N

tion and mutation (dashed arrows for S, U, and V).

The three panels of Fig. 11.3B refer to the equilibrium distributions of allele frequencies at one locus in many finite subpopulations connected by some degree of gene flow. The forces that dictate the distribution of allele frequencies are now genetic drift

(arrows labeled — where n is the effective popula-4n

Figure 11.3 Wright's schematic representation of the simultaneous action of multiple population genetic processes leading to equilibrium distributions of allele frequencies. Each distribution represents the allele frequencies of many replicate populations or an ensemble distribution (in (A) numerous populations that make up a species are independent while in (B) subpopulations are interdependent in an island model). The magnitude and direction of the effects of a process on the distribution of allele frequencies is indicated by arrows bearing letters. Solid arrows indicate stronger processes and dashed arrows indicate weaker processes. For example, in the left-most distribution of (B) strong migration relative to drift maintains subpopulation allele frequencies with little divergence while weak genetic leads to a modest spread of subpopulation allele frequencies around the average allele frequency of the total population. In all panels, the frequency of the wild-type allele (x) is given on the x axis and the frequency of populations with a given allele frequency is given on the y axis. The probability on the y axis is given by the equation at the top of (A) and (B) for the allele frequency on the x axis given values for the population parameters. Original caption: "Random variability of a gene frequency under various specified conditions." From Wright (1932); reproduced with permission.

Figure 11.3 Wright's schematic representation of the simultaneous action of multiple population genetic processes leading to equilibrium distributions of allele frequencies. Each distribution represents the allele frequencies of many replicate populations or an ensemble distribution (in (A) numerous populations that make up a species are independent while in (B) subpopulations are interdependent in an island model). The magnitude and direction of the effects of a process on the distribution of allele frequencies is indicated by arrows bearing letters. Solid arrows indicate stronger processes and dashed arrows indicate weaker processes. For example, in the left-most distribution of (B) strong migration relative to drift maintains subpopulation allele frequencies with little divergence while weak genetic leads to a modest spread of subpopulation allele frequencies around the average allele frequency of the total population. In all panels, the frequency of the wild-type allele (x) is given on the x axis and the frequency of populations with a given allele frequency is given on the y axis. The probability on the y axis is given by the equation at the top of (A) and (B) for the allele frequency on the x axis given values for the population parameters. Original caption: "Random variability of a gene frequency under various specified conditions." From Wright (1932); reproduced with permission.

tion size of demes) and migration (arrows labeled m for the rate of migration in an island model). Here Wright assumed that migration was much stronger than mutation and selection so these later two processes could be ignored. At one extreme shown in the left-hand panel of Fig. 11.3B, a narrow distribution of allele frequencies among demes is expected when 4nm is large because migration rates are high (solid arrows) and and/or genetic drift is relatively weak due to large effective population size (dashed arrows). The middle panel of Fig. 11.3B shows the case when genetic drift and migration approximately balance, leading to a wide distribution of intermediate allele frequencies in demes. At the other extreme, shown in the right-hand panel of Fig. 11.3B, the distribution of allele frequencies is horseshoe-shaped (most populations near fixation or loss) when 4nm is small because migration rates are low and and/or genetic drift is strong due to small effective population size.

Evolutionary scenarios imagined by Wright

With the allele-frequency distributions established, Wright then returned to the movement of populations on fitness surfaces given different parameters for the processes of natural selection, mutation, genetic drift, and migration. Wright saw the position of populations on the landscape, the area occupied by populations on the landscape, and the very topography of the landscape itself as subject to change over time. His goal was to illustrate scenarios with sufficient trial and error (or genetic drift) that the tendency of natural selection to strand a population on a single fitness peak could be overcome. Figure 11.4 illustrates the six possibilities that Wright considered. In each of these six cases, the allele-frequency distributions in Fig. 11.3 define the range of variation in fitness expected among individuals in a population or deme. The connection arises if each locus in the allele-frequency distributions of Fig. 11.3 is interpreted as having a phenotypic effect and genotypes homozygous for the wild-type allele have the highest fitness. Broader allele-frequency distributions then lead to a larger number of possible allele combinations that would produce a wider range of fitness values.

Panels A and B in Fig. 11.4 show Wright's ideas about the area of the adaptive landscape that would be occupied by a species in the context of large 4NS and 4NU values. Imagine a population initially

Figure 11.4 Wright's representation of the action of drift/mutation balance (dictated by the magnitude of 4NU), drift/selection balance (dictated by the magnitude of 4NS), and drift/migration balance in the island model (dictated by the magnitude of 4nm). Wright's parameters are N for effective population size, U for mutation rate, S for the selection coefficient in directional selection, and 4nm for the effective migration rate in the infinite island model. The word "inbreeding" is used in the population sense where finite population size leads to genetic drift. Original caption: "Field of gene combinations occupied by a population within the general field of possible combinations. Type of history under specified conditions indicated by relation to initial field (heavy broken contour) and arrow." From Wright (1932); reproduced with permission.

Figure 11.4 Wright's representation of the action of drift/mutation balance (dictated by the magnitude of 4NU), drift/selection balance (dictated by the magnitude of 4NS), and drift/migration balance in the island model (dictated by the magnitude of 4nm). Wright's parameters are N for effective population size, U for mutation rate, S for the selection coefficient in directional selection, and 4nm for the effective migration rate in the infinite island model. The word "inbreeding" is used in the population sense where finite population size leads to genetic drift. Original caption: "Field of gene combinations occupied by a population within the general field of possible combinations. Type of history under specified conditions indicated by relation to initial field (heavy broken contour) and arrow." From Wright (1932); reproduced with permission.

occupies some area around a fitness peak, as shown by the dashed circle inside the shaded circle in Fig. 11.4A. If the selection coefficient against genotypes with non-wild-type alleles were to decrease or the forward mutation rate were to increase, the area a population occupies around the adaptive peak would spread out (larger shaded circle). This would correspond to the allele-frequency distribution changing from one like that in the left-hand panel of Fig. 11.3A to one like that in the middle panel of Fig. 11.3A. In contrast, when selection against genotypes with alleles other than the wild type becomes stronger or forward mutation rates decrease in the context of large 4NS and 4NU, the area on the fitness surface occupied by a population shrinks because populations take on a narrower range of allele frequencies (compare the circle made by a dashed line to the smaller shaded circle in Fig. 11.4B). This case corresponds to the allele-frequency distribution changing in the opposite direction, from one like the middle panel of Fig. 11.3A to one like that in the left-hand panel of Fig. 11.3A. In the case of Fig. 11.4A, the average fitness of the species decreases, making it possible that ". . . the spreading of the [fitness surface] field occupied may go so far as to include another and higher peak ..." or that a fitness valley is crossed. It is also possible that the fitness peak itself could become taller if beneficial mutations occurred in a population and were fixed by selection. However, Wright pointed out that rates of mutation are very low so that evolutionary change of this sort would be very slow.

Wright also considered how the shape of the adaptive landscape itself might change. Figure 11.4C shows Wright's concept of how the adaptive landscape might change over time due to changes in the environmental context of a population (still in the context of large values of 4NS and 4NU). Because genotypic fitness values are defined by the physical and biological environment a species experiences, the fitness values of allele combinations may very well change over time. This would lead to a reshaping of the fitness surface itself, with peaks and valleys changing elevation or the position of peaks on the adaptive landscape shifting over time. While such change in the fitness surface would cause populations to track high fitness peaks, Wright saw this as "change without advance in adaptation" because populations were not necessarily occupying a number of peaks in the fitness landscape nor were populations necessarily evolving to higher levels of mean fitness.

This theme of constant environmental change driving a continual redefinition of the genotypes having highest fitness in a population was emphasized by Fisher (1999). Under this view, rugged adaptive landscapes are less problematic since a population can be thought of as occupying a region of allele-frequency space where the topography of the fitness elevations changes over time. If the fitness landscape is continually remodeling itself, a population will not be stranded on a fitness peak since eventually the peak itself will move or change position. This view is also the foundation of the so-called Red Queen or arms race model of Van Valen (1973), where a species must constantly experience adaptive change to keep pace with continually changing genotypic fitness values ultimately caused by a perpetually changing environmental context defined by other species that themselves are constantly changing.

Another set of possibilities that Wright considered, diagrammed in Figs 11.4D and 11.4E, focused on effective population size. Wright pointed out that if the effective population size were very small relative to the selection coefficient and the mutation rate (Fig. 11.4D), a population would likely experience fixation or loss at all loci due to genetic drift (see the allele-frequency distribution in the right-hand panel of Fig. 11.3A). As a consequence, a population would cease attraction to fitness peaks, would wander at random around the fitness landscape, and would also experience the fixation of deleterious alleles, leading to inbreeding depression. If the effective population size became small rapidly, then after fixation and loss at most loci, movement on the landscape would be very slow since most new mutations would be unlikely to segregate for long. In contrast, a finite population with a medium effective population size relative to the selection coefficient and the mutation rate (Fig. 11.4E) would occupy a fairly large area on the surface and would experience some random movement around a fitness peak but would not stray too far from the peak. This would occur because the population would experience an approximate balance between natural selection and genetic drift and would also have the input of new mutations over time (see the allele-frequency distribution in the center panel of Fig. 11.3A). Wright saw populations experiencing a balance of genetic drift, natural selection, and mutation (medium values of 4NU and 4NS) as being able to shift fitness peaks and a means by which "the species may work its way to the highest peaks in the general field." The limitation is that peak shifting by one such population was expected by Wright to be a very slow process that would only occur if the mutation rate was approximately equal to the reciprocal of the effective population size.

The final case Wright considered, shown in Fig. 11.4F, was the situation where a species was subdivided into a number of finite demes (or "small local races") that were nearly genetically isolated but did experience some gene flow. Here Wright was thinking of the allele-frequency distribution in the center panel of Fig. 11.3B, where there is a balance between genetic drift leading to population differentiation and gene flow leading to homogenization of allele frequencies that produces a broad distribution of allele frequencies among demes. Wright's idea was that many semi-independent finite demes would move positions on the fitness landscape more rapidly than a single panmictic population. Wright also conjectured that those demes that did reach higher fitness peaks would produce more migrants. The effect of more migrants would be for a deme on a higher fitness peak to shift the allele frequencies of the demes that received those migrants toward the positions of higher fitness peaks. This process of higher rates of gene flow from those demes on higher fitness peaks is often called interdemic selection since it is equivalent to natural selection acting at the level of demes with different levels of demographic productivity. Thus, Wright envisioned that a species made up of many subdivided demes experiencing approximately equal pressures of natural selection and genetic drift could explore more of the fitness surface and would be more likely to find more of the higher fitness peaks than natural selection alone. Wright concluded that "subdivision of a species into local races provides the most effective mechanism for trial and error in the field of gene combinations."

The shifting balance process is often summarized by the simultaneous operation of three "phases" of population genetic change in a subdivided population. Phase I involves genetic drift within demes that causes the allele-frequency position of each deme to shift randomly with respect to the position of fitness peaks. Phase II is the operation of natural selection on demes such that the allele-frequency position of demes is shifted toward and higher up fitness peaks, with taller peaks exerting a stronger influence on allele frequencies. Phase III is interdemic selection such that the rates of emigration from demes are proportional to the mean fitness of a population. Thus, demes at higher fitness peak elevations export more migrants and comprise a larger proportion of the immigrant pool of other demes, shifting allele frequencies of all demes toward the allele-frequency locations of taller fitness peaks.

Critique and controversy over shifting balance

Although Wright's metaphor of the adaptive landscape and proposal of the shifting balance theory has stimulated the thinking of biologists for decades, his ideas have also generated sustained controversy. The fitness surface metaphor itself has been one focus of critique because the original fitness surface described by Wright is problematic in some respects. As Provine (1986) describes, Wright employed two distinct versions of the fitness surface. One version of the fitness surface illustrates the fitness of each genotype based on an ordering of the allele combinations in genotypes. In this version of the fitness surface, each combination of alleles has a relative fitness and defines one point on the landscape. This type of surface has been compared with the pixels that make up a photographic print or digital image (Ruse 1996). In the genotype version of the fitness surface, what is represented biologically by the dimensions other than that representing fitness is not clear since the genotype axes do not relate to the frequency of genotypes or alleles in a population. Another version of the fitness surface plots the mean fitness of a population for all possible allele frequencies (examples of population mean fitness surfaces can be found in Chapters 6 and 7). Contemporary usage of the fitness surface metaphor is often in the population mean fitness sense, with axes representing allele frequencies and one dimension representing the mean fitness of a population at those allele frequencies, although there are exceptions (e.g. Weinreich et al. 2005). Wright often switched back and forth between these two types of fitness surface in his writing, leading to ambiguity and confusion (Provine 1986). Fitness surfaces have been constructed and interpreted in a wide variety of ways since Wright's work (Gavrilets 2004; Skipper 2004).

Coyne et al. (1997) presented a detailed and vigorous critique of Wright's shifting balance theory that examined evidence for and against operation of the three phases in actual populations. They reexamined the theoretical basis of the shifting balance theory with the benefit of more than 60 years of work in theoretical population genetics, and considered empirical evidence for the shape of fitness surfaces and operation of the stages of the shifting balance process. They concluded that "although there is some evidence for the individual phases of the shifting balance process, there are few empirical observations explained better by Wright's three phase mechanism than by simple mass selection." Other authors responded in defense of shifting balance theory or to offer alternative points of view (e.g. Peck et al. 1998; Wade and Goodnight 1998), generating a cascade of replies and counter-replies (Coyne et al. 2000; Goodnight and Wade 2000; Peck et al. 2000). While it is not possible here to consider in detail all of the points raised in that debate, disagreements over elements of the shifting balance process serve to highlight difficulties that arise when attempting to predict the outcome of multiple population genetic processes operating simultaneously.

The third phase of the shifting balance process, production of migrants in proportion to the population mean fitness and shifting of demes via differential contributions to the immigrant pool, is particularly problematic (see Crow et al. 1990). The difficulty is that the migration rate must be low enough to permit population subdivision into semi-isolated demes but at the same time high enough to permit the exchange of individuals (or gametes) among subpopulations that leads to interdemic selection. A general objection is that interdemic selection is a form of group selection, a process where there is greater survival or reproduction of a population of individuals compared to other populations such that some populations go extinct while others persist and expand. Williams (1966, 1992) has presented the classical arguments that natural selection on additive genetic variation among individual genotypes is expected to act more rapidly than selection on groups because the frequencies of individuals can change more rapidly than the frequencies of populations. Nonetheless, possible evidence for group selection in the context of differential migration has been shown in experiments with the flour beetle Tribolium castaneum (Wade and Goodnight 1991). Large changes in number of individuals per population were observed over nine generations by selecting individuals to be founders of the next generation based on the total number of individuals in a population. In contrast, the size of populations did not change over time when founding individuals were selected at random with respect to population size. The interpretation of numerous Tribolium experiments of this type (reviewed by Goodnight and Stevens 1997) has been controversial since there is disagreement over what exactly constitutes group and individual selection and what type of selection is imposed by the experimental procedures (see Coyne et al. 1997; Getty 1999; Wade et al. 1999).

Another aspect of the disagreement over shifting balance theory involves the dual nature of the concept of epistasis (see Cheverud and Routman 1995; Whitlock et al. 1995; Fenster et al. 1997; Brodie 2000; Cordell 2002). Epistasis exists when genotypes at two or more loci result in a genotypic value that is greater or less than the sum of the genotypic effects of the loci when taken individually (see Chapter 9). The existence of an interaction between two or more loci indicates the existence of physiological epistasis (also known as functional or mechanistic epistasis). The term physiological epistasis simply recognizes that certain genotypes at two or more loci interact in the production of a phenotype. The contribution, if any, of such physiological epistasis to population level quantities is a function of the frequencies of interacting genotypes in a population. The term statistical epistasis is used to refer to the amount of standing population variation in genotypic values caused by interactions among loci. In the symbols and concepts of Chapters 9 and 10, statistical epistasis is Vr The amount of statistical epistasis present in a population is a function of the frequencies of interacting multilocus genotypes and therefore a function of population allele frequencies, as it is for additive and dominance variance (VA and VD), as well as a function of mating system and the rate of recombination.

Wright implicitly assumed that statistical epistasis was abundant in natural populations. While there is evidence that statistical epistasis exists in natural and laboratory populations (MacKay 2001; Cordell 202; Carlborg and Haley 2004; see chapters in Wolf et al. 2000), statistical epistasis is not widespread in populations, although it remains difficult to estimate. There is currently no consensus over the relative contribution of epistasis to overall quantitative trait variation, although there is recognition that empirical detection of epistasis is limited by experimental designs and statistical power (see Whitlock et al. 1995). Some conclude that there is a lack of evidence for strong or frequent statistical epistasis in natural populations. Others suggest that there is some evidence for epistasis in natural populations, and since epistasis is difficult to detect, it is premature to draw a conclusion about the prevalence of epistasis. These disparate views translate into difficulty summarizing the nature of adaptive landscapes in populations that are genetically variable.

When a population is at fixation and loss for all loci there can be no statistical epistasis since there is no variation in genotypic value, even though physiological epistasis may exist and even be very strong. An alternative definition of epistasis is useful for populations that may exhibit little statistical epi-stasis and yet have abundant physiological epistasis. Sign epistasis is a special case of physiological epistasis in populations with little or no genetic variation (Weinreich et al. 2005). A locus exhibits sign epistasis when a new mutation exhibits higher-than-average fitness on some genetic backgrounds defined by other loci but lower-than-average fitness on other genetic backgrounds. The sign of the fitness value is therefore a function of the other loci that make up the genetic background of the allele. (This is in contrast to a more general definition of epistasis where a new mutation might always be deleterious, but it is more or less deleterious depending on the genetic background.) An example of sign epistasis in the context of a haploid system would be if the mean fitness of a new mutation at the B locus was positive if it was paired with an A allele and negative if it was paired with an a allele. This leads to an alternative view of how to define and test for epistasis that is amenable to empirical study.

Weinreich et al. (2006) examined five single-nucleotide mutations in the P-lactamase gene of bacteria. Four of these mutations result in missense versions of the P-lactamase gene, so that they are deleterious individually and selected against in antibiotic environments. The fifth mutation is a non-coding change 5' to the gene. However, when all five mutations occur simultaneously they lead to a version of the P-lactamase gene that confers resistance to P-lactam antibiotic drugs such as penicillin. When each mutation occurs on a genetic background with the other four mutations present its fitness is positive since the five-mutation version of the gene has high fitness in antibiotic environments. This situation constitutes an example of sign epistasis.

Even with these various objections and complications, the shifting balance theory has had an enduring impact on the imaginations of population geneticists The basic problem that motivated Wright to propose the shifting balance theory - that natural selection cannot lead to decreases in mean fitness - remains a difficulty that continues to attract attention and motivate researchers many decades later.

Chapter 11 review

• The synthesis of Darwin's concept of natural selection with Mendelian particulate inheritance that forms that basis of population genetics is called neo-Darwinism.

• The classical hypothesis predicted that directional natural selection was the dominant process. This led to a prediction that genetic variation was limited at most loci. What genetic variation that existed was thought to be caused mostly by deleterious mutations, along with some neutral mutations and very few beneficial mutations.

• The balance hypothesis predicted that balancing natural selection caused by overdominance for fitness was the dominant process. This led to the prediction that levels of genetic variation should be high for many loci since balancing selection maintains alleles at intermediate frequencies indefinitely. The balance hypothesis also predicted selection would cause gametic disequilibrum over large regions of the genome, producing supergenes or coadapted gene complexes.

• Genetic load results from the selective deaths (either reproductive or actual) that must occur as frequencies of mutations or genotypes change under natural selection. In principle, the amount of natural selection is limited by the genetic load a population can tolerate. Genetic load arguments were used to estimate the upper limit on the rate of substitution in mammals and to argue for the neutral theory of molecular evolution.

• The novel technique of allozyme electrophoresis first used in the mid-1960s revealed that about 30% of the loci in Drosophila were heterozygous. This observation set off a long-running debate over how to best explain levels of genetic polymorphism in natural populations.

• The proposal of the neutral theory of molecular evolution sparked a controversy between neutralists and those who favored selection-based explanations of rates of divergence and levels of polymorphism. This debate lead to many innovations in the theory of both genetic drift and natural selection. Explanations such as the nearly neutral theory that combine the relative contributions of drift and selection and place them on a continuum are now common in population genetics.

• Wright's metaphor of the adaptive landscape is a heuristic device designed to articulate how the process of natural selection alone is con strained since it can only increase population mean fitness.

• Sewall Wright's shifting balance theory was designed as a hypothesis about how the simultaneous action of natural selection, genetic drift, mutation, and population subdivision might lead to the exploration of a larger portion of the adaptive landscape than would be possible under selection alone.

• While shifting balance theory and its key assumption of statistical epistasis remains controversial, adaptive landscapes are an enduring metaphor in population genetics.

Further reading

For a history of early population genetics beginning with Darwin and Mendel and ending with Fisher, Haldane, and Wright, see:

Provine WB. 1971. The Origins of Theoretical Population Genetics. University of Chicago Press, Chicago, IL (this book was originally published in 1971 while the 2001 edition has an afterword by Provine).

For a wide-ranging consideration and critique of aspects of the classical/balance hypothesis debate written in the midst of the allozyme era in population genetics, see:

Lewontin RC. 1974. The Genetic Basis of Evolutionary Change. Columbia University Press, New York.

For Kimura's view on why the classical and balance hypotheses failed to explain patterns of genetic variation see the following (especially the first chapter):

Kimura M. 1983. The Neutral Theory of Molecular Evolution. Cambridge University Press, Cambridge (Kimura also reviews the manifold arguments in support of the neutral and nearly neutral theories).

An illuminating history of the development of the neutral and nearly neutral theories is provided in:

Ohta T and Gillespie JH. 1996. Development of neutral and nearly neutral theories. Theoretical Population Biology 49: 128-42.

For a review of elements of the selectionism/ neutralism debates see:

Nei M. 2005. Selectionism and neutralism in molecular evolution. Molecular Biology and Evolution 22: 2318-42.

A highly readable review of the selectionist/neutralist debate written shortly after the proposal of the neutral theory can be found in:

Crow JF. 1972. Darwinian and non-Darwinian evolution. Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, vol. V, pp. 1-22. University of California Press, Berkeley, CA.

For background and explanation of the original fitness surface along with some response to criticisms, see:

Wright S. 1988. Surfaces of selective value revisited. American Naturalist 131: 115-23.

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