plant speciation. Science 317:910–914.

Rieseberg, L. H., M. A. Archer, and R. K. Wayne. 1999a. Transgressivesegregation, adaptation, and speciation. Heredity 83:363–372.

Rieseberg, L. H., J. Whitton, and K. Gardner. 1999b. Hybrid zones and thegenetic architecture of a barrier to gene flow between two sunflowerspecies. Genetics 152:713–727.

Romero, I. G., I. Ruvinsky, and Y. Gilad. 2012. Comparative studies of gene ex-pression and the evolution of gene regulation. Nat. Rev. Genet. 13:505–516.

Schluter, D. 2009. Evidence for ecological speciation and its alternative. Sci-ence 323:737–741.

Schumer, M., R. Cui, G. G. Rosenthal, and P. Andolfatto. 2015. Reproductiveisolation of hybrid populations driven by genetic incompatibilities. PLoSGenetics 11(3):e1005041. doi: 10.1371/journal.pgen.1005041.

Seehausen, O. 2004. Hybridization and adaptive radiation. Trends Ecol. Evol.19:198–207.

Seehausen, O., R. K. Butlin, I. Keller, C. E. Wagner, J. W. Boughman, P.A. Hohenlohe, C. L. Peichel, G.-P. Saetre, C. Bank, A. Braennstroem,et al. 2014. Genomics and the origin of species. Nat. Rev. Genet. 15:176–192.

Sweigart, A., L. Fishman, and J. Willis. 2006. A simple genetic incompatibilitycauses hybrid male sterility in Mimulus. Genetics 172:2465–2479.

Teeter, K. C., L. M. Thibodeau, Z. Gompert, C. A. Buerkle, M. W. Nachman,and P. K. Tucker. 2010. The variable genomic architecture of isolationbetween hybridizing species of house mouse. Evolution 64:472–485.

True, J., and E. Haag. 2001. Developmental system drift and flexibility inevolutionary trajectories. Evol. Dev. 3:109–119.

Tulchinsky, A. Y., N. A. Johnson, W. B. Watt, and A. H. Porter. 2014. Hy-brid incompatibility arises in a sequence-based bioenergetic model oftranscription factor binding. Genetics 198:1155–1166.

Turelli, M., and H. A. Orr. 2000. Dominance, epistasis and the genetics ofpostzygotic isolation. Genetics 154:1663–1679.

Vuilleumier, S., G. Goudet, and N. Perrin. 2010. Evolution in heterogeneouspopulations: from migration models to fixation probabilities. Theor.Popul. Biol. 78:250–258.

Wu, C. I. 2001. The genic view of the process of speciation. J. Evol. Biol.14:851–865.

Associate Editor: R. AzevedoHandling Editor: M. Servedio

EVOLUTION AUGUST 2015 2 0 0 3

D. LINDTKE AND C. A. BUERKLE

Supporting InformationAdditional Supporting Information may be found in the online version of this article at the publisher’s website:

Text S1: Supplemental Methods.Text S2: Supplemental Results and Discussion.Table S1: Genotype fitnesses for the DMI model, generalized form.Table S2: Genotype fitnesses for the pathway model, generalized form.Table S3: Example for genotype fitnesses for a three-locus DMI.Table S4: Example for genotype fitnesses for a three-locus pathway.Figure S1: Genetic architectures of epistatic hybrid incompatibilities investigated in the main article.Figure S2: Additional genetic architectures of epistatic hybrid incompatibilities investigated in the Supporting Information.Figure S3: Locus-specific patterns of admixture proportion for DMI and pathway models along demes for single replicates and mean over replicates.Figure S4: Locus-specific patterns of intersource ancestry for DMI and pathway models along demes for single replicates and mean over replicates.Figure S5: As in Figure 3, but for complex genetic architectures of epistasis with s = 0.2.Figure S6: As in Figure 4, but for complex genetic architectures of epistasis with s = 0.9.Figure S7: As in Figure 2, but with finite source populations on either side of the chain of demes.Figure S8: As in Figure 2, but for parapatric contact.Figure S9: As in Figure 2A, B, for DMI models with population size Nc = 50 and Nc = 5000.Figure S10: As in Figure 2C, D, for pathway models with population size Nc = 50 and Nc = 5000.Figure S11: As in Figure 2, with epistatic loci tightly linked, unlinked or partially linked.Figure S12: As in Figure 4, with epistatic loci tightly linked, unlinked or partially linked.Figure S13: As in Figure 2, but for complex genetic architectures of epistasis with four pairwise interactions on different chromosomes.Figure S14: As in Figure 2, but for complex genetic architectures of epistasis with multilocus interactions on a single chromosome.Figure S15: As in Figure 2B, for DMI models involving two epistatic interactions from various architectures and m = 0.2.Figure S16: As in Figure 3B, for DMI models involving two epistatic interactions from various architectures with s = 0.2 and m = 0.2.Figure S17: As in Figure 4B, for DMI models involving two epistatic interactions from various architectures with s = 0.9 and m = 0.2.Figure S18: As in Figure 2D, for pathway models involving two epistatic interactions from various architectures and m = 0.2.Figure S19: As in Figure 4D, for pathway models involving two epistatic interactions from various architectures with s = 0.9 and m = 0.2.Figure S20: As in Figure 2A, B, but for DMI models including selection against ancestral variants.Figure S21: As in Figure 3A, B, but for DMI models including selection against ancestral variants and with epistatic selection of strength 0.2.Figure S22: As in Figure 4A, B, but for DMI models including selection against ancestral variants and with epistatic selection of strength 0.9.Figure S23: As in Figure 2A, B, but for DMI models with codominant and recessive incompatible interactions.Figure S24: As in Figure 4A, B, but for DMI models with codominant and recessive incompatible interactions with s = 0.9.Figure S25: As in Figure 2C, D, for a two-locus pathway and a simple genetic network.Figure S26: As in Figure 2B, but for DMI models including ecologically based divergent selection and m = 0.2.Figure S27: As in Figure 2D, but for pathway models including ecologically based divergent selection and m = 0.2.Figure S28: Genome-wide admixture proportion for DMI and pathway models along demes and over 100 generations.Figure S29: Genome-wide intersource ancestry for DMI and pathway models along demes and over 100 generations.Figure S30: Fitness of individuals for DMI and pathway models along demes and over 100 generations.Figure S31: Numbers of junctions for DMI and pathway models along demes and over 100 generations.Figure S32: Two-dimensional plots of pairwise linkage disequilibrium for DMI and pathway models after 10 or 80 generations since contact in the hybriddeme.

2 0 0 4 EVOLUTION AUGUST 2015