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Non-Genetic Inheritance
Mini-review • DOI: 10.2478/ngi-2013-0003 • NGI • 2013 • 27-32
Non-genetic Inheritance in Evolutionary Theory: a Primer
Abstract
Evolutionary biology traditionally equates inheritance with transmission
of genes from parents to offspring. However, recent literature calls for
considering ‘non-genetic inheritance’ in evolutionary theory. These calls
have met with substantial scepticism. What is more, they appear to have
caused further confusion both with respect to what inheritance is and
what types of inheritance mechanisms are evolutionarily consequential.
Building on previous work, we make use of the Price Equation to outline
a general discussion of how non-genetic inheritance can affect phenotypic
change within populations, exemplified by epigenetic inheritance. This
shows that integrating non-genetic inheritance in evolutionary theory will
require specific attention to the developmental processes that shape the
relationship between the fitness of parents and the phenotype of their
offspring.
Tobias Uller1*,
Edward Grey Institute,
Department of Zoology,
University of Oxford.
1
Heikki Helanterä2
Centre of Excellence in Biological
Interactions, Department of Biosciences,
University of Helsinki
2
Keywords
Heredity • Price Equation • Maternal effects • Parental effects • Plasticity
© 2013 Tobias Uller et al., licensee Versita Sp. z o. o.
This work is licensed under the Creative Commons Attribution-NonCommercialNoDerivs license (http://creativecommons.org/licenses/by-nc-nd/3.0/), which
means that the text may be used for non-commercial purposes, provided credit
is given to the author.
Introduction
In biology, inheritance or heredity typically refers to the
phenomenon that offspring resemble their parents. Many modern
definitions of inheritance specifically refer to the transmission of
genes between generations as the causal mechanism behind this
similarity (e.g., [1,2]). Indeed, the reason that offspring resemble
their parents more than they resemble unrelated individuals can
often be linked to differences in the DNA sequences that they
inherited from their parents. This goes both for inheritance of
species-typical phenotypes (e.g., why human babies look human
rather than chimpanzee and vice versa) and for inheritance of
differences between lineages within populations (e.g., why each
of the authors of this paper resembles their father). In many areas
of biology, including evolutionary theory, the focus is on the latter
of these inheritance concepts, i.e., inheritance of differences
in phenotypes within populations rather than inheritance of
species-typical phenotypes [3].
DNA is clearly important for the inheritance of differences
in phenotypes, but any mechanism that contributes to
parent-offspring similarity within populations is potentially of
evolutionary relevance. This could be due to causal effects of
the parental phenotype on offspring phenotype, which are often
referred to as parental effects [4]. These include molecules
associated with DNA, amount and location of egg mRNA, yolk
nutrients, and different forms of behavioural interactions. In all
those cases, the contribution from the parent can depend on
Received 10 July 2013
Accepted 22 August 2013
various aspects of the parental phenotype. But inheritance also
involves stable transmission of biomolecules down generations,
where this transmission does not depend on the parental
phenotype. For example, the amount and sequence of DNA that
is transferred from parent to offspring is typically not affected by
the phenotype of the parent. The stability during transmission
is one of the crucial features of DNA that makes it warranted to
speak of DNA as an inheritance system in a more strict sense
than most parental effects [5]. However, DNA is not unique in
this regard. Recent findings that also epigenetic variants can
be stably transmitted down generations mean that long-run
transgenerational inheritance of differences in phenotypes
could be epigenetic rather than genetic [6,7]. Furthermore,
it is possible that the action of the parent ‘reconstructs’ the
environmental conditions that are conducive to the expression of
the same phenotype in the next generation, thereby generating
transgenerationally stable differences between lineages [4]. This
is true, for example, when animals return to their natal habitat
type (e.g., host plant) for reproduction [8], thereby setting
the stage for transgenerationally stable differences between
lineages.
In addition to the classic treatments of the biology of
inheritance (see e.g. discussion in Ch. 7 in Ref. [9]), there is
now a small but growing literature that discuss conceptual
challenges that arise from non-genetic inheritance (accessible
introductions include [6,10-13]). We will not review this literature
here. Instead, our aim is to show how non-genetic inheritance
* E-mail: [email protected]
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T. Uller, H. Helanterä
can be integrated into evolutionary theory using a mainstream
mathematical approach to phenotypic evolution. In doing so,
we do not wish to imply that this is all there is to integrating
non-genetic inheritance in evolutionary thinking (indeed, we
argue elsewhere that more fundamental conceptual shifts
are needed, [11,14]). But we do believe that it will be helpful
to see that the consequences of non-genetic inheritance for
phenotypic evolution can be approached without the need to
endorse more radical claims about the need for an extended
evolutionary synthesis.
Because the Price Equation does not make any assumptions
of the underlying mechanisms of parent-offspring similarity it
can of course be used to derive the standard single-locus and
quantitative genetic formulations of evolutionary change that
are found in evolutionary biology and genetics textbooks [23].
However, none of the terms in Eq. (1) are obviously referring
to the covariance between parental and offspring phenotypes,
which makes this difficult to see. Assuming that the parentoffspring regression is linear, we can rewrite the equation as
1
(2)
∆z =
β o Cov w, z + E ∆z + Cov( w, e)
w
Non-genetic inheritance and the Price Equation
∆z =
1
( Cov ( w, z ) + E ( w∆z ) )
w
(
)
(
βz
( )
)
)
, z , which is referred to as the heritability of the phenotype
(using selected parents, [25]; the slope of the regression is equal
to the phenotypic covariance between parents and offspring
divided by the total phenotypic variance in parents. Also note
that in quantitative genetics, heritability is often defined in terms
of genetic and phenotypic variance instead of a regression; see
chapter 7 in Ref [23] for discussion). Thus, if the remaining terms
are zero, this equation corresponds to the breeder’s equation,
usually written as R=h2S [28], which can be found in every
undergraduate textbook on evolution. The second term, E ( ∆z ) ,
represents the expected phenotypic change in the absence of
fitness differences. This is often referred to as ‘transmission bias’
[25], but it is important to realise that this term can be affected
by a variety of developmental processes, including those that
are independent of the parents [23]. Mathematically this is
represented by the intercept of the regression and could be,
for example, changes that occur because of intergenerational
environmental change that affects phenotypic development
(i.e., phenotypic plasticity) [23]. The third term consists of the
covariance between fitness and the scatter around the regression
line (i.e., the residuals, e), Cov( w, e) [25].
Equation 2 assumes that the regression is linear. If we are not
making this assumption, Equation 2 becomes
(1)
where ∆z is the change in the average phenotype (e.g.,
height) in the population, w is the mean number of descendants
per individual, cov w, z is the covariance between fitness and
trait value, and E w∆z is the expected value of the product
of fitness and the average phenotypic difference between
parent and offspring in the absence of selection [20]. The terms
within the parenthesis can be interpreted as the change due to
differential reproduction and survival and the change that occurs
as a result of reproduction and the mechanisms of inheritance,
respectively (Ch 6 in [23]). The latter can be the result of any
process that causes phenotypic change between generations,
be it through the actual mechanisms of inheritance or changes in
environmental conditions that affect development. Thus, not only
parent-offspring covariance, but also developmental responses
to environmental change that are shared among members of
the population will affect the magnitude of the expected value
of phenotypic change between generations [24]. Division by the
mean number of descendants means that fitness is relative and
not absolute.
(
(
z ,z
This decomposes change in population mean phenotype
into three components (see [23,25,26] and Ch. 14 in [27] for
mathematical details and how to get from Eq. 1 to Eq. 2). The first
term on the right hand side consists of the covariance between
fitness and trait value, Cov w, z , known as the selection
differential, times the slope of the parent offspring regression,
If we want to understand the consequences of different
mechanisms of inheritance for phenotypic evolution, it is
sensible to start with a model that does not make any a priori
assumptions about those mechanisms [5,16] (perhaps counterintuitively, population genetic approaches can also be useful
for modelling evolution under non-genetic inheritance, e.g.,
[17,18]). The Price Equation allows us to do this as it does not
make any assumptions with respect to the underlying biology
(indeed, the ‘ancestors’ and ‘descendants’ need not even be
biological entities [19,20]; see [21-23] for discussion). Both
Helanterä and Uller [15] and Day and Bonduriansky [16] have
used the Price Equation to outline some potential evolutionary
implications of non-genetic inheritance. Our approach here
differs somewhat from both of these. Specifically, our main
purpose in this brief paper is to use the Price Equation to
explain, in a non-technical way, why non-genetic inheritance
will affect phenotypic evolution, not to contrast different
mechanisms of inheritance [15] or build mathematical models
of specific scenarios [16].
The Price Equation can be written as
(
)
)
o
∆z =
1
β o Cov ( w, z ) + E ( ∆z ) + Cov( w, z 0 z )
w z ,z
(
) (3)
(see [25],Ch 14 in [27] for derivation). The difference to Eq. 2
is now that β z o , z is the best linear regression given the data, and
that Cov( w, z 0 z ) is the covariance between the residuals for
the regression of fitness on parental phenotype and the residuals
for the regression of offspring phenotype on parental phenotype
(i.e., parent-offspring regression; [25]) (Figure 1).
Although it is not obvious that the residuals should ever
covary, this is possibly quite common. As shown in Figure 1,
the reason is that when we describe evolutionary change in
this form of the Price Equation we are forcing the slope of the
regression to be linear even if it may not be [27]. In fact, empirical
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Non-genetic Inheritance in Evolutionary Theory: a Primer
Figure 1. Illustration of a situation that gives rise to a spurious response to selection. The relationship between parental phenotype and fitness (top left)
and the relationship between parental and offspring phenotype (top right) are non-linear. As a result, the residuals for the best fitting linear
regressions are non-random. This results in a negative covariance between the residuals (bottom graph), which is the spurious response to
selection, Cov( w, z 0 z ) , in Equation 3. Figure adopted with modifications from [25,27].
studies suggest that the relationship between phenotypes of
parents and offspring can be non-linear [24,29]. When we are
forcing a linear regression through these data the residuals are
biased across parental phenotypic values (Figure 1). Because
fitness may also show non-linear relationships with phenotype
(probably a common phenomenon), the residuals can be
0
correlated and hence Cov( w, z z ) will be non-zero. Heywood
[25] termed this a ‘spurious response to selection’ to emphasize
that this is the response that occurs once we have removed the
direct (linear) effect of the parental phenotype on both fitness
and the phenotype of its offspring. Thus, this response is not
adaptive and may even counteract the response to selection.
An alternative reason for why Cov( w, z 0 z ) could be non-zero is
that, even if one or both regressions are linear, the residuals are
correlated via a third variable [25]. Thus, for a given phenotypic
trait, z , there may be a third variable that is correlated with
both the residuals of trait z on fitness and the residuals of the
parent-offspring regression. Heywood [25] discusses a case
with breeding date in birds, where there is a spurious response
to selection even when both regressions are linear. This is
because a third variable, nutritional status, covaries with both
the residuals of breeding date on fitness and the residuals of
parental breeding date on offspring breeding date.
In summary, Equation 2 describes the change in the
population mean phenotype from one generation to the next in
terms of the product of the covariance between phenotype and
fitness (‘selection differential’) and the parent-offspring regression
(‘heritability’) and two terms that can be affected by mechanisms
of inheritance and development, including environmental effects
(‘transmission bias’ and ‘spurious response to selection’). These
components can subsequently be given biological meaning in
models that track evolutionary trajectories under different forms
of selection or establish evolutionarily stable equilibria (e.g.,
[26,30]). Quantitative genetics typically assume that the last
two terms are zero (hence the Breeder’s Equation), but they
may be non-zero even under pure genetic inheritance due to,
for example, dominance [25,27]. However, both terms are more
likely to be of significance if we include some additional biological
reality by allowing non-genetic mechanisms of inheritance.
For example, Day and Bonduriansky [16] constructed several
models by explicitly separating the evolutionary response in a
focal trait in terms of its genetic and non-genetic components,
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T. Uller, H. Helanterä
and the environment make it more likely that there will be nonlinear relationships between parent and offspring phenotype or
biased distribution of residuals of the regressions in Figure 1. In
fact, non-linearity may be common whenever there are parental
effects as they tend to skew the distribution of phenotypes
from that expected under additive genetic variance [23]. For
example, biased transmission stability of DNA methylation may
result from passive loss of methylation with age. This can result
in spurious responses for both reasons mentioned above (Figure
1). Firstly, it could lead to non-linear relationships between
phenotypes in parents and offspring and hence residuals
may become correlated even in the absence of a causal link.
Secondly, age may covary both with the residuals of fitness for
a focal trait (e.g., older individuals may be more experienced
and thus have higher breeding performance for a given trait
value) and the residuals of the parent-offspring regression (e.g.,
older parents may be less likely to transmit the same epigenetic
mark as they themselves inherited because of stochastic loss
of DNA methylation with age). This line of reasoning suggests
that establishing the pattern of parent-offspring similarity (e.g.,
if it is linear), and its underlying mechanism (e.g., if there is
environment-specific transmission of epigenetic states), is an
important task if we are to understand and predict the extent
to which epigenetic mechanisms contribute to short- and longterm evolution [16,24].
In summary, we advocate a perspective on inheritance that
encompasses all the genomic and non-genomic resources by
which parents contribute to offspring development and hence
the recurrence of phenotypes (Ch. 4 in [39,40]) . Non-genetic
inheritance contributes to more or less persistent recurrence of
differences in phenotypes between lineages within populations
and the heritability of phenotypes phenotypes can partly be
due to non-genetic inheritance. Furthermore, non-genetic
inheritance may be more likely than genetic inheritance to cause
transmission bias and a spurious response to selection. Nongenetic mechanisms of inheritance are therefore potentially
important for both short- and long-term phenotypic evolution.
As our understanding of the role of developmental processes
in evolution improves, the part of those processes that underlie
heredity should take on a central role in evolutionary theory
[6,12,14,16,24,41].
for which transmission rules were specified (their model differs
somewhat from our discussion here as it did not address the
role of the spurious response to selection). These models show
that a wide range of non-genetic inheritance mechanisms can
have consequences for the rate and direction of phenotypic (and
genetic) evolution.
Here we exemplify this with epigenetic inheritance, which
has attracted substantial interest recently (e.g., [7,31-33]; see
also [16] for a worked example). Epigenetic inheritance, such as
DNA methylation, differs from genetic inheritance in several ways
(e.g., [6]). Although epigenetic variants can be stably inherited
through meiosis in multicellular organisms, such stability seems
to be relatively rare and short lived compared to transmission of
DNA sequence variation. Like DNA mutation, epigenetic variation
can be environmentally induced but, unlike mutation, a broader
range of environments are apparently able to modify epigenetic
states, perhaps in non-random directions. The degree to which
offspring pass on the same ‘epiallele’ as they received from their
parents could therefore depend on the similarity of environments
across generations, the parental phenotype, and perhaps the
epigenetic state itself (discussion in [6,11,34,35]). Each of these
has potential consequences for how epigenetic mechanisms
contribute to phenotypic evolution.
Firstly, transmission of epigenetic variants means that
epigenetic mechanisms can cause offspring to resemble their
parents, i.e., that the (linear) slope of regression of offspring
phenotype on parental phenotype is non-zero. Thus, epigenetic
mechanisms contribute to the overall heritability of a character
[12,36,37]. The increasing evidence for transgenerational
stability of epigenetic variants (at least partly) independently of
DNA sequence [7,31] also suggest the potential for cumulative
adaptive evolution via epigenetic inheritance. Naturally, the
long-term consequences of epigenetic inheritance will depend
on the stability of these variants, which itself can be a function
of genetic, phenotypic and environmental change. Day and
Bonduriansky [16] have shown that differences in the stability of
epialleles can affect both evolutionary trajectories and equilibria
of genotype and phenotype values within populations (see also
[38]).
Secondly, the environment-dependence of epigenetic
inheritance is likely to cause significant transmission bias, which
makes E ( ∆z ) non-zero as well. This affects the predicted
evolutionary change from one generation to the next because
epigenetic inheritance, or environmental epigenetic effects,
causes phenotypes to change more or less predictably from one
generation to the next even in the absence of parent-offspring
covariance (e.g., due to a common plastic response in the
population).
Finally, epigenetic inheritance may be more likely than
genetic inheritance to generate a spurious response to
selection. The stochastic nature of epigenetic inheritance and
its dependence on the phenotypic character state of the parent
Acknowledgements
We are grateful to Neil Youngson for the invitation to contribute
this paper, two reviewers for their comments, and to all our
colleagues who have taken their time to discuss non-genetic
inheritance with us. TU is supported by the Royal Society
of London and the European Union’s Seventh Framework
Programme (FP7/2007-2011) under grant agreement no 259679.
HH is supported by the Academy of Finland (grant number
135970).
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Non-genetic Inheritance in Evolutionary Theory: a Primer
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