Natural selection. II. Developmental variability and evolutionary rate.

Natural selection. II. Developmental variability and evolutionary rate
Steven A. Frank∗
Department of Ecology and Evolutionary Biology,
University of California, Irvine, CA 92697–2525 USA
In classical evolutionary theory, genetic variation provides the source of heritable phenotypic vari-
ation on which natural selection acts. Against this classical view, several theories have emphasized
that developmental variability and learning enhance nonheritable phenotypic variation, which in
turn can accelerate evolutionary response. In this paper, I show how developmental variability al-
ters evolutionary dynamics by smoothing the landscape that relates genotype to fitness. In a fitness
landscape with multiple peaks and valleys, developmental variability can smooth the landscape to
provide a directly increasing path of fitness to the highest peak. Developmental variability also
allows initial survival of a genotype in response to novel or extreme environmental challenge, pro-
viding an opportunity for subsequent adaptation. This initial survival advantage arises from the
way in which developmental variability smooths and broadens the fitness landscape. Ultimately, the
synergism between developmental processes and genetic variation sets evolutionary rateab.
In evolutionary biology, environmentally induced
modifications come under unfinished business . . .
There have been repeated assertions of both their
importance and their triviality, a lot of discussion
with no consensus. . . . Yet the debate has contin-
ued over such concepts as genetic assimilation,
the Baldwin effect, organic selection, morphoses,
and somatic modifications. So much controversy
over the span of a century suggests that a prob-
lem of major significance remains unsolved [1,
p. 498].
I. INTRODUCTION
A single genotype produces different phenotypes. De-
velopmental programs match the phenotype to differ-
ent environments. Intrinsic developmental fluctuations
spread the distribution of phenotypes. Extrinsic en-
vironmental fluctuations perturb developmental trajec-
tory. These nonheritable types of phenotypic variation
are common.
Nonheritable phenotypic variation is not transmitted
through time. Thus, nonheritable variation would seem
to be irrelevant for evolutionary change, which instead
depends on the genetic component of variation. However,
nonheritable phenotypic variation can, in principle, affect
evolutionary rate. At first glance, that contribution of
nonheritable phenotypic variation to evolutionary rate
appears to be a paradox.
Many different theories, commentaries, and controver-
sies turn on this paradox (Box 2). The literature has
followed a consistent pattern. Detailed theories relate de-
velopmental variability to accelerated evolution. Coun-
terarguments ensue. Listings of complicated examples
∗ email: safrank@uci.edu; homepage: http://stevefrank.org
a doi: 10.1111/j.1420-9101.2011.02373.x in J. Evol. Biol.
b Part of the Topics in Natural Selection series. See Box 1.
claim to support the theory. Refinements to the theory
develop.
In the end, few compelling examples relate nonheri-
table phenotypic variability to evolutionary rate. The
literature is hard to read. Enthusiasts extend the con-
cepts and keep the problem alive. Through the enthusi-
asts’ promotions, many have heard of the theory. But,
in practice, few consider the role of nonheritable phe-
notypic variability in their own analyses of evolutionary
rate. Almost everyone ignores the problem.
In this article, I emphasize simple theory that re-
lates nonheritable phenotypic variability to evolutionary
rate. Understanding the paradoxical relation between
nonheritable phenotypic variability and evolutionary rate
is an essential step in reasoning about many evolutionary
problems.
This article is primarily a concise tutorial to the ba-
sic concepts (see Box 1). I briefly mention some of the
history (Box 2) and recent, more advanced literature
(Box 3).
II. SMOOTHING THE EVOLUTIONARY PATH
The distribution of phenotypes for a given genotype
is called the reaction norm. All theories come down to
the fact that a broad reaction norm smooths the path of
increasing fitness. Once one grasps the smoothing pro-
cess, many apparently different theories become easy to
understand.
The next section gives the mathematical expression for
the smoothing of fitness by the reaction norm. Fig. 1
explains the mathematics with a simple example.
A. The reaction norm smooths fitness
We need to track three quantities. First, fitness, f(x),
varies according to the particular phenotype expressed,
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2Box 1. Topics in the theory of natural selection
This article is part of a series on natural selection. Al-
though the theory of natural selection is simple, it remains
endlessly contentious and difficult to apply. My goal is to
make more accessible the concepts that are so important, yet
either mostly unknown or widely misunderstood. I write in
a nontechnical style, showing the key equations and results
rather than providing full derivations or discussions of math-
ematical problems. Boxes list technical issues and brief sum-
maries of the literature.
Second, the phenotype expressed varies according to
the reaction norm. Read p(x|x¯) as the probability of ex-
pressing the phenotype x given a genotype with average
phenotype x¯.
Third, we must calculate F (x¯), the expected fitness
for a genotype with average phenotype x¯. We obtain
the expected fitness by summing up the probability, p, of
expressing each phenotype multiplied by the fitness, f ,
of each phenotype. That sum is
F (x¯) =
∑
p(x|x¯)f(x), (1)
taken over all the different phenotypes, x. We often mea-
sure x as a continuous variable. The sum is then equiv-
alently written as
F (x¯) =
∫
p(x|x¯)f(x)dx. (2)
This equation shows how one averages the fitness, f(x),
for each phenotypic value, x, over the reaction norm,
p(x|x¯), to obtain the expected fitness of a genotype, F (x¯).
We label each genotype by its average phenotype, x¯. The
expected fitness of a genotype, F (x¯), is what matters for
evolutionary process [2].
The averaging of expected fitness over the reaction
norm is the key to the entire subject. Averaging over the
reaction norm, p, flattens and smooths the fitness func-
tion, f . This smoothing makes the curve for expected
fitness, F , have lower peaks and shallower valleys than
the original fitness curve, f . The smoothing of F changes
evolutionary dynamics. The whole problem comes down
to understanding how reaction norms smooth fitness, and
the consequences of a smoother relation between geno-
type and fitness.
B. Example of continuous smoothing
Fig. 1 shows an example of smoothing with discrete
distributions. It will often be convenient to consider
smoothing of continuous variables. Fig. 2 shows an ex-
ample. The following expressions describe the underlying
mathematics.
Box 2. Historical overview
Schlichting and Pigliucci [3] and West-Eberhard [1] thor-
oughly review the subject. Here, I highlight a few key points
in relation to this article. I treat learning and developmental
plasticity as roughly the same with regard to potential con-
sequences for evolutionary rate, although one could certainly
choose to focus on meaningful distinctions.
In my own reading during the 1980s, I had found the re-
lation between learning and evolutionary rate intriguing but
confusing. Baldwin’s [4] idea that learning can accelerate evo-
lutionary rate seemed attractive. Mayr [5], in his monumen-
tal review of biological thought, also discussed various ways
in which behavior or flexible developmental programs might
alter evolutionary dynamics. Those ideas seemed potentially
important, but it was not easy to grasp the essence. The
literature at that time was not helpful, with a lot of jargon
and sometimes almost mystical commentary mixed in with
intriguing and creative ideas.
It was clear that learning could slow evolutionary rate.
Different genotypes could, through learning, end with the
same phenotype. Reducing the phenotypic distinction be-
tween different genotypes would generally slow evolutionary
rate. The more intriguing problem concerns the origin of evo-
lutionary novelty or the response to novel or extreme environ-
mental challenge. Environmental novelty and acceleration of
evolutionary response were the primary concern of Baldwin
[4], Waddington [6, 7], and West-Eberhard [1]. My article
also focuses on acceleration of evolutionary response.
Hinton and Nowlan [8] clarified the subject with their sim-
ple conclusion that:
Learning alters the shape of the search space
in which evolution operates and thereby pro-
vides good evolutionary paths towards sets of co-
adapted alleles. We demonstrate that this effect
allows learning organisms to evolve much faster
than their nonlearning equivalents, even though
the characteristics acquired by the phenotype are
not communicated to the genotype.
During the past few decades, the fundamental role of
smoothed fitness surfaces in biology has not always been rec-
ognized as fully as it should be, in spite of several fine pa-
pers along that line (see Box 3). Interestingly, certain com-
puter optimization algorithms take advantage of the increased
search speed provided by a process similar to smoothed fitness
landscapes [9, 10].
In Fig. 2, the reaction norm follows a normal distribu-
tion. In symbols, we write
p(x|x¯) ∼ N (x¯, γ2),
which we read as the probability, p, of a phenotype, x,
for a reaction norm centered at x¯, follows a normal dis-
tribution with mean x¯ and variance γ2.
For fitness, we write in symbols
f(x) ∼ N (0, σ2),
which we read as the fitness, f , of a phenotype, x, has the
shape of a normal distribution with mean 0 and variance

3...
-3 -3 -2 -3 -2 -1 0 1 2 3
f(x)
(a) (b) (c)
p(x|x)
F(x)
Phenotype
FIG. 1. The reaction norm smooths the fitness landscape. This simple example illustrates the calculation of the expected
fitness for each genotype, following Eq. (1). (a) The calculation of expected fitness, F (x¯), for the smallest average phenotype,
x¯ = −3. For that average phenotype, the reaction norm, p(x|x¯), shows the probabilities of expressing different phenotypes,
x. In this case, the peak of the reaction norm matches the average value, and each phenotype ±1 occurs half as often as the
peak value. To get the expected fitness for a reaction norm centered at x¯ = −3, one sums up the probability p(x|x¯) for each
phenotype, x, multiplied by the fitness for each phenotype, f(x). The arrows illustrate the summation. (b) The expected
fitness, F (x¯), for each increase in x¯, is calculated by the same summation process, shifting the reaction norm to the right by
one to get the proper value for each x¯. (c) The full transformation is shown between the fitness for each phenotypic value, f(x),
and the expected fitness, F (x¯), for each genotype with reaction norm p(x|x¯) and average phenotype x¯. The reaction norm
smooths the multipeaked fitness function, f(x), into the single-peaked fitness function F (x¯). Evolutionary dynamics depend
on genotypic fitnesses, F . Thus, the reaction norm transforms fitness into a smooth function that allows a direct increasing
path to the fitness peak from any starting value for average phenotype.
σ2. In this case, we assume the center of the fitness
distribution is at a phenotypic value of zero to give a
fixed point for comparison—any value to center fitness
could be used. The important issue is that fitness falls
off from its peak by the pattern of a normal distribution.
The width of the fitness function is set by the variance
parameter, σ2.
We can now use Eq. (2) to calculate the expected fit-
ness of a genotype with average phenotype x¯, yielding
F (x¯) ∼ N (0, γ2 + σ2). (3)
This equation shows that smoothing by the reaction
norm, p, flattens and widens the shape of the fitness func-
tion by increasing the variance of the expression for F .
C. Evolutionary response to novel or extreme
challenge
If a genotype expresses an average phenotype close to
the maximum fitness, then a narrow reaction norm has
higher fitness than a broad reaction norm. The lower
plots of F (x¯) in Fig. 2 illustrate contrasting widths of
reaction norms. Near the peak, the average phenotype
closely matches the optimum, and the narrower reaction
norm has higher fitness. This advantage occurs because a
narrow reaction norm expresses fewer phenotypes in the
tails, away from the optimum.
For genotypes with an average phenotype far from the
maximum fitness, a broad reaction norm has higher fit-
ness than a narrow reaction norm. Fig. 3 illustrates this
advantage for broad reaction norms. In that figure, both
reaction norms are centered at x¯. Only those phenotypes
above the fitness truncation point survive. The broad re-
action norm produces some individuals with phenotypes
above the truncation point, whereas the narrow reaction
norm has zero fitness.
If the environment poses a novel or extreme challenge,
the broad reaction norm wins. By contrast, in a stable
environment for which the current average phenotype is
close to the fitness optimum, the narrow reaction norm
wins. Thus, extreme or novel environmental challenges
or intense competition favor a broad reaction norm.
Haldane [11] made a similar point when he said: “In-
tense competition favors variable response to the envi-
ronment rather than high average response. Were this
not so, I expect that the world would be much duller
than is actually the case.” Holland’s [12] emphasis on
exploration versus exploitation is perhaps closer to the
problem here. Broad reaction norms are favored when
exploration of novel challenges dominates, whereas nar-
row reaction norms are favored when exploitation domi-
nates. Fluctuating environments may also favor a broad

4Phenotype
(a) (b)
f(x)
p(x|x)
F(x)
FIG. 2. Reaction norms and fitness for continuous pheno-
types. Each column shows how the reaction norm, p(x|x¯),
smooths the fitness function, f(x), to give the expected fit-
ness, F (x¯), for a genotype with average phenotype x¯. The
smoothing follows Eq. (2). These examples use normal distri-
butions that lead to Eq. (3). (a) The solid and dashed reaction
norms follow N (x¯, 1/2) and N (x¯, 5), respectively. Fitness,
f(x), has the shape of a normal distribution with vanishingly
small variance, N (0, σ2 → 0). Thus, expected fitness, F (x¯),
is the same as the reaction norm. (b) The same structure
as in (a), except that f(x) is much wider, following N (0, 7).
Thus, F (x¯) now has curves N (0, 7.5) and N (0, 12) for solid
and dashed curves, respectively. In each plot, the baseline is
set to 4.3% of the peak in that plot. The baseline truncates
phenotypes with low vigor, setting their fitnesses to zero.
reaction norm to increase the chance of matching what-
ever is favored at any time [2]. Here, I focus on constant
challenges to extreme or novel environments.
D. Smoothly increasing fitness path in a multipeak
fitness landscape
Much discussion in evolutionary theory concerns how
populations shift from a lower fitness peak to a higher
fitness peak [13]. For example, in the fitness landscape,
f(x), of Fig. 4b, a population starting on a lower peak
must evolve through a valley of lower fitness in order to
follow an increasing path to a higher fitness peak. Natu-
ral selection typically follows a path of increasing fitness,
so a population may be trapped on a lower peak.
Most evolutionary analyses use a fitness landscape that
relates phenotype, x, to fitness, f(x). However, the
proper measure should relate the average phenotype of a
genotype, x¯, to the expected fitness, F (x¯) [2].
A sufficiently broad reaction norm smooths a multi-
peak fitness landscape, f(x), into a smooth landscape,
p(x|x)
Phenotype, x
x
Fitness
truncation
FIG. 3. Novel environmental challenge or intense competi-
tion favors a broad reaction norm. In this example, both the
broad and narrow reaction norms are centered at x¯. Pheno-
types above the truncation point survive. Phenotypes below
the truncation point die. None of the phenotypes for the nar-
row reaction norm are above the truncation point, so all die.
Some of the phenotypes of the broad reaction norm survive.
Those surviving phenotypes may evolve so that their average
phenotype, x¯, moves toward the truncation point, improv-
ing fitness over time. Improvement occurs if there is genetic
variation for the average phenotype, x¯, of the reaction norm.
F (x¯), with a single peak (Fig. 4c). A broad reaction norm
will typically perform badly near a fitness peak, but allow
much more rapid evolutionary advance to a higher fitness
peak. Once again, we see that broad reaction norms ex-
ploit current fitness opportunities relatively poorly but
gain by enhanced exploration and achievement of novel
adaptations.
III. DIMENSIONALITY AND DISCOVERY
The reaction norm may be generated randomly by per-
turbations in development. If so, then exploration of the
fitness landscape by a broad reaction norm is a type of
random search. Figs. 3 and 4 show that random search
can greatly increase the rate of adaptation, particularly
to novel environmental challenges.
Those previous examples showed the reaction norm
and fitness both varying across a single dimension. A
broad reaction norm spreads phenotypes along that sin-
gle dimension, increasing the chance that some individu-
als will have high fitness.
Now consider the much more difficult search problem
that arises in higher dimensions [14]. Suppose, for ex-
ample, that adapting to a novel environmental challenge
requires multiple phenotypic changes to work together in
a harmonious way. Think of each particular phenotypic
change as a trait in its own dimension, so that the search
now occurs in multiple dimensions. If the reaction norm
simply generates random phenotypes in each dimension,
then there is little chance of getting simultaneous match-

5f(x)
p(x|x)
F(x)
Phenotype
(a)
(b)
(c)
FIG. 4. A broad reaction norm smooths a multipeak fitness
landscape. (a) The dashed curve shows the broader reaction
norm, p(x|x¯). (b) The fitness landscape for each particular
phenotype, f(x), has multiple peaks. (c) The broad reaction
norm smooths the fitness landscape to a single peak for the
relation between the average phenotype for a genotype, x¯,
and fitness, F (x¯). In this example, the narrow and broad
reaction norms follow N (0, γ2) distributions with variances
of 0.04 and 0.16, respectively. Fitness is given by f(x) =∑1
i=−1(3|1 + i|
2 + 1)N (i, σ2), with σ2 = 0.0225. The value
of F (x¯) is calculated from Eq. (2), yielding the expression
for f(x) in the prior sentence with the variance replaced by
σ2 + γ2. The baseline truncates small values.
ing phenotypes in multiple dimensions.
To visualize the multidimensional problem, begin with
the one-dimensional fitness landscape in Fig. 4b. Now
consider two phenotypic dimensions. Assume that fit-
ness concentrates along one dimension, as in Fig. 5a. In
that plot, only a narrow band of phenotypes along the
second phenotypic dimension produces viable individu-
als. In the first dimension, fitness rises and falls along
the same peaks and valleys as in Fig. 4b. Thus, both
figures show essentially the same fitness landscape, but
in the second case the nearly one-dimensional landscape
is embedded in a second dimension (fitnesses scale loga-
Phenotype
log
[F
(x
)]
(d)
(c)
(b)
(a)
FIG. 5. A broad reaction norm performs poorly when fit-
ness is concentrated in a lower dimension. (a) The bivariate
analogy of the fitness landscape in Fig. 4b, scaled logarith-
mically. The primary dimension has variance σ21 = 0.0225
corresponding to standard deviation σ1 = 0.15, as in Fig. 4b.
The secondary (narrow) dimension has standard deviation
σ2 = 0.1σ1. (b) Fitness landscape smoothed by a reaction
norm concentrated in the same dimension as fitness. The
variance of the reaction norm in the primary dimension is
γ21 = 0.16, and standard deviation is γ1 = 0.4, as in the
dashed reaction norm of Fig. 4a. The standard deviation in
the secondary dimension is γ2 = 0.01γ1. The smoothed fit-
ness surface rises steadily to a peak along its ridge in the pri-
mary dimension, tracing the same path as the dashed curve
in Fig. 4c. (c and d) Increasingly broad reaction norms in the
secondary dimension with standard deviations of 0.1γ1 and
γ1, respectively. The baseline truncates small fitness values,
which are considered inviable.
rithmically in Fig. 5).
In two dimensions, the reaction norm will smooth phe-
notypes along both trait axes. When the reaction norm
varies mostly along the same dimension as the variation
in fitness, as in Fig. 5b, then we obtain the same smooth-
ing as in one dimension (dashed curve of Fig. 4c). When
the reaction norm varies in both directions, as in Fig. 5d,
then the smoothed surface has very low fitness even at its