Wright's Shifting Balance Theory Research Articles

Theories that narrate the world: Ronald A. Fisher's mass selection and Sewall Wright's shifting balance

Theories are composed of multiple interacting components. I argue that some theories have narratives as essential components, and that narratives function as integrative devices of the mathematical components of theories. Narratives represent complex processes unfolding in time as a sequence of stages, and hold the mathematical elements together as pieces in the investigation of a given process. I present two case studies from population genetics: R. A. Fisher's “mas selection” theory, and Sewall Wright's shifting balance theory. I apply my analysis to an early episode of the “R. A. Fisher – Sewall Wright controversy.”

Sewall Wright, shifting balance theory, and the hardening of the modern synthesis

The period between the 1940s and 1960s saw the hardening of the modern synthesis in evolutionary biology. Gould and Provine argue that Wright's shifting balance theory of evolution hardened during this period. But their account does not do justice to Wright, who always regarded selection as acting together with drift. This paper presents a more adequate account of the development of Wright's shifting balance theory, paying particular attention to his application of the theory to the geographical distribution of flower color dimorphism in Linanthus parryae. The account shows that even in the heyday of the hardened synthesis, the balance or interaction of evolutionary factors, such as drift, selection, and migration, occupied pride of place in Wright's theory, and that between the 1940s and 1970s, Wright developed the theory of isolation by distance to quantitatively represent the structure of the Linanthus population, which he argued had the kind of structure posited by his shifting balance theory. In the end, Wright arrived at a sophisticated description of the structure of the Linanthus population, where the interaction between drift and selection varied spatially.

Parallel Experimentation: A Basic Scheme for Dynamic Efficiency

My topic is the process of parallel experimentation which I take to be a process of multiple experiments running concurrently with some form of common goal, with some semi-isolation between the experiments, with benchmarking comparisons made between the experiments, and with the migration of discoveries between experiments wherever possible to ratchet up the performance of the group. The thesis is that parallel experimentation is a fundamental dynamic efficiency scheme to enhance and accelerate variation, innovation, and learning in contexts of genuine uncertainty or known ignorance. Within evolutionary biology, this type of parallel experimentation scheme was developed in Sewall Wright's shifting balance theory of evolution. It addressed the rather neglected topic of how a population on a low fitness peak might eventually be able to go downhill against selective pressures, traverse a valley of low fitness, and then ascend a higher fitness peak. The theme of parallel experimentation is used to recast and pull together dynamic and pluralistic theories in economics, political theory, philosophy of science, and social learning.

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.

Transposable elements and an epigenetic basis for punctuated equilibria

Evolution is frequently concentrated in bursts of rapid morphological change and speciation followed by long-term stasis. We propose that this pattern of punctuated equilibria results from an evolutionary tug-of-war between host genomes and transposable elements (TEs) mediated through the epigenome. According to this hypothesis, epigenetic regulatory mechanisms (RNA interference, DNA methylation and histone modifications) maintain stasis by suppressing TE mobilization. However, physiological stress, induced by climate change or invasion of new habitats, disrupts epigenetic regulation and unleashes TEs. With their capacity to drive non-adaptive host evolution, mobilized TEs can restructure the genome and displace populations from adaptive peaks, thus providing an escape from stasis and generating genetic innovations required for rapid diversification. This "epi-transposon hypothesis" can not only explain macroevolutionary tempo and mode, but may also resolve other long-standing controversies, such as Wright's shifting balance theory, Mayr's peripheral isolates model, and McClintock's view of genome restructuring as an adaptive response to challenge.

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.

Batesian Mimicry: Can a Leopard Change Its Spots — and Get Them Back?

Can undefended mimics survive outside the range of their noxious models? Two recent studies on Batesian mimicry suggest they can, but alternative survival strategies and morphologies are then favoured.

STOCHASTICITY, COMPLEX SPATIAL STRUCTURE, AND THE FEASIBILITY OF THE SHIFTING BALANCE THEORY

Abstract Sewall Wright's shifting balance theory of evolution posits a mechanism by which a structured population may escape local fitness optima and find a global optimum. We examine a one-locus, two-allele model of underdominance in populations with differing spatial arrangements of demes, both analytically and with Monte Carlo simulations. We find that inclusion of variance in interpatch connectivities can significantly reduce the number of generations required for fixation of the more favorable allele relative to island and stepping-stone models. Although time to fixation increases with migration rate in all cases, the presence of one or two relatively isolated demes may reduce the number of generations by 80% or more. These results suggest that the shifting balance process may operate under less restrictive conditions than those found with a simple spatial arrangement of demes.

STOCHASTICITY, COMPLEX SPATIAL STRUCTURE, AND THE FEASIBILITY OF THE SHIFTING BALANCE THEORY

Sewall Wright's shifting balance theory of evolution posits a mechanism by which a structured population may escape local fitness optima and find a global optimum. We examine a one-locus, two-allele model of underdominance in populations with differing spatial arrangements of demes, both analytically and with Monte Carlo simulations. We find that inclusion of variance in interpatch connectivities can significantly reduce the number of generations required for fixation of the more favorable allele relative to island and stepping-stone models. Although time to fixation increases with migration rate in all cases, the presence of one or two relatively isolated demes may reduce the number of generations by 80% or more. These results suggest that the shifting balance process may operate under less restrictive conditions than those found with a simple spatial arrangement of demes.

Stability and instability of polymorphic populations and the role of multiple breeding seasons in phase III of Wright's shifting balance theory.

It is generally difficult for a large population at a fitness peak to acquire the genotypes of a higher peak, because the intermediates produced by allelic recombination between types at different peaks are of lower fitness. In his shifting-balance theory, Wright proposed that fitter genotypes could, however, become fixed in small isolated demes by means of random genetic fluctuations. These demes would then try to spread their genome to nearby demes by migration of their individuals. The resulting polymorphism, the coexistence of individuals with different genotypes, would give the invaded demes a chance to move up to a higher fitness peak. This last step of the process, namely, the invasion of lower fitness demes by higher fitness genotypes, is known as phase III of Wright's theory. Here we study the invasion process from the point of view of the stability of polymorphic populations. Invasion occurs when the polymorphic equilibrium, established at low migration rates, becomes unstable. We show that the instability threshold depends sensitively on the average number of breeding seasons of individuals. Iteroparous species (with many breeding seasons) have lower thresholds than semelparous species (with a single breeding season). By studying a particular simple model, we are able to provide analytical estimates of the migration threshold as a function of the number of breeding seasons. Once the threshold is crossed and polymorphism becomes unstable, any imbalance between the different demes is sufficient for invasion to occur. The outcome of the invasion, however, depends on many parameters, not only on fitness. Differences in fitness, site capacities, relative migration rates, and initial conditions, all contribute to determine which genotype invades successfully. Contrary to the original perspective of Wright's theory for continuous fitness improvement, our results show that both upgrading to higher fitness peaks and downgrading to lower peaks are possible.

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.

Maize Agriculture Evolution in the Eastern Woodlands of North America: A Darwinian Perspective

David Rindos' coevolution theory remains the most comprehensive application of Darwinian theory to issues of prehistoric agriculture evolution. While his theory has drawn attention, there has been a lack of subsequent development of the application of Darwinian theory to prehistoric agricultural evolution. Combining Sewall Wright's shifting balance theory of evolution with aspects of Rindos' coevolution theory provides important new insights into the processes of crop transmission between regions. Using these theories, a model is developed for the adoption and subsequent evolution of maize agriculture in the Eastern Woodlands of North America.

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

PERSPECTIVE: THE THEORIES OF FISHER AND WRIGHT IN THE CONTEXT OF METAPOPULATIONS: WHEN NATURE DOES MANY SMALL EXPERIMENTS.

We critically review the two major theories of adaptive evolution developed early in this century, Wright's shifting balance theory and Fisher's large population size theory, in light of novel findings from field observations, laboratory experiments, and theoretical research conducted over the past 15 years. Ecological studies of metapopulations have established that the processes of local extinction and colonization of demes are relatively common in natural populations of many species and theoretical population genetic models have shown that these ecological processes have genetic consequences within and among local demes. Within demes, random genetic drift converts nonadditive genetic variance into additive genetic variance, increasing, rather than limiting, the potential for adaptation to local environments. For this reason, the genetic differences that arise by drift among demes, can be augmented by local selection. The resulting adaptive differences in gene combinations potentially contribute to the genetic origin of new species. These and other recent findings were not discussed by either Wright or Fisher. For example, although Wright emphasized epistatic genetic variance, he did not discuss the conversion process. Similarly, Fisher did not discuss how the average additive effect of a gene varies among demes across a metapopulation whenever there is epistasis. We discuss the implications of such recent findings for the Wright-Fisher controversy and identify some critical open questions that require additional empirical and theoretical study.

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.

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.