Download Conditions for sympatric speciation

Evolutionary Ecology 1996, 10, 187-205
Conditions for sympatric speciation: a diploid model
incorporating habitat fidelity and non-habitat
assortative mating
P A U L A. J O H N S O N 1., F. C. H O P P E N S T E A D T 2, J A M E S J. S M I T H 3 and G U Y L.
BUSH 4
1NSF Center for Microbial Ecology, Michigan State University, East Lansing, MI 48824, USA
2Department of Mathematics, Department of Statistics and Probability and NSF Center for Microbial Ecology,
Michigan State University, East Lansing, MI 48824, USA
3Department of Zoology and NSF Center for Microbial Ecology, Michigan State University, East Lansing, MI 48824,
USA
4Department of Entomology, Department of Zoology and NSF Center for Microbial Ecology, Michigan Stale
University, East Lansing, M1 48824, USA
Summary
Three types of genes have been proposed to promote sympatric speciation: habitat preference genes,
assortative mating genes and habitat-based fitness genes. Previous computer models have analysed these
genes separately or in pairs. In this paper we describe a multilocus model in which genes of all three types
are considered simultaneously. Our computer simulations show that speciation occurs in complete sympatry
under a broad range of conditions. The process includes an initial diversification phase during which a slight
amount of divergence occurs, a quasi-equilibrium phase of stasis during which little or no detectable
divergence occurs and a completion phase during which divergence is dramatic and gene flow between
diverging habitat morphs is rapidly eliminated. Habitat preference genes and habitat-specific fitness genes
become associated when assortative mating occurs due to habitat preference, but interbreeding between
individuals adapted to different habitats occurs unless habitat preference is almost error free. However, 'nonhabitat assortative mating', when coupled with habitat preference can eliminate this interbreeding. Even when
several loci contribute to the probability of expression of non-habitat assortative mating and the contributions
of individual loci are small, gene flow between diverging portions of the population can terminate within less
than 1000 generations.
Keywords: speciation, habitat-sympatric divergence, divergent selection, habitat preference, assortative
mating, linkage disequilibrium, penetrance
Introduction
A number of biologists, including Mayr (1963), Futuyma and Mayer (1980), Paterson (1981) and
Futuyma (1986), pointed out limitations for sympatric divergence between co-adapting portions of
a population. These limitations support the idea that speciation under sympatric conditions may be
insignificant and rare events in nature. The claims of these biologists are supported by models (e.g.
Felsenstein, 1981) which demonstrate that a major obstacle to sympatric speciation is the
homogenizing effect of recombination (see Rice, 1987). By continually combining genes of two
portions of a population adapting to different habitats, recombination can oppose natural selection
in 'choosing' adaptive genes and gene combinations within each habitat.
* Present address: Swedish University of Agricultural Sciences, Department of Plant Breeding Research, Box 7003, S750 07 Uppsala, Sweden.
0269-7653
© 1996 Chapman & Hall
188
Johnson
A number of other biologists such as Bush (1975), White (1978), Kondrashov and Mina (1986),
Bush and Howard (1986), Rice (1987) and Tauber and Tauber (1989) presented arguments
suggesting that sympatric speciation in some animal groups may not be rare because in these
groups the homogenizing effect of recombination can be reduced or circumvented. Rosenzweig
(1978), Slatkin (1982), Rice (1984) and Diehl and Bush (1989), for example, developed models
that support these arguments.
Laboratory studies by Rice and Salt (1990) suggested that sympatric speciation may indeed have
a role in nature and observations appear to confirm this: sympatric sister species (or races) exist for
several organisms, such as parasitic insect species in the genus Megarhyssa (Heatwole and Davis,
1965), fruit flies in the genus Rhagoletis (Bush, 1969; Feder et al., 1989), fig wasps in the family
Agaonidae (Murray, 1990), human-commensal flour beetles of the genus Tribolium (Wade et al.,
1994) and the Enchenopa binotata complex of six treehopper species (Wood and Guttman, 1983).
Also, endemic speciation occurs in isolated areas such as the Galapagos Islands (Lack, 1947; Grant,
1986), the Seychelles in the Indian Ocean (R'Kha et al., 1991) and the Juan Fernandez Islands near
Chile (Crawford et al., 1992).
Kondrashov and Mina (1986) and Tauber and Tauber (1989) compared theoretical investigations
of sympaWic speciation with data collected from naturally occurring populations of insects, fish and
molluscs. They concluded that sympatric speciation may be an important component in
evolutionary diversification for certain taxa, especially those subject to disruptive selection. Bush
(1992) argued that non-allopatric speciation (i.e. without geographical isolation) may be common
among small animals such as insects, mites and nematodes. In these taxa, mating often occurs
within a preferred habitat. If an alternative habitat becomes available to a population, individuals
may select the new or original habitat based on genetically controlled habitat preference. Since
mating is restricted to different habitats (habitat-based mating), two habitat races can arise.
The objective of this paper is to determine, in theory, whether a diploid population having
alternative habitats can develop sufficient linkage disequilibrium to speciate sympatrically. To
approach this problem, we developed a model that incorporates the biological attributes likely to
promote sympatric speciation and then used computer simulations of the model to analyse
speciation under conditions of complete sympatry. Our model differs from previous models by
taking into account both habitat-based and non-habitat-based (e.g. ethological) factors contributing
to assortative mating.
Non-habitat-mating and habitat-mating sympatric divergence
Divergence between populations or portions of a population is sympatric when the probability of
mating between two individuals depends only on their genotypes (Kondrashov and Mina, 1986).
Sympatric divergence that leads to speciation involves two components (Maynard Smith, 1966).
First, diversification of portions of an ancestral population, followed by the evolution of
reproductive isolation between those portions. Barton and Charlesworth (1984) described the first
component as the splitting of an ancestral population into populations located at different equilibria
under selection.
Hutchinson (1968) explains how different types of regions within niche space affect speciation
processes. Integrating Hutchinson's (1968) ideas with the concepts of adaptive landscapes and
intraspecific competition, Rosenzweig (1978) described, with a biological model, how certain
regions of niche space can allow divergence under sympatric conditions and how divergence can
result in sympatric speciation. These regions of niche space contain 'islands' separated by
disruptive gaps.
Conditions for sympatric speciation
189
For a population, these islands represent adaptively discrete habitats that individuals can select.
If each individual in the population mates and places its progeny within its selected habitat, then
mating is 'habitat-based' and the divergence that develops will be called habitat-mating sympatric
divergence (HMSD). Sympatric divergence that might develop when mating is not habitat-based
will be called non-habitat-mating sympatric divergence (NMSD). Note that HMSD is consistent
with pure sympatry only if individuals of the population do not 'remember' the habitat in which
they were born (A.S. Kondrashov, personal communication). This requires absence of conditioning,
i.e. an individual's habitat choice is not altered by the habitat in which it was born.
Levene (1953) and Maynard Smith (1962, 1966) broadly outlined the dynamics for NMSD using
models with single loci both for fitness and for non-habitat assortative mating. Later, Gibbons
(1979) analysed an NMSD model in which non-habitat assortative mating alleles are associated
through linkage or pleiotropy with fitness alleles involved in intraspecific competition for a
resource that varies over a spectrum. Along similar lines, Kondrashov (1983a, 1983b, 1986) studied
the effects on NMSD of multiple loci pleiotropically controlling fitness and non-habitat assortative
mating. Finally, besides fitness and non-habitat assortative mating, Seger (1985) included
genetically controlled niche preference in an NMSD model.
In NMSD, intraspecific competition drives divergence unassisted by habitat-based mating,
whereas in HMSD, habitat assortative mating assists intraspecific competition. Although HMSD is
in a sense just an elaboration of NMSD (see Levene, 1953, pp. 332-3), the difference in dynamics
between these two types of sympatric divergence is considerable. Selection is disruptive for
NMSD, but in HMSD, because habitat-based mating partitions individuals into separate mating
pools which correspond to different habitats, selection is divergent (Pimental et al., 1967; Soans et
al., 1974; Bush, 1982; Shaw and Platenkamp, 1993). In addition, habitat assortative mating cannot
occur in NMSD because habitat-based mating is required, but it can occur during HMSD (Maynard
Smith, 1962, 1965) if genes control habitat preference.
Bush (1969, 1975), Tauber and Tauber (1977), Rice (1984), Diehi and Bush (1989) and De
Meeus et al. (1993) analysed biological and mathematical models to explore the dynamics of
HMSD when habitat assortative mating is unassisted by non-habitat assortative mating, while
Dickinson and Antonovics (1973), Felsenstein (1981) and Fialkowski (1988, 1992) analysed
HMSD models in which non-habitat assortative mating is unassisted by habitat assortative mating,
i.e. only intraspecific competition drives divergence. In our simulations, we analyse the dynamics
of HMSD when habitat assortative mating and non-habitat assortative mating complement one
another to facilitate speciation.
A basic two-habitat model for HMSD
The model is patterned after a population of phytophagous insects in an area where there are two
alternative host plants (habitats). A set of genes (hab genes) controls genotype-dependent migration
in the form of habitat preference and individuals mate and place their offspring in the selected
habitat. Habitat assortative mating develops because individuals are genetically predisposed to
select a given host plant and thus have a high probability of mating with an individual with similar
host preference. This mode of habitat or host-dependent mate recognition, which satisfies the
characterizing requirements for HMSD, is common in many phytophagous and parasitic insects,
mites and nematodes.
Another set of genes (fit genes) controls habitat-specific survival by enabling individuals to
utilize more effectively one host plant or the other. Individuals that select the host plant for which
they are best adapted have a selective advantage, so association of habitat preference alleles and
fitness alleles is favoured. If this association develops, a selective advantage occurs for individuals
190
Johnson
who not only select the 'correct' host plant, but who also mate homogamously. Thus, a third set of
genes (asm genes) for controlling non-habitat assortative mating operates to reduce interbreeding
between individuals adapted to different habitats who happen to be in the same habitat due to less
than absolute genetic control of habitat selection.
The principle simulations of the model discussed in this paper involve either one or two fitness
loci (fit loci), two habitat preference loci (hab loci), and two non-habitat assortative mating loci
(asm loci). The hab, fit and asm loci are not linked and each locus has two alleles. Selection (s) acts
directly on fit loci and indirectly on hab and asm loci. Generations are discrete and nonoverlapping, and soft selection occurs independently in each of the two habitats so that density is
regulated independently in each. This allows simultaneous variation at fit and hab loci (Rausher,
1984).
Habitat-specific selection and fitness
Selection is directional in each habitat because at each fit locus, one allele contributes to fitness
only in the original habitat and the other allele only in the new habitat. Therefore selection is also
habitat specific and divergent. Let k be the number of fit loci and s be a selection factor. If an
individual in a given habitat carries b homozygous fit loci with both alleles contributing to fitness
in that habitat and c heterozygousfit loci, where (b + c) = k, its fitness value is (1 + ps) b (1 + Os)c
if the loci interact multiplicatively and 1 + s (pb + 0c) if the loci interact additively.
The ratio of p/0 is a measure of the fitness of heterozygotes relative to homozygotes.
Underdominance occurs for p/0 > 2, while overdominance occurs for p/0 < 2. In our model, as in
the model of Diem and Bush (1989), p = 2 and 0 = 1. Since underdominance is then minimal for
the metapopulation, there is no direct selection against individuals that are heterozygous atilt loci.
Results of simulations by Fialkowski (1988, 1992) suggest that p/0 --- 2 is a necessary condition for
sympatric speciation and that the rate of speciation increases (to a point) as p/0 increases beyond
2 due to selection against heterozygotes.
Migration
The probability that an individual will live within its 'correct' habitat (i.e. where it is most fit) and
place its young there is controlled by hab alleles. We denote this probability by g and call it the
'hab penetrance' of the individual because it is the probability that an individual will express its
expected phenotype, based on its genotype, by selecting its preferred habitat.
At each hab locus there are two alleles: one confers preference for the original habitat and the
other for the new habitat. The model assumes that hab loci interact additively to determine the rate
Ph~ of production of a 'pathway product'. Hab penetrance g, which is a function of Ph~b, is scaled
so that penetrance is complete (g = 1.0) for an individual if ehab ~ 1.0. Individuals with complete
hab penetrance are certain to express their habitat preference by selecting their genetically
preferred habitat.
Only homozygous loci confer preference for a habitat, because for simplicity we assume that
alleles at heterozygous loci cancel each others effect. Let Lh~b denote the contribution by each
homozygous hab locus to Phab" Contributions of hab loci to penetrance are additive if ehab < 1.0 for
the individual and then g = Phab" If Phab< 1.0, then g = 1 regardless of the nature of interaction
between the hab loci. If Phab = 0, the individual randomly selects a habitat and g = 0. If m is the
number of hab loci, Phag is at most mLha b (i.e. max Phab = mLhab).
We assume that max Phab can be less than sufficient for complete penetrance (Phab< 1.0 for all
individuals in the population) or more than sufficient (Phab> 1.0 for some individuals). If max Phab
is more than sufficient, individuals with Phab> 1.0 have an extra pathway product termed
'penetrance excess'. This extra pathway product increases the probability that offspring of such an
191
Conditions for sympatric speciation
Table 1. Computed migration probabilities as proportions of individuals
leaving or staying in a habitat for each habitat-preference genotype
Habitat
Reside in
Prefer
Proportion that stay
for mating
Proportion that
migrate for mating
Original
Original
New
New
Original
New
Original
New
g+
0.5
0.5
g+
0.5
g+
g+
0.5
0.5 (l-g)
(l-g)
(l-g)
0.5 (l-g)
(l-g)
0.05 (l-g)
0.5 (l-g)
(l-g)
Each genotype has an associated penetrance g, which determines the probability that
an individual will either leave or stay in a given habitat for mating based on its
genotype. The factor 0.5 reflects the fact that genotype-independentmigration for all
individuals is maximized and that divergenceis truly sympatric. After Diehl and Bush
(1989).
individual will have complete penetrance, despite the effects of recombination. We call a
population 'saturated' with respect to hab penetrance if individuals of at least one pair of genotypes
prefer different habitats and have ehab ~- 1.0 SO that they always select their preferred habitat
(g = 1o0). In our simulation models, a population is saturated when max Phab>- 1.0.
Table 1 shows how migration probabilities are computed. The probability that an individual for
whom g = 0 will migrate to a new habitat is used as a measure of genotype-independent migration.
Since divergence is truly sympatric in our simulations, this probability is the maximum, 0.5 (see
Table 1).
In our model, Lhab is the same for all hab loci. Therefore, if b homozygous loci confer preference
for one of the habitats and d for the other and if b is greater than d, then Phab ~" (b - d)Lha b. The
preferred habitat for an individual is that for which most of the hab loci confer preference.
Non-habitat assortative mating
In our model, all three types of loci (hab, fit and asm) contribute to the pattern of mating. Positive
habitat assortative mating evolves indirectly as a correlated character of hab loci because mating
occurs only within a preferred habitat and mate choice is associated with habitat preference.
However, habitat assortative mating also occurs as a correlated character of fit loci in response to
habitat-specific divergent selection: each generation, within each habitat, natural selection increases
the proportion of individuals adapted to that habitat, thereby increasing the probability within each
habitat that the most fit individuals will mate with one another.
Asm loci control traits not specifically associated with either habitat (e.g. pheromone synthesis)
and non-habitat assortative mating occurs as an outcome of differences between individuals in
these traits. There are three non-habitat assortative mating phenotypes: A, B and C and individuals
of each phenotype mate at random with one another. Each asm locus is diallelic, with one allele
favouring phenotype A and the other favouring phenotype B.
Let r be the number of asm loci (therefore 2r is the number of asm alleles) and -q denote the
number of asm alleles that favour phenotype A. If qq > r for an individual, then asm penetrance, p,
is the probability that the individual will express phenotype A by mating homogamously, that is, by
mating with other such individuals. Conversely, 1 - p is the probability that this individual will
express phenotype C by mating at random with other individuals of phenotype C. If an individual
has "q < r, the individual has a probability p that it will express phenotype B, with 1-p again the
probability of expressing phenotype C. If "q = r, the individual has phenotype C.
Johnson
192
Let easm (an analogue to Phab) be the rate of production of a pathway product for determining asm
penetrance p (an analogue to hab penetrance g). asm penetrance p is complete for any individual
in which Pasta >- 1.0, which means that such individuals mate homogamously with certainty. We
assume that p is independent of the relative frequencies of the alleles favouring phenotypes A and
B. The value o f p for an individual is computed in the same manner as hab penetrance g, with each
asm locus contributing additively and equally an a m o u n t Las m to the rate Pasta" We scale p so that
penetrance is complete (p = 1.0) for an individual if easm ~ 1.0. The concept of penetrance excess
with respect to asm loci is analogous to that described for hab loci. We call a population saturated
with respect to asm penetrance if individuals of at least one pair of genotypes, X and Y, for
example, have complete penetrance (Pa~m>
-- 1.0 and p = 1). Therefore, individuals of these
genotypes always mate homogamously with individuals of their same phenotype.
As the proportion of individuals of phenotype C decreases, interbreeding between the two
subpopulations adapting to different habitats decreases. In cases in which phenotype C is
eliminated, all heterozygotes are eliminated and speciation is completed. Thus, the proportion of
individuals of phenotype C is a useful measure of the amount of interbreeding between the two
diverging portions of the population.
Life-cycle dynamics of the model
The model can be described mathematically as follows. Let u denote the total number of hab, fit
and asm loci and Gj the jth gamete, where j = 1, 2, 3 . . . . . 2u-l, 2u. Let q and Q denote the
frequency of an arbitrary genotype (G~, Gj) in the original and new habitat, respectively. At
generation n, just after migration, q = x~j(") and Q = Xu("). (Lower and upper case letters represent
the original and new sympatric habitats, respectively.)
We now follow the frequencies q and Q of (G i, Gj) through one life cycle. After reproduction,
which marks the beginning of generation n + 1, q has changed to Yij(n+l) and Q to y/j(n+l),
where
E v(n) v(n) D
Akl Ak'I' ,t klk,l,ij,
y!.~+l) = klk'v
tj
(1)
E "~kl'(n)x(n,/eklk'l'iT
klk'l'iy'
Yij(n+ 1) is obtained with an analogous equation. Pktk,l,ij,l is the probability that an individual of
genotype kl and an individual of genotype k T mate and produce an offspring of genotype ij.
Selection follows, changing q to zi/'+ 1) and Q to Z/j(~+ 1), where
7!.m+l) =
-'J
V(.n+l) (1 +
Jq
sq)
E y}~,+l)(l + si~,)
(2)
iT
Zij(n+ 1) is obtained with an analogous equation. Here s~i is the selection coefficient for genotype
ij. After selection, migration occurs, changing q to xij(~+ 1) and Q to Xij('+ 1) where
(1 + hij) 7 (.n+l) "Jr"Hi.~//; +1)
x(n+l) _~_
U
-'J
E [(1 + hiT) -`"+1)
~itjt +n/~,zi~,,n+l)]
(3)
iT
Xij(n 4-1) is obtained with an analogous equation. Here h 0 denotes the probability that an
individual of genotype ij in the original habitat will migrate to the new habitat and Hij denotes the
Conditions f o r sympatric speciation
193
probability that an individual of genotype ij in the new habitat will migrate to the original habitat
(see Table 1). The next generation n + 2 now proceeds, etc.
Methods
Simulations were run using various combinations of fit, asm and hab loci. The majority of the
results presented were obtained using one fit locus, two hab loci and two asm loci. Simulations
using more loci tended to be computationally prohibitive. Each simulation begins with identical
populations in an original and a new habitat. All hab, fit and asm loci are in Hardy-Weinberg
equilibrium (i.e. within-locus equilibrium) and linkage equilibrium (i.e. between-locus equilibrium). Recombination is free. Each locus contains a low-frequency allele for promoting adaptation
to the new habitat. In all simulations, initial relative frequencies for alleles of the three types of loci
are hab ° = f i t ° = asm a = 0.99 and hab" = f i t ~ = asm b = 0.01 in each habitat, where the super-script (°)signifies the original habitat and superscript (") the new habitat. Superscripts (a) and (b) are
used for the asm alleles because they are unassociated with either habitat. The only things different
in the system initially are the habitats.
Pair-wise linkage disequilibria were calculated for each subpopulation (within-population
equilibrium) and the metapopulation (total linkage disequilibrium). Between-population linkage
disequilibria were calculated using the Wahlund distribution of disequilibrium for two subpoputations. Since the ancestral population diverges into two portions utilizing different habitats in our
models, total disequilibrium (Otot) between pairs of loci is a combination of the following.
(1) The Wahlund disequilibrium (Obet) , which occurs when differences in allele frequencies at
two loci co-vary between the diverging portions of the population (Smouse and Neel, 1977).
(2) The disequilibrium within each of the diverging portions Dorig and Onew.
Nei and Li (1973) showed that at total disequilibrium Dtot = D b e t -k-(Oorig +D,ew)/2. The
Wahlund disequilibrium is unaffected by the homogenizing effects of recombination.
Speciation sensu stricto (Templeton, 1989) occurs in our simulations when gene flow terminates
and the diverging populations form two completely isolated gene pools, each adapted to a different
habitat (Kondrashov, 1986). We recognize that speciation is completed when two portions of a
diverging population become committed to different evolutionary pathways and does not require
the complete elimination of all gene flow. However, accurate determination of the time and
conditions for this bifurcation in simulations is not yet possible. Other criteria for completion of
speciation must therefore be used.
In all simulations, we determined the number of generations required for speciation. When
alleles at each locus were within 1/100 of the frequencies they were approaching asymptotically,
we considered speciation sensu stricto to have occurred, since linkage disequilibria between asm
loci and fit loci was essentially completed, with virtually no gene flow between the two sibling
species. In nature, under similar circumstances of approach to fixation, random drift completes the
process.
Results
Simulations with at least one type o f locus absent
To confirm results of earlier models and analyses pertaining to sympatric speciation, initial
simulations were carried out using various combinations o f fit, asm and hab loci, but not all three
together. With regard to HMSD models, we confirmed (1) the establishment of polymorphism by
194
Johnson
divergent selection when onlyfit loci are involved (Levene, 1953; Maynard Smith, 1966; Diehl and
Bush, 1989), (2) the joint action of genotype-dependent and genotype-independent population
regulation when only hab loci are involved (Nagylaki and Moody, 1980; Moody, 1981) and (3) the
establishment of polymorphism and of linkage disequilibrium between hab loci and fit loci when
habitat assortative mating occurs as a result of habitat preference and only fit and hab loci are
segregating (Diehl and Bush, 1989).
We also confirmed the results of Felsenstein (1981) and Diehl and Bush (1989) that if nonhabitat assortative mating and adaptation to different habitats are not accompanied by habitat
preference, then no linkage disequilibrium develops between a s m loci and fit loci irrespective of
selection factor s and a s m penetrance, if the fitness loci interact additively. However, if there are
at least two fit loci that interact multiplicatively, then very strong selection and non-habitat
assortative mating can generate some linkage disequilibrium between fit and a s m loci. But as
Felsenstein (1981) pointed out, such cases are unrealistic.
Finally, we also corroborated data showing that higher numbers of loci weaken the effectiveness
of individual loci to reduce speciation time. This was true for all three types of traits. With NMSD
models, Kondrashov (1986) obtained similar results.
S i m u l a t i o n s w i t h all three types o f loci p r e s e n t
Figure 1 illustrates speciation times over a range of values for gene penetrances Lasm and Lha b when
there is a single fit locus (s = 0.1) and a s m and hab penetrance are each controlled by two loci.
When speciation is completed, between-population pairwise linkage disequilibrium is maximum
for all pair combinations of the three types of loci. Speciation occurs when Las ~ >-- 0.5 and gha b > 0
(see Figs 1 and 2). Simulations were not run for values of Lha b < 0.2 because the time required for
Generations
4,000
4,000
3,000
3,000
2,000
!,000
,000
to Speciation
Generations
to Speciation
1,00(
I
S=0.1
~netrance
sm
Gene
0.8
Figure 1. Generations to speciation as a function of both hab gene penetrance (Lhab) and asm gene
penetrance (L,sm).Lha b varies in the range 0.2-0.8 and Lasm in the range 0.5-0.8. The selection factor s is set
at 0.1. Computer rounding of values creates a slight asymmetry in the first generation that determines the
fit allele with which the asm a (or asm b) allele becomes associated. When the rare asm allele asm b becomes
associated with the frequent fit° alleles favouring fitness in the original habitat (light bars), time to speciation
is slightly greater than when the rare asm b allele becomes associated with the rare fit" alleles for fitness in
the new habitat (dark bars).
195
Conditions for sympatric speciation
4,000 -
l
3,000
Generations
to Speciation
s=0.1
L ~ b = 0.7
2,000
1,000
0
0.45
I
I
0.475
I " - ~ saturation (asm)
0.5
gene penetrance
0.525
0.55
L asm
Figure 2. An illustration of the nature of the asm penetrance threshold for the occurence of speciation. The
population is saturated with respect to hab penetrance (Lh~b = 0.7 ~ 0.5), S = 0.1 and La,m varies from 0.45
to 0.55. Generations to speciation are shown as a function of asm gene penetrance. With Lasm = 0.5, the
population is also saturated with respect to asm penetrance and speciation occurs rapidly (approximately
1000 generations). As Las,, drops below the threshold of 0.5 so that the population is no longer saturated
with respect to asm penetrance, the time to speciation increases sharply towards infinity.
the process became computationally prohibitive. The number of generations to speciation ranged
from less than 1000 when Zas m ~---0.5 and Lha b = 0.8 to more than 3000 when Zas m > 0.5 and
Zha b = 0.2.
Our results illustrate the role of habitat preference in facilitating sympatric speciation. Observe
that if the population is saturated with respect both a s m and hab penetrance (Lasm >I 0.5,Lh~b I> 0.5),
speciation occurs within approximately 1000 generations if s = 0.1 (see Fig. 1) and the sister
species confine themselves to the habitat in which they are specifically adapted. Now consider the
minimal condition for linkage disequilibrium to develop if there are no hab loci to facilitate the
speciation process via habitat preference. Instead of just one f i t locus, there must be at least two that
interact multiplicatively. If L,s m = 0.5 and s = 0.1, we obtain a speciation time of approximately
10 500 generations instead of 1000. Besides this 10-fold increase in speciation time, the resulting
sympatric sister species migrate randomly between the two habitats. Correspondingly, within- and
not between-population linkage disequilibrium becomes maximum.
Enough simulations beyond those shown in Fig. i were run to construct a depiction (Fig. 3) of
speciation times over the entire range of Lasm and Lhab values. We observe the following: (1)
sympatric speciation occurs in our HMSD model only if the population is saturated with respect to
a s m penetrance, (2) given that speciation does occur, Lh~ b determines the time required and (3)
speciation is achieved in the shortest time when the population is saturated with respect to both hab
and a s m penetrance (i.e. the 'complete habitat-fidelity' region where Las m and Lhab are ~ 0.5). ~n
this region of complete habitat-fidelity (Fig. 3), gene flow between the sympatric sister species that
emerge is impossible because homogamous mating and preference for the habitat in which an
individual is adapted become errorless due to the elimination by natural selection of individuals
with less than complete a s m and hab penetrance.
The 'incomplete habitat-fidelity' region in Fig. 3 corresponds with cases when the population is
only saturated with respect to a s m penetrance. Then speciation occurs because interbreeding
between individuals of the two divergent portions of the population is terminated, even though
some individuals of the sister species migrate between habitats due to incomplete h a b penetrance.
196
Johnson
Although speciation is completed, individuals of the species adapted specifically to one of the
habitats can sometimes be found in the other 'wrong' habitat (Fig. 4). The percentage of such
individuals increases linearly as Lhab decreases. At Lhab = 0, this value becomes 50% and
individuals of the sympatric sister species migrate at random between habitats.
However, by the time the speciation process has reached the advanced stage of speciation, there
is a fitness penalty against individuals that select the wrong habitat. Not only are they homozygous
for the wrong fitness allele in that habitat, but they must mate with other such individuals since f i t
and a s m alleles are completely associated. Offspring of these matings will also be maximally unfit,
except those offspring that select the other 'correct' habitat to which they are adapted. Hence, the
proportion of individuals of the sister species found in their respective 'wrong habitats' will in
theory diminish and eventually disappear due to the selective advantage of mutations that increase
habitat preference penetrance. This intrinsic process of increase in habitat fidelity can be facilitated
by mutant f i t loci that introduce habitat preference pleiotropically or mutant hab loci linked to f i t
loci ('hitchhiking').
When there are ten loci contributing to a s m penetrance, saturation results when gene penetrance
Lasm = 0.1 and when there are 20 such loci, Lasm = 0.05 is sufficient for saturation; similarly for hab
penetrance. This suggests that when enough hab and a s m loci are involved in HMSD, speciation
can occur for a population almost regardless of how small the additive contributions of individual
loci to penetrance may be. In theory, the complete habitat-fidelity region could expand (see Fig. 3)
until the 'incomplete habitat-fidelity' region and the 'no speciation' region disappear.
O0
20,000
20,000
15,000
15,000
10,000 Generations
to Speciation
Generations 10,00(
to Speciation
,000
5,00
s=0.1
trance
GE
[]
[]
[]
complete namtat-rme.ty
incomplete habitat-fidelity
no speciation
1.0 1.0
complete
gene penetrance
Figure 3. Delineation of three distinct forms of HMSD as a function of Zhab and La+m. Simulations were run
with two hab loci, two asm loci and onefit locus (s = 0.1). Speciation is most rapid when both asm and hab
penetrance are saturated, In this 'complete habitat-fidelity' region, both asm and hab penetrance become
saturated. In the 'incomplete habitat-fidelity' region, speciation occurs even though only asm penetrance is
saturated. Speciation does not occur when/_,asm< 0.5, i.e. when asm penetrance is not saturated. This is the
'non-occurence of speciation' region and bars are not shown.
Conditions for sympatric speciation
197
Additional fitness loci
Figure 5 shows the speciation times for conditions identical to those represented in Fig. 1, excepL
for s, which is reduced by half, from 0.10 to 0.05. We observe that this approximately doubles the
time to speciation. In the opposite direction, doubling the selection factor s for a single fit locus
(0.05-0.10), which doubles the fitness of homozygous individuals, decreases speciation time by
approximately half. On the other hand, the addition of a second fit locus with the same selection
factor s as the first, which also doubles the fitness of homozygous individuals, decreases the time
to speciation by less than one-third (Fig. 6) when s is > 0.05. This demonstrates the weakened
effect of selection when the number of loci contributing to fitness increases. The weakening
becomes greater as the additive contributions of each locus to fitness increases: when s is 0.50
(10-fold higher than 0.10), including a second locus reduces speciation time by less than one-sixth
(Fig. 6).
Having two fit loci interact multiplicatively reduced time to speciation only slightly and can be
less effective than an additive interaction at values of s less than 0.05. When s was set above 0.2,
increasing the additive or multiplicative contribution per fit locus did not significantly reduce
speciation time.
Migration of Sister Species Adapted to New Habitat
O
t...
o
o.
0
0.2
0.4
0.6
0.8
1
Gene Penetrance
L hab
Figure 4. The percent of individuals that migrate to the wrong habitat, where they are at a fitness
disadvantage, is shown as a function of Lhab. This occurs for simulations that fall in the 'incomplete habitatfidelity' region of Fig. 3 where Lhab < 0.5. In these cases, some individuals of both new sister species
disperse across the two habitats after speciation has occured. This figure only shows dispersal for the
species specifically adapted to the new habitat.
198
Johnson
4,000
4,000
3,000
3,000
Generations 2,00C
to Speciation
2,000 Generations
to Speciation
,000
1,00,
S = 0.05
~netmnce
Genq
tsm
Figure 5. Generations to speciation as a function of both hab gene penetrance (Lhab) and asm gene
penetrance (L,~m)when the selection factor s = 0.05. As in Fig. 1, Lhab varies in the range 0.2-0.8 and Las,~
in the range 0.5-0.8. The light and dark shading of the bars is explained in the legend to Fig. 1.
Development of linkage disequilibrium
To illustrate basic features of HMSD divergence, the trajectory for development of pair-wise
linkage disequilibrium between fit loci and asm loci was examined (Fig. 7). In the specific case
used (Fig. 6, arrow), speciation occurred within approximately 850 generations.
During a relatively short initial phase of population diversification, the rare hab allele rapidly
becomes common and habitat preference initiates a reduction in gene flow between habitats within
less than 50 generations. Soon after, the rare fit allele increases in frequency and some linkage
disequilibrium develops between all loci. Within less than 200 generations, within-population
linkage disequilibrium between the two asm loci reaches 0.099 or 40% of maximum, although the
frequency of the rare asm allele has increased very little. However, the amount of disequilibrium
between asm loci and fit loci is minuscule.
A quasi-equilibrium is reached within less than 500 generations, which begins a period of stasis
before the rare asm alleles begin to exhibit a noticeably rapid increase in frequency across habitats
(the beginning of the speciation phase). During the period of stasis, the highest between-habitat
linkage disequilibrium (0.038, 15% of maximum) occurs between the two hab loci and the next
highest (0.0084, 3% of maximum), between hab loci andfit loci. In the absence of asm loci, this
would be the final equilibrium state, as in the models analysed by Diehl and Bush (1989).
The last component and phase of the speciation process, completion of speciation by
reproductive isolation, is a short dramatic process (approximately 100 generations). Linkage
disequilibrium suddenly increases to maximum for all pairs of loci. Interbreeding between
individuals adapted to different habitats rapidly diminishes to zero as all intermediate forms
disappear, resulting in the elimination of gene flow between the two diverging co-adapted
subpopulations. Kondrashov (1986) observed a similar phenomenon for sympatric speciation in
some of his NMSD models, namely, a prolonged initial stage of speciation when polymorphisms
are developing, followed by a stage of rapid elimination of intermediate individuals (Kondrashov
and Mina, 1986).
199
Conditions for sympatric speciation
Although within-habitat linkage disequilibrium between fit and asm loci is predominant initially
over between-population linkage disequilibrium, eventually a sudden shift to the latter occurs. This
happens because the population is saturated with respect to both hab and asm penetrance (the
complete habitat-fidelity region in Fig. 3). Should the population be only saturated with respect to
asm penetrance (the incomplete habitat-fidelity region), some of the within-habitat disequilibrium
would have been retained throughout the speciation process and each sympatric sister species
would utilize both habitats to some extent (see Fig. 4).
In summary, for populations that are saturated with respect to asm penetrance, the process of
sympatric speciation via HMSD includes (1) an initial diversification phase during which a slight
amount of divergence occurs, (2) a quasi-equilibrium phase of stasis, which can be long and during
which little or no detectable divergence occurs and (3) a completion phase during which divergence
is dramatic and gene flow between diverging habitat races is rapidly eliminated.
Discussion
This study expands earlier HMSD models by incorporating all three basic types of loci that
facilitate sympatric divergence: habitat-based fitness (fit) loci, habitat preference (hab) loci and
assortative mating (asm) loci. We found that each type of locus facilitates the effectiveness of the
other two types so that the three types operate together to promote HMSD. Sympatric speciation is
then theoretically quite plausible. If any one of the three types of loci is absent, then speciation
2,500
2,000
N u m b e r of Fitness Loci
t w o (multiplicative interaction)
o
t w o (additive interaction)
\
W C
.9o 1,ooo
500
,
0
0
I
0.1
i
I
0.2
,
I
,
0.3
I
0.4
,
I
,
0.5
Selection Factor s
Figure 6. Generations to speciation as a ftmction of the selection factor s. In these simulations, there are
two asm loci and two hab loci with L~s,, = Lh~b = 0.6. The contribution s of each fit allele to total fitness is
the same, so when two fit loci interact additively, total fitness is doubled for homozygous individuals. The
arrow is a reference mark for Figure 7.
200
Johnson
completion
(speciation
in progress)
stasis
(no speciation)
sister species
(speciation completed)
I ~ 1
Maximum
025
®
E
..~
e"
L
.10
o n
, m
O"
P_
r~
500
600
700
800
900
1000
Generations
Figure 7. The development of a pair-wise linkage disequilibrium between fit and asm loci. In this
simulation (see arrow in Fig. 6), there are two fit loci interacting additively, two hab loci and two asm loci
(s = 0.1, Lasm = Lh~b = 0.6). Linkage disequilibrium increases suddenly to the maximum (0.25) from values
difficult to detect, within less than 100 generations.
becomes less likely and requires special genetic conditions such as underdominance or divergent
selection on habitat preference (Rice, 1984). Diehl and Bush (1989) analysed a three-locus haploid
HMSD model where variation at two unlinked loci affects fitness and a third locus influences host
preference (no non-habitat assortative mating occurs). Although considerable progress towards
speciation can occur in this model, sympatric speciation (sensu stricto) is possible only if habitat
preference is error free, in which case habitat preference alone is sufficient for reproductive
isolation.
The role o f habitat preference
Kondrashov (1983a,-b, 1986) showed with NMSD models that once reproductive isolation is
virtually estabfished, then linkage disequilibrium between asm loci and fit loci can increase and
complete the speciation process by eliminating interbreeding within a population between divergent
morphs adapting to different niches or habitats. This occurs even when the intensity of disruptive
selection is less than 10% and without involvement of hab loci. His results suggest that once
linkage disequilibrium between asm loci and fit loci has developed sufficiently during HMSD, then
NMSD is sufficient to bring about speciatlon. Habitat-based mating and niche or habitat preference
become unnecessary.
Conditions for sympatric speciation
201
This observation suggests that the role of habitat preference in sympatric speciation via HMSD
is to initiate the process and allow development of disequilibrium between asm loci and fit loci to
proceed until a threshold value is reached at which a self-sustaining momentum results in rapid
completion.
The execution of the role of habitat preference in HMSD can be explained as follows. Even if
only hab loci are segregating, those loci rapidly proceed to polymorphism and reduce gene flow
between habitats in the process (Diehl and Bush, 1989). Due to habitat preference, within each
habitat the relative frequency of individuals that are homozygous for preferring that habitat
increases relative to those that are homozygous for preferring the other habitat. Consequently,
individuals that are heterozygous for habitat preference decrease in frequency across habitats due
strictly to density-dependent selection and recombination at hab loci. This strengthens habitat
assortative mating and facilitates the development of linkage disequilibrium between hab and fit
alleles. Such linkage disequilibrium promotes linkage disequilibrium between asm and fit alleles
and vice versa. The result is mutual enhancement of all combinations of pair-wise linkage
disequilibria for the three types of loci.
Liberman and Feldman (1989) showed that mutations that introduce additional hab loci which
increase the level of hab penetrance can become established due to a selective advantage so that
habitat preference can indeed perform the role of initiating the speciation process. They studied a
model involving a multiple-allele modifier of migration rate between two habitats and found that
although the modifier locus and a fit locus may achieve linkage equilibrium in each of the habitats
(Hardy - Weinberg equilibrium), the equilibrium is externally unstable to alleles that reduce
migration rates.
The role of non-habitat assortative mating
The role of non-habitat assortative mating in HMSD is apparent, namely, to reduce interbreeding
between the diverging portions of a population that occurs when individuals of both portions are',
found in the same habitat. As mentioned above, the selective advantage of non-habitat assortatiw~
mating during HMSD is increased whenfit and hab loci become associated. The diverging portions
of the population can develop different mate recognition systems (e.g. pheromones, courtship
behaviours, displays, etc.). If the population is saturated with respect to asm penetrance, the
outcome is completion of speciation even though migration between habitats may still occur.
Within a 'homogamy pool,' individuals are certain to mate only among themselves because the
genotypes within the pool have complete asm penetrance. A metapopulation is saturated with
respect to asm penetrance if it contains at least two homogamy pools. Due to recombination, some
of the offspring of individuals with less than complete penetrance and therefore in neither
homogamy pool, can have complete penetrance and therefore fall within one or the other
homogamy pool. The set of genotypes within such a pool therefore constitutes an 'absorbing state',
in that all descendents of an individual having one of those genotypes remain in that pool. If there
are no homgamy pools, there is no means of eliminating interbreeding between individuals adapted
to different habitats unless habitat prefererence is error free. The critical role of homogamy pools
in sympatric speciation (sensu stricto) is confirmed by Kondrashov's (1983a,b, 1986) models.
A population that is saturated with respect to asm penetrance can include individuals (or
genotypes) with penetrance excess. The probability of the offspring of such an individual having
complete penetrance is enhanced, since both homozygous and heterozygous offspring can yield the
phenotype of a parent that has penetrance excess. A relationship between penetrance excess .and
dominance is suggested by Haldane (1930) who proposed that the evolution of dominance can be
achieved by the strengthening of the wild type allele, so that optimal rates of enzyme production
can be attained even in the heterozygote. Sved and Mayo (1970) called such genes 'haplo-
202
Johnson
sufficient'. Selection pressure and consequent evolution leading to some 'extra' pathway product,
as suggested by Haldane (1970), seems plausible, unless one can think of a biological limitation on
the capacity of metabolic pathways to produce more product than is sufficient to ensure the
occurrence of a particular behaviour (or other phenotype). Even though there may be some
physiological cost in producing 'extra' product, such cost must be weighed against the advantage
of being able to pass the benefit of optimal rates of enzyme production to offspring who otherwise,
due to a recombination event, are burdened by less than optimal rates. Behavioural characters,
whose expression is often contingent on circumstances other than physiological, may be
particularly amenable to penetrance excess.
Natural populations of similar species existing in the same area but that do not interbreed due to
differences in mate recognition systems controlled by more than one gene can theoretically be
viewed as a metapopulation that is saturated with respect to a s m penetrance. The intermediate
forms happen to have been largely eliminated in these cases. Such populations are not uncommon.
The closely related sulfur butterflies Colias eurytheme and Colias philidiee are an example of this.
These species occur together in most of North America but are sexually isolated under most natural
conditions due to female response to species-specific visual and pheromonal signals (Taylor, 1972;
Grula and Taylor, 1979).
Non-habitat assortative mating models
By including at least two a s m loci in our simulations, we take into account cases of non-habitat
assortative mating (e.g. Grula and Taylor, 1979; Roelofs et al., 1987) in which one set of a s m loci
is needed for variation in the display characters of one sex (for example, pheromone composition),
and another set is needed for variation in preference by the other sex (for example, increased
attraction for a specific pheromone composition).
When a mutant a s m allele first occurs in a population, it will be heterozygous for the individual
carrying the mutant. In our model, these mutant individuals are of phenotype C, so they easily find
mates since that portion of the population continues to be large until the speciation process nears
completion. But if the initial frequency of the rare a s m allele is too low, as may be the case in our
simulation models (frequency = 0.01), the problem arises for individuals with nearly complete
a s m penetrance and homozygous a s m loci. Those individuals may occur so infrequently as to
seldom encounter one another, yet they are assumed to mate homogamously in our model. As a
consequence, our model applies to HMSD when the a s m alleles have become frequent enough so
that individuals with homozygous a s m loci and complete penetrance can be quite certain of finding
mates.
Although our model is a basic HMSD model in that it takes into account all three types of loci,
it does not take into account mating success. It assumes that each generation all individuals succeed
in mating and with one partner only. A more general HMSD model is needed that takes into
account not only frequency-dependent mating success, but also mating success that is genotype
dependent and habitat dependent (regardless of frequency dependence). Mating success is expected
to be genotype dependent if changes in the genome by mutation can improve the probability of an
individual finding mates and accomplishing successful courtships. It can also be habitat dependent,
in particular under the conditions of HMSD. Genotype- and habitat-dependent mating success may
particularly apply to species in which males compete for the number of females they
inseminate.
If mating success is habitat and genotype dependent for a population undergoing HMSD, natural
selection will favour traits that increase habitat-specific mating success. Since habitat-specific
homogamy occurs as a correlated trait, a s m alleles can reach the frequency at which our model
applies, independent of natural selection on habitat-specific survival traits. Once HMSD is well
Conditions for sympatric speciation
203
under way, the frequency dependence of asm penetrance can lead to a 'runaway' process that
enhances the dramatic increase in linkage disequilibrium demonstrated in our model.
Conclusions
Under sympatric conditions and biologically reasonable intensities of selection and penetrance for
habitat preference and non-habitat assortative mating, genetically controlled habitat preference can
promote linkage disequilibrium between asm loci and fit loci in diploid populations. After a period
of 'incubation', maximum linkage disequilibrium between all loci (completely correlated traits) can
develop quickly and complete the speciation process. No further interbreeding (gene flow) is
possible between the habitat-specific sister populations because linkage disequilibrium between fit
loci and asm loci is complete.
The dynamics of our model suggests that the process of sympatric speciation can be selfenhancing and gain momentum over generations and that clear differences between diverging
morphs of a population, each morph adapting to different habitats, may only occur during the final
relatively brief completion stage. This may explain the mixed success (Barton et al., 1988) in the
search for the evolution of correlated change in hab genes and fit genes, which provides an
opportunity for non-habitat assortative mating to develop.
Acknowledgements
Helpful comments or reviews were provided by Scott Diehl, Richard Lenski, John Jenkins, Brian
Charlesworth, Alexey Kondrashov, Michael Rosenzweig and anonymous reviewers. NSF Grants
BIR 9120006 and DMS 9206677 (F.C.H.) supported the work.
References
Barton, N.H. and Charlesworth, B. (1984) Genetic revolutions, founder effects, and speciation. Ann. Rev.
Ecol. Syst. 15, 133-64.
Barton, N.H., Jones, J.S. and Mallet, J. (1988) No barriers to speciation. Nature 336, 13-14.
Bush, G.L. (1969) Sympatric host race formation and speciation in frugivorous flies of the genus Rhagoletis.
Evolution 23, 237-51.
Bush, G.L. (1975) Sympatfic speciation in phytophagous parasitic insects. In Evolutionary strategies of
parasitic insects (P.W. Price, ed.), pp. 187-206. Plenum, London.
Bush, G.L. (1982) What do we really know about speciation? In Perspectives on evolution (R. Milkman, ed.),
pp. 119-28. Sinauer Associates, Sunderland, MA.
Bush, G.L. (1992) A reaffirmation of Santa Rosalia, or why are there so many kinds of small animals, h
Evolutionary patterns and processes (D. Edwards and D.R. Lees, eds), pp. 229-49. Academic Press,
New York.
Bush, G.L. and Howard, D.J. (1986) Allopatric and non-allopatric speciation; assumptions and evidence. In
Evolutionary processes and theory (S. Karlin and E. Nevo, eds), pp. 411-38. Academic Press, New
York.
Crawford, D.J., Stuessy, T.F., Haines, D.W., Cosner, M.B., Silva, O.M. and Lopez, P. (1992) Allozyme
diversity within and divergence among four species of Robinsonia (Asteraceae: Senecioneae), a genus
endemic to the Jan Fernandez Islands, Chile. American Journal of Botany 79~ 962-6
De Meeus, T., Michalakis, Y., Renaud, F. and Olivieri, I. (1993) Polymorphism in heterogeneous
environments, evolution of habitat selection and sympatric speciation: soft and hard selection models.
Evol. Ecol. 7, 175-98.
Dickinson, H. and Antonovics, J. (1973) Theoretical considerations of sympatric divergence. Am. Nat. 107',
256-74.
204
Johnson
Diehl, S.R. and Bush, G.L. (1989) The role of habitat preference in adaptation and speciation. In Speciation
and its consequences (D. Otte and J. Endler, eds), pp. 345-65. Sinauer Associates, Sunderland, MA.
Feder, J.L., Chilcote, C.A. and Bush, G.L. (1989) Are the apple maggot, Rhagoletis pomonella, and blueberry
maggot, R. mendax, distinct species? Implications for sympatric speciation. Entomol. Exp. Appl. 51,
113-23.
Felsenstein, J. (1981) Scepticism towards Santa Rosalia, or why are there so few kinds of animals. Evolution
35, 124-38.
Fialkowski, K.R. (1988) Lottery of sympatric speciation computer model. J. Theor. Biol. 130, 379-90.
Fialkowski, K.R. (1992) Sympatric speciation: a simulation model of imperfect assortative mating. J. Theor.
Biol. 157, 9-30.
Futuyma, D. (1986) Evolutionary Biology, 2nd edn. Sinauer Associates, Sunderland, MD.
Futuyma, D. and Mayer, G.C. (1980) Non-allopatric speciation in animals. Syst. Zool. 29, 254-71.
Gibbons, R.H. (1979) A model for sympatric speciation in Megarhyssa (Hymenoptera: Ichneumonidae):
competitive speciation. Am. Nat. 114, 719-41.
Grant, P.R. (1986) Ecology and Evolution of Darwin's Finches. Princeton University Press, Princeton, NJ.
Grula, J.W. and Taylor, O.R., Jr (1979) The inheritance of pheromone production in the sulphur butterflies
Colias eurytheme and C. philodice. Heredity 42, 359-71.
Haldane, J.B.S. (1930) A note on Fisher's theory of the origin of dominance. Am. Nat. 64, 87-90.
Heatwole, H. and Davis, D.M. (1965) Ecology of three species of parasitic insects of the genus Megarhyssa
(Hymenoptera: Ichneumonidae). Ecology 46, 140-50.
Hutchinson, G.E. (1968) When are species necessary? In Population biology and evolution (R.C. Lewontin,
ed.) pp. 177-86. Syracuse University Press, Syracuse, NY.
Kondrashov, A.S. (1983a) Multilocus model of sympatric speciation. I. One character. Theor. Pop. Biol. 24,
121-35.
Kondrashov, A.S. (1983b) Multilocus model of sympatric speciation. 11. Two characters. Theor. Pop. Biol. 24,
121-35.
Kondrashov, A.S. (1986) Multilocus model of sympatric speciation. 111. Computer simulations. Theor. Pop.
BioL 29, 1-15.
Kondrashov, A.S. and Mina, M.V. (1986) Sympatric speciation: when is it possible? BioL J. Linn. Soc. 27,
201-23.
Lack, D. (1947) Darwin's Finches. Cambridge University Press, Cambridge.
Levene, H. (1953) Genetic equilibrium when more than one ecological niche is available. Am. Nat. 87,
331-33.
Liberman, U. and Feldman, M.W. (1989) The reduction principle for genetic modifiers of the migration rate.
In Mathematical evolutionary theory (M.W. Feldman, ed.), pp. 111--44. Princeton University Press,
Princeton, NJ.
Maynard Smith, J. (1962) Disruptive selection, polymorphism and sympatric speciation. Nature 195,
60-2.
Maynard Smith, J. (1965) Mr. J. Maynard Smith (comments). Proc. R. Entomol. Soc. London 30, 22-3.
Maynard Smith, J. (1966) Sympatric speciation. Am. Nat. 100, 637-50.
Mayr, E. (1963) Animal Species and Evolution. Harvard University Press, Cambridge, MA.
Moody, M. (1981) Polymorphism with selection and genotype-dependent migration. J. Math. Biol. 11,
245-67.
Murray, M.G. (1990) Comparative morphology and mate competition of flightless male fig wasps. Anim.
Behav. 39, 434--43.
Nagylaki, T. and Moody, M. (1980) Diffusion model for genotype-dependent migration. Proc. Natl Acad. Sci.
USA 77, 4842-6.
Nei, M. and Li, W.H. (1973) Linkage disequilibrium in subdivided populations. Genetics 75, 213-19.
Paterson, H.E.H. (1981) The continuing search for the unknown and the unknowable: a critique of
contemporary ideas on speciation. South Africa J. Sci. 77, 119-33.
Pimentel, D., Smith, G.J.C. and Soans, J.S. (1967) A population model of sympatric speciation. Am. Nat. 101,
493-504.
Conditions for sympatric speciation
205
Rausher, M.D. (1984) The evolution of habitat preference in subdivided populations. Evolution 38,
596--608.
Rice, W.R. (1984) Disruptive selection on habitat preference and the evolution of reproductive isolation: a
simulation study. Evolution 38, 1251-60.
Rice, W.R. (1987) Selection via habitat specialization: the evolution of reproductive isolation as a correlated
character. EvoL Ecol. 1, 301-14.
Rice, W.R. and Salt, G.W. (1990) The evolution of reproductive isolation as a correlated character under
sympatfic conditions: tall evidence. Evolution 44, 1140-52.
R'Kha, S., Capy, P. and David, J.R. (1991) Host-plant specialization in the Drosophila melanogaster species
complex: a physiological, behavioral, and genetical analysis. Proc. Nat Acad. Sci. USA 88, 1835-9.
Roelofs, W.R., Glover, T., Tang, X., Sreng, I., Robbins, D., Eckenrode, C., Lofstedt, G., Hannon, B.S. and
Bengtsson, B.O. (1987) Sex pheromone production and perception in European corn borer moths is
determined by both autosomal and sex-linked genes. Proc. Natl Acad. Sci. USA 84, 7585-9.
Rosenzweig, M.L. (1978) Competitive speciation. Biol.J. Linn. Soc. 10, 275-89.
Seger, J. (1985) Intraspecific resource competition as a cause of sympatric speciation. In Evolution (P.J.
Greenwood, P.H. Harveyand and M. Slatkin, eds), pp. 43-53. Cambridge University Press,
Cambridge.
Shaw, R.G. and Platenkamp, G.A.J. (1993) Quantitative genetics of response to competitors in Nemophila
menziesii: a greenhouse study. Evolution 47, 801-12.
Slatldn, M. (1982) Pleiotropy and parapatfic speciation. Evolution 36, 263-70.
Smouse, P.E. and Neel, J.V. (1977) Multivariate analysis of gametic disequilibrium in the Yanomama.
Genetics 85, 733-52.
Soans, A.B., Pimentel, D. and Soans, J.S. (1974) Evolution of reproductive isolation in allopatfic and
sympatdc populations. Am. Nat. 108, 117-24.
Sved, J.A. and Ma, O. (1970) The evolution of dominance. In Mathematical topics in population genetics (K.
Kojima, ed.), pp. 289-316. Springer-Verlag, New York.
Tauber, C.A. and Tauber, M.J. (1977) A genetic model for sympatric speciation through habitat
diversification and seasonal isolation. Nature 268, 702-5.
Tauber, C.A. and Tauber, M.J. (1989) Sympatric speciation in insects: perception and perspective. In
Speciation and its consequences (D. Otte a,ad J. Endler, eds), pp. 307-343. Sinauer Associates,
Sunderland, MA.
Taylor, O.R., Jr (1972) Random vs. non-random mating in the sulfur butterflies, Colias eurytheme and C.
philodice (Lepidoptera, Pieridae). Evolution 26, 344-56.
Templeton, A.R. (1989) The meaning of species and speciation: a genetic perspective. In Speciation and its
consequences (D. Otte and J. Endler, eds), pp. 3-27. Sinaner Associates, Sunderland, MA.
Wade, M.J., Patterson, H., Chang, N. and Johnson, N.A. (1994) Postcopulatory, prezygotic isolation in flour
beetles. Heredity 72, 163-7.
White, M.J.D. (1978)Modes of Speciation. W.H. Freeman, San Francisco.
Wood, T.K. and Guttman, S.I. (1983) Enchenopa binotata complex: sympatric speciation? Science 220,
310-12.