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Epigenetic Inheritance, Genetic Assimilation and Speciation
CSABA PAD L*
AND ISTVAD N
MIKLOD S
Department of Plant ¹axonomy and Ecology, ¸oraH nd EoK tvoK s ;niversity, Budapest,
¸udovika 2, H-1083, Hungary
(Received on 1 December 1998, Accepted in revised form on 20 May 1999)
Epigenetic inheritance systems enable the environmentally induced phenotypes to be transmitted between generations. Jablonka and Lamb (1991, 1995) proposed that these systems have
a substantial role during speciation. They argued that divergence of isolated populations may
be "rst triggered by the accumulation of (heritable) phenotypic di!erences that are later
followed and strengthened by genetic changes. The plausibility of this idea is examined in this
paper. At "rst, we discuss the &&exploratory'' behaviour of an epigenetic inheritance system on
a one peak adaptive landscape. If a quantitative trait is far from the optimum, then it is
advantageous to induce heritable phenotypic variation. Conversely, if the genotypes get closer
to the peak, it is more favorable to canalize the phenotypic expression of the character. This
process would lead to genetic assimilation. Next we show that the divergence of heritable
epigenetic marks acts to reduce or to eliminate the genetic barrier between two adaptive peaks.
Therefore, an epigenetic inheritance system can increase the probability of transition from one
adaptive state to another. Peak shift might be initiated by (i) slight changes in the inducing
environment or by (ii) genetic drift of the genes controlling epigenetic variability. Remarkably,
drift-induced transition is facilitated even if phenotypic variation is not heritable. A corollary of
our thesis is that evolution can proceed through suboptimal phenotypic states, without
passing through a deep adaptive valley of the genotype. We also consider the consequences of
this "nding on the dynamics and mode of reproductive isolation.
1999 Academic Press
1. Introduction
Mostly we "nd that variation is not continuous
in a single geographical region. There are separated species with genetical, morphological, behavioural di!erences. Why should this be so?
One possible answer is that species are adapted
to discontinuous ecological niches, and the less
"t intermediate forms are selectively eliminated.
Imagine that there is a bimodal distribution of
some resource combined with di!erences in resource use between the genotypes. The resource
* Author to whom correspondence should be addressed.
E-mail: [email protected]
0022}5193/99/017019#19 $30.00/0
is assumed to be unlimited, so that individual
"tnesses do not depend on the current distribution of the genotypes (no frequency dependent
selection). These assumptions generate a bimodal
relation between individual "tness and the value
of a quantitative trait (Barton, 1989b). How can
traits evolve from one adaptive state to another,
if intermediates are at a selective disadvantage?
This problem can be visualized by the adaptive
landscape, originally addressed by Sewall Wright
(1932, 1980). Adaptive landscape is a surface in
a multidimensional space, showing the mean
"tness of the population as a function of the
possible genetical states (e.g. gene frequency).
Adaptation is a &&hill-climbing'' process of the
1999 Academic Press
20
C. PAD L AND I. MIKLOD S
population reaching a local maximum. The peaks
of the adaptive landscape separated by valleys
de"ne the possible stable states of the populations. Peak shift is the transition between these
states.
The possible mechanisms driving the population to a new peak are of interest from two points
of view. First, the rate of evolution in a given
lineage may crucially depend on, how it can proceed through suboptimal stages. Second, speciation can also be envisaged as a movement on
a "tness surface. In the classic view, speciation
occurs by accident. If populations are isolated
from each other, they diverge genetically from
each other because of the appearance and spread
of di!erent mutations. Reproductive isolation
evolves gradually in these populations as a side
e!ect of this process. The evolutionary dynamics
of divergence depends on the strength of the
barrier to gene #ow and the rate of transitions
between the peaks (Barton & Charlesworth,
1984). Remarkably, both depend on the depth of
the valley separating two peaks: weak selection
makes the transition more probable, but the degree of isolation is also lowered. An obvious
limitation of this approach is that it does not
include any explicit ecological factors, so it cannot say anything about the coexistence of diverged populations. Nevertheless, the population
genetic approach may highlight the genetic and
environmental factors that can potentially facilitate speciation.
What drives divergence if selection opposes
any shift from the status quo? Genetic drift has
attracted substantial attention as a possible candidate. Genetic drift can presumably knock out
a population from a local optimum, suggesting
that it can cause reproductive isolation even under unchanging ecological circumstances. Nevertheless, the probability of stochastic transitions
quickly diminishes with increasing population
size (Barton & Charlesworth, 1984; Charlesworth
& Rouhani, 1987; Lande, 1985). How can we
remove this problem? Wright argued for the importance of population structure, which enables
the species to continually "nd its way from lower
to higher peaks by the combination of stochastic
and selective forces (Wright, 1932). His analysis
included population subdivision, "nite population size and inbreeding. In spite of the intellec-
tual merit of his work, recent theoretical issues
and empirical facts do not support the shiftingbalance theory (Coyne et al., 1997).
Because of the ambiguities of drift-induced
transition, it is necessary to look for other possibilities that could initiate peak-shift alone or with
the combination of stochastic forces. Changing
environmental conditions can be one candidate.
Environment has two di!erent e!ects on phenotypic pattern: it generates variation and selects
the variants. As "rst emphasized by Fisher (1930),
under a new selective environment, isolated
populations can evolve to di!erent adaptive
peaks. The environment can also induce di!erent
phenotypic variants. According to Kirkpatrick
(1982), the mean of a quantitative trait may be
shifted to the neighboring optimal state deterministically, provided that the phenotypic variance exceeds a critical value. Is this change in
phenotypic variance solely due to changes in
extrinsic conditions? We know that there is
a genetic variation for the degree to which phenotypes are a!ected by environmental di!erences
(Waddington, 1957; Scheiner, 1993; Via et al.,
1995). Therefore, the genes specifying the genetic}environmental interaction can also evolve,
and as a by-product they can in#uence the probability of peak shift. It is particularly interesting
when the induced phenotypes are transmitted
between generations. Because dual inheritance of
a trait separates the e!ects of selection on phenotypes and genotypes (PaH l, 1998), divergence might
be a hierarchical process (see below). In this
paper, we examine the consequences of inherited
phenotypic variation on the probability of peak
shift.
2. Epigenetic Inheritance Systems
and Speciation
We have got a growing number of experimental facts showing the inheritance of non-DNA
variation (for details and references see Jablonka
& Lamb 1995; Russo et al., 1996). The systems
enabling the transmission of phenotypic information have been recently called epigenetic inheritance systems (EIS), (Maynard Smith, 1990). The
epigenetic variants are mostly not reversed in
a predictable manner, and are not as stable
as genetic mutations. Environment can induce
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
di!erent phenotypes, and the changed phenotypic pattern can be inherited even if the original
stimuli are absent (for references see Jablonka
& Lamb 1995, Table 6.1). Several types of cellular
epigenetic inheritance systems are known (for
di!erent classi"cations see Jablonka & Lamb,
1995; SzathmaH ry, 1999). The most prominent of
them is the chromatin marking system which is
carried and transmitted to the chromosomes
during DNA replication. Chromatin marks*including DNA methylation pattern, or proteins
attached to the DNA*do not change the coding
properties of the genes, they rather a!ect the
nature and long-term stability of gene expression
(e.g. Holliday, 1987). Recent studies convincingly
demonstrated that epigenetic states are sometimes meiotically heritable (e.g. Grewal & Klar,
1996; Hollick & Chandler, 1998; Cavalli & Paro,
1998; Kakutani et al., 1999).
According to Jablonka & Lamb (1991, 1995),
both genetic and epigenetic variation can contribute to speciation and reproductive isolation.
They stated that while two parts of the population are geographically or ecologically separated,
they accumulate di!erent epigenetic marks that
are followed by the "xation of DNA mutations.
They proposed that epigenetic changes alone can
lead to some reduction of hybrid viability or
fertility. This idea seems to be very plausible,
because (i) the rate of new epigenetic variation
produced can be much higher, than the rate of
genetic changes. Therefore, an EIS can initiate
evolutionary divergence. (ii) Selection can force
the stabilization of (favourable) epigenetic variants by genetic changes, ensuring more reliable
transmission of information. In the following,
we examine the theory in the light of recent
experiments:
(1) Changes in epigenetic marks of related
species can cause inviability or sterility of hybrids.
Jablonka & Lamb (1995, 1998) claimed that divergence of epigenetic marks could alone lead to
some "tness reduction in hybrids. They considered the nuclear transplantation experiments
in mouse (Mcgrath & Solter 1984, Surani et al.,
1984) as a support of their ideas. These studies
demonstrated that zygotes with two maternal or
parental set of genomes of the same species show
abnormal development. Although these results
are very impressive, we cannot conclude that
21
divergence of epigenetic marks would solely
cause "tness reduction in hybrids (Johnson,
1998). Nevertheless, they do show that epigenetic
compatibility is necessary for normal development (Jablonka & Lamb, 1998). Sometimes, alleles or characters of interspecies hybrids show
species-speci"c expression (e.g. Reeder, 1985;
Zakian et al., 1991). In other cases, interspecies
crosses display parent-of-origin defects (Forejt
& Gregova, 1992; Signoret & David, 1986; Vrana
et al., 1998).
It is clear from these examples that species
sometimes carry di!erent epigenetic marks that
a!ect gene expression in hybrids. Nevertheless,
these "ndings do not demonstrate directly that
the epigenetic divergence anticipated genetic
changes. It is possible that the epigenetic states
are strictly determined by the genetic system,
without any epigenetic variability. Accordingly,
epigenetic changes might be only a manifestation
of the accumulation of di!erent mutations in
di!erent species.
(2) Epigenetic marks change under a new selection pressure. We know that highly inbred
populations sometimes exhibit high epigenetic
variation (Ruvinsky et al., 1983). More remarkably, selection experiments showed the capacity
of inbred strains to adapt to new environmental
conditions (Brun, 1965; Fitch & Atchley, 1985;
Shaposhnikov, 1966). Although other explanations can be given to these "ndings, it is conceivable that the environment induced heritable
phenotypic variation, and the bene"cial variants
spread in the population. We do not know,
whether these results are the tip of an iceberg, or
simple contamination errors, but the paradox
can be resolved by a series of selection experiments using inbred strains.
(3) Epigenetic divergence can occur prior to
genetic changes. West-Eberhard (1986, 1989) argued that new ecological innovations begin with
the bifurcation of developmental or behavioural
programs giving rise to intraspeci"c alternative
phenotypes. This enables the genotype to occupy
a new niche without abandoning the old one.
Some conditions may favour the "xation or exclusive expression of one of the alternatives that
are followed by rapid genetic changes. WestEberhard documented rather good examples that
make her idea highly plausible. Nevertheless, she
22
C. PAD L AND I. MIKLOD S
did not consider the case when the di!erent
phenotypes have heritable capacities. We know
a few cases when we might suspect that the divergence of heritable epigenetic marks*e.g. methylation*has been responsible for the isolation.
Shaposhnikov (1966) showed that a clone of
aphids allowed to reproduce parthenogenetically
on a novel host diverged rapidly and acquired
a new host preference. If sexual reproduction was
permitted, the derived clone failed to produce
a viable o!spring with the original population.
Even more remarkably, the new strain displayed
close morphological resemblance to a conspeci"c
species living on the host to which it had become
adapted. Because of the genetical similarity of the
ancient and the derived clones, it is probable that
epigenetic marks diverged during the experiment.
This proposition is strengthened by the "nding
that heritable phenotypic variation in aphids
correlates with changes in methylation (Field
et al., 1989).
(4) Epigenetic changes can be strengthened by
genetic mutations. We know some cases when
environmentally induced phenotypic variants resemble the e!ects of known genetic mutations
(phenocopies; Scharloo, 1991). Series of selection
experiments demonstrated that the phenotypic
response became expressed even in the absence of
the stimuli that were initially necessary to induce
it (Scharloo, 1991). Waddington (1953) introduced the concept of genetic assimilation to highlight
this phenomenon. According to his interpretation, there is a variation in the dependence of
gene expression on environmental conditions.
Selection can act on this variation, producing
genetic variants with constitutive expression of
the required phenotype.
Unfortunately, we still do not know exactly
whether EIS plays an important role in the assimilation of an environmentally induced trait.
Nevertheless, there is at least one remarkable example. Ho et al. (1983) found that the
assimilation of the Bithorax phenocopy can
also occur in inbred lines of Drosophila.
Maybe epigenetic variants were induced during
the experiment, and they were transmitted for
the subsequent generations (Jablonka & Lamb,
1995, p. 167). It has also been proposed that
these epigenetic variants can be later "xed by
genetic mutations.
That epigenetic changes of a given gene might
help the population to move across an adaptive
valley is obvious from the following elementary
example. Consider a diploid sexual organism
with two di!erent possible alleles at a locus. We
de"ne the "tness of genotypes (AA,Aa,aa) as
=(AA)"1, =(Aa)"1!s and =(aa)"1, respectively. This "tness scheme can arise due to
epistatic interaction between the alleles. Consider
now a large panmictic population "xed for one of
the alleles (A). Because of the selective disadvantage of heterozygotes, a rare a allele has negligible
chance to spread. Nevertheless, gene expression
might be suppressed on an epigenetic variant of
the common allele (denoted by A). Now the rare
a can be coupled either with A or A. It has a
clear disadvantage as Aa. In contrast, the Aa
type mimics a hemyzygous * (a0) stage. If di!erences in the amount of gene products do not cause
serious phenotypic di!erences, then Aa may be
indistinguishable from aa. Therefore, the "tness
of the suboptimal (heterozygote) genotype is enhanced. Consequently, the probability of peak
shift is also enlarged.
In this paper, we improve the theory "rst suggested by Jablonka & Lamb (1991, 1995). Using
the adaptive landscape metaphor, we consider
the plausibility of epigenetically triggered peakshift of a quantitative trait.
3. Preliminary Assumptions
Historically, the notions of multiple inheritance systems and Lamarckian evolution have
been coupled. The mechanism of Lamarckian
evolution can be summarized in three statements:
(i) the change in a character can be induced by the
environment, (ii) the induced change can be
transmitted to the following generations, even if
the original inducing stimuli are no longer present, and (iii) the induced phenotypes are adaptive
in the given environment. The &&soft'' version of
Lamarckism includes only the "rst two points,
while the &&hard'' version covers all three points. If
we agree with the former, we do not think that
the environment induces the required phenotype.
Rather good and bad phenotypes are induced
alike. In this paper, we deal only with the latter
possibility: we do not assume directed epigenetic
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
variation. However, we heavily rely on the following assumptions:
(1) The genetic system speci"es only the limiting
conditions: the possible epigenetic states of
the genotype. However, the genotype does
not specify which transmissible state is
actually present in a given individual. Therefore, we do not address directly the adaptive
value of genomic imprinting (Hurst, 1997).
Imprints are abolished and reset each generation in a parental-speci"c manner, and the
expression states seem to be strictly determined by the genetic system.
(2) The genetic factors controlling epigenetic
variation do not act in a genome wise manner, but rather localize their action to particular regions in the genome. This enables
certain traits to evolve rapidly, while also
ensuring the conservation of other genes
(similar to the e!ects of certain hypermutable
loci, Moxon et al., 1994). In this way, the ratio
of bene"cial to harmful variants is enhanced.
We think that it is reasonable to assume
locus-speci"c epigenetic state modi"er genes.
In certain cases, multiprotein complexes
assemble at speci"c sites in the genome to
mediate the propagation of discrete states of
gene expression by organizing heritable
chromatin structures (Klar, 1998). Changes in
the regulatory proteins or cis-acting control
regions seem to have only local e!ects on the
establishment or propagation of these states
(Grewal and Klar, 1996; Cavalli and Paro,
1998). Nevertheless, we admit that there are
known cases, when mutation of certain genes
caused meiotically stable reduction in the
methylation level of the whole genome (e.g.
Kakutani et al., 1999).
(3) The establishments of di!erent expression
states are mechanistically (or genetically) separable from the heritable maintenance of expression states. In the light of recent experimental
"ndings (e.g. Pirrotta, 1997; Cavalli and Paro,
1998) this assumption seems to be plausible.
4. The Basic Model
In this section, we examine the e!ect of the
environment on a quantitative, polygenic trait.
23
The environment modi"es the phenotypic pattern in two di!erent ways: it generates
phenotypic variation and selects the variants.
Throughout the paper, we restrict our attention
to a constant environment. This means the following: only microenvironmental #uctuation is
present, inducing di!erent phenotypes, but the
individual "tness function remains unchanged. It
is assumed that the reaction of phenotypes on
environmental changes is determined genetically.
According to Gavrilets and Scheiner (1993), the
value of an arbitrary individual trait ( y) can be
given by a polynomial of the form
y"x#P m#P m#2#P mL,
L
(1)
where the quantities x, and the P 's depend on the
G
genotype and m is a single environmental parameter. The P 's specify the reaction norm of the
G
genotype to microenvironmental changes. The
distribution of m is assumed to be Gaussian with
mean m and variance d. As a "rst approximation,
K
we omit the quadratic and higher-order term, so
eqn (1) reduces to
y"x#P m.
(2)
This linear relationship between phenotype
and environment can be a good approximation if
the e!ect of the microenvironments on the trait is
small (Gavrilets & Hastings, 1994). The mean
phenotype of a genotype across environments is
yN "x#P m, and the phenotypic variance of the
genotype is < "P d. Without the loss of genW
K
erality*possibly by rede"ning the scale*we set
m"0, so yN "x. Therefore, the phenotypic distribution of a given genotype is also Gaussian
1
!(x!y)
u (y)"
exp
,
2<
(2n<
W
W
(3)
with mean x and variance < . For a simpler
W
denotation, we change P to P, and call it epi
genetic variability. Epigenetic variability determines the capability of the genotype to generate
phenotypic variants di!erent from the genetically
hard-wired one (x), regardless of their adaptive
states. It has nothing to do with adaptive
24
C. PAD L AND I. MIKLOD S
phenotypic plasticity, because we do not assume
speci"c responses to changing selective conditions. Presumably, epigenetic variability crucially
depends on the possible number of epigenetic
states of the trait.
If an EIS is present, then phenotypes are not
only generated, but are also inherited. The mean
number of generations through which the phenotypes are transmitted is measured by the memory
(m). In the model, epigenetic variability and memory characterize the EIS from a functional point
of view.
The mean phenotype (x), the epigenetic variability (P) and the memory (m) of a given trait are
assumed (i) to be determined by the genetic system; (ii) to be genetically independent of each
other and any other traits; and (iii) to evolve, like
any other character.
5. The Adaptive Landscape of the Genotype
The adaptive landscape metaphor has di!erent
interpretations. In the "rst version, which is quite
common although sometimes misleading, the
adaptive landscape shows the relationship between the possible genetic state and the mean
"tness of the population. This interpretation is
based on a more fundamental version: the adaptive landscape of the genotype. This shows the
"tness of the genotype as plotted against the
possible genetic states of the characters (Gavrilets, 1997). A discrete point on the landscape
does not represent a possible state of a population, but rather a single genotype. Population is
given here as a cloud of points. We also have to
make a clear distinction between genotypic and
individual "tnesses. The latter shows the "tness of
a given phenotype as a function of the possible
phenotypic states. Due to phenotypic variation,
the genotypic "tness is a weighted average over
the "tnesses of all possible phenotypes.
The "tness of the genotype with an epigenetic
inheritance system is given as follows (see also
PaH l, 1998). The "tness of an individual with
phenotype y is =(y). This phenotype is induced
with frequency u(y) in the "rst generation. The
phenotypes are transmitted to subsequent generations speci"ed by the memory. After m generation selection the frequency of the y phenotype
is proportional to u(y)=(y)K. Therefore, the
frequency of the (x, P, m) genotype after m
generation is proportional to u(y)=(y)K dy.
The expected "tness of the (x, P, m) genotype
is the geometric mean over the memory span.
We obtain that
=(x, P, m)"
u(y)=(y)K dy
K
.
(4)
In the case of P'0 and m"1 the phenotypes are only induced but not inherited. The
"tness of a genotype with epigenetic inheritance
is reasonable only if memory is much shorter
than the expected time it takes the trait to
mutate. Because the transmission e$ciency of
epigenetic information is much lower than that of
genetic information, this assumption seems to be
ful"lled. Accordingly, the time-scales of phenotypic variation and selection is di!erent from the
time-scale of genetic evolution.
The central question of our work is the following: when is it favourable for the genotype to
enlarge or to suppress phenotypic variability?
How can evolution of an EIS modify the probability of peak shift? Before exploring these questions on a multi-peak "tness surface, we have to
examine the behaviour of these systems if the
landscape has only one global optimum.
6. The One-peak Adaptive Landscape
We assume Gaussian stabilizing selection on
the character. Accordingly, the individual "tness
function is
=(y)"exp
!(y !y)
MNR
,
2<
Q
(5)
where y
gives the optimal phenotype and
MNR
1/< measures the intensity of selection. If we
Q
ignore the e!ect of linkage disequlibrium, or
frequency}dependent selection, then the mean
phenotype will tend to the maximum. How does
selection change epigenetic variability during the
evolution of the mean? Applying eqns (3) and (5),
the evaluation of eqn (4) gives
=(x, P, m)"
<
K
!(x!y )2
Q
MNR .
exp
2(<#Pmd)
< #P md
Q
K
Q
K
(6)
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
If phenotypic variation is suppressed (P"0),
eqn (6) reduces to =(y), with y"x. We assume
that the mean and the epigenetic variability
evolve synchronously on the adaptive landscape,
leaving the memory unaltered. Now we can
examine the optimal epigenetic variability for
a given point of the landscape (x) and for a given
memory (m). Solving * ln =(x,P,m)/*P"0, we
obtain
< 1
.
P " (x!y )! Q
MNR
MNR
m d
K
(7)
Increasing epigenetic variability is advantageous in the following cases [see eqn (7)]:
(1) The character is far from the peak of the
landscape. On the peak of the landscape
(x"y ) selection forces to suppress epigenetic
MNR
variability. This is due to the fact that in this case
phenotypic variance produces only suboptimal
phenotypes.
(2) The intensity of selection is high. It ensures
that the possibility of "nding a much better epigenetic variant is high.
(3) The microenvironmental variance (d) is
K
low. If d decreases, epigenetic variability has
K
to increase to ensure unchanging phenotypic
variation.
(4) The memory is long. Memory increases the
strength of phenotypic selection. It allows the
rarely induced, but advantageous phenotypes to
spread. On the other hand, if the phenotypes are
not heritable (m"1), the genotype &&regenerates''
its variants in every generation, so that they are
always present with the same frequency. Epigenetic inheritance systems enable phenotypic
variability to be high, even if the intensity of
selection is low, and the mean is close to its
optimum.
7. Genetic Assimilation:
Theory and Consequences
By de"nition, we "nd the critical point of the
landscape, where the optimal epigenetic variability is zero:
x "y $
APGR
MNR
<
Q.
m
(8)
25
If the phenotypes are generated but not
inherited (m"1), the critical point coincides
with the in#ection point of the landscape
(x "y $(< ). This relationship can also be
APGR
MNR
Q
realized by elementary algebra using the Jensen
inequality (see appendix A). As a result of a very
di!erent theoretical framework, Rice (1998)
arrived at the same conclusion. Increasing
phenotypic variance is advantageous if the adaptive landscape is convex, and disadvantageous if
it is concave.
It has been widely demonstrated that environmental sensitivity (plasticity) is a trait that can
respond to selection, and this response is partly
independent of a change in the mean of that trait
(Scheiner, 1993). Our model predicts that (i) directional selection pressure on the mean could
lead to changes in plasticity. (ii) In contrast, selection on plasticity is expected to leave the mean of
the trait unchanged. (iii) Increasing intensity of
selection on the mean would lead to higher plasticity [eqn (7)]. The "rst two, (i) and (ii), predictions have been already con"rmed by the experiment of Scheiner & Lyman (1991). Nevertheless,
the third point suggests some new empirical tests.
In a truncation selection experiment similar to
that mentioned above, it would be quite easy to
manipulate the intensity of selection by resetting
the threshold (see also Rice, 1998). It has also
been shown that as long as the trait is far from the
adaptive peak, heritable epigenetic variation is
especially favourable. Near the optimum, the
stabilizing e!ect of selection dominates, so it
forces to suppress epigenetic variation.
The capacity of the organisms to ensure the
production of a standard phenotype in spite of
environmental disturbances is called canalization
(Waddington, 1942). Under stabilizing selection,
canalization can bu!er against phenotypic variation, without changing the average expression of
the character. If the trait is under directional
selection, the optimal phenotype appears with
a very low frequency at the beginning, and it is
probably induced by the environment. The frequency of the optimal phenotype increases, as
epigenetic variability increases, and the mean
evolves closer to the optimal phenotype. Reaching the critical point of the landscape, the suppression of phenotypic variation is selectively
advantageous. Genetic assimilation occurs much
26
C. PAD L AND I. MIKLOD S
closer to the peak, if an epigenetic inheritance
system is present [m'1, eqn (8)].
Waddington (1953) showed how phenotypic
variation can be converted to genetic changes
without hurting the central dogma. However,
Williams (1966) claimed that genetic assimilation
cannot contribute signi"cantly to adaptive evolution, because the e!ects of environmental challenges are mostly harmful for the organisms. Under a new selection pressure never experienced
before, we cannot expect the organisms to give
immediate speci"c responses. Adaptive phenotypic plasticity can only be achieved under regularly changing selective conditions, through the
slow process of natural selection. It is obviously
true, but irrelevant for us. We considered the
evolution of phenotypic variability under directional selection forces, and not the evolution of
speci,c responses under changing (selective) environments. We do not assume any correlation between selective demands and inducing factors
(for a similar, detailed argument see Eshel
& Matessi, 1998). Thus, changing inducing conditions do not necessarily lead to "tter phenotypes.
It is enough, if only a fraction of the induced
phenotypes is adaptive: directed epigenetic variation is not necessary for the process to go on.
Genetic assimilation is an inevitable consequence
of the selection acting on the mean and epigenetic
variability.
The inheritance of phenotypic variation seems
to be especially favourable if new favourable genetic variants turn up very rarely. This can occur
under a wide range of circumstances: if the size of
the population is low, recombination is limited or
absent, etc.
8. Multiple Adaptive Peaks
Using the results of the previous sections, we
address the question, how can epigenetic inheritance modify the evolution of a trait if there are
multiple "t states for the individuals. We will see
that even if there is a bimodal relation between
individual "tness and the value of a quantitative
trait, the "tness surface of the genotype can be
both uni- or bimodal, depending on the phenotypic variance and the memory. We also examine
the selection pressure acting on epigenetic variability.
Kirkpatrick (1982) designed a bimodal "tness
function of the individuals. According to his
formula, the "tness of an individual with phenotype y is
!(y!y
)
MNR
2<
Q
!(y!y
)
MNR ,
#H exp
2<
Q
=(y)"exp
(9)
where the two phenotypic maxima are located at
y
and y
, 1/< measures the intensity of
MNR
MNR
Q
selection, and H gives the relative heights of the
peaks. Using eqns (3) and (9) the integration in
eqn (4) can be evaluated to give
=(x, P, m)"
<
K K m
K
Q
,
HI exp(b/4a!c)
<#m<
k
Q
W
I
(10a)
where
a"m/2< #1/2< ,
Q
W
b"x/< #(y
k#y
(m!k))/< ,
W
MNR
MNR
Q
(10b)
(10c)
c"x/2< #(y k#y (m!k))/2< . (10d)
W
MNR
MNR
Q
[For the derivation of eqn (10) see Appendix B.]
One of the disadvantages of this formula is that
the derivatives with respective to x and P are
transcendental functions, hence the minima and
maxima cannot be solved analytically. Therefore,
we used numerical simulations to see the behaviour of the model.
8.1. THE TRANSITION BETWEEN PEAKS
Generally, peak shift is described as a movement along the population "tness surface. However, because population clusters around one
genotype, it is enough to envisage the e!ects of an
EIS on the adaptive landscape of the genotype.
We considered a bimodal, asymmetric individual
"tness function; therefore two isolated optimal
states are present in the absence of phenotypic
variation (Fig. 1). With epigenetic variability, the
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
27
"tnesses of the intermediate genotypes are enhanced. This is a result of the environmental
deviations producing individuals with phenotypes of the other peak (Kirkpatrick 1982). This
e!ect is especially pronounced with large memory [Fig. 1(a) and (b)]. Because the transition rate
primarily depends on the valley depth, an EIS is
expected to facilitate the shift between adaptive
states.
Why is it so? Phenotypes between the optimal
states still su!er selective elimination. Nevertheless, a genotype with intermediate mean (x) need
not reside in a "tness valley, because it may
contain a mixture of more or less "t phenotypes
(Coyne et al., 1997). The transmission of phenotypic information ensures that the rarely induced
favorable variants are not lost in the next generation, and they can increase in frequency. The
e$ciency of phenotypic selection depends on the
epigenetic variability (P) and the memory (m).
This process leads to the epigenetic divergence of
a given genotype: the intermediates are selectively eliminated, and the more "t phenotypes
accumulate in the population. We can conclude
that an EIS enables the genotypes to "nd a
new adaptive zone, without abandoning the old
one.
As phenotypic variation increases, the adaptive valley shallows, until the lower peak vanishes
(Fig. 2). This would lead to the evolution of the
FIG. 1. The e!ects of an epigenetic inheritance system on
the adaptive landscape of the genotype. The dashed line
shows the individual "tness function. Increasing memory
reduces the depth of the adaptive valley (a). Nevertheless,
memory must be quite high, to be favourable in the vicinity
of the lower adaptive peak (a) and (b). The genotypes with
epigenetic inheritance (P'0, m'1) su!er selective disadvantages on the higher adaptive peak (c). Therefore, near the
global optimum, canalization of phenotypic expression is
favourable. Data: m"10, 100, < "0.1, < "1, y
"0,
W
Q
MNR
y
"2.4, H"1.2.
MNR
genotypic optima do not coincide with the peaks
of the individual "tness function, but are displaced towards the other peak. The attraction of
the higher peak is extended. In addition, the
FIG. 2. Changing positions of the minima and maxima
on the adaptive landscape as phenotypic variance of the
genotype increases. Epigenetic variability diminishes the distance between the peak and the bottom of the valley. Reaching the critical phenotypic variance, the lower peak vanishes,
and only the upper maximum remains. Data: m"10,
< "1, y
"0, y
"2.4, H"1.2.
Q
MNR
MNR
28
C. PAD L AND I. MIKLOD S
mean by mass selection alone. As the mean gets
to the vicinity of the neighboring peak, it is disadvantageous to generate epigenetic variation.
Once the optimal genotype is found, exploration
away from this optimum only reduces "tness
[Fig. 1(c), Sections 6 and 7].
8.2. THE EFFECT OF SELECTION ON EPIGENETIC
VARIABILITY
Previously, we argued that a given epigenetic
inheritance system can in#uence the evolutionary
dynamics of a trait. However, another problem
arises. Generally, evolution is regarded to be
myopic, an event happening now would not
be selected for just because it will turn out to be
advantageous in the distant future. Therefore, it
is not enough to show that dual inheritance
of a trait enhances the transition towards a
higher peak. We also have to know how the genes
controlling non-zero epigenetic variability are
maintained in the population. The possible answer is either (a) the presence of an EIS is a side
e!ect of other evolutionary forces or structural
constraints, or (b) the genetic control of
phenotypic variation has been directly shaped by
natural selection. Although, we may never know
whether (a) holds in general, we put forth an
argument in favour of (b).
Consider now the genotypic "tness as a function of epigenetic variability and the mean. If the
mean (x) coincides with a maximum, the mutants
with phenotypic variance slightly higher than
zero necessarily su!er "tness reduction (Fig. 3.) In
this case, the phenotypes of the new adaptive
zone do not appear frequently enough to compensate the disadvantage of generating suboptimal variants. Thus, although the population may
evolve from y
to y
along various paths on
MNR
MNR
the x}P plane, it still has to move across an
adaptive valley. We propose two di!erent ways
to solve the problem:
(1) Changes in the inducing e!ect of the
environment, leaving the selective conditions
unaltered can initiate peak shift (Fig. 4). If microenvironmental variance (d) temporarily inK
creases, the population may cross the adaptive
valley of epigenetic variability without genetic
changes. Consequently, the mean (x) evolves to
the neighbouring peak purely by selection. This
FIG. 3. Fitness as a function of phenotypic variance on
the lower "tness peak. The adaptive valley shallows, as
memory increases. x:0, < "1, y
-y
"2.5, H"1.2.
Q
MNR MNR
FIG. 4. A possible way on the x}P plane in which two
isolated peaks may be connected. The contours of the adaptive landscape are also indicated. The most likely path for
transition passes the saddle point. Changes in the inducing
e!ects of the environment (represented by mM and d) may
K
help the population overcome suboptimal phenotypic states.
Note that the zone of attraction extends to the valley as the
epigenetic variability increases.
mechanism has been originally suggested by Kirkpatrick (1982). Nevertheless, he did not consider
the possibility of heritable phenotypic variation.
=ith growing memory both the depth of the valley
and the distance of the neighbouring adaptive zone
are lowered (Figs 3 and 4, Table 1). This e!ect is
especially pronounced, if there is a large discrepancy in peak height in favour of the new peak
[Table 1(b)]. This is due to the increased strength
of phenotypic selection. It is also possible that
the mean (m) of the environmental distribution
changes. The epigenetic e!ect would di!er from
genetic mutations in an important aspect: it
29
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
TABLE 1
¹he position of the saddle point and its ,tness
value. P"0 corresponds to the situation, when
epigenetic variability is not allowed to evolve.
Data: (a) H"1.2, y
"0, y
"3, <"1,
MNR
MNR
Q
d"1. (b) H"1.4, y
"0, y
"3, < "1,
K
MNR
MNR
Q
d"1
K
(a)
Position of the saddle point
P"0
m"1
m"10
m"50
x"1.390
x"0.799, P"0.871
x"0.413, P"0.840
x"0.166, P"0.549
Fitness in the
saddle point
="0.709
="0.857
="0.927
="0.988
(b)
P"0
m"1
m"10
m"50
Position of the saddle point
Fitness in the
saddle point
x"0.760
x"0.677, P"0.757
x"0.33, P"0.690
x"0.131, P"0.422
="0.759
="0.890
="0.945
="0.996
yields novel phenotypes in many individuals of the
population at the same time (Jablonka & Lamb,
1995, pp. 222}224). If the suboptimal phenotypic
state is passed through, then the transformed
population "nds itself under a new selective regime. After phenotypic inducement, the population can evolve by genetic changes to the other
adaptive state. Because increasing memory enlarges the attraction domain of the higher peak,
the initial increase of phenotypic variation can be
driven even by slight changes in the environment.
Summarizing, the rate of evolution may depend
on the speci"c distribution of the (inducing)
environment.
(2) In Section 3, we assumed that the epigenetic variability and the mean are genetically
independent, evolving traits. Therefore, the rate
of stochastic shift may be augmented by the simultaneous changes of x and P. Each path on the
x}P plane has certain probabilities. In a multidimensional adaptive surface, the most probable
#ux between alternative states passes a single
saddle point (Barton & Rouhani, 1987). The frequency of stochastic shifts is proportional to
the ratio =
M /=
where =
and =
are the popuQ N
N
Q
lation "tnesses on the peak and saddle, respec-
tively. With an EIS, genotypic "tness value of the
saddle point is highly enhanced (Table 1). Thus,
the rate of drift-induced transition is also expected to increase. We in turn examine the details
of this possibility.
9. The Expected Time for Peak Shift Under
Finite Population Size and Evolving
Genetic}environmental Interaction
In the preceding section, we stated that an EIS
substantially reduces the depth of the valley
separating peaks (Fig. 3, Table 1). Because the
probability of drift-induced transition primarily
depends on the valley depth (Barton & Charlesworth 1984, Lande 1985), the evolutionary
dynamics of divergence is expected to increase.
This statement is in turn investigated explicitly.
We restrict our attention to the case when phenotypes are induced but not inherited (P'0,
m"1). Intuitively, this seems to be the least
hopeful situation, because any initial increase of
epigenetic variability only reduces "tness (Fig. 3).
In spite of this, the simulation experiments demonstrated that the evolution of epigenetic variability substantially enhances the rate of stochastic
shifts (see below). Because valley depth diminishes with increasing memory (Fig. 3, Table 1), we
may extrapolate our "nding to those cases, when
epigenetic inheritance is present (m'1). We plan
to study the e!ect of phenotypic transmission
on the probability of drift-induced peak shift in
a future work.
9.1. MATHEMATICAL TREATMENT
If phenotypic variation is induced, but not
inherited (m"1), then eqn (10) reduces to
=(x, P, 1)" u (y) =(y) dy
"
<
!(x!y
)
Q
MNR
exp
< #Pd
2(< #Pd)
Q
K
Q
K
#H exp
!(x!y
)
MNR .
2(< #Pd)
Q
K
(11)
Presumably, the mean (x) and the epigenetic
variability (P) are genetically independent of each
30
C. PAD L AND I. MIKLOD S
other. Accordingly, we neglect the possibility of
pleiotropic mutations and the e!ects of linkage
disequilibrium. The latter might be generated
directly under strong selection or genetic drift
(Barton, 1989a). Nevertheless, this problem does
not seem to be too severe. There is evidence from
similar simulation experiments (Phillips, 1996)
that the assumption of linkage equilibrium does
not jeopardize the qualitative picture. Thus,
x and P in the population in the t-th generation
may be described by two independent distributions, denoted by p(x, t) and p(P, t), respectively.
Accordingly, the mean "tness of the population
becomes
=
(t)"
p(x, t)p(P, t) =(x, P, 1) dP dx. (12)
The strength of stabilizing selection on the mean
(x) is generally higher than that on canalization
(P) (for details see Rice, 1998; Wagner et al., 1997).
We also know that the genetic variance of
phenotypic variation is generally lower than the
genetic variance of the mean (Scheiner, 1993).
Therefore, we have a good reason to think that
the distribution of epigenetic variability does not
have a substantial e!ect on the mean "tness.
Therefore, we approximate eqn (12) by
(t): p(x, t) =(x, P , 1) dx,
=
(13)
where P is the population mean of epigenetic
variability. Generally, it is assumed that continuously varying traits have normal distributions.
Therefore, the frequency of x in generation t may
then be written as
1
!(x!xN (t))
p(x, t)"
exp
,
2<
(2n<
EV
E V
(14)
where x (t) is the population mean and < is the
EV
genetic variance of x. Using (14), eqn (13) can be
evaluated to give
<
!(xN (t)!y
)
Q
MNR
=
(t):
; exp
< #< #<
2(< #< #< )
Q
W
EV
Q
W
EV
#H exp
!(xN (t)!y
)
MNR ,
2(< #< #< )
Q
W
EV
(15)
where < "( PM (t)d ). We used Monte Carlo
W
K
simulations to examine the evolutionary dynamics of x and PM under a given selection pressure
and random genetic drift. The simulations were
semi deterministic (Kimura, 1980), and expressed
the changes of x and PM as the sum of deterministic
and random variable terms:
DxN (t)"<
EV
* ln =
M (t)
#d ,
V
*x (t)
(16a)
DxN (t)"<
E.
* ln =
M (t)
#d ,
.
*PM (t)
(16b)
where < is the genetic variance of P in the
E.
population. The deterministic part expresses that
selection causes the population to climb the surface of the mean "tness along the greatest slope
(Lande, 1976). The stochastic terms (d and d )
V
.
represent the e!ects of genetic drift. They are
generated as pseudo-random Gaussian deviates
with mean 0, variances < /2N and < /2N ,
EV
C
E.
C
respectively. (N is the e!ective population size).
C
This method provides an excellent approximation of the Fisher}Wright individual sampling
process, and it also takes several magnitudes
shorter to complete. The genetic variances were
taken constant throughout a simulation run. The
validity of this presumption is not straightforward, because the genetic variances are likely to
change in the long term (Barton, 1989a). Nevertheless, increasing genetic}environmental interaction diminishes the strength of selection on the
mean (x), so the genetic variance (< ) under
EV
mutation-selection equilibrium is expected to increase. Because growing genetic variation usually
facilitates the transition from one adaptive state
to another (Charlesworth & Rouhani, 1988,
Kirkpatrick, 1982; Whitlock, 1995), our treatment overestimates the expected time for peak
shift.
9.2. SIMULATION METHODS
All simulations were conducted by starting the
population close to the smaller peak (xN (0):
y
), showing well canalized phenotypic expresMNR
sion (P(0)"0). Each run was continued until
the population mean (xN ) reached the vicinity
of the higher peak and epigenetic variability was
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
approximately zero (x (¹):y
, P (¹):0). In
MNR
all cases, 200 replicates were run for each set of
parameters. The expected time before shift (¹M )
was the mean of the individual replicate times.
We used this procedure with preset parameter
values (Fig. 5). If < "0, epigenetic variability
E.
remained zero throughout the simulation. This
special case has been analysed previously by
Lande (1985). He gave an approximate formula
[Lande, 1985, eqn (7)] for the expected time until
shift of the mean phenotype. To shorten computer time, we used this approach, when < "0
E.
and N 53000.
C
9.3. RESULTS
The results of the simulations can be summarized in three statements (Fig. 5): (i) The
expected time (¹ ) is de"nitely lower when
epigenetic variability is allowed to evolve
(< '0), compared with the case, when phenoE.
typic variation is suppressed (< "0). (ii) The
E.
di!erences increase exponentially with the e!ective size of the population. (iii) Moderate changes
of < do not cause substantial di!erences in the
E.
expected time. Clearly, this is what we expected.
According to Barton & Charlesworth (1984) and
Lande (1985), ¹ increases exponentially with the
population size and the valley depth. The latter is
signi"cantly lowered if epigenetic variability is an
evolving trait.
31
FIG. 5. The expected time for peak shift as a function of
the e!ective population size at di!erent genetic variances of
phenotypic variability (< ). See text for details. Note that
E.
the expected time is on a logarithmic scale. Data: < "0.13,
Q
< "0.7, < "0, 0.3 and 0.7, y
!y "2, H"1.1,
EV
E.
MNR
MNR
m"1, d"1. Key: < "0 (simulation results) (䊏); < "0
K
E.
E .
(analytic approach) (;); < "0.7 (䉱); < "0.3 (䊏 ).
E .
E .
FIG. 6. The self-reinforcing e!ects of selection on
phenotypic variance. Increasing epigenetic variability (P)
has dual e!ects on the mean. At "rst, it reduces the strength
of selection on the trait, therefore the mean (x) is allowed to
evolve, leading to further increase of P. This direct e+ect has
been analysed explicitly in Section 9. However, epigenetic
variability might also have a variance directed e!ect. Increasing P enhances the genetic variance of the trait (< ), allowEV
ing further displacement of the mean.
9.4. THE SELF-REINFORCING EFFECT OF SELECTION
ON EPIGENETIC VARIABILITY
Why should evolving genetic}environmental
variance cause such a huge di!erence? One possible answer is that it is an extra dimensional
bypass, where the population can evolve. However, we think that this is only a partial answer.
The strength of stabilizing selection on the mean
(x) is generally higher than that on canalization
(P). Therefore, the genes controlling some slight
increase in epigenetic variability can be "xed
in the population without signi"cant "tness
reduction. Epigenetic variability produces some
individuals whose phenotypes place them in
the domain of the other peak. This results in the
displacement of the population optimum towards the other peak. Thus, selection acts to
change the mean, so that further increase in epi-
genetic variability might be selectively favourable
(or only slightly detrimental). Accordingly, selection is expected to push the mean further. The
initial slight increase of phenotypic variation
could lead to subsequent genetic changes of the
mean (Fig. 6). We can conclude that evolution of
the genes specifying the reaction norm can help the
population to pass through suboptimal phenotypic
states. In the vicinity of the neighbouring peak,
phenotypic variation is suppressed, leading to relatively high ,tness reduction of the suboptimal
(hybrid) genotypes.
10. The Evolution of Reproductive Isolation
Mostly, phenotypic variability is limited by
some structural reasons. Therefore, we propose
32
C. PAD L AND I. MIKLOD S
that reproductive isolation evolves gradually in
a series of successive shallow peak shifts rather
than a large single one. As long as new adaptations are available, selection forces the epigenetic
variability to enhance, triggering new peak shifts.
This chain reaction is expected to stop, if
the population reaches a global optimum*or a
highly isolated peak. Once the optimal genotype is found, exploration away from this
optimum only reduces "tness. This raises an intriguing possibility*the reversible evolution
of the genes controlling epigenetic variability
(Fig. 7). The presence of an EIS is favourable
during the transition from one adaptive state to
another, but is expected to be selectively eliminated near the global optimum. This is in agreement with the results of sections 5 and 6. Inducing epigenetic variation is favorable under directional selection, but it is supposed to remain
suppressed as the stabilizing e!ect of selection
dominates. Reproductive isolation arises as
a side-e!ect of genetic and epigenetic divergence,
and it is completed by the canalization of
phenotypic expression. After the suppression of
phenotypic variation, "t phenotypic states are
not available for the hybrids.
The expected properties of hybrids with an EIS
di!er from those formed when such a system is
not present and when the adaptive peaks
FIG. 7. The adaptive landscape of the genotype as a
function of the phenotypic variance and the mean. Two
separated peaks are connected by the ridge of epigenetic
variability. Consequently, no deep valley should be crossed
if P and x evolve synchronously. Data: m"30, < "1,
Q
y
"0, y
"2.4, H"1.
MNR
MNR
are isolated. In the latter case, any deviation
from a coadapted combination of genes leads to
signi"cant reduction in "tness (Barton, 1989b).
In contrast, a hybrid genotype with epigenetic
inheritance is expected to have viable phenotypic
variants resembling one of the parent species.
Perhaps the most widely cited example of one
factor peak shift is the evolution of new karyotypes. There are many cases of related species
"xed for di!erent chromosome rearrangements.
The interpopulation hybrids often show improper segregation, or abnormal chromosome
pairing leading to reduced fertility. Therefore, the
"xation of a new karyotype has been advocated
as an evidence that evolution sometimes proceeds through an adaptive valley. Nevertheless,
these examples do not show directly that the new
rearrangements are "xed when drift overcomes
the strong underdominance of heterozygotes.
Sometimes, heterokaryotypes vary widely in "tness (Coyne et al., 1991, 1993, 1997), and there are
clear-cut examples of reduction in hybrid viability or fertility being non-detectable (Coyne et al.,
1991). Is this only due to the genetic heterogeneity of the hybrids? It has been previously proposed that equivalent phenotypic e!ects can be
obtained either by genetic or epigenetic changes
(Zuckerlandl & Villet, 1988). Maybe, the "tness
reduction of hybrids depends on the ability of an
EIS to compensate for genetic changes and mask
the incompatibilities of the parental genomes. Of
course, we do not argue that this mechanism
would be a special adaptation for the hybrids,
rather it seems to be an accidental by-product of
the EIS initiating divergence.
For example, pericentric inversions could theoretically lead to aneuploid gametes through
crossing over. However, recombination is often
nearly absent in the inverted region for some
unknown reason. There are experimental evidences that the epigenetic state of chromatin affects the frequency of recombination (Ashley,
1988). In general, chiasma cannot form in highly
condensed regions (John, 1988; Wu & Lichten,
1994). Therefore, the fertility of heterozygotes
might be due to the accumulation of chromatin
marks in the inverted regions, leading to heterochromatinization and inhibition of crossing overs.
Finally, we must emphasize that we do not
want to give an alternative explanation for the
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
Haldane's rule (the preferential sterility or inviability of hybrids of the heterogametic sex), which
is usually explained by speci"c properties of the
sex chromosomes or sexual selection (Orr, 1997).
Our speciation theory is not limited to the action
of the sex chromosomes.
11. Di4erences Between Epigenetic and
Behavioural Inheritance
Throughout the paper, we restricted our attention to cellular epigenetic inheritance systems,
and we did not mention behavioural inheritance
of animals and man. The analogy seems to be
straightforward: new patterns of behaviour, "rst
acquired by chance or through individual learning in a new condition, may be transmitted to the
following generations through social learning
(Heyes & Galef, 1996; Jablonka et al., 1998).
Surely, there is an increasing acceptance that
learning precedes mutations, and the acquired
behaviour may be augmented by genetic assimilation (Hinton & Nowlan, 1987). It is also known
that behavioural #exibility can play a crucial role
in evolution and speciation (Wyles et al., 1983;
Baker and Jenkins, 1987; Laland, 1994; Whitehead, 1998).
However, we do not think that our results
would be directly applicable in the context of
behavioural inheritance. First, it is often argued
that animals acquire bene"cial traits by learning.
In this paper, we avoided discussing the possibility of directed phenotypic variation*the possibility of &&hard'' Lamarckism. Second, we only
investigated the vertical*parent}o!spring*
transmission of phenotypic information, which is
naturally true in the case of cellular inheritance.
On the contrary, in the case of behavioural inheritance animals may acquire information from
(i) their parents (strict vertical transmission), (ii)
relatives or (iii) anyone else in the population
with given probabilities (strict horizontal transmission). In the third case, naive animals copy the
behaviour of individuals with di!erent genetic
backgrounds, so the linked transmission of genetic and phenotypic information is not ful"lled.
We suspect that the horizontal transmission of
phenotypic information greatly alters the dynamics of evolution and the possibility of genetic
assimilation (PaH l, unpublished data).
33
12. Discussion
The dual inheritance of a character separates
the e!ects of selection on genotypes and phenotypes. Therefore, adaptation can be viewed as
a hierarchical process. At "rst, new epigenetic
variants of a given genotype appear in the population, that are later followed by the "xation of
DNA mutations. The bene"t of phenotypic
selection depends on the possibility of "nding
much better phenotypes than the genetically
hard-wired ones. Accordingly, genetic adaptation limits the e$ciency of the &&exploratory
behaviour'' of epigenetic inheritance systems.
This paper showed that an EIS can have a temporary e!ect on adaptation and divergence, but it
is selectively eliminated at the global optimum.
Thus, the question remains: How can an EIS be
permanently maintained? Are these side e!ects of
structural constraints, other selective forces, or
do they have an important role in evolution?
Previously, it has been argued that random
(Jablonka et al., 1995), or periodically #uctuating
(Lachmann & Jablonka, 1996) environment favours the spread of an EIS. Our framework can
also consider this e!ect. We have to incorporate
that both the inducing and the selective conditions may change in time and space.
In this paper, we investigated the behaviour of
an epigenetic inheritance system, if there are multiple "t states for the individuals. We arrived at
the conclusion that evolution can proceed
through suboptimal phenotypic states, without
passing through a deep adaptive valley of the
genotype. We suggest that epigenetic changes
might contribute to the evolutionary divergence
of populations. This "nding may alter our view
on the dynamics and mode of reproductive
isolation. In the following, we summarize our
speciation scenario:
(1) The preliminary condition to epigenetically
induced divergence is the presence of the genes
controlling non-zero epigenetic variability. The
initial increased frequency of an epigenetic modi"er may be driven by slight changes in the inducing environment or by genetic drift.
(2) New epigenetic variants appear in the
population. Some of them can be selectively
favourable and can accumulate in the population. This enables the genotypes to occupy a new
34
C. PAD L AND I. MIKLOD S
adaptive zone without abandoning the old one.
The extent of epigenetic divergence crucially
depends on the transmission e$ciency of phenotypic information. Low e$ciency prevents the
spread of these variants.
(3) Selection forces the favourable epigenetic
variants to be conserved by genetic changes. As
a result, the favourable variants are transmitted
to the o!spring in a more reliable way. Genetic
assimilation of phenotypic variants leads to the
genetic divergence of the populations. It is possible that this process*epigenetic changes followed by genetic "xation*is reiterated as long
as new adaptive peaks are available.
(4) As the derived population is genetically
close to an optimal state, and no higher adaptive
peaks are available, selection acts to suppress
epigenetic variability. Canalization of phenotypic
expression strengthens the reproductive barrier,
because no "t epigenetic states are available for
the hybrids.
In one of his papers, Wright (1932) said that
there must be some trial and error mechanism by
which the species may explore a small portion of
the "eld (genotypic space) which it occupies. He
thought that this mechanism works at the level of
subpopulation (demes). We rather think that epigenetic inheritance systems enable this localized
search at the phenotypic level, guiding the genetical system to new optima. Epigenetic variability
opens new dimensions on the adaptive landscape,
where the population can evolve. Therefore, our
work is in a good accordance with Fisher's view.
Fisher (1930) rejected the existence of isolated
peaks, arguing that as the number of traits considered increases, the probability that a given
equilibrium would be stable to perturbations decreases. He thought that our imagination is limited by viewing the population at equilibrium,
and by neglecting the complicated "tness surface
that channels evolution. Dobzhansky's (1937)
model also laid special emphasis on the &&ridges''
of quasi well-"t genotypes, connecting reproductively isolated genotypes. The existence of an
adaptive valley separating current genotypes is
not an evidence that this valley has been crossed
during divergence.
This idea has become a point of renewed interest (for a review see Gavrilets, 1997). Based on
a theoretical framework, Gavrilets & Gravner
(1997) stated that ridges must be a general property of multidimensional adaptive landscapes.
According to this view, populations become reproductively isolated when they are on the opposite sides of a &&hole'' on the landscape (Gavrilets,
1997). This strict geometrical view of evolution
gives ample scope to any special genetic trait
(dimensions) that could routinely facilitate divergence. In this work, we argued that heritable
non-DNA changes open new routes for evolution.
The exploratory behaviour of an EIS is responsible for the &&ridges'' connecting the otherwise
separated adaptive peaks. After reaching a new
adaptive zone, these ridges are eliminated by the
canalization of phenotypic expression, leading to
the regeneration of the genetic barrier.
Throughout the paper C.P. is responsible for the
theoretical treatments, while I.M. is responsible for the
computer simulations. We would like to thank EoK rs
SzathmaH ry, BeaH ta Oborny and the anonymous referees for the critical comments, and IstvaH n Scheuring
for an extremely useful suggestion. We are also grateful to GaH bor KutrovaH cz for his help in preparing the
manuscript.
REFERENCES
ASHLEY, T. (1988). G-band position e!ects on meiotic synapsis and crossing over. Genetics 118, 307}317.
BAKER, A. J. & JENKINS, P. F. (1987). Founder e!ect and
cultural evolution in an isolate population of cha$nches
Fringilla coelebs. Anim. Behav. 35, 1793}1803.
BARTON, N. H. (1989a). The divergence of a polygenic system under stabilizing selection, mutation and drift. Genet.
Res. 54, 59}77.
BARTON, N. H. (1989b). Founder e!ect speciation. In: Speciation and its Consequences, (Otte, D., Endler, J. A., eds),
Sunderland, MA: Sinauer.
BARTON, N. H. & CHARLESWORTH, B. (1984). Genetic revolutions, founder e!ects and speciation. Ann. Rev. Ecol. Syst.
15, 133}164.
BARTON, N. H. & ROUHANI, S. (1987). The frequency of
shifts between alternative equilibria. J. theor. Biol. 125,
397}418.
BRUN, J. (1965). Genetic adaptations in Caenorhabditis
elegans (Nematoda) to high temperatures. Science 150, 1467.
CAVALLI, G. & PARO, R. (1998). The Drosophila Fab-7
chromosomal element conveys epigenetic inheritance during mitosis and meiosis. Cell 93, 505}518.
CHARLESWORTH, B. & ROUHANI, S. (1988). The probability
of peak shifts in a founder population. II. An additive
polygenic trait. Evolution 42, 1129}1145.
COYNE, J. A., AULARD, S. & BERRY, A. (1991). Lack of
underdominance in a naturally occurring pericentric inversion in Drosophila Melanogaster and its implication for
chromosomal evolution. Genetics, 129, 791}802.
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
COYNE, J. A., BARTON, N. H. & TURELLI, M. (1997). Perspective: a critique of Sewall Wright's shifting balance
theory of evolution. Evolution, 51, 643}671.
COYNE, J. A., MEYERS, W., CRITTENDEN, A. P. &
SNIEGOWSKY, P. (1993). The fertility e!ects of pericentric
inversions in Drosophila Melanogaster. Genetics 134,
487}496.
DOBZHANSKY, T. (1937). Genetics and the Origin of Species.
New York: Columbia University Press.
ESHEL, I. & MATESSI, C. (1998). Canalization, genetic assimilation and preadaptation: A quantitative genetic
model. Genetics 149, 2119}2133.
FIELD, L. M., DEVONSHIRE, A. L., FFRENCH CONSTANT,
R. H. & FORDE, B. G. (1989). Changes in DNA methylation are associated with loss of insecticide resistance in
the peach potato aphid Myzus persicae (Sulz.). FEBS ¸ett.
243, 323}337.
FISHER, R. A. (1930). ¹he Genetical ¹heory of Evolution.
Oxford: Oxford University Press.
FITCH, W. M. & ATCHLEY, W. R. (1985). Rapid mutations in
mice? Science 230, 1408}1409.
FOREJT, J. & GREGOROVA, S. (1992). Genetic analysis of
genomic imprinting: an Imprintor-1 gene controls inactivation of the paternal copy of the mouse ¹me locus. Cell 70,
443}450.
GAVRILETS, S. (1997). Evolution and speciation on holey
adaptive landscape. ¹rend. Ecol. Evol. 12, 307}312.
GAVRILETS, S. & GRAVNER, J. (1997). Percolation on the
"tness hypercube and the evolution of reproductive isolation. J. theor. Biol. 184, 51}64.
GAVRILETS, S. & HASTINGS, A. (1994). A quantitative genetic model for selection on developmental noise. Evolution
48, 1478}1486.
GAVRILETS, S. & SCHEINER, S. (1993). The genetics of
phenotypic plasticity. V. Evolution of reaction norm
shape. J. Evol. Biol. 6, 31}48.
GREWAL, S. I. S. & KLAR, A. J. S. (1996). Chromosomal
inheritance of epigenetic states in "ssion yeast during mitosis and meiosis. Cell 86, 95}101.
HEYES, C. M. & GALEF, B. G. (eds) (1996). Social ¸earning in
Animals: the Roots of Culture. New York: Academic Press.
HINTON, G. E. & NOWLAN, S. J. (1987). How learning can
guide evolution. Complex systems 1, 495}502.
HO, M. W., TUCKER, C., KEELEY, D. & SAUNDERS, P. T.
(1983). E!ects of succesive generations of ether treatment
on penetrance and expression of the Bithorax phenocopy
in Drosophola melanogaster. J. Exp. Zool. 225, 357}368.
HOLLICK, J. B. & CHANDLER, V. L. (1998). Epigenetic allelic
states of a maize transcriptional regulatory locus exhibit
overdominant gene action. Genetics, 150, 891}897.
HOLLIDAY, R. (1987). The inheritance of epigenetic defects.
Science 238, 163}170.
HURST, L. D. (1997). Evolutionary theories of genomic imprinting. In Genomic Imprinting (Reik, W. & Surani, A.,
eds). Oxford: IRL Press.
JABLONKA, E. & LAMB, R. M. (1991). Sex chromosomes and
speciation. Proc. Roy. Soc. ¸ond. B 243, 203}208.
JABLONKA, E. & LAMB, R. M. (1995). Epigenetic Inheritance
and Evolution. Oxford: Oxford University Press.
JABLONKA, E. & LAMB, R. M. (1998). Epigenetic inheritance
in evolution. J. Evol. Biol. 11, 159}183.
JABLONKA, E. & LAMB, R. M. & AVITAL, E. (1998). Lamarckian mechanisms in Darwinian evolution. ¹rends. Ecol.
Evol. 13, 206}210.
35
JABLONKA, E., OBORNY, B., MOLNAD R, I., KISDI, E., HOFBAUER, J. & CZAD RAD N, T. (1995). The adaptive advantage of
phenotypic memory in changing environments. Phil.
¹rans. R. Soc. ¸ond. B 350, 133}141.
JOHN, B. (1988). The biology of heterochromatin. In Heterochromatin: Molecular and Structural Aspects (Verma, R. S.,
eds), pp. 1}147. Cambridge: Cambridge University Press.
JOHNSON, N. A. (1998). Postzygotic reproductive isolation:
Epigenetics for an epiphenomenon? J. Evol. Biol. 11,
207}212.
KAKUTANI, T., MUNAKATA, K., RICHARDS, E. J. &
HIROCHIKA, H. (1999). Meiotically and mitotically
stable inheritance of DNA hypomethylation induced by
ddm1 mutation of Arabidopsis thaliana. Genetics 151,
831}838.
KIMURA, M. (1980). Average time until "xation of a
mutant allele in a "nite population under continued
mutation pressure: studies by analytical, numerical, and
pseudo-sampling methods. Proc. Nat. Acad. Sci. ;SA 77,
522}526.
KIRKPATRICK, M. (1982). Quantum evolution and punctuated equilibrium in continuous genetic characters. Am.
Nat. 119, 833}848.
KLAR, A. J. S. (1998) Propagating epigenetic states through
meiosis: where Mendel's gene is more than a DNA moiety.
¹rends Genet. 14, 299}301.
LACHMANN, M. & JABLONKA, E. (1996) The inheritance of
phenotypes: an adaptation against #uctuating environments. J. theor. Biol. 181, 1}9.
LALAND, K. N. (1994) On the evolutionary consequences of
sexual impriting. Evolution 48, 477}489.
LANDE, R. (1976). Natural selection and random
genetic drift in phenotypic evolution. Evolution 30,
314}334.
LANDE, R. (1985). Expected time for random genetic drift of
a population between stable phenotypic states. Proc. Nat.
Acad. Sci. ;SA 82, 7641}7645.
MAYNARD SMITH, J. (1990). Models of a dual inheritance
system. J. theor. Biol. 143, 41}53.
MCGRATH, J. & SOLTER, D. (1984). Completion of mouse
embryogenesis requires both the maternal and the paternal
genomes. Cell 37, 179}183.
MOXON, E. R., RAINEY, P. B., NOWAK, M. A., & LENSKI,
R. E. (1994). Adaptive evolution of highly mutable loci in
pathogenic bacteria. Curr. Biol. 4, 24}33.
ORR, H. A. (1997). Haldane's rule. Ann. Rev. Ecol. Syst. 28,
195}218.
PAD L, C. (1998). Plasticity, memory and the adaptive landscape of the genotype. Proc. Roy. Soc. ¸ond. 265,
1319}1323.
PHILIPS, P. C. (1996). Waiting for compensatory mutation:
phase zero of the shifting-balance process. Gen. Res. 67,
271}283.
PIRROTTA, V. (1997). Chromatin-silencing mechanisms in
Drosophila maintain patterns of gene expression. ¹rends
Gen., 13, 314}318.
REEDER, R. H. (1985). Mechanisms of nucleolar dominance
in Xenopus hybrids. J. Cell. Biol. 101, 2013}2016.
RICE, S. H. (1998). The evolution of canalization and the
breaking of von Baer's laws: modeling the evolution of
development with epistasis. Evolution 52, 647}656.
RUSSO, V. E. A., MARTIENSSEN, R. A. & RIGGS, A. D. (eds)
(1996). Epigenetic Mechanisms of Gene Regulation. New
York: Cold Spring Harbor Laboratory Press.
36
C. PAD L AND I. MIKLOD S
RUVINSKY, A. O., LOBKOV, Y. I. & BELAYEV, D. K. (1983).
Spontaneous and induced activation of genes a!ecting the
phenotypic expression of glucose 6 phosphate dehydrogenase in Daphnia Pulex. I. Intraclonal variations in the
electrophoretic mobility of G6PD. Mol. Gener. Gen. 189,
485}489.
SCHARLOO, W. (1991). Canalization: genetic and developmental aspects. Ann. Rev. Ecol. Syst. 22, 65}93.
SCHEINER, S. M. (1993). Genetics and evolution of
phenotypic plasticity. Annu. Rev. Ecol. Syst. 24, 35}68.
SCHEINER, S. M. & LYMAN, R. F. (1991). The genetics of
phenotypic plasticity. II. Response to selection. J. Evol.
Biol. 4, 23}50.
SHAPOSHNIKOV, G. K. (1966). Origin and breakdown of
reproductive isolation and the criterion of the species. Ent.
Rev. 45, 1}18.
SIGNORET, J. & DAVID, J. C. (1986). DNA-ligase activity in
axolotl early development: evidence for a multilevel regulation of gene expression. J. Embryol. Exp. Morph. 97
(Suppl.), 85}95.
SURANI, M. A., BARTON, S. C. & NORRIS, M. L. (1984).
Development of reconsituted mouse eggs suggests imprinitng of the genome during gametogenesis. Nature 308,
548}550.
SZATHMAD RY, E. (1999). Chemes, genes, memes. A revised
classi"cation of replicators. ¸ect. Math. ¸ife. Sci. 26,
1}10.
VIA, S., GOMULKIEWICZ, R., SCHEINER, S. M., SCHLICHTING, C. D. & TIENDEREN, P. H. V. (1995). Adaptive
phenotypic plasticity: consencus and controversy. ¹rends
Ecol. Evol. 10, 212}217.
VRANA, P. B., GUAN, X.-J., INGRAM, R. S. & TILGHAM, S. H.
(1998). Genomic imprinting interspeci"c Peromyscus hybrids. Nature Gen. 20, 362}365.
WADDINGTON, C. H. (1942). Canalization of development
and the inheritance of acquired characters. Nature 251,
314}315.
WADDINGTON, C. H. (1953). Genetic assimilation of an
acquired character. Evolution 7, 118}126.
WADDINGTON, C. H. (1957). ¹he Strategy of the Genes.
London: Allen and Unwin.
WAGNER, G. P., BOOTH, G. & BAGHERI-CHAICHIAN, H.
(1997). A population genetic theory of canalization. Evolution 51, 329}347.
WEST-EBERHARD, M. J. (1986). Alternative adaptations,
speciation and phylogeny (A review). Proc. Nat. Acad. Sci.
;SA 83, 1388}1392.
WEST-EBERHARD, M. J. (1989). Phenotypic plasticity
and the origins of diversity. Ann. Rev. Ecol. Syst. 20,
249}278.
WHITEHEAD, H. (1998). Cultural selection and genetic diversity in matrilineal whales. Science 282, 1708}1711.
WHITLOCK, M. C. (1995). Variance induced peak-shifts.
Evolution 49, 252}259.
WILLIAMS, G. C. (1966). Adaptation and Natural Selection.
NJ: Princeton University Press.
WU, T. C. & LICHTEN, M. (1994). Meiosis-induced doublestrand break sites determined by yeast chromatin structure. Science, 263, 515}518.
WRIGHT, S. (1932). The roles of mutation, inbreeding, crossbreeding and selection in evolution. Proc. 6th Int. Cong.
Genetics, Vol. 1, pp. 356}366.
WRIGHT, S. (1980). Genic and organismic selection. Evolution 34, 825}843.
WYLES, J. S., KUNKEL, J. G., & WILSON, A. C. (1983). Birds,
behavior and anatomical evolution. Proc. Nat. Acad. Sci.
;SA 80, 4394}4397.
ZAKIAN, S. M., NESTEROVA, T. B., CHERYAUKENE, O. V.
& BOCHKAREV, M. N. (1991). Heterochromatin as a factor
a!ecting X-inactivation in interpeci"c female vole hybrids
(Microtidae, Rodentia). Gen. Res. 58, 105}110.
ZUCKERLANDL, E. & VILLET, R. (1988). Concentrationa$nity equivalence in gene regulation: convergence of
genetic and environmental e!ects. Proc. Nat. Acad. Sci.
;SA 85, 4784}4788.
APPENDIX A
Let us start by recalling the Jensen inequality.
A function = de"ned on some interval I is said
to be strictly convex if
= p y ( p =(y ),
G G
G
G
(A.1)
where y , y , 2 , y 3l, the p 's are positive num L
G
bers and p "1. We apply eqn (A.1) to show
G
that increasing phenotypic variation is advantageous if the adaptive landscape is convex, and
disadvantageous if it is concave. The p 's may
G
de"ne the frequency by which an y phenotype is
G
induced, and = may give the "tness function of
the phenotypes. In the main text we approximated the distribution of phenotypes by
Gaussian. Because of the symmetry of this distribution around the mean (x), any x!e , x#e
G
G
phenotype is generated with the same p freG
quency. Therefore, in this special case, p y "x.
G G
Accordingly, inequality (A.1) can be rearranged
to give
=(x)( p =( y )
G
G
(A.2)
We can conclude that it is bene"cial to generate
y phenotypes, instead of the genetically deterG
mined x, if the arithmetic mean "tness of the
induced phenotypes is higher than the "tness of
x. Inequality (A.2) is satis"ed if and only if the
"tness function is convex on the given interval.
APPENDIX B
The "tness of the genotype with an epigenetic
inheritance system is
=(x, P, m)"
u (y) =(y)K
,
(B.1)
37
DIVERGENCE OF DUAL INHERITANCE SYSTEMS
where u ( y) gives the initial phenotypic distribution of the genotypes, and
=(y)"exp
!(y!y
)
MNR
2<
Q
#H exp
!(y!y
)
MNR
2<
Q
;exp
(B.2)
gives the "tness of individuals with y phenotype.
If m is an integer, then we can use the binomial
expansion
K m
AK\I BI
(A#B)K" k
I
in eqn (B.1) to give
u
=(x, P, m)"
K m
(y) k
I
;HI exp
!(m!k) (y!y
)
MNR
2<
Q
K
!k(y!y
)
MNR dy
.
2<
Q
(B.3)
Changing the order of summation and integration in eqn (B.3) leads to
K m
HI u (y)
=(x, P, m)" k
I
;exp
!(m!k)(y!y
)
MNR
2<
Q
;exp
K
!k(y!y
)
MNR dy
. (B.4)
2<
Q
Evaluating the integration in eqn. (B.4) and
after some rearrangements we get eqn (10).