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Natural Selection. II. Developmental Variability and Evolutionary Rate

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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 claim to support the theory. Refinements to the theory modifications come under unfinished business ::: develop. There have been repeated assertions of both their In the end, few compelling examples relate nonheri- importance and their triviality, a lot of discussion table phenotypic variability to evolutionary rate. The with no consensus. ::: Yet the debate has contin- literature is hard to read. Enthusiasts extend the con- ued over such concepts as genetic assimilation, cepts and keep the problem alive. Through the enthusi- the Baldwin effect, organic selection, morphoses, asts' promotions, many have heard of the theory. But, and somatic modifications. So much controversy in practice, few consider the role of nonheritable phe- over the span of a century suggests that a prob- notypic variability in their own analyses of evolutionary lem of major significance remains unsolved [1, rate. Almost everyone ignores the problem. p. 498]. In this article, I emphasize simple theory that re- lates nonheritable phenotypic variability to evolutionary rate. Understanding the paradoxical relation between I. INTRODUCTION nonheritable phenotypic variability and evolutionary rate is an essential step in reasoning about many evolutionary A single genotype produces different phenotypes. De- problems. velopmental programs match the phenotype to differ- This article is primarily a concise tutorial to the ba- ent environments. Intrinsic developmental fluctuations sic concepts (see Box 1). I briefly mention some of the spread the distribution of phenotypes. Extrinsic en- history (Box 2) and recent, more advanced literature vironmental fluctuations perturb developmental trajec- (Box 3). tory. These nonheritable types of phenotypic variation are common. Nonheritable phenotypic variation is not transmitted II. SMOOTHING THE EVOLUTIONARY PATH through time. Thus, nonheritable variation would seem to be irrelevant for evolutionary change, which instead The distribution of phenotypes for a given genotype depends on the genetic component of variation. However, is called the reaction norm. All theories come down to nonheritable phenotypic variation can, in principle, affect the fact that a broad reaction norm smooths the path of arXiv:1109.5633v1 [q-bio.PE] 26 Sep 2011 evolutionary rate. At first glance, that contribution of increasing fitness. Once one grasps the smoothing pro- nonheritable phenotypic variation to evolutionary rate cess, many apparently different theories become easy to appears to be a paradox. understand. Many different theories, commentaries, and controver- The next section gives the mathematical expression for sies turn on this paradox (Box 2). The literature has the smoothing of fitness by the reaction norm. Fig. 1 followed a consistent pattern. Detailed theories relate de- explains the mathematics with a simple example. velopmental variability to accelerated evolution. Coun- terarguments ensue. Listings of complicated examples A. The reaction norm smooths fitness ∗ email: [email protected]; homepage: http://stevefrank.org We need to track three quantities. First, fitness, f(x), a doi: 10.1111/j.1420-9101.2011.02373.x in J. Evol. Biol. varies according to the particular phenotype expressed, b Part of the Topics in Natural Selection series. See Box 1. x. 2 Box 1. Topics in the theory of natural selection Box 2. Historical overview This article is part of a series on natural selection. Al- Schlichting and Pigliucci [3] and West-Eberhard [1] thor- though the theory of natural selection is simple, it remains oughly review the subject. Here, I highlight a few key points endlessly contentious and difficult to apply. My goal is to in relation to this article. I treat learning and developmental make more accessible the concepts that are so important, yet plasticity as roughly the same with regard to potential con- either mostly unknown or widely misunderstood. I write in sequences for evolutionary rate, although one could certainly a nontechnical style, showing the key equations and results choose to focus on meaningful distinctions. rather than providing full derivations or discussions of math- In my own reading during the 1980s, I had found the re- ematical problems. Boxes list technical issues and brief sum- lation between learning and evolutionary rate intriguing but maries of the literature. 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 Second, the phenotype expressed varies according to alter evolutionary dynamics. Those ideas seemed potentially the reaction norm. Read p(xjx¯) as the probability of ex- important, but it was not easy to grasp the essence. The pressing the phenotype x given a genotype with average literature at that time was not helpful, with a lot of jargon phenotypex ¯. and sometimes almost mystical commentary mixed in with Third, we must calculate F (¯x), the expected fitness intriguing and creative ideas. for a genotype with average phenotypex ¯. We obtain It was clear that learning could slow evolutionary rate. Different genotypes could, through learning, end with the the expected fitness by summing up the probability, p, of same phenotype. Reducing the phenotypic distinction be- expressing each phenotype multiplied by the fitness, f, tween different genotypes would generally slow evolutionary of each phenotype. That sum is rate. The more intriguing problem concerns the origin of evo- lutionary novelty or the response to novel or extreme environ- X F (¯x) = p(xjx¯)f(x); (1) 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 taken over all the different phenotypes, x. We often mea- also focuses on acceleration of evolutionary response. sure x as a continuous variable. The sum is then equiv- Hinton and Nowlan [8] clarified the subject with their sim- alently written as ple conclusion that: Z Learning alters the shape of the search space F (¯x) = p(xjx¯)f(x)dx: (2) in which evolution operates and thereby pro- vides good evolutionary paths towards sets of co- adapted alleles. We demonstrate that this effect This equation shows how one averages the fitness, f(x), allows learning organisms to evolve much faster for each phenotypic value, x, over the reaction norm, than their nonlearning equivalents, even though p(xjx¯), to obtain the expected fitness of a genotype, F (¯x). the characteristics acquired by the phenotype are We label each genotype by its average phenotype,x ¯. The not communicated to the genotype. expected fitness of a genotype, F (¯x), is what matters for During the past few decades, the fundamental role of evolutionary process [2]. smoothed fitness surfaces in biology has not always been rec- The averaging of expected fitness over the reaction ognized as fully as it should be, in spite of several fine pa- norm is the key to the entire subject. Averaging over the pers along that line (see Box 3). Interestingly, certain com- reaction norm, p, flattens and smooths the fitness func- puter optimization algorithms take advantage of the increased tion, f. This smoothing makes the curve for expected search speed provided by a process similar to smoothed fitness fitness, F , have lower peaks and shallower valleys than landscapes [9, 10]. 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 In Fig. 2, the reaction norm follows a normal distribu- the consequences of a smoother relation between geno- tion. In symbols, we write type and fitness. p(xjx¯) ∼ N (¯x; γ2); which we read as the probability, p, of a phenotype, x, B. Example of continuous smoothing for a reaction norm centered atx ¯, follows a normal dis- tribution with meanx ¯ and variance γ2. Fig. 1 shows an example of smoothing with discrete For fitness, we write in symbols distributions. It will often be convenient to consider f(x) ∼ N (0; σ2); smoothing of continuous variables. Fig. 2 shows an ex- ample. The following expressions describe the underlying which we read as the fitness,
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