Wright's Shifting-balance Research Articles

PHASE III OF WRIGHT'S SHIFTING BALANCE PROCESS AND THE VARIANCE AMONG DEMES IN MIGRATION RATE

Interdemic selection by the differential migration of individuals out from demes of high fitness and into demes of low fitness (Phase III) is one of the most controversial aspects of Wright's Shifting Balance Theory. I derive a relationship between Phase III migration and the interdemic selection differential, S, and show its potential effect on FST . The relationship reveals a diversifying effect of interdemic selection by Phase III migration on the genetic structure of a metapopulation. Using experimental metapopulations, I explored the effect of Phase III migration on FST by comparing the genetic variance among demes for two different patterns of migration: (1) island model migration and (2) Wright's Phase III migration. Although mean migration rates were the same, I found that the variance among demes in migration rate was significantly higher with Phase III than with island model migration. As a result, FST for the frequency of a neutral marker locus was higher with Phase III than it was with island model migration. By increasing FST , Phase III enhanced the genetic differentiation among demes for traits not subject to interdemic selection. This feature makes Wright's process different from individual selection which, by reducing effective population size, decreases the genetic variance within demes for all other traits. I discussed this finding in relation to the efficacy of Phase III and random migration for effecting peak shifts, and the contribution of genes with indirect effects to among-deme variation.

Wright's Shifting Balance Theory and the Diversification of Aposematic Signals

Despite accumulating evidence for selection within natural systems, the importance of random genetic drift opposing Wright's and Fisher's views of evolution continue to be a subject of controversy. The geographical diversification of aposematic signals appears to be a suitable system to assess the factors involved in the process of adaptation since both theories were independently proposed to explain this phenomenon. In the present study, the effects of drift and selection were assessed from population genetics and predation experiments on poison-dart frogs, Ranitomaya imitator, of Northern Peru. We specifically focus on the transient zone between two distinct aposematic signals. In contrast to regions where high predation maintains a monomorphic aposematic signal, the transient zones are characterized by lowered selection and a high phenotypic diversity. As a result, the diversification of phenotypes may occur via genetic drift without a significant loss of fitness. These new phenotypes may then colonize alternative habitats if successfully recognized and avoided by predators. This study highlights the interplay between drift and selection as determinant processes in the adaptive diversification of aposematic signals. Results are consistent with the expectations of the Wright's shifting balance theory and represent, to our knowledge, the first empirical demonstration of this highly contested theory in a natural system.

Mid-Century Controversies in Population Genetics

Beginning in the 1930s, evolution became an experimental subject. New techniques, especially in Drosophila, made possible quantitative analysis of natural populations. In addition to a large number of studies on many species, there were four major controversies that dominated much of the discussion and experimentation. Some of the arguments were quite heated. These controversies were: Wright vs Fisher on Wright's shifting-balance theory; dominance vs overdominance as an explanation of heterosis; the classical vs balance hypothesis for genetic variability; the neutral theory of molecular evolution. Curiously, most of these issues were not really resolved. Rather they were abandoned in favor of more tractable studies made possible by the new molecular methods.

ADAPTATION AND SPECIES RANGE

Phase III of Sewall Wright's shifting-balance process involves the spread of a superior genotype throughout a structured population. However, a number of authors have suggested that this sort of adaptive change is unlikely under biologically plausible conditions. We studied relevant mathematical models, and the results suggest that the concerns about phase III of the shifting-balance process are justified, but only if environmental conditions are stable. If environmental conditions change in a way that alters species range, then phase III can be effective, leading to an enhancement of adaptedness throughout a structured population.

Spatial Mosaic and Interfacial Dynamics in a Müllerian Mimicry System

Uncovering why spatial mosaics of mimetic morphs are maintained in a Müllerian mimicry system has been a challenging issue in evolutionary biology. In this article, we analyze the reaction diffusion system that describes two-species Müllerian mimicry in one- and two-dimensional habitats. Due to positive frequency-dependent selection, a local population first approaches the state where one of the comimicking patterns predominates, which is followed by slow movement of boundaries where different patterns meet. We then analyze the interfacial dynamics of the boundaries to find whether a stable cline is maintained and to obtain the wave speed if the cline is unstable. The results are: (1) In a spatially uniform habitat the morph with greater base fitness spreads both in one and two species system. (2) The strength of cross-species interaction determines whether the mimetic morph clines of model and mimic species coalesce into the same geographical region or pass through each other. The joint wave speed of clines decreases by increasing the number of comimicking species in the mimicry ring. (3) In spatial heterogeneous habitats, stable clines can be maintained due to the balance between the base fitness gradient and the biased gene flow by negative curvature of boundary. This allows the persistence of a spatial mosaic even if one of the morphs is in every place advantageous over the other. A balanced cline is also maintained if there is a gradient in the population density. (4) A new advantageous morph occurring at a local region is doomed to go to extinction in a finite time if the “radius” of initial distribution is below a threshold. Possible applications to the heliconiine butterfly mimicry ring, heterozygous disadvantage systems of chromosomal rearrangement and hybrid zone, the third phase of Wright's Shifting Balance theory, and cytoplasmic incompatibility are discussed.

Towards a more synthetic view of evolution

The 21st century will be the century of biology, and evolutionary biology will be the linchpin. Yes, this is a bold statement, but it is certainly in keeping with Dobzhansky's famous dictum about evolution. Dobzhansky was one of the major architects of the Modern Synthesis. This book by Schlichting and Pigliucci (SP the Final Synthesis is just gathering steam. Note that these dates are just rough guides and not meant to imply that significant work did not occur outside those periods. What is critical is that within these periods the relevant disciplines all become focussed on the same research program. We are now in the midst of this final joining of biological disciplines. This joining, if history is a guide, will take the next couple of decades. This joining will be driven from the evolutionary side. It is the evolutionary side within which the disciplines are linked by a synthetic theory. The molecular side is primarily linked by a shared set of techniques and a viewpoint that centers all questions ultimately on DNA sequences. Because the evolution side is much more theory driven, that is where synthetic concepts tend to arise. This book by S&P is an excellent example of such theorydriven synthesis. Also, if truth be told, as a whole evolutionary biologists tend to have a larger perspective than those in many other biological disciplines. Looking back on the Modern Synthesis is useful for the task ahead (Mayr and Provine, 1980). In particular, if we learn anything from that episode in our history, we

A Spatially Explicit Stochastic Model Demonstrates the Feasibility of Wright's Shifting Balance Theory

A Spatially Explicit Stochastic Model Demonstrates the Feasibility of Wright's Shifting Balance Theory

A SPATIALLY EXPLICIT STOCHASTIC MODEL DEMONSTRATES THE FEASIBILITY OF WRIGHT'S SHIFTING BALANCE THEORY.

Recently there has been a resurgence of theoretical papers exploring Wright's Shifting Balance Theory (SBT) of evolution. The SBT explains how traits which must pass through an adaptive valley may evolve in substructured populations. It has been suggested that Phase III of the SBT (the spread of new advantageous traits through the populations) proceeds only under a very restricted set of conditions. We show that Phase III can proceed under a much broader set of conditions in models that properly incorporate a key feature of Wright's theory: local, random migration of discrete individuals.

ON PHASE THREE OF THE SHIFTING-BALANCE THEORY.

A common conclusion in several recent publications devoted to the deterministic analysis of the third phase of Wright's shifting-balance theory is that under reasonable conditions phase three should proceed easily. I argue that the mathematical equations analyzed in these papers do not correspond to the biological situation they were meant to describe. I present a more appropriate study of the third phase of the shifting balance. My results show that the third phase can proceed only under much more restricted conditions than the previous studies suggested. Migration should be neither too strong not too weak relative to selection. The higher peak should be sufficiently dominant over the lower peak. Recombination can greatly reduce the plausibility of this phase or completely preclude peak shifts. A very important determinant of the ultimate outcome of the competition between different peaks is the topological structure of the network of demes. Peak shifts in two-dimensional networks of demes are more difficult than in one-dimensional networks. Phase three can be accomplished easiest if it is initiated in one of the peripheral demes.

MAINTENANCE OF POLYGENIC VARIATION VIA A MIGRATION-SELECTION BALANCE UNDER UNIFORM SELECTION.

Population subdivision is often invoked to explain the large amount of heterozygosity found at single loci in natural populations (Felsenstein 1976; Hedrick et al., 1976; Karlin 1982; Hedrick 1986). Surprisingly, relatively few studies describe the effects of population structure on the maintenance of variance for polygenic (quantitative) traits. Felsenstein (1977) and Slatkin (1978) presented models in which additive variance can be maintained via migration along a cline (see also Barton and Turelli 1989). Goldstein and Holsinger (1992) used simulations to show that variance for quantitative traits could be maintained under uniform selection in a population subject to isolation by distance (see also Lande [1991]), and Slatkin and Lande (1994) demonstrated that the segregation variance generated by betweenpopulation crosses depends on how variance is generated within each population. Here I analyze the amount of variance that can be maintained deterministically via a migration-selection balance under uniform selection and conclude that a potentially large amount of variance can be generated in this way. This is true only when migration is very weak, so as not to overcome the influence of selection. When variance is maintained, it is maximal at the critical balance between migration and selection. The deterministic interaction between migration and selection has been the subject of a great deal of analysis in the context of Wright's shifting-balance theory (Crow et al. 1990; Barton 1992; Kondrashov 1992; Phillips 1993). These studies have shown that migration can be very effective at overcoming the effects of selection and driving populations to uniformity. For the shifting-balance process, this means that once a population has undergone a peak shift, it might be expected to drive peak shifts in neighboring populations, depending on the details of the system and population structure (Barton 1992; Phillips 1993). The purpose here is to explore regions of the parametric space in which this does not happen, but instead both populations remain polymorphic. Results from this deterministic approach will be contrasted with models that include stochastic effects and make somewhat different predictions (Lande 1991; Goldstein and Holsinger 1992; Barton and Rouhani 1993). Uniform stabilizing selection on an additive character generates disruptive selection at the level because various combinations of alleles can yield the same optimal phenotype, but the marginal fitness of any allele depends on the background in which it is found (Wright 1935). This is called genetic redundancy by Goldstein and Holsinger [1992]). Two populations can thus display the same phenotype but be fixed for different genotypes. If these populations were to exchange migrants, the mixing of the different genotypes would generate variance within each population. This would be a somewhat cryptic source of variation because there would be no obvious differentiation between the populations. Depending on the strength of migration, most of the variance generated by migration would then be quickly eliminated by selection, creating a migration-selection balance. This is the multilocus equivalent of a migration-selection polymorphism generated by underdominance at a single locus (Karlin and McGregor 1972). Because many characters are assumed to be under stabilizing selection, and because population structure is undoubtedly an important feature of natural populations, the interaction of migration and selection could obviously be an important influence on the maintenance of variance.

Population structure, fitness surfaces, and linkage in the shifting balance process

Wright first introduced the idea that random genetic drift and classical mass-action selection might combine in such a way as to allow populations to find the highest peak in complicated adaptive surfaces. His theory assumes large but structured populations, in which mating is spatially local. If gene flow is sufficiently low, and the subpopulations (demes) are small enough, they will be subject to genetic drift. Distant demes drift independently, allowing many independent searches of the adaptive surface to take place. A deme that has shifted to a higher peak can, by emigration, cause the rest of the demes to shift to the higher peak. The probability of this shift depends on the migration rate. Previous studies have concluded that very little migration is necessary to effect the shift in adaptive peaks that characterizes the last phase of Wright's Shifting Balance Process (SBP). Here we present the results of a computer study that investigates the roles of dispersal distance, the degree of epistasis in the fitness surface, and recombination on the shifting balance process. In particular, we measure their effect on the population's mean fitness. We show that over a range of dispersal distances the advantage of the SBP is a monotonically increasing function of the amount of epistasis. Our results show that the extent of dispersal that results in the greatest effect of the SBP in increasing mean fitness depends on the extent of epistasis. Finally, for low levels of epistasis, higher recombination performs better, while for intermediate levels, lower recombination results in a greater advantage of the SBP.

EPISTASIS AND THE INCREASE IN ADDITIVE GENETIC VARIANCE: IMPLICATIONS FOR PHASE 1 OF WRIGHT'S SHIFTING-BALANCE PROCESS.

Central to Wright's shifting-balance theory is the idea that genetic drift and selection in systems with gene interaction can lead to the formation of "adaptive gene complexes." The theory of genetic drift has been well developed over the last 60 years; however, nearly all of this theory is based on the assumption that only additive gene effects are acting. Wright's theory was developed recognizing that there was a "universality of interaction effects," which implies that additive theory may not be adequate to describe the process of differentiation that Wright was considering. The concept of an adaptive gene complex implies that an allele that is favored by individual selection in one deme may be removed by selection in another deme. In quantitative genetic terms, the average effects of an allele relative to other alleles changes from deme to deme. The model presented here examines the variance in local breeding values (LBVs) of a single individual and the covariance in the LBVs of a pair of individuals mated in the same deme relative to when they are mated in different demes. Local breeding value is a measure of the average effects of the alleles that make up that individual in a particular deme. I show that when there are only additive effects the covariance between the LBVs of individuals equals the variance in the LBV of an individual. As the amount of epistasis in the ancestral population increases, the variance in the LBV of an individual increases and the covariance between the LBVs of a pair of individuals decreases. The divergence in these two values is a measure of the extent to which the LBV of an individual varies independently of the LBVs of other individuals. When this value is large, it means that the relative ordering of the average effects of alleles will change from deme to deme. These results confirm an important component of Wright's shifting-balance theory: When there is gene interaction, genetic drift can lead to the reordering of the average effects of alleles and when coupled with selection this will lead to the formation of the adaptive gene complexes.

Epistasis and the Increase in Additive Genetic Variance: Implications for Phase 1 of Wright's Shifting-Balance Process

Epistasis and the Increase in Additive Genetic Variance: Implications for Phase 1 of Wright's Shifting-Balance Process

VARIANCE-INDUCED PEAK SHIFTS

The increase in phenotypic variance that occurs in some populations as a result of bottlenecks and founder events can cause a dramatic increase in the probability of a peak shift from one adaptive state to another. Periods of small population size allow drift in the amount of phenotypic variance. Increases in phenotypic variance, coupled with a constant individual fitness function with multiple peaks, can cause the mean fitness landscape to change from bimodal to unimodal, thereby allowing the population's mean phenotype to change deterministically by selection. As the amount of phenotypic variance is returned to an equilibrium state, the multiple peaks reemerge, but the population has moved from one stable state to another. These variance-induced peak shifts allow punctuational evolution from one peak to another at a rate that can be much higher than that predicted by Wright's shifting-balance process alone.

A Simulation of Wright's Shifting-Balance Process: Migration and the Three Phases

A Simulation of Wright's Shifting-Balance Process: Migration and the Three Phases

PEAK SHIFTS AND POLYMORPHISM DURING PHASE THREE OF WRIGHT'S SHIFTING-BALANCE PROCESS.

The third phase of Wright's shifting-balance theory involves the export of adaptive gene combinations from one subpopulation to another. Previous results have demonstrated that this can occur at very low migration rates, but it has been argued that this simply reflects the ability of migration to overcome selection and fix any (even deleterious) alleles. Here, previous analyses are extended by concentrating on the critical balance between forward and reverse migration rates that still allows phase III to proceed. It is shown that selective advantage, dominance, recombination rate, and the number of loci all affect the ability of a genotype to invade and become fixed in a new subpopulation, but it is unlikely that phase III will occur in the absence of differential migration unless the invading genotype consists of a few dominant loci with a large selection advantage, spreading into a few populations of lower fitness. Therefore, as was envisioned by Wright, differential migration from more to less fit populations will be necessary for phase III to occur under most circumstances.

THE GENETICS OF CENTRAL AND MARGINAL POPULATIONS OF DROSOPHILA SERRATA. II. HYBRID BREAKDOWN IN FITNESS COMPONENTS AS A CORRELATED RESPONSE TO SELECTION FOR DESICCATION RESISTANCE.

Multiple-peak epistasis is one of the four premises that underlie Wright's shifting-balance theory of evolution. A selection experiment was conducted in an attempt to push different geographic populations to different fitness peaks as a correlated response to selection for an additively controlled character (desiccation resistance). Four populations of Drosophila serrata, sampled from central and marginal areas of its distribution along a 3000-km stretch of Australia's east coast, underwent selection for desiccation resistance for 14 generations. After selection had ceased, control lines from each of the populations were crossed to determine the amount of hybrid breakdown that existed before selection and selected lines were crossed to determine the amount of hybrid breakdown after selection. Hybrid breakdown was measured in three fitness traits: developmental time, viability, and fecundity. When the individual crosses were examined, virtually no evidence was found for hybrid breakdown between these populations. However, the level of hybrid breakdown in development time in the control lines increased as the distance between the populations in the field increased. This relationship was lost in the selected lines. Therefore, selection for desiccation resistance influenced the level of hybrid breakdown in a fitness trait, although selection may need to be maintained for longer than 14 generations if a new relationship between hybrid breakdown and distance is to be formed.

Bottlenecks, soft selection, and Phase III of Wright's ?Shifting Balance? theory

An argument is presented, using the spread of the African honeybee through the American tropics, Mexico, and into the southern United States, that the geographic spread of a novel, highly successful gene combination does not necessarily occur as commonly viewed under Phase 3 of Wright's shifting-balance theory. Rather, migrants from the deme possessing the new genetic system may populate sites previously left vacant and subsequently, when their numbers have swelled, overwhelm the populations in previously occupied sites. The outcome, the argument continues, gives the (false) appearance of the species having gone through a bottleneck.

The Third Phase of Wright's Shifting-Balance: A Simple Analysis of the Extreme Case

The Third Phase of Wright's Shifting-Balance: A Simple Analysis of the Extreme Case

On the Spread of New Gene Combinations in the Third Phase of Wright's Shifting-Balance

On the Spread of New Gene Combinations in the Third Phase of Wright's Shifting-Balance