Genotype-by-environment interaction and the Dobzhansky±Muller
model of postzygotic isolation
S. R. BORDENSTEIN* & M. D. DRAPEAU *Department of Biology, The University of Rochester, Rochester, NY 14627, USA
Department of Ecology and Evolutionary Biology, 321 Steinhaus Hall, University of California, Irvine, CA 92697±2525, USA
Keywords:
Abstract
hybrid inviability;
postmating reproductive isolation;
reaction norm;
sterility;
underdominance.
The Dobzhansky±Muller (D±M) model of reproductive isolation (RI) posits
that hybrid sterility and inviability result from negative epistatic interactions
between alleles at a minimum of two genes. This standard model makes
several implicit assumptions, including a lack of environmental effects and
genotype-by-environment interactions (GEI) involving hybrid sterility and
hybrid inviability loci. Here we relax this assumption of the standard D±M
model. By doing so, several patterns of the genetic architecture of RI change.
First, a novel single-locus model of postzygotic RI emerges. Several indirect
lines of evidence are discussed in support of the model, but we conclude that
this new single-locus model is currently no more supported than previous
ones. Second, when multilocus D±M models incorporating GEI are considered,
we ®nd that the number of potential negative epistatic interactions increases
dramatically over the number predicted by the standard D±M model, even
when only the most simple case of two-allele interactions are considered.
Third, these multilocus models suggest that some previous generalizations
about the evolutionary genetics of postzygotic RI may not necessarily hold.
Our ®ndings also suggest that the evolution of postzygotic RI may be more
likely when the expression of traits driving speciation is affected by the
environment, since there appears to be a greater spectrum of potential hybrid
incompatibilities under the D±M model incorporating GEI.
Introduction
Traditionally it has been argued that at least two
interacting genes underlie the traits intrinsically involved
in postzygotic reproductive isolation: hybrid sterility
and inviability (Bateson, 1909; Dobzhansky, 1937; Muller,
1942). Consider a one-locus, two-allele model in which
a substitution in a population of genotype aa yields a
derived population with genotype AA (Fig. 1A). A hybrid
formed between these two populations (Aa) is unlikely to
be sterile or inviable, because AA evolved from this
heterozygous genotype, which would have been an
evolutionary dead end had it been maladaptive. Even if
heterozygotes are only partially sterile, they would not
persist in the population, since they would enter at a
Correspondence: Seth R. Bordenstein, Department of Biology,
The University of Rochester, Rochester, NY 14627, USA.
e-mail: sbst@troi.cc.rochester.edu
490
frequency of 1/2N, where N is the population size, and
are therefore likely to be lost by genetic drift. In addition,
they would be disfavoured by natural selection if they
drifted to an appreciable frequency.
The problem then is to explain how hybrid sterility or
inviability evolves if the genes causing such hybrid
incompatibilities do not pass through a maladaptive
intermediate step. Bateson (1909), Dobzhansky (1937)
and Muller (1940) proposed an answer ± the addition of a
second interacting locus bypasses the maladaptive intermediate step of a one-locus model (Fig. 1B). Assume
aabb is the genotype of the ancestral lineage, which
consists of two allopatric populations. In the ®rst population, a substitution at the A locus yields genotype AAbb,
which is compatible with the ancestral lineage. In the
second population, a substitution at the B locus yields
another derived lineage with genotype aaBB, likewise
compatible with the ancestral line. The hybrid genotype
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
Evolution of hybrid incompatibility
491
Fig. 1 (A) The traditional single-gene model for the evolution of a hybrid incompatibility. C ˆ compatible hybrid genotype,
I ˆ incompatible hybrid genotype. (B) The `standard' Dobzhansky±Muller (D±M) two-locus model for the evolution of a hybrid
incompatibility. After initial divergence of the two populations, one incompatible interaction is possible (A-B).
formed from crosses between individuals from different
populations, AaBb, can now be un®t by the following
reasoning: The derived A and B alleles function normally
within their own, nonhybrid, genetic background, but
epistatically interact in a hybrid background to produce
either sterility or inviability. In this case, the term
`epistatic' denotes the between-locus nonadditive component of the genetic variance of a trait (Wade, 1992).
Genetic analyses of interspeci®c hybrid sterility and
inviability are generally consistent with this two-locus
model, commonly known as the Dobzhansky±Muller
(D-M) model, which we will refer to as the `standard'
D-M model (reviewed in Orr, 1997; Naviera & Maside,
1998; Wu & Hollocher, 1998; Johnson, 2000). A particularly clear example of sterility or inviability being
caused by complementary gene interactions is the
extensive work on the genetics of hybrid male sterility
between Drosophila simulans and D. mauritiana, in which
numerous alleles only have a large effect on hybrid
sterility when brought together in speci®c combinations
(reviewed by Wu & Hollocher, 1998). Such experiments
provide strong evidence that epistatically interacting loci
can cause reproductive isolation.
The standard D±M model makes a number of speci®c
predictions about the evolution of postzygotic RI (Muller,
1942; Orr, 1995). These include the following: (1) All
hybrid incompatibilities must initially be asymmetric,
since the derived alleles (A-B) can cause a hybrid
incompatibility, but the ancestral alleles (a-b) cannot.
(2) Derived alleles are involved in incompatible interactions in hybrids more often than ancestral alleles. The
reason is that of the three types of allelic interactions,
derived±derived, derived±ancestral and ancestral±
ancestral, only the latter type cannot be incompatible.
(3) Later substitutions are more likely to be involved in
hybrid incompatibilities than earlier ones, since the Kth
substitution can negatively interact with K ) 1 loci from
the other population. For example, while the second
substitution (e.g. B) can negatively interact with an allele
at one locus (e.g. A), the third substitution (e.g. C) can
interact with alleles at two loci (e.g. B and a), and so
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
forth. (4) The total number of possible negative epistatic
interactions leading to hybrid incompatibilities increases
at least as fast as the square of the number of substitutions separating two taxa, for the same reason as
prediction (3).
Because of the standard D±M model's great utility for
explaining the origin and evolution of RI, and its wide
acceptance, it is important to test the robustness of the
above predictions. Indeed, one may consider the standard D±M model to be the null hypothesis for genetic
studies of postzygotic isolation. The model makes a
number of implicit assumptions, among which are the
following: (1) alleles at interacting `speciation loci' are
®xed within populations, (2) alleles at a given speciation
locus are limited to two ± one ancestral allele and one
derived allele, (3) only two-locus interactions causing
sterility or inviability are allowed and (4) hybrid incompatibilities are not subject to speci®c environmental
in¯uences. While the ®rst three assumptions have been
theoretically investigated (Orr, 1995; Johnson & Porter,
2000), assumption (4) has not been considered to our
knowledge. Given the prevalence of environmental
in¯uences and genotype-by-environment interactions
(GEI) for a wide variety of characters in laboratory,
domesticated and natural populations (Lynch & Walsh,
1998, chapter 22, and references contained therein),
we suggest that studying the effects of these sources of
environmental variation in the D±M model is both
warranted and important.
Environmental variation in hybrid incompatibilities
can be broadly divided into two categories, which are
based upon whether hybrid genotypes and nonhybrid
genotypes demonstrate the same or a different degree of
environmental sensitivity for fertility and viability. First,
genotypes may show parallel responses to environmental change, meaning that individuals of different genotypes react equally in their degree of fertility, for
example, in a second environment. This source of
environmental variation is characterized as a parallel
reaction norm (Gordon, 1992; Roff, 1997). In contrast,
nonparallel reaction norms, when different genotypes
492
S. R. BORDENSTEIN AND M. D. DRAPEAU
respond to environmental change in different ways,
indicate the existence of GEI. Two examples are (a)
when certain hybrid genotypes react either more or less
strongly to an environmental change than others, and
(b) when the inferior hybrid genotype in one environment is superior to some or all other genotypes in a
second environment. There have been few studies of
GEI for hybrid traits (but see Wade et al., 1999), though
observations of natural animal and plant hybridizations
demonstrate that hybrid zone evolution is typically
in¯uenced by environmental components, and that GEI
can fashion the genetic structure of hybrid zones
(Arnold, 1997).
The aim of this paper is to explore how GEI can affect
the evolution of both single- and multilocus (Dobzhansky±
Muller) hybrid incompatibilities. We ®rst examine the
evolution of single-locus hybrid incompatibilities that are
conditional on the environment. We make several
predictions related to the single-locus model and survey
the literature to compile cases in support of these
predictions. Likewise, we extend the Dobzhansky±Muller
model to include GEI and analyse several issues related to
the genetics of postzygotic isolation, including the asymmetry of hybrid incompatibilities, the proportion of
derived vs. ancestral alleles conferring hybrid sterility or
lethality, and the involvement of late vs. early substitutions in hybrid incompatibilities.
Extension of a single-locus hybrid
incompatibility model to include GEI
The model
Our one-locus model of postzygotic isolation is depicted
in Fig. 2(A). It differs from the standard D±M model in
that it relaxes the assumption that the intermediate
hybrid state is maladaptive when a new allele arises in
the population at the locus under consideration. After a
lineage AA evolves by selection or drift from an ancestor
aa, an environmental change may induce a maladaptive
phenotypic alteration in heterozygotes. This alteration
does not occur in either homozygote. In this speci®c case,
Aa hybrids are fertile until the environmental change
triggers a hybrid incompatibility that renders Aa hybrids
fully or partially sterile. As a simple example, Aa hybrids
could be fertile at 19 °C, yet sterile at 26 °C.
Predictions of the model
This new single-locus model makes at least three predictions that can be tested with our current knowledge of
environmentally in¯uenced genetically based characters.
The ®rst prediction follows from the key assumption of
the model: expression of hybrid sterility or inviability,
regardless of genetic basis, should be subject to environmental in¯uence. While the conditionality of hybrid
incompatibilities has not been widely investigated, every
case study that we found con®rms this assumption of our
model. The second prediction is that levels of sterility and
inviability caused by a single locus should change across
systematic changes in the environment. A survey of
Mendelian mutants shows that many alleles which cause
sterility or inviability display reaction norms for these
phenotypes. The third prediction is that single-locus
heterozygous genotypes (regardless of the trait they
express) should also have reaction norms. Such cases
would imply that the phenotypes produced by withinlocus allelic interactions are sensitive to the environment. We found a remarkable amount of evidence in
support of single-locus heterozygote reaction norms.
Fig. 2 (A) A single-locus model for the evolution of a hybrid incompatibility following an environmental change. An incompatibility does
not arise between the derived populations until a change in the environment causes a change in the hybrid phenotype, e.g. sterility or
inviability. DE ˆ environmental change, C ˆ compatible hybrid genotype, I ˆ incompatible hybrid genotype. (B) A modi®ed two-locus
model of the evolution of hybrid incompatibilities. After initial divergence of the two populations, only one incompatible interaction is
possible (A-B). Following the change in environment, there are four potential incompatible interactions (A-B, A-a, B-b and a-b).
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
Evolution of hybrid incompatibility
Notable among these are heterozygotes that yield sterility
or inviability phenotypes. In sum, a survey of the
literature lent support to the three predictions of the
model presented here. However, we caution that support
of these predictions only reveals the plausibility of the
model.
Prediction 1: the environment in¯uences postzygotic
isolation between populations or species
We compiled cases in which the environmental sensitivity of hybrid incompatibilities was speci®cally tested. Our
criteria for selecting cases were the following: (1) the
organisms considered must be sexually reproducing
diploids or haplodiploids, (2) hybrid sterility or inviability
must be genetically based, and (3) hybrid sterility or
inviability was measured in more than one environment.
We de®ne the environment as any extrinsic factors
which may affect the ®tness of the organism. Most
studies relevant to these criteria and the predictions
tested below have investigated the effects of temperature
changes on hybrid incompatibilities. This bias is likely
due to the practical ease of manipulating temperature
in a laboratory setting, rather than an indication that
493
temperature is the dominant environmental in¯uence on
hybrid incompatibilities.
Table 1 shows the results of our literature survey. The
®ndings are striking: all 19 case studies found signi®cant
environmental effects on hybrid incompatibilities, particularly in F1 hybrids. Although the genetic basis of each
of these characters is probably not due to a single locus,
these ®ndings are persuasive evidence against the notion
that hybrid incompatibilities are unconditional. Indeed,
Darwin (1859) writes: `The fertility ¼ of hybrids is more
easily affected by unfavourable conditions than is the
fertility of pure species ¼ their [the hybrids'] degree of
fertility is often found to differ greatly in the several
individuals raised from seed out of the same capsule and
exposed to exactly the same conditions' (Chapter VIII, p.
256), though he of course found it mechanistically
confusing at the time. We note that these data in Table 1
pertain as well to a multilocus D±M model (see below).
Prediction 2: single-locus homozygotes causing sterility
or inviability have reaction norms
The key point of this second prediction is that we can
assess whether intrinsic postzygotic isolation having a
Table 1 Examples of environmentally in¯uenced postzygotic hybrid incompatibilities.
Taxa
4 Animal
5
Hybridization
Hybrid trait
Environmental
in¯uence
Representative
reference
Drosophila virilis/D. lummei
Drosophila melanogaster
Drosophila melanogaster/D. simulans,
D. mauritiana, D. sechellia
Drosophila virilis/D. lummei
Drosophila melanogaster/D. simulans
Daphnia galeata/D. hyalina
F2 female inviability
F1 female sterility
Temperature
Temperature
Mitrofanov & Sidorova (1981)
Ronsseray et al. (1984)
male inviability
eye anomaly
female inviability
clutch size and intrinsic
rate of increase
F1 female sterility
F1 male and female
inviability, morphological
anomalies, longevity
F1 female inviability
F1 and F2 male and female
survival
F1 and F2 male and female
inviability
F1 male sterility
F1 female inviability
F1 male inviability and
morphological anomalies
F1 male and female
growth rate
F1 female inviability
Temperature
Temperature
Temperature
Diet
Hutter & Ashburner (1987)
Heikkinen (1991)
Sawamura et al. (1993)
Weider (1993)
Temperature
Temperature
Torti et al. (1994)
Thomson et al. (1995)
Temperature
Diet
Stouthamer et al. (1996)
Grant & Grant (1993)
Host plant
Craig et al. (1997)
Temperature
Temperature
Temperature
Maside et al. (1998)
Coyne et al. (1998)
Wade et al. (1999)
Habitat
Hat®eld & Schluter (1999)
Temperature
Carracedo et al. (2000)
F2 spikelet sterility
F1 male sterility
Field hybrid seed
germination, seedling
survivorship, and ¯owering
percentage
Temperature
Photoperiod
Habitat
Li et al. (1997)
Murai & Tsunewaka (1993)
Wang et al. (1997)
Ceratitis capitata
Tribolium castaneum
6
Trichogramma deion
Geospiza fortis/G. fuliginosa/G. scandens
Eurosta solidagnis
Drosophila melanogaster/D. simulans
Drosophila melanogaster/D. simulans
Tribolium castaneum/T. freemani
Gasterosteus aculeatus complex
Drosophila melanogaster/D. simulans
Plant
Oryza sativa indica/O.s. japonica
Aegilops crassa/Triticum aestivum
Artemisia tridentata
F1
F1
F1
F1
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494
S. R. BORDENSTEIN AND M. D. DRAPEAU
simple genetic basis (i.e. a single locus) is conditional on
the environment. To test this prediction, we surveyed the
Drosophila melanogaster genes in Lindsley & Zimm (1992)
for loci that have at least one known allele that when
homozygous, or, for X-linked genes, male hemizygous,
are (1) associated with a sterile or lethal phenotype and
(2) display a reaction norm for that sterility or inviability
phenotype. We found 37 D. melanogaster genes which
show temperature-related reaction norms for sterility,
and 156 genes which show temperature- or diet-related
reaction norms for inviability (detailed gene information
is available from the corresponding author). Virtually all
of the examples are either spontaneous Mendelian
mutants or those generated by mutagenesis; such genotypes are most certainly not the `stuff' of speciation.
Nevertheless, the numerous examples in support of this
second prediction show that maladaptive phenotypes (of
which the genetic basis is known and simple) are
sensitive to environmental conditions. [We note that of
the sets of 37 sterility and 156 inviability loci, there are 8
loci that are common to both data sets].
Prediction 3: single-locus heterozygotes
have reaction norms
Our model posits that underdominances caused by
interallelic interactions can be in¯uenced by the environment. Due to a lack of ®ne-scale genetic analyses
measuring the conditions associated with this phenomenon, we cannot directly assess the validity of environmentally sensitive underdominances. However, there is
a comparable prediction that can be tested: single locus
heterozygotes (regardless of the trait) should show
reaction norms. The key point of this prediction is that
we can assess the degree of environmental in¯uences on
within-locus allelic interactions ± the types of interactions
that may be involved in hybrid sterility or inviability.
Our evidence for heterozygote reaction norms
comes from two organisms: Culex pipiens and
D. melanogaster.
Plasticity of dominance in C. pipiens.
Dominance of an insecticide-resistance gene (Ace) was
characterized under several different environmental conditions, such as concentration of insecticide and type of
larval food (Bourguet et al., 1996). Resistance was scored
through mortality assays, from which the ratio of heterozygous to homozygous mortality was used as a measure of
dominance of resistance to the insecticide. Dominance
relationships dramatically changed with systematic
changes in the environment. In particular, the resistance
phenotype tended to be recessive in more demanding
environments. The ®ndings support the notion that
variation in dominance levels, and thus intralocular
interactions, can be caused by environmental conditions.
Dominance, a phenotype by de®nition only manifested in
heterozygotes, is thus not an unconditional trait.
Heterozygote reaction norms in D. melanogaster.
We surveyed all of the D. melanogaster genes in Lindsley &
Zimm (1992) for loci which have at least one heterozygous reaction norm. Examples of D. melanogaster loci
which have environment-dependent phenotypes in the
heterozygous state are shown in Table 2. Table 2A
includes all such heterozygotes except those which cause
sterility or inviability, which are shown in Table 2B.
In sum, the heterozygote norms of reaction in Table 2
con®rm the third prediction of our model. While they are
not direct evidence for our model's relevance to natural
populations (only extremely ®ne-scale genetic experiments on hybrid incompatibilities in different environments could provide direct evidence for our model),
they, along with the evidence for Predictions 1 and 2,
reveal the plausibility of an environmentally sensitive
single-locus underdominance.
Extension of a multilocus hybrid
incompatibility model to include GEI
The model
Figure 2(B) depicts a two-locus model of hybrid incompatibility incorporating a single environmental change
after population divergence. Although only one incompatible interaction is possible following initial divergence
of the two populations, an environmental change that
affects the hybrid phenotype allows for four incompatible
allelic interactions (Fig. 2B), increasing the likelihood that
divergence will occur. Under the standard D±M model, the
one possible interaction which causes a hybrid incompatibility is that of A-B (Figs 1B and 2B). Under our model,
which incorporates GEI after the divergence of two
populations, the four possible incompatible interactions
are A-B, A-b, a-B and a-b. Thus, A-B may be the least ®t
genotype under the standard D±M model in environment
1, but when GEI is considered, a-b, for example, may be the
least ®t of the four genotypic classes in environment 2. The
key point is that the alleles not shared between the derived
populations all have the potential to negatively interact in
a particular environment.
The two-locus model outlined above can be extended to
multilocus incompatibility systems. Assuming two alleles
at each locus, as the number of loci involved increases, the
number of possible two±allele incompatible interactions
increases as the square of the number of loci. For example,
with three loci A, B and C, there are six alleles, A, a, B, b, C
and c, which can interact with each other in hybrid
individuals after an environmental change, in nine
combinations: A-a, A-B, A-c, b-a, b-B, b-c, C-a, C-B and C-c
(Fig. 3; This assumes that the two diverged populations
are of ®xed genotypes AAbbCC and aaBBcc. The number of
interactions remains the same but the precise interactors
change with different divergent population genotypes.
This assumes solely two-way allelic interactions). With
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Evolution of hybrid incompatibility
495
Table 2 Drosophila melanogaster genes at which a heterozygote genotype displays a norm of reaction for its phenotype. For some loci listed
here, multiple combinations of alleles meet these criteria. `Ancestral' alleles are `wild-type' alleles and `derived' alleles are `mutant' alleles.
Most loci are affected by the change in environment at the developing (preadult) stage, but a minority are affected at the adult stage. All data
are taken from Lindsley & Zimm (1992). Detailed information is available from the corresponding author. (A) Heteroallelic combinations
with nonsterile and nonlethal phenotypes. (B) Heteroallelic combinations with sterile or lethal phenotypes.
Environmental
in¯uence
Ancestral±derived (A-D) or
derived±derived (D-D) alleles
Temperature
Temperature
Temperature
Temperature
Temperature
Temperature
D-D
D-D
A-D
A-D
A-D
A-D
N: Ax, N,
spl, nd
Ocd
Pfd
Pin
Pl
Tcp
Jumping, ¯ying, courtship
Enzyme activity
Eye shape
Wing size and shape
Wing shape and eye morphology
Bristle size, eye morphology,
developmental time, viability
Female eye, bristle, and wing
morphology
Female leg and wing movement
Wing spread
Thoracic bristle size
Wing, bristle, and eye morphology
Paralysis
Temperature
A-D and D-D
Temperature
Temperature
Temperature
Temperature
Temperature
A-D
A-D
A-D
A-D
A-D
vg
Wing size and shape
Temperature
D-D
Gl
l(2)25 Ca
Lethality
Lethality
Temperature
Temperature
D-D
A-D
l(2)DTS
Lethality
Temperature
A-D
l(3)DTS
M(2)21AB
N: Ax, N, nd
Lethality
Female sterility
Lethality
Temperature
Temperature
Temperature
A-D
A-D
D-D
ogre
su(f)
Tcp
Lethality
Lethality
Lethality
Temperature
Temperature
Temperature
D-D
D-D
A-D
b-Tb85D
Sterility
Temperature
A-D
Name
Abbreviation
Affected phenotype(s)
(A) Non-sterile and nonlethal phenotypes
a-Actinin
Alcohol dehydrogenase
Barlike eye
Jammed
Jagged
Minute (3) 80
Actn
Adh
Ble
J
Jag
M(3)80
Notch: Abruptex, Notch,
split, notchoid
Out cold
Pufdi
Pin
Pearl
Third-chromosome
cold-sensitive paralytic
vestigial
(B) Sterile and lethal phenotypes
Glued
lethal (2) 25 Ca
lethal (2) Dominant
Temperature Sensitive
lethal (3) Dominant
Temperature Sensitive
Minute (2) 21 AB
Notch: Abruptex, Notch,
notchoid
optic ganglia-reduced
suppressor of forked
Third chromosome
cold-sensitive paralytic
b-Tubulin 85D
four diallele loci, there are 16 possible two-allele interactions, and so forth. In contrast, under the standard D±M
model, only six interactions are possible given the same
assumptions. In fact, the difference between the number
of potential interactors of the two models, when K
divergent loci are considered, is equal to the number of
possible interactions under the standard D±M model with
K + 1 divergent loci. Therefore with GEI, there can be a
dramatically greater number of incompatible genotypes.
The contrast between Orr's (1995) Fig. 1 and our Fig. 3
reveals a more complex web of potential negative interactions when loci conferring sterility and inviability
phenotypes are subject to GEI. In addition, the simplifying
assumption that only two-allele interactions are possible
does not necessarily hold, and so the square of the number
of loci is an underestimate of the total number of possible
interactions conferring hybrid incompatibility. There is in
fact empirical evidence for higher-level allelic interactions
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
from studies of both sterility (Cabot et al., 1994) and
inviability (Carvajal et al., 1996).
Evaluation of predictions of the standard
D±M model
Incorporating GEI into the standard D±M model also
changes several previous conclusions concerning the
population genetics of speciation (Orr, 1995), among
which are: (1) Following Muller (1942), all incompatibilities are initially asymmetric ± both A-B and a-b cannot be
incompatible because one of the two combinations was
present in either the common ancestor of the two
populations or in an intermediate evolutionary step
(Fig. 1B). (2) Evolutionarily derived alleles are involved
more often in hybrid incompatibilities than ancestral ones,
because no ancestral±ancestral interactions are possible.
(3) More incompatibilities result from later substitutions
496
S. R. BORDENSTEIN AND M. D. DRAPEAU
Fig. 3 The differential ®xation of alleles in two populations, and the
evolution of incompatible interactions between them, allowing for
GEI. Following Orr (1995; Fig. 1), time runs upward, lowercase
letters represent ancestral allelic states, and capital letters represent
newly arising and ®xed allele states. Arrows show potential
incompatibilities between two alleles. Horizontal arrows are drawn
in an arbitrary direction.
rather than earlier ones. When the environment in¯uences the expression of hybrid incompatibilities, these three
conclusions are not necessarily general patterns of the
evolution of RI. We discuss these predictions below.
Standard D±M Prediction 1: all incompatibilities
are initially asymmetric
Consider a two-locus, two-allele model, with ancestral
population aabb and subsequent diverged populations
AAbb and aaBB. A-B and a-b cannot both negatively
epistatically interact in hybrid individuals, because one of
these combinations necessarily existed in an ancestral or
transitional state of the populations. In this case, a-b is a
combination which existed in the ancestor. Under the
standard D±M model, this reasoning is correct; however,
we demonstrate below that this line of reasoning does
not hold when GEI is considered. Imagine the following
scenario: ancestral population aabb in Environment 1
(E1) diverges into populations AAbb and aaBB, both
located in E1 but allopatric to each other. Now, the two
diverged populations meet and form a hybrid zone in E2,
a geographical area separating their populational ranges.
The combination of either A-B or a-b could be incompatible, because a-b could be ®t in E1 but sterile or
inviable in E2. Hence, incompatibilities are not necessarily asymmetric as the standard D±M model predicts. In
fact, this example shows that the direction of the
asymmetry could even swing the other way ± a-b
interactions may arise before those of A-B.
The amount of asymmetry (summed across all loci) in
these two epistatic interactions, A-B and a-b, will depend
upon whether one arises more often than the other. For
simplicity, assume that the derived hybrid genotype,
AABB, has a certain probability (d) of being sterile or
inviable, given some arbitrary divergence time, and that
its ®tness in E1 and E2 is the same. For the same amount
of time, we would like to calculate the likelihood that the
ancestral hybrid genotype, aabb, is sterile or inviable in
E2. This value will be precisely related to the product of
the probability of an environmentally sensitive hybrid
incompatibility (s), and the probability of being present in
a new environment where that hybrid incompatibility
will be expressed (e). If se ˆ d, then there is no
asymmetry since one of these epistatic interactions is
just as likely to arise as the other. If se does not equal d,
then the asymmetry holds, but the predicted direction of
the asymmetry depends upon the value of the product.
For example, if se > d, then there will be more incompatibilities caused by a-b interactions than by A-B ones.
Furthermore, even if the predicted direction of the
asymmetry holds (d > se), the scale of the asymmetry
will likely be different than that predicted by the standard
D±M model, in which the product of s and e is implicitly
assumed to equal 0.
Standard D±M Prediction 2: derived alleles are involved
in negative epistatic interactions conferring hybrid
incompatibilities more often than ancestral ones
This prediction follows from the fact that only derived±
derived and derived±ancestral epistatic incompatibilities
can occur under the standard D±M model (Orr, 1995).
However, in a model that incorporates GEI for hybrid
incompatibilities, ancestral±ancestral interactions are also
possible.
Following Orr (1995), we calculate the probabilities of
various incompatibilities under the standard D±M model,
as well as under a D±M model incorporating GEI.
Consider two populations incurring independent substitutions. A fraction f of these substitutions occur in
population 1 and a fraction 1 ± f occur in population 2. In
the same way, a fraction 1 ± f of these loci in population
1 and a fraction f in population 2 are ancestral alleles.
Under the standard D±M model, the probability that a
derived allele in population 1 (D1) will be incompatible
with an ancestral allele in population 2 (A2) is equal to
f 2, the product of the proportion of derived alleles in
population 1 (f), and the proportion of ancestral alleles
in population 2 (f). Thus, the probabilities of hybrid
incompatibilities under the standard D±M model are
simply
P…D1 A2 † ˆ …f 2 †;
P…A1 D2 † ˆ …1 ÿ f †2 ;
P…D1 D2 † ˆ 2f …1 ÿ f †:
1†
When the model is extended to include ancestral±
ancestral incompatibilities, that result from GEI, a fourth
probability is added that depends upon the probability of
environmentally sensitive hybrid incompatibilities (s)
and the probability of occurring in an environment
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
Evolution of hybrid incompatibility
where that incompatibility will be expressed (e). In
addition, since the probability of these incompatibilities is
independent of the probability of standard D±M model
incompatibilities (which is assumed to equal 1 in the
above equations), the probability of a D±M hybrid
incompatibility (d) also must be added to the equations.
It then follows that under a D±M model with GEI,
P…D1 A2 † ˆ f 2 …d†;
P…A1 D2 † ˆ …1 ÿ f †2 …d†;
P…D1 D2 † ˆ 2f …1 ÿ f †…d†;
P…A1 A2 † ˆ 2f …1 ÿ f †…se†:
2†
With these probabilities, we can calculate the expected
frequency of derived and ancestral alleles involved in
hybrid incompatibilities:
P…D1 † ˆ df …2 ÿ f †=2
P…A1 † ˆ …1 ÿ f †‰d ÿ f …d ÿ 2se†Š=2
P…D2 † ˆ d…1 ÿ f †…1 ‡ f †=2
P…A2 † ˆ f ‰df ‡ 2se…1 ÿ f †Š=2:
3†
We then obtain the intuitive result that P(D1) +
P(A1) ˆ P(D2) + P(A2), since every incompatibility results
from an interaction between an allele from each species
(Orr, 1995). In other words, the total frequency of
population 1 alleles involved in hybrid incompatibilities
must equal that of population 2 alleles.
Using these frequencies, we can calculate the amount
of asymmetry in derived vs. ancestral alleles involved in
hybrid incompatibilities. The ratio P(D):P(A) for hybrid
incompatibilities is
d‰1 ‡ 2f …1 ÿ f †Š : d‰1 ÿ 2f …1 ÿ f †Š ‡ 4sef …1 ÿ f †:
4†
This ®nding means that the number of derived and
ancestral alleles involved in postzygotic isolation
depends upon the fraction of substitutions that occur
in each population, the probability of a standard D±M
hybrid incompatibility (d), and the probability of an
environmentally sensitive hybrid incompatibility (i.e. the
product of s and e). Under the standard D±M model,
when there are equal rates of allelic substitution in the
two populations (f ˆ 0.5) and no environmentally
sensitive incompatibilities (se ˆ 0), the asymmetry of
D:A is 3:1 (eqn 4; see also Orr, 1995). Put simply,
derived alleles are three times more likely to be
involved in incompatibilities than ancestral alleles.
However, whenever d ˆ se, f can take on any value
and the `asymmetry' of D:A is 1:1. There is no
asymmetry under these conditions. From this we
conclude that derived alleles are not necessarily
involved in more hybrid incompatibilities than ancestral
alleles. In fact, when se > d, the asymmetry swings the
other way. For example, when f ˆ 0.5, d ˆ 0.25 and
se ˆ 1, the P(D):P(A) ratio is 1:3, the reciprocal of the
asymmetry predicted by the standard D±M model. With
values of se < d, the asymmetry holds, but the amount
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
497
of asymmetry depends upon the precise value of se. For
example, when f ˆ se ˆ 0.5, and d ˆ 1, then P(D):P(A) is
3:2. Since se is unlikely to equal d, we conclude that the
scale and/or direction of the asymmetry will tend to
differ from that predicted by the standard D±M model,
in which the product of s and e is implicitly assumed to
equal 0.
Standard D±M Prediction 3: later allelic substitutions
are involved in negative epistatic interactions conferring
hybrid incompatibilities more often than earlier ones
Similar to Prediction 2 (above), Orr (1995) concluded
that later allelic substitutions (L) are involved in postzygotic RI more often than earlier substitutions (E). This
is because under the standard D±M model, the Kth
substitution in one diverging population can be incompatible with K ± 1 loci from the other population. Hence,
the greater the rank-order of a given substitution, the
more epistatic incompatibilities the substitution could
be involved in. In our model, however, the number of
incompatibilities that an allele could be involved in is
equal to K (Fig. 3). Therefore, later substitutions are not
necessarily involved in more incompatible interactions
than are earlier substitutions.
Here we have a conclusion similar to that for Prediction 2. If se ˆ d, then L and E substitutions have an equal
likelihood of being involved in hybrid incompatibilities
(Fig. 3). If se < d, then the asymmetry will hold, but the
amount of asymmetry of L and E alleles expressing a
hybrid incompatibility depends upon the value of se.
Notably, this does not change an additional, secondary,
conclusion ± the strength of RI between two populations
increases faster than linearly with time (Orr, 1995). In
fact, our model predicts that RI should increase over time
faster than the standard D±M model, and hence the
general conclusion concerning the rate of speciation
remains true.
Predictions of the multilocus D±M model
incorporating GEI
Our model of the evolution of postzygotic isolation
makes at least two predictions that can be tested with our
current knowledge of the genetic basis of hybrid sterility
and inviability.
Prediction 1: The environment in¯uences postzygotic
isolation between populations or species
This prediction is identical to Prediction 1 of our singlegene model. A literature survey of studies which tested
the conditionality of hybrid incompatibilities revealed 19
out of 19 studies which found a positive result. That is, all
19 studies found environmentally sensitive hybrid
incompatibility phenotypes (Table 1). We note that the
evidence presented in support of this particular prediction is more relevant to multilocus RI than single locus RI
(see above), because although the genetic architecture of
498
S. R. BORDENSTEIN AND M. D. DRAPEAU
RI in the systems is largely unknown (but see Sawamura
et al., 1993 and Carracedo et al., 2000, for example),
multilocus epistatic incompatibilities tend to be the rule
rather than the exception (Orr, 1997; Naviera & Maside,
1998; Wu & Hollocher, 1998). Hence, the studies in
Table 1 which detected environmental effects on hybrid
incompatibilities constitute strong evidence for the
notion that hybrid incompatibilities are sometimes, and
perhaps often, in¯uenced by the environment.
petitively inferior in either environment of the nonhybrids (AA or aa), have also been developed (Pimm, 1979;
Udovic, 1980). While ecological underdominances exist
(Rohwer & Manning, 1990; Grant & Grant, 1993;
Schluter, 1996; Hat®eld, 1997), resolving their genetic
basis is still in its infancy. Admittedly, direct support for
any single-locus model of the evolution of postzygotic
isolation is marginal at best (Portin, 1974; Li et al., 1997;
Axenovich et al., 1998).
Prediction 2: the ratio of D:A alleles involved in hybrid
incompatibilities will be smaller than that predicted
by the standard D±M model
Molecular mechanisms of single-locus
hybrid incompatibilities
The reason is that as shown above, a model incorporating
GEI allows for ancestral±ancestral interactions to contribute to hybrid sterility and/or inviability, thereby
increasing the number of ancestral alleles involved in
hybrid incompatibilities. Indeed, the fraction of ancestral
alleles involved in hybrid sterility or inviability may be
greater than that of derived alleles if the probability of an
environmentally sensitive incompatibility (se) is greater
than that of a standard D±M incompatibility (d). Unfortunately, to our knowledge there exists no direct empirical evidence to assess this prediction.
Very little is known about speci®c genes (and hence
allelic substitutions) which cause sterility or inviability
in hybrids between populations or species. Consequently,
we also have very little information about the ancestral
vs. derived states of alleles at such genes. The abundance
of genetic data that will emerge on postzygotic isolation
in the next decade will undoubtedly make this prediction
testable.
Discussion
Alternative single-locus models of RI
We explored how single- and multilocus models of
speciation can change when postzygotic isolating barriers
are conditional on the environment. We presented a
novel model for the evolution of single locus hybrid
incompatibilities which incorporates environmental in¯uences on `underdominances'. A `contracomplementation' model of single-locus incompatibilities was
proposed by Portin (1974) and Nei et al. (1983), who
each suggested that multiple substitutions at a single
locus could bypass the maladaptive intermediate step of
single gene speciation. Brie¯y, after divergence at locus A
between Populations 1 and 2 (e.g. Population 1 has a
substitution at A from allele A1 to A2, and Population 2
has a similar substitution, but from A1 to A3), these
`derived' alleles could then interact in hybrids to cause
postzygotic isolation. Portin supported his model with
data from crosses between several D. melanogaster strains
that carried different alleles of the sex-linked Abruptex
locus (see below). Single-locus models of ecological
underdominance, in which hybrids (e.g. Aa) are com-
How might within-locus allelic interactions occur on a
biochemical scale? One example of biochemical interactions at a single locus contributing to RI are those which
occur at the Abruptex (Ax) locus of D. melanogaster to
cause postzygotic RI between laboratory strains harbouring different Ax alleles (Portin & Ruohonen, 1972; Portin,
1974, 1975). Portin (1974, 1975) demonstrated that
while strains which are ®xed for alleles Ax 28, Ax 16172,
Ax 71d, Ax E2 and Ax 9B2 are fully viable, the transheterozygotes Ax 28/Ax 16172, Ax 28/Ax 71d, Ax 9B2/Ax E2,
Ax 9B2/Ax 16172 and Ax 9B2/Ax 71d are lethal (and genotype
Ax 28/Ax E2 is semilethal, i.e. some proportion <1 die).
Additional within-locus allelic interactions causing postzygotic isolation (lethality) are seen at the lesser-studied
D. melanogaster X-linked short wing (sw) locus, which has
four known trans-heterozygote lethal combinations.
Alleles sw 1, sw 2, sw 5, sw 6 and sw 7 are homozygous
viable below 31 °C, but combinations of sw 2, sw 5, sw 6
and sw 7 with sw 1 are unconditionally lethal within the
same temperature range.
What is occurring at these loci on a biochemical level?
Studies of the Ax locus provide some insight. Portin
& Ruohonen (1972) suggest that heterozygote lethality at
Ax is `due to an active process, probably some kind of
interaction between two different mutant gene products'
(p. 70). One could argue that lethality is due to lack of
function of the mutant protein products, but it is known
that the Ax alleles involved in the hybrid±lethal interactions are not lack-of-function, or `null', alleles (Portin,
1975; Flybase, 1999). Portin (1975) proposes three
nonmutually exclusive molecular mechanisms for negative complementation at Ax: (1) Because Ax acts at two
distinct times during development, if one mutation causes
a de®ciency at one time in development, and another
mutation similarly causes a de®ciency at the other, the
combined effect causes a lethal negative complementation. (2) If Ax is a tandem repeat coding for two subunits
of a molecule, then hybridization of two mutant proteins
might reduce that enzyme's activity below a critical
threshold, resulting in lethality. (3) If Ax has a regulatory
function, then a trans-heterozygote of hypo- and hypermorphic alleles (those with less-than and greater-than
wild-type phenotypes, respectively) could cause a canalization imbalance, again resulting in lethality. While the
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
Evolution of hybrid incompatibility
basis of negative complementation at Ax is not currently
known (P. Portin, personal communication), any of these
three mechanisms may be general explanations of withinlocus allelic interactions which result in sterility or
lethality. Kerr (1997) discusses additional mechanistic
hypotheses for interallelic interactions, speci®cally in
relation to single-locus sex determination, which is
common in certain insect groups, particularly the
Hymenoptera. Single-locus sex determination is a solid
demonstration of how novel phenotypes can be caused by
intralocular interactions. H. J. Muller independently
foresaw the plausibility of single-locus hybrid incompatibilities through this reasoning as well:
`It is true that a special type of allelic interaction does
sometimes occur where the combined action of two
different alleles is enabled to transcend these limits of
effect, as in the production of the ``femaleness'' reaction
by heterozygous sex alleles in Habrobracon [ ˆ Bracon]
(Whiting) ¼ Thus it is conceivable that lethality and
sterility also may on rare occasions result from heterozygosis in respect to alleles that by themselves would
have no such in¯uence.' (1942, p. 84)
GEI in nature may diminish the scarcity of such `rare'
allelic interactions.
Evolution of hybrid incompatibilities subject to GEI
How might our single- or multilocus model incorporating
GEI explain naturally occurring RI? One scenario is
when two divergent allopatric populations come into
contact and subsequently hybridize in a new environment. We will simplify the genetics of the following
scenario by only considering a single-locus, two-allele
model; however, it is important to note that the genetics
may be extended to any number of loci with similar
results. Consider the case in which AA and aa individuals
occur separately in a pair of allopatric populations, but
upon hybridization in a new environment (i.e. a hybrid
zone), Aa individuals may suffer from hybrid sterility or
inviability. In other words, the Aa heterozygote and the
AA and aa homozygotes are ®t in the environments of
the allopatric populations, but Aa individuals are un®t in
the hybrid zone. Alternatively, the reciprocal is possible:
Aa individuals are ®t only in the relatively narrow hybrid
zone, and are un®t outside of it (i.e. in the `parental'
habitats). Hence, hybrids may persist but not spread,
essentially maintaining the genetic boundaries of developing species. Indirect evidence for the latter scenario
exists in a hybrid zone between two plant species,
Ipomopsis aggregata and I. tenuituba, in Poverty Gulch,
Gunnison County, Colorado. Brie¯y, there are signi®cant
differences in survival between hybrid individuals from
reciprocal parental crosses in both species' habitats, but
this survival difference disappears in the hybrid zone
between the species (Campbell & Waser, 2001). In fact,
J. EVOL. BIOL. 14 (2001) 490±501 ã 2001 BLACKWELL SCIENCE LTD
499
both types of F1 hybrids have higher survival in the
hybrid zone than the nonhybrids of I. aggregata. Although the genetic basis of hybrid survival in this species
pair is unknown, this is a clear example of variation in
hybrid ®tness across naturally varying environments.
More relevantly for this population genetic model, for
hybrids derived from one of the parental cross directions,
hybrid ®tness is highest within the hybrid zone and
lower when in either of the parental habitats. As implied
above, hybrid zone size should be limited by the size of
the habitat which is favourable to the hybrids, and this
will help to reinforce isolation between the forming
species. Arnold (1997) has comprehensively reviewed
the literature on this topic and has amassed many
examples where hybrids and speci®c hybrid genotypes
show varying degrees of ®tness in and outside of natural
hybrid zones. He shows that the genetic architecture of
hybrid populations is not unconditional and can depend
upon the availability of environments for those hybrids.
Conclusions
We conclude by suggesting a few lines of research relevant
to testing aspects of our models. First, while ®eld studies of
hybrid incompatibilities encompass a broad range of
environments that may demonstrate environmental
in¯uences on hybrid traits, laboratory studies are needed
in most cases to classify GEI precisely. Hybrid genotypes
must be reproducible (e.g. through sibship analysis, hybrid
inbred lines, or marker-assisted introgression lines) and
tested in well-de®ned environments. Studies of GEI for
hybrid incompatibilities should be tractable in many
systems by characterizing nonparallel reaction norms for
hybrid sterility and inviability (e.g. Wade et al., 1999).
Second, researchers investigating species pairs with genetic tools can test speci®c hybrid genotypes for nonparallel
reaction norms to characterize which loci are involved in
GEI more precisely. Additionally, mapping of QTL for
hybrid incompatibilities in different environments may
reveal that the genetic architecture of hybrid incompatibility can vary across environments. To our knowledge, no
such QTL mapping studies have been performed. Finally,
once the resolution of genetic studies of RI moves from loci
to genes, we will be able to determine the derived vs.
ancestral state of alleles involved in hybrid incompatibilities, and therefore whether ancestral±ancestral incompatibilities arise during the evolution of RI.
It is clear that much work needs to be done concerning the population genetics of speciation. The relative
importance of GEI in the speciation process is not
currently known. The combination of increasingly realistic population genetic models of the evolution of
reproductive isolation and more detailed empirical genetic studies of incipient species pairs will greatly increase
our knowledge of the process of speciation.
500
S. R. BORDENSTEIN AND M. D. DRAPEAU
Acknowledgments
We thank S. Frank, C. Kennedy, N. Leung, T. Long,
A. Peek, P. Portin, D. Presgraves, S. Schrodi and
J. Werren for helpful discussions and suggestions. We
thank D. Campbell for sharing her unpublished data with
us. We thank N. Johnson and an anonymous referee
for helpful comments on an earlier version of this
manuscript.
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Received 30 September 2000; accepted 1 December 2000