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Note that as gene flow becomes more and more restricted (m approaches zero), Mi converges to wi. This means that conditions 14.8 and 14.9 become nearly identical when gene flow is highly restricted. Thus, under highly restricted gene flow the ecological distinction between soft and hard selection becomes irrelevant for the conditions under which coarse-grained spatial heterogeneity protects polymorphisms. This work therefore illustrates the danger of considering one factor in isolation, such as hard versus soft selection. What we see here is strong interaction between ecology (hard and soft selection), population structure (here measured by m), and natural selection. Even a complete knowledge of the spatial heterogeneity of fitnesses and of the ecological conditions determining local densities is insufficient to predict the evolutionary outcome: You also must know about population structure.

One general conclusion to emerge from the contrast of inequalities 14.8 and 14.9 is that as gene flow becomes more and more restricted, populations show greater and greater adaptation to the local rather than the global environment. Indeed, for highly restricted gene flow in both cases, it is local conditions and only local conditions that determine if a polymorphism is protected (the first of the alternative inequalities in 14.8 and 14.9). The role of gene flow as a modulator of local adaptation in the face of spatial heterogeneity is illustrated by studies on industrial melanism.

Industrial melanism is the evolution of dark coloration in various species (mostly insects) in response to a darkening caused by air pollution of the background color upon which the species rests or lives. Industrial melanism is one of the classic examples of natural selection (Kettlewell 1955, 1973; Lees 1981). Although this example has been questioned (Majerus 1998; Hooper 2002), an exhaustive review of the literature and the continuing studies on this system strongly support the role of natural selection, of which predation is one part (Cook 2003). Several species of moths in England have melanic (dark) morphs that are controlled by a single autosomal locus with two alleles. Many of these moths rest upon tree trunks and limbs during the day. There they are subject to predation by a variety of bird species, and such bird predation has been directly observed and recorded under natural conditions (Murray et al. 1980), including on the trunk in an area before any experimentation was performed [Murray, personal communication, and contrary to claims reported in Hooper (2002)]. One type of protection from bird predation during that time is simply being cryptic, that is, matching the background upon which they are resting such that they are difficult to see. The trees normally had a light-colored background due to the growth of epiphytic lichens and bryophytes upon the bark, but air pollution, particularly sulfur oxides and acid rain, can kill these epiphytes, leading to a dark background on the tree trunks. Great Britain has a long history of people collecting butterflies and moths, so collections were available to show that before industrialization the light-colored morphs dominated throughout the island and melanic forms were extremely rare. However, with industrialization and its attendant air pollution, there was a marked increase in the frequency of melanic forms in many species. Of course, not all areas of Great Britain are equally polluted, and different local areas vary from extreme air pollution to areas, mostly in the countryside, that remained unpolluted. As a consequence, as industrialization proceeded, Great Britain became a spatial patchwork of polluted and unpolluted areas, and many moth species responded to this spatial heterogeneity with a corresponding genetic heterogeneity in the frequency of melanic alleles. For example, Figure 14.4 shows the frequency of melanic forms in different local populations of the peppered moth, Biston betularia. The melanic morphs are most frequent in areas with much industrial activity and air pollution, whereas the light morphs are most frequent in nonindustrialized areas. Thus, on this coarse

Organic Theory Map

Figure 14.4. Distribution of melanic forms of peppered moth B. betulariaon island of Great Britain. Black segments of each pie diagram indicate phenotype frequency of melanic form in sample at particular location. Modified from Fig 5.10 in Lees (1981). Copyright © 1981 by Academic Press, Inc. (London). Reprinted by permission of Elsevier.

Figure 14.4. Distribution of melanic forms of peppered moth B. betulariaon island of Great Britain. Black segments of each pie diagram indicate phenotype frequency of melanic form in sample at particular location. Modified from Fig 5.10 in Lees (1981). Copyright © 1981 by Academic Press, Inc. (London). Reprinted by permission of Elsevier.

geographical scale of the entire island of Great Britain, the moths are adapting to local conditions.

There is considerable spatial variation in the degree of pollution on a finer geographical scale as well. For example, the nearby cities of Manchester and Liverpool have much pollution as compared to the nearby Welch countryside (Bishop and Cook 1975; Bishop

Figure 14.5. Distribution of melanic peppered moths in Manchester/Liverpool area in England and adjacent areas of Wales. The height of the surface gives the proportion of the population in that locale that is melanic. The surface is viewed from the southwest, from rural Wales looking toward Liverpool and Manchester. Modified from Bishop and Cook (1975). Copyright © 1975 by Gabor Kiss.

Figure 14.5. Distribution of melanic peppered moths in Manchester/Liverpool area in England and adjacent areas of Wales. The height of the surface gives the proportion of the population in that locale that is melanic. The surface is viewed from the southwest, from rural Wales looking toward Liverpool and Manchester. Modified from Bishop and Cook (1975). Copyright © 1975 by Gabor Kiss.

et al. 1978). Figure 14.5 shows the frequency of the melanic form of B. betularia in this area of England and Wales. As can be seen, the frequency surface has two distinct parts: a plateau of more than 90% melanic in Liverpool, Manchester, and the area between them and a descending portion that drops to less than 10% in Northern Wales. However, there is even finer scale heterogeneity in the degree of pollution in the Manchester/Liverpool area. There are some wooded areas to the south and east of this urban area, and even in the urban corridor there is variation in the amount of pollution. However, the peppered moth adapts to the Manchester/Liverpool area as if it were uniformly polluted.

The scalloped hazel moth also lives in this region, and it is also polymorphic for a melanic locus subject to the same type of selective pressures as observed in the peppered moth. As was the case with the peppered moth, this species also shows geographical variation in the frequency of the melanic forms such that melanic forms are most common in polluted areas. Figure 14.6 shows the geographical distribution of the frequency of melanic forms in the scalloped hazel moth in the Manchester/Liverpool urban area, a subset of the area shown in Figure 14.5 that is fully contained with the >90% melanic plateau of the peppered moth. The scalloped hazel moth shows considerable variation in the frequency of melanic forms in this area of England in a manner that corresponds to polluted and relatively unpolluted local areas, but the peppered moth does not show any significant variation in the frequency of melanic forms in this same area. Why do these two moth species, each with a melanic polymorphism subject to similar selection, respond to spatial heterogeneity in such distinct fashions? The answer seems to stem from differences in the amount of gene flow between the two species. The scalloped hazel moth populations are very dense in this area, with as many as 50,000-100,000 moths per square kilometer. In contrast, the peppered moth density is about 10 per square kilometer. This implies that a peppered moth is likely to have to travel

Figure 14.6. Distribution of melanic scalloped hazel moths (Gonodontis bidentata) in Manchester/ Liverpool area in England. The height of the surface gives the proportion of the population in that locale that is melanic. The surface is viewed from the southwest, looking toward Liverpool center and Manchester. Modified from Bishop and Cook (1975). Copyright © 1975 by Gabor Kiss.

Figure 14.6. Distribution of melanic scalloped hazel moths (Gonodontis bidentata) in Manchester/ Liverpool area in England. The height of the surface gives the proportion of the population in that locale that is melanic. The surface is viewed from the southwest, looking toward Liverpool center and Manchester. Modified from Bishop and Cook (1975). Copyright © 1975 by Gabor Kiss.

much farther than a scalloped hazel moth to encounter a mate. Mark/recapture experiments confirm this difference, with many peppered moths flying more than a kilometer but with scalloped hazel moths rarely flying more than 150 meters. As shown by conditions 14.8 or 14.9, when the gene flow parameter is very small, the top condition of having just a single local environment favoring an allele is sufficient to protect it. This occurs because with very restricted gene flow the local population is able to adapt to its local environment in a manner not strongly influenced by the influx of genes from other local populations adapted to a different environment. As the amount of gene flow increases, the role of the local environment in protecting polymorphisms is diminished and is replaced increasingly by the lower conditions in 14.8 or 14.9. In this case, the adaptive outcome is determined more by an averaging across several local environments rather than the local conditions per se. In the case of the scalloped hazel moth, the amount of dispersal and gene flow is so low and the densities so high that populations can adaptively respond to local environments on the scale of just a kilometer of two. In contrast, the peppered moth experiences spatial heterogeneity at this small geographical scale as individuals rather than as breeding populations and hence as a population adapts to coarse-grained spatial heterogeneity on a much larger geographical scale. Conditions 14.8 and 14.9 and this example all show that the adaptive response to spatial heterogeneity arises from an interaction of natural selection and gene flow. Thus, we see a reinforcement of the theme developed in Chapter 12: Adaptation arises from the interaction of natural selection with population structure such that natural selection alone cannot explain how a population adapts to its environment.

The peppered moth (Figure 14.5) and the scalloped hazel moth (Figure 14.6) illustrate how the evolutionary response to spatial heterogeneity emerges from the balance of selection favoring local differentiation versus gene flow which diminishes local differentiation. Another way of characterizing spatial heterogeneity that is sensitive to the balance of selection versus gene flow is ecotones versus gradients. An ecotone is a spatially abrupt change from one environment (and hence selective regimen) to another, whereas a gradient is a gradual change over space from one environment to another. There is no absolute geographical scale that distinguishes between an ecotone and a gradient because that distinction depends upon how the organism moves and reproduces through space. To see this, consider a single-locus, two-allele codominant model with a spatial transition between two environments that influences the fitnesses such that waa(x) = 1 - 2bA w Aa (x) = 1 Waa(x) = 1 + 2 bA w AA(x) = 1 + bx W Aa (x) = 1 waa(x) = 1 - bx w aa(x ) = 1 + 2 bA w Aa (x) = 1 waa(x) = 1 - 2bA

where x is the spatial position in a transect between the two environments in which one environment ends at point —x0 and the second environment begins at point x0, b measures the slope of the fitness effect in the transition space between the two environmental types, and A is the transition distance between the two environments (Endler 1977). If fitnesses are changing continuously along some transect, then A is the distance between the two most distant points in the transect. Let gene flow be characterized by an isolation-by-distance model in which an individual born at a particular point has a probability m of dispersing from the deme of birth and given dispersal it moves an average distance of d. Then gene flow is measured by the root-mean-square gene flow distance (Endler 1977):

The parameter t is the same parameter as a in the continuous isolation-by-distance models discussed in Chapter 6 (equations 6.37). Hence, t is a direct measure of gene flow restricted by isolation by distance. This gene flow tends to diminish local adaptation. The measure of the strength of selection in counteracting gene flow is s = bA, which is the magnitude of the maximum fitness change in a homozygote in response to this spatial heterogeneity. The balance of gene flow and selection is then given by (Endler 1977)

The quantity tc is known as the characteristic length of variation in allele frequencies and represents the spatial scale over which selection is effectively averaged by gene flow. Note that this characteristic length is directly proportional to our measure of gene flow (equation 14.11) and inversely proportional to the intensity of the spatial change in fitnesses (measured by b) and the spatial scale over which the fitnesses change (measured by A). If tc > A, the organism experiences the environment as an ecotone because the transition between the two environments occurs on a spatial scale less than individual gene flow relative to selection. If tc < A, the organism experiences the environmental transition as a gradient in which adaptation to transitional, intermediate environments is possible. Either situation can result in a genetic cline, a gradual shift of gamete frequencies over geographical space. In the case of an ecotone, populations far away from the transitional zone will tend to be fixed for either the A or a alleles depending upon which environment they are in, but populations near the environmental transition zone will have intermediate allele frequencies due to the mixing via gene flow of gametes coming from the two alternative environments. The width of this cline is on the order of tc. In the case of a gradient, there is more potential for geographic differentiation for a given strength of selection 5. Populations in the transition zone can show local adaptation to the transitional environment. This means that the width of the cline is greater than tc and tends to approach A.

Note that equation 14.12 tells us that there is no absolute difference between a gradient and an ecotone. The distinction between the two depends upon the physical scale of the environmental heterogeneity (A), the population attribute of degree of isolation by distance (t), and the locus-specific attribute of phenotypic response to the spatial heterogeneity (b). Hence, not only can different species experience the same physical heterogeneity (measured by A) in different fashions because they differ in t but also even within a species one locus may respond to the spatial heterogeneity as if it were an ecotone, another respond to the same heterogeneity as if it were a gradient, and yet other loci not respond at all to the spatial heterogeneity because of variation in b across loci.

These points can be illustrated by an examination of a population of the fruit fly Drosophila mercatorum in the Kohala Mountains on the Island of Hawaii near the town of Kamauela (also known as Waimea) that was discussed in Chapter 6 (see Figure 6.9). There is an extreme rainfall and humidity gradient on the windward side of Kohala, with a rainforest existing at the top and extending down the slope and then rapidly transitioning into a desert. Site A in Figure 6.9 is close to the rainforest and is extremely humid. However, site B, only 300 meters downhill from site A, is much drier, and sites F and IV are extremely dry. As the distance from site A to F is only about 1 km, this environmental transition from rainforest to desert seems very abrupt and dramatic to most human observers. However, how does a fly experience this 1-km transition? As discussed in Chapter 6, there is sufficient gene flow across this space to result in a nonsignificant fst for nuclear genes, but gene flow is sufficiently restricted to result in fst statistics that are significantly different from zero for mtDNA and Y-DNA, indicating that the variance effective number of migrants across this area is about 8.5 using the island model as our ideal reference population (Chapter 6). The inference of restricted but significant gene flow over this area is confirmed by direct studies on dispersal (Johnston and Templeton 1982). This area of Hawaii is very windy, as noted in a traditional Hawaiian chant about this locale: Hole waimea ika ihe a ka makani ("Tousled is Waimea by spear sharp thrusts of wind"). Under normal conditions, the wind blows down the mountainside shown in Figure 6.9 between 15 and 35 km/h, occasionally gusting higher. The flies live in patches of the prickly pear cactus Opuntia megacantha, and these patches block the wind. However, both laboratory and field observations reveal that the flies will not disperse between these cactus patches unless the wind speed drops and remains below 10 km/h (Johnston and Templeton 1982). Days with such low winds are relatively rare in this area, occurring on average only about four to five days per month. When these relatively still days occur, 31% of the adult D. mercatorum population disperse, and the dispersing adults move an average of 43 meters/day, roughly the average distance between neighboring large cactus patches. This nearest-neighbor pattern of dispersal represents a type of isolation by distance. The amount of gene flow associated with this dispersal is also a function of how long the flies live as adults, for it is only in the adult stage that flies can disperse. Adult survivorship data from the field (to be discussed in Chapter 15) indicates that most flies will have only one or two days on average in their lifetime in which dispersal is possible. Putting all these data together yields t = 28.8 meters. In terms of the two-dimensional neighborhood model in equation 6.37, this means that the radius of the neighborhood area in which parents can be treated as if drawn at random is 2a = 2t = 57.6 meters. Hence, there is isolation by distance over the 1-km transect, but apparently the densities are sufficiently high (recall that fst emerges from the balance of gene flow to drift and not just gene flow alone) that there is no significant subdivision over the transect for most nuclear loci (DeSalle et al. 1987).

However, what would happen at a locus for which the genotype-fitness relationship is directly affected by the humidity gradient to create fitness differences across this gradient? One such locus is abnormal abdomen (aa). As will be detailed in Chapter 15, aa is not really a single locus, but rather a cluster of genes that are tightly linked on the X chromosome. Recombination is sufficiently rare that we can treat this X-linked region for now as a single Mendelian superlocus (Chapter 13) with two alleles, aa+ and aa. In Chapter 15 we will investigate in detail the phenotypic consequences of genetic variation at this super-locus, but for now it suffices to say that the aa allele is favored by natural selection under dry environmental conditions whereas the aa+ allele is favored under humid conditions. Templeton et al. (1990a) estimated that the magnitude of the selective difference between aa homozygotes at the extreme of the transect is s = 0.0245. Hence, the characteristic length for the aa locus over this transect is 28.8/V0.0245 = 184 meters, which is much less than the length A = 1000 meters of the transect. With respect to the aa locus, these populations of D. mercatorum experience this abrupt environmental transition not as an ecotone, but as a gradient in which local adaptation should result in a genetic cline within the transitional zone. Indeed, there is a significant genetic cline for aa across this humid-dry environmental transition (Figure 14.7). However, there was no significant cline for the allozymes, considered either together or individually. One of the isozyme loci is another X-linked locus, glucose-6-phosphate dehydrogenase (G6PD), which is located at the other end of the X from aa. The allele frequency changes for the G6PD S allele are also shown in Figure 14.7. In this case, there is no cline and no statistically significant differentiation across this transect, illustrating how gradients are locus specific, as expected from equation 14.12.

Although G6PD appears to be a neutral marker in the Kohala populations of D. mercatorum, the X-linked G6PD locus in humans is involved with malarial resistance (Chapter 11). The island of Sardinia lies off the west coast of Italy. The coastal areas of Sardinia historically have had a high incidence of malaria, but the central mountainous region does not. The estimated relative fitnesses of the genotypes associated with the active (A+) and deficient (A-) alleles at this locus in Sardinia are given in Table 14.2 (from Livingstone 1973). Figure 14.8 shows the frequencies of the A- allele along the 130-km transect bisecting the island going from the east coast through the central mountains to the west coast. The actual transition from the lowland malarial areas to the highland nonmalarial region occurs in just

Figure 14.7. Frequencies of the aa allele at X-linked abnormal abdomen locus and S allele at X-linked G6PD locus in populations of D. mercatorum over transect on leeward side of Kohala in Hawaii. The position of the sites is indicated in Figure 6.9. Vertical solids lines indicate ± one standard deviation above and below the estimated frequency of the S allele, and vertical dotted lines indicate ± one standard deviation above and below the estimated frequency of the aa allele.

Figure 14.7. Frequencies of the aa allele at X-linked abnormal abdomen locus and S allele at X-linked G6PD locus in populations of D. mercatorum over transect on leeward side of Kohala in Hawaii. The position of the sites is indicated in Figure 6.9. Vertical solids lines indicate ± one standard deviation above and below the estimated frequency of the S allele, and vertical dotted lines indicate ± one standard deviation above and below the estimated frequency of the aa allele.

a few kilometers on both the east and west sides of this transect. People have inhabited this area for over 2000 years with relatively constant densities. Livingstone (1973) simulated the evolutionary response to the fitness values shown in Table 14.2 in a manner that tried to mimic the movements of peasant populations in Europe. A good fit to the observed pattern shown in Figure 14.8 was obtained by assuming that the environmental transition was sharp with A < 2.65 km (the average distance between adjacent villages in the simulations) and that 25% of the people left their village of birth, with those dispersing going primarily to adjacent villages and other nearby villages, yielding an average dispersal distance of d = 3.34 km, which yields I = 3.34^1 = 1.67 km. The cline in this case is driven by the fitness effects of A- in hemizygous males and in heterozygous females (Table 14.2). From Table 14.2, 5 = 0.97 - 0.90 = 0.07 in males, and the 5 for females is 1.07 - 0.98 = 0.09.

Table 14.2. Relative Fitness of Male and Female Genotypes Created by A+ and A- Alleles at Human X-Linked G6PD Locus in Malarial (Coastal) and Nonmalarial (Mountain) Regions on Island of Sardinia

Fitness for Fitness for

Male Genotype Female Genotype

Mountains 1 0.90 1 0.98 0.90

Source: Livingstone (1973).

Figure 14.8. Frequencies of the A- alleles at X-linked G6PD locus in human populations along east-west transect of island of Sardinia. Modified from Fig. 8 in Livingstone (1973). Copyright © 1973 by the School of American Research, University of New Mexico Press.

Averaging across the two sexes, 5 = 0.08. Then, from equation 14.12, lc = 5.91. Hence, the characteristic length of this cline is more than twice the transitional distance A, implying that the ecotone model explains the cline observed in Figure 14.8. Note that the geographic distance of the transition in the environment is larger in this human example than the transition distance in the Drosophila example, yet the larger physical distance in the human example defines an ecotone whereas the smaller physical distance in the Drosophila example defines a gradient. The distinction between an ecotone and a gradient is not a function of absolute distance but rather depends upon the balance among physical distance, gene flow, and selective strength.

In addition to genetic clines, there are also phenotypic clines, gradual shifts of pheno-typic frequencies or mean phenotypes over geographical space. In the case of abnormal abdomen, the genetic cline is accompanied by a phenotypic cline (the phenotypes associated with aa will be discussed in Chapter 15). However, premise 3 (Chapter 1) states that phenotypes arise from the interaction of genotypes and environments. The interactions of genotypes with environments that are changing over ecotones or gradients can result in complex, even counterintuitive relationships between genetic and phenotypic clines. For example, populations of the green frog Rana clamitans live on the east coast of the United States and into the Appalachian Mountains (Berven et al. 1979). Populations were sampled in ponds along an elevational transect from 10 to 1250 meters above sea level. The growth rates of the tadpoles were measured, and it was discovered that tadpoles in the lowland ponds had the largest growth rates and tadpoles in the montane ponds had the smallest growth rates. However, growth rates in amphibians are strongly influenced by temperature, and the average temperature varies greatly over this transect. In particular, low temperatures decrease the growth rate whereas warm temperatures increase it. Consequently, the phenotypic cline in growth rates along this elevational transect could be due just to the temperature effects with no genetic component at all. To test this hypothesis, Berven et al. (1979) performed laboratory experiments under controlled temperature conditions on egg masses sampled from both lowland and montane ponds. They discovered that for a given temperature the montane forms had higher growth rates than the lowland forms—exactly the opposite of the observed phenotypic cline!

De Jong (1988) produced a simple model to show how genetic and phenotypic clines can go in opposite directions. Consider first a one-locus model with two alleles, Aand a. Let all genotypes have linear norms of reaction (Chapter 10) to temperature such that the genotypic values of growth are

where T is the temperature, c is the slope of the linear norm of reaction to temperature and is shared in common by all genotypes, and a > 0 defines the genotypic specific intercepts of the norm of reaction (note that the heterozygote is always intermediate between the two homozygotes such that no heterozygote superiority for growth rate is possible in this model). For simplicity, we also assume that the environmental variance is zero for any given temperature; that is, all individuals sharing the same genotype have the same phenotype at a specific temperature.

Under equations 14.13, the norms of reaction of the genotypes are all parallel lines when plotted against temperature, but with some genotypes having uniformly higher or lower growth rates for a specific temperature, as shown in Figure 14.9. In this simple model, the AA genotype always has the highest growth rate at any given temperature, the aa genotype the lowest, and the Aa genotype an intermediate growth rate. Now suppose that the fitnesses assigned to individuals on the basis of their actual growth rates are constant throughout the transect with a single optimal growth rate, say j, being associated with the highest fitness, as also shown in Figure 14.9. A fitness function that has a single optimal value j with fitness dropping off symmetrically about j is given by w(P) = 1 - a(j - P)2 (14.14)

where P is the individual's phenotype (in this case growth rate) and a determines how rapidly fitness drops off in individuals with growth rates that deviate from j. Note that this is a fitness of the type commonly used in ecological theory; it is a fitness assigned to an individual's phenotype for some trait besides fitness, and it is not a fitness assigned to genotypes. However, in order to predict the selective response at this locus, we need to

Mean growth rate

Mean growth rate

Figure 14.9. Hypothetical norms of reaction over temperature and fitnesses assigned to phenotype of growth rate for one-locus, two-allele model. The fitness curve assigned to the phenotype of growth rate is shown on the left of the figure. The right side plots the growth rate response of each genotype to temperature. Three points on the temperature gradient are indicated, along with their effects on the fitnesses assigned to genotypes.

Figure 14.9. Hypothetical norms of reaction over temperature and fitnesses assigned to phenotype of growth rate for one-locus, two-allele model. The fitness curve assigned to the phenotype of growth rate is shown on the left of the figure. The right side plots the growth rate response of each genotype to temperature. Three points on the temperature gradient are indicated, along with their effects on the fitnesses assigned to genotypes.

assign genotypic values of fitness. This is done by using the norm of reaction for frogs reared at any particular temperature. Figure 14.9 shows three possible temperatures. Even though fitness for growth rates is constant regardless of temperature, the genotypic values of fitness vary as temperature changes. The AA genotype has the highest fitness at temperature 1 in Figure 14.9, the Aa genotype at temperature 2, and the aa genotype at temperature 3. Hence, the relative genotypic fitnesses vary dramatically over this temperature gradient. This discrepancy between phenotypic and genotypic fitnesses shows why it is essential to distinguish the cases in which fitness is assigned to another phenotype versus the cases in which fitness is assigned to genotypes.

Fitnesses alone do not determine the evolutionary response to natural selection. Another important factor in determining that response is population structure. We will assume that the species is distributed over this temperature regimen such that there is random mating in any local area, the local densities are large so that drift can be ignored, and there is substantial isolation by distance such that local allele frequencies reflect the local selective conditions. Under these assumptions, selection is expected to drive the local allele frequency to 1 (fixation for A) whenever the fitness of AA is greater than the fitness of Aa and aa. Combining equations 14.13 and 14.14, this occurs whenever

1 - ^ - a - cT)2 > 1 - ^ - cr)2 T < ^ (14.15)

Similarly, selection will cause the local fixation of the a allele whenever

1 - ot(P + a - cT)2 > 1 - a(fi - cT)2 T > r (14.16)

Within the temperature range (2ß - a)/2c < T < (2ß + a)/2c the heterozygote has highest fitness (even though the heterozygote is always intermediate between the two homozygotes for the phenotype of growth rate), and from equation 11.13, we predict that selection will stabilize the local allele frequency at

The average phenotype of growth rate in these locally polymorphic populations is

Figure 14.10 shows a plot of how allele frequency and mean phenotype change over a temperature gradient. As the temperature increases, the local populations go from fixation of the A allele through a steadily declining allele frequency and end up with fixation of the a allele. Thus, there is a genetic cline such that those genotypes with the slower growth rates increase in frequency with increasing temperature. However, the mean growth rate

GAA GAa Gaa

GAA GAa Gaa

2c Temperature 2c

Figure 14.10. Graph of genetic and phenotypic clines obtained with model of de Jong (1988). The temperature axis is subdivided into three sections: T < (2fi - a)/(2c), in which there is fixation of the A allele (p = 1); (2fi - a)/(2c) < T < (2p + a)/(2c), in which there is a balanced polymorphism with 0 < p < 1; and T > (2fi + a)/(2c), in which there is fixation of the a allele (p = 0). The solid line indicates the allele frequency cline over these temperatures. The thick dashed line indicates the mean phenotype of the local population as a function of the temperature gradient. For T < (2fi - a)/(2c) the phenotypic response follows the norm of reaction for the AA genotype, the sole genotype in the population under those conditions, and for T > (2fi + a)/(2c) the phenotypic response follows the norm of reaction for the aa genotype, the sole genotype in the population under those conditions. The norms of reaction for all the genotypes are indicated by the thin dashed lines.

2c Temperature 2c

Figure 14.10. Graph of genetic and phenotypic clines obtained with model of de Jong (1988). The temperature axis is subdivided into three sections: T < (2fi - a)/(2c), in which there is fixation of the A allele (p = 1); (2fi - a)/(2c) < T < (2p + a)/(2c), in which there is a balanced polymorphism with 0 < p < 1; and T > (2fi + a)/(2c), in which there is fixation of the a allele (p = 0). The solid line indicates the allele frequency cline over these temperatures. The thick dashed line indicates the mean phenotype of the local population as a function of the temperature gradient. For T < (2fi - a)/(2c) the phenotypic response follows the norm of reaction for the AA genotype, the sole genotype in the population under those conditions, and for T > (2fi + a)/(2c) the phenotypic response follows the norm of reaction for the aa genotype, the sole genotype in the population under those conditions. The norms of reaction for all the genotypes are indicated by the thin dashed lines.

is also increasing with increasing temperature. The phenotypic and genetic clines are going in exactly opposite directions! As the mean growth rate increases in the intermediate temperature range, there is actually an increase in the frequency of genotypes with slower growth rates. In the extremes of the temperature range, there is a continuation of the phe-notypic cline with temperature but there is no genetic cline whatsoever because there is no genetic variation in the extremes of the temperature range. Figure 14.10 and the example of R. clamitans illustrate well the dangers of equating phenotypic clines to genetic clines.

Figure 14.10 represents some of the complexity that emerges from an interaction effect, in this case the interaction of genotypes with environments to produce phenotypes. Epista-sis is another type of interaction that can modulate the evolutionary response to selection and gene flow in spatially heterogeneous environments. Suppose the unit of selection is a multilocus architecture with much epistasis for the phenotype of fitness. Hadany (2003) considered the evolutionary fate of such a coadapted gene complex in an environment showing heterogeneity in the intensity of selection rather than direction, with some areas showing intense selection and other areas showing weak selection. Such multilocus, epistatic complexes generate the rugged adaptive landscapes associated with Wright's shifting balance theory (Chapter 12). Hadany modeled shifting balance by defining a two-locus, two-allele genetic architecture (say A and a at locus 1 and B and b at locus 2) with epistasis in a haploid population such that the cis AB and ab combinations had higher fitness than the trans Ab and aB combinations. However, the combination AB had higher fitness than ab, but the populations started out fixed for ab. Mutation and recombination create variation in this model, and a shift to a higher peak occurs when AB arises, spreads, and becomes the most common form. Two neighboring subpopulations were then considered, each with the same fitness pattern, but one in which the fitness differences between cis and trans were large and the other in which the fitness differences between cis and trans were small. The effectiveness of shifting balance was measured by the average waiting time to a peak shift (the ab-to-AB transition). Hadany discovered that shifting balance was most effective when there was some, but limited, gene flow between the two subpopulations. The waiting times were increased if there was extensive gene flow between the subpopulations, and likewise they were increased if there were no gene flow between the subpopulations (that is, two independently evolving subpopulations, one subject to intense selection and one to weak selection). The reason for this is that selective intensity has contrasting effects at different stages of the shifting balance process. When selection is weak, the intermediate Ab and aB forms are more frequent, and the advantageous combination AB appears easily. However, weak selection also means that this advantageous combination is readily broken down by recombination (Chapter 13), making it difficult for this combination to persist and spread. The opposite is true when selection is strong. Now the intermediate Ab and aB forms are extremely rare, making it very difficult to generate the favored AB combination, but once that combination arises, strong selection can cause its rapid spread. When there is spatial heterogeneity in selective intensities and positive but limited gene flow, the AB combination can arise in those areas with weak selection, and when placed in areas of strong selection via gene flow, the favored combination can rapidly increase in frequency and then spread back into the areas of weak selection by subsequent gene flow after the favored combination has become the common form in areas of intense selection. The adaptive response emerges in this model from a three-way interaction between selection, population structure, and genetic architecture. Adaptive evolution cannot be explained in terms of natural selection alone.

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