Rugged Fitness Landscapes Research Articles

The impact of population size on the evolution of asexual microbes on smooth versus rugged fitness landscapes

BackgroundIt is commonly thought that large asexual populations evolve more rapidly than smaller ones, due to their increased rate of beneficial mutations. Less clear is how population size influences the level of fitness an asexual population can attain. Here, we simulate the evolution of bacteria in repeated serial passage experiments to explore how features such as fitness landscape ruggedness, the size of the mutational target under selection, and the mutation supply rate, interact to affect the evolution of microbial populations of different sizes.ResultsWe find that if the fitness landscape has many local peaks, there can be a trade-off between the rate of adaptation and the potential to reach high fitness peaks. This result derives from the fact that whereas large populations evolve mostly deterministically and often become trapped on local fitness peaks, smaller populations can follow more stochastic evolutionary paths and thus locate higher fitness peaks. We also find that the target size of adaptation and the mutation rate interact with population size to influence the trade-off between rate of adaptation and final fitness.ConclusionOur study suggests that the optimal population size for adaptation depends on the details of the environment and on the importance of either the ability to evolve rapidly or to reach high fitness levels.

Natural Selection Fails to Optimize Mutation Rates for Long-Term Adaptation on Rugged Fitness Landscapes

The rate of mutation is central to evolution. Mutations are required for adaptation, yet most mutations with phenotypic effects are deleterious. As a consequence, the mutation rate that maximizes adaptation will be some intermediate value. Here, we used digital organisms to investigate the ability of natural selection to adjust and optimize mutation rates. We assessed the optimal mutation rate by empirically determining what mutation rate produced the highest rate of adaptation. Then, we allowed mutation rates to evolve, and we evaluated the proximity to the optimum. Although we chose conditions favorable for mutation rate optimization, the evolved rates were invariably far below the optimum across a wide range of experimental parameter settings. We hypothesized that the reason that mutation rates evolved to be suboptimal was the ruggedness of fitness landscapes. To test this hypothesis, we created a simplified landscape without any fitness valleys and found that, in such conditions, populations evolved near-optimal mutation rates. In contrast, when fitness valleys were added to this simple landscape, the ability of evolving populations to find the optimal mutation rate was lost. We conclude that rugged fitness landscapes can prevent the evolution of mutation rates that are optimal for long-term adaptation. This finding has important implications for applied evolutionary research in both biological and computational realms.

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen's model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a {\it quasispecies} which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or step-like) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.

The Frequency of Fitness Peak Shifts Is Increased at Expanding Range Margins Due to Mutation Surfing

Dynamic species' ranges, those that are either invasive or shifting in response to environmental change, are the focus of much recent interest in ecology, evolution, and genetics. Understanding how range expansions can shape evolutionary trajectories requires the consideration of nonneutral variability and genetic architecture, yet the majority of empirical and theoretical work to date has explored patterns of neutral variability. Here we use forward computer simulations of population growth, dispersal, and mutation to explore how range-shifting dynamics can influence evolution on rugged fitness landscapes. We employ a two-locus model, incorporating sign epistasis, and find that there is an increased likelihood of fitness peak shifts during a period of range expansion. Maladapted valley genotypes can accumulate at an expanding range front through a phenomenon called mutation surfing, which increases the likelihood that a mutation leading to a higher peak will occur. Our results indicate that most peak shifts occur close to the expanding front. We also demonstrate that periods of range shifting are especially important for peak shifting in species with narrow geographic distributions. Our results imply that trajectories on rugged fitness landscapes can be modified substantially when ranges are dynamic.

Reflections on Researching the Rugged Fitness Landscape

Introduction At the core of the informing sciences is the need to better understand the interplay between the components of an informing system: the sender, the client, the delivery system, and the task to be performed. Implicit in this understanding is a notion of fit. For example, if the client is in a rural area of a developing country served only by telephone lines that are subject to intermittent failure and the sender wishes to convey large amounts of information in video format, then the use of an Internet-based delivery system is unlikely to be a good fit with the informing need. Similarly, if the task to be performed is highly interactive and requires ongoing exchange of information with the client, then a system providing two-way communication is likely to be a better fit than a system that only allows one-way broadcast of information. If we attach a numerical or ordinal value to the level of fit, we can refer to that value as a fitness value. If we were to consider a whole variety of different possible informing systems for achieving the same purpose and were to attach a fitness value to each one, we have the beginnings of a fitness landscape. To develop a complete fitness landscape, we would need to develop a function that can take any combination of informing system characteristics and map them to an associated fitness value. The optimal possible system would then be that collection of characteristics that maps to the highest fitness value. It is probably not an exaggeration to assert that most research in the informing sciences is motivated by the desire to contribute, directly or indirectly, to our understanding of the fitness landscape associated with informing. In our goal to better understand the fitness landscape for informing systems, it is useful to learn from other disciplines--many of which have their own versions of the fitness function. In economics, for example, consumers strive to maximize utility--a function that maps the bundle of goods and services they consume to a satisfaction-related value. Producers are frequently modeled as attempting to maximize shareholder value, another measure of fitness. In computer science, the concept of fitness is routinely employed in evaluator functions. A chess program, for example, will normally choose its move based upon assessing the fitness of the alternative board positions that may result. Genetic algorithms use reproductive and mutation rules originally observed in natural systems in an effort to seek solutions of maximal fitness. The concept of fitness is particularly prevalent in biological sciences. Evolutionary biologists, for example, view fitness as a survivability function representing the likelihood of reproductive success that may be applied at many different levels--from the gene to an entire species. If fitness is insufficient, the gene or species ultimately disappears if it fails to evolve or adapt. The present paper is intended to as a non-mathematical introduction to the nature of fitness landscapes, with particular attention being paid to the potential implications for research in the informing sciences. It begins by presenting a continuum used to characterize fitness landscapes that was first introduced in evolutionary biology (e.g., Kauffman, 1993). In this model, landscapes range from decomposable to rugged to chaotic. The paper then demonstrates how the continuum strongly resembles another continuum: that of science and art. The remainder of the paper focuses specifically on rugged landscapes, emphasizing two main themes. First, it argues that the conditions that are likely to lead to a rugged fitness landscape are nearly always going to be present in informing systems. Second, it considers the many ways in which rigorous research conducted on a rugged fitness landscape can--or, more precisely, should--differ from research that assumes underlying decomposability. …

Research Themes in Complex Informing

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Evolution of the genetic code: partial optimization of a random code for robustness to translation error in a rugged fitness landscape

BackgroundThe standard genetic code table has a distinctly non-random structure, with similar amino acids often encoded by codons series that differ by a single nucleotide substitution, typically, in the third or the first position of the codon. It has been repeatedly argued that this structure of the code results from selective optimization for robustness to translation errors such that translational misreading has the minimal adverse effect. Indeed, it has been shown in several studies that the standard code is more robust than a substantial majority of random codes. However, it remains unclear how much evolution the standard code underwent, what is the level of optimization, and what is the likely starting point.ResultsWe explored possible evolutionary trajectories of the genetic code within a limited domain of the vast space of possible codes. Only those codes were analyzed for robustness to translation error that possess the same block structure and the same degree of degeneracy as the standard code. This choice of a small part of the vast space of possible codes is based on the notion that the block structure of the standard code is a consequence of the structure of the complex between the cognate tRNA and the codon in mRNA where the third base of the codon plays a minimum role as a specificity determinant. Within this part of the fitness landscape, a simple evolutionary algorithm, with elementary evolutionary steps comprising swaps of four-codon or two-codon series, was employed to investigate the optimization of codes for the maximum attainable robustness. The properties of the standard code were compared to the properties of four sets of codes, namely, purely random codes, random codes that are more robust than the standard code, and two sets of codes that resulted from optimization of the first two sets. The comparison of these sets of codes with the standard code and its locally optimized version showed that, on average, optimization of random codes yielded evolutionary trajectories that converged at the same level of robustness to translation errors as the optimization path of the standard code; however, the standard code required considerably fewer steps to reach that level than an average random code. When evolution starts from random codes whose fitness is comparable to that of the standard code, they typically reach much higher level of optimization than the standard code, i.e., the standard code is much closer to its local minimum (fitness peak) than most of the random codes with similar levels of robustness. Thus, the standard genetic code appears to be a point on an evolutionary trajectory from a random point (code) about half the way to the summit of the local peak. The fitness landscape of code evolution appears to be extremely rugged, containing numerous peaks with a broad distribution of heights, and the standard code is relatively unremarkable, being located on the slope of a moderate-height peak.ConclusionThe standard code appears to be the result of partial optimization of a random code for robustness to errors of translation. The reason the code is not fully optimized could be the trade-off between the beneficial effect of increasing robustness to translation errors and the deleterious effect of codon series reassignment that becomes increasingly severe with growing complexity of the evolving system. Thus, evolution of the code can be represented as a combination of adaptation and frozen accident.ReviewersThis article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.Open Peer ReviewThis article was reviewed by David Ardell, Allan Drummond (nominated by Laura Landweber), and Rob Knight.

Evolutionary dynamics of the most populated genotype on rugged fitness landscapes

We consider an asexual population evolving on rugged fitness landscapes which are defined on the multidimensional genotypic space and have many local optima. We track the most populated genotype as it changes when the population jumps from a fitness peak to a better one during the process of adaptation. This is done using the dynamics of the shell model which is a simplified version of the quasispecies model for infinite populations and standard Wright-Fisher dynamics for large finite populations. We show that the population fraction of a genotype obtained within the quasispecies model and the shell model match for fit genotypes and at short times, but the dynamics of the two models are identical for questions related to the most populated genotype. We calculate exactly several properties of the jumps in infinite populations, some of which were obtained numerically in previous works. We also present our preliminary simulation results for finite populations. In particular, we measure the jump distribution in time and find that it decays as t(-2) as in the quasispecies problem.

Deterministic and stochastic regimes of asexual evolution on rugged fitness landscapes.

We study the adaptation dynamics of an initially maladapted asexual population with genotypes represented by binary sequences of length L. The population evolves in a maximally rugged fitness landscape with a large number of local optima. We find that whether the evolutionary trajectory is deterministic or stochastic depends on the effective mutational distance d(eff) up to which the population can spread in genotype space. For d(eff) = L, the deterministic quasi-species theory operates while for d(eff) < 1, the evolution is completely stochastic. Between these two limiting cases, the dynamics are described by a local quasi-species theory below a crossover time T(x) while above T(x) the population gets trapped at a local fitness peak and manages to find a better peak via either stochastic tunneling or double mutations. In the stochastic regime d(eff) < 1, we identify two subregimes associated with clonal interference and uphill adaptive walks, respectively. We argue that our findings are relevant to the interpretation of evolution experiments with microbial populations.

Fitness landscape of human immunodeficiency virus type 1 protease quasispecies.

Here we show, at a high resolution (1%), the human immunodeficiency virus type 1 (HIV-1) protease gene quasispecies landscape from three infected naïve individuals. A huge range of genetic configurations was found (67%, 71%, and 80% of the nucleotide clones from the three individuals, respectively, were different), and these configurations created a dense net that linked different parts of the viral population. Similarly, a vast diversity of different protease activities was also found. Importantly, 65% of the analyzed enzymes had detectable protease activity, and 11% of the minority individual variants showed similar or better fitness than the master (most abundant) enzyme, suggesting that the viral complexity in this genomic region does not exclusively depend on the enzyme's catalytic efficiency. Several high-fitness minority variants had only one substitution compared to the master sequence, supporting the possibility that the rugged HIV-1 protease quasispecies fitness landscape may be formed by a continuous network that can be traversed by single mutational steps without passing through defective or less-adapted proteins.

Red Queen strange attractors in host–parasite replicator gene-for-gene coevolution

We study a continuous time model describing gene-for-gene, host–parasite interactions among self-replicating macromolecules evolving in both neutral and rugged fitness landscapes. Our model considers polymorphic genotypic populations of sequences with 3 bits undergoing mutation and incorporating a ‘‘type II’’ non-linear functional response in the host–parasite interaction. We show, for both fitness landscapes, a wide range of chaotic coevolutionary dynamics governed by Red Queen strange attractors. The analysis of a rugged fitness landscape for parasite sequences reveals that fittest genotypes achieve lower stationary concentration values, as opposed to the flattest ones, which undergo a higher stationary concentration. Our model also shows that the increase of parasites pressure (higher self-replication and mutation rates) generically involves a simplification of the host–parasite dynamical behavior, involving the transition from a chaotic to an ordered coevolutionary phase. Moreover, the same transition can also be found when hosts ‘‘run’’ faster through the hypercube. Our results, in agreement with previous studies in host–parasite coevolution, suggest that chaos might be common in coevolutionary dynamics of changing self-replicating entities undergoing a host–parasite ecology.

THE POPULATION GENETICS OF ADAPTATION ON CORRELATED FITNESS LANDSCAPES: THE BLOCK MODEL

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.

THE POPULATION GENETICS OF ADAPTATION ON CORRELATED FITNESS LANDSCAPES: THE BLOCK MODEL

Several recent theoretical studies of the genetics of adaptation have focused on the mutational landscape model, which considers evolution on rugged fitness landscapes (i.e., ones having many local optima). Adaptation in this model is characterized by several simple results. Here I ask whether these results also hold on correlated fitness landscapes, which are smoother than those considered in the mutational landscape model. In particular, I study the genetics of adaptation in the block model, a tunably rugged model of fitness landscapes. Considering the scenario in which adaptation begins from a high fitness wild-type DNA sequence, I use extreme value theory and computer simulations to study both single adaptive steps and entire adaptive walks. I show that all previous results characterizing single steps in adaptation in the mutational landscape model hold at least approximately on correlated landscapes in the block model; many entire-walk results, however, do not.

Rugged fitness landscapes of Kauffman models with a scale-free network

We study the nature of the fitness landscapes of a "quenched" Kauffman's Boolean model with a scale-free network. We have numerically calculated the rugged fitness landscapes, the distributions, their tails, and the correlation between the fitness of local optima and their Hamming distance from the highest optimum found, respectively. We have found that (a) there is an interesting difference between random and scale-free networks such that the statistics of the rugged fitness landscapes is Gaussian for the random network while it is non-Gaussian with a tail for the scale-free network; (b) as the average degree [k] increases, there is a phase transition at the critical value of [k]=[k]c=2, below which there is a global order and above which the order goes away.

Evolutionary trajectories in rugged fitness landscapes

We consider the evolutionary trajectories traced out by an infinite population undergoingmutation–selection dynamics in static, uncorrelated random fitness landscapes. Startingfrom the population that consists of a single genotype, the most populated genotype jumpsfrom one local fitness maximum to another and eventually reaches the global maximum.We use a strong selection limit, which reduces the dynamics beyond the first time stepto the competition between independent mutant subpopulations, to study thedynamics of this model and of a simpler one-dimensional model which ignores thegeometry of the sequence space. We find that the fit genotypes that appear along atrajectory are a subset of suitably defined fitness records, and exploit severalresults from the record theory for non-identically distributed random variables.The genotypes that contribute to the trajectory are those records that are notbypassed by superior records arising further away from the initial population. Severalconjectures concerning the statistics of bypassing are extracted from numericalsimulations. In particular, for the one-dimensional model, we propose a simple relationbetween the bypassing probability and the dynamic exponent which describesthe scaling of the typical evolution time with genome size. The latter can bedetermined exactly in terms of the extremal properties of the fitness distribution.

RNA viruses as complex adaptive systems

RNA viruses have high mutation rates and so their populations exist as dynamic and complex mutant distributions. It has been consistently observed that when challenged with a new environment, viral populations adapt following hyperbolic-like kinetics: adaptation is initially very rapid, but then slows down as fitness reaches an asymptotic value. These adaptive dynamics have been explained in terms of populations moving towards the top of peaks on rugged fitness landscapes. Fitness fluctuations of varying magnitude are observed during adaptation. Often the presence of fluctuations in the evolution of physical systems indicates some form of self-organization, or where many components of the system are simultaneously involved. Here we analyze data from several in vitro evolution experiments carried out with vesicular stomatitis virus (VSV) looking for the signature of criticality and scaling. Long-range fitness correlations have been detected during the adaptive process. We also found that the magnitude of fitness fluctuations, far from being trivial, conform to a Weibull probability distribution function, suggesting that viral adaptation belongs to a broad category of phenomena previously documented in other fields and related with emergence.

From Self-Organization to Evolution of RNA Molecules: The Origin of Biological Information

Autocatalytic chemical reactions may lead to spatio-temporal patterns if processed under non-equilibrium conditions. The patterns disappear when the conditions change and information stored in these non-equilibrium structures is lost since precise reconstructions are impossible. Replication of molecules, in particular of polynucleotides RNA or DNA, is an autocatalytic process too. The storage of information in polynucleotide sequences, however, allows for reconstruction of the molecules under suitable conditions. Conservation of information in polymer sequences constitutes the basic difference between chemical and biological self-organization. Evolution of RNA molecules is considered as pattern formation in sequence space, which manifests itself as another pattern in the space of minimum-free-energy structures. In addition, optimization of RNA structures and properties is visualized as an evolutionary trial-and-error process. This process can be interpreted as a simple form of learning at the level of ensembles or populations of molecules. Evolutionary optimization of RNA molecules occurs in steps: Short adaptive periods are interrupted by long epochs of quasi-stationarity during which the mean replication rate of the populations is essentially constant. Understanding of evolution is largely facilitated through consideration of sequence-structure relation as a many-to-one or non-invertible mapping from sequence space into structure space. Neutrality of sequences with respect to structure formation is highly relevant for evolutionary optimization on rugged fitness landscapes.

Sequence analysis of an artificial family of RNA-binding peptides.

Diverse peptide sequences recognizing the lambda boxB RNA hairpin were previously isolated from a library encoding the 22-residue lambda N peptide with random amino acids at positions 13-22 using mRNA display. We have statistically analyzed amino acid distributions in 65 unique sequences from rounds 11 and 12 of this selection and evaluated the resulting structural and functional predictions by alanine-scanning mutagenesis and circular dichroism spectrometry. This artificial sequence family has a consensus structure that continues the bent alpha helix of lambda N up to position 17 when bound to lambda boxB. A charge pair (E(14)R(15)) and hydrophobic patch (A(21)L(22) or V(21)L(22)) have important functional roles in this context. Notably, amino acid covariance reveals six specific pairs of random region positions with >95% significant linkage and strong overall helical (i+1, i+3, and i+4) couplings. The covariance analysis suggests that (1) the sequence context of every residue in each insert has been optimized, (2) selected sequences are local optima on a rugged fitness landscape, and (3) it is possible to detect more subtle structural features with artificial protein sequence families than natural homologs. Our results provide a framework for investigating the structures of in vitro selected proteins by functional minimization, reselection, and covariance analysis.

The complex dynamics of technological innovation: a comparison of models using cellular automata

AbstractArthur's (1988, 1989) model of the ‘lock‐in’ predicates the dominance of a single technology, while Kauffman's (1993, 1995) NK‐model investigates the existence of different suboptima in a ‘rugged fitness landscape’. Can the two mechanisms also be offset against each other? Under what conditions can one expect a technological monopoly or an oligopoly to prevail? What can serve as a discursive ground for making comparisons among the results of these sophisticated models? In this study, the two models are first reconstructed using a common language for the coding. The results of the simulations are made visual on the screen by means of a cellular automaton that represents the diffusion of different technologies in terms of different colours. By using a single platform for the interpretation, one can specify the conditions under which the models compete for the explanation. Second, I address the question of how one model interacts with the other. The reduction of the complexity in the coding enables us to focus on the theoretical assumptions. The introduction of a Schumpeterian dynamics of ‘creative destruction’, for example, can be shown to introduce variation in ‘rugged fitness landscapes’. Copyright © 2002 John Wiley &amp; Sons, Ltd.

Presidential Politics: Constrained by Complexity?

During the U.S. presidential campaign, there has been considerable discussion about the degree of similarity between the platforms of the Democratic and Republican candidates ([1][1]). Mallaby sees the “irrelevant election” as a consequence of globalization, noting that “the next U.S. president will find his ideals on a wide range of foreign policy issues boxed in by new systemic constraints” ([2][2]). This boxing in of the executive office is reminiscent of the complexity catastrophe described by Kauffman in his NK model of rugged fitness landscapes ([3][3]) used to simulate evolutionary patterns in biological systems. In this model, networks are constructed randomly to simulate the large number of conflicting interactions found in complicated systems. Each of the N components is randomly assigned an initial state, is randomly connected to K other components, and exerts at random favorable or unfavorable interactions on each of its K neighbors. Despite these random assignments, systems having moderate amounts of interconnectivity (lower values of K ) can be readily configured to achieve primarily favorable interactions. However, in systems with higher amounts of interconnectivity (higher values of K ), a nagging load of unfavorable interactions becomes unavoidable. In the limit of maximum interconnectedness ( K = N - 1), configurations have, on average, as many favorable as unfavorable interactions, and a given configuration contains no information about neighboring configurations. Hence, overly connected, highly frustrated networks guarantee that (i) a search for better configurations can do no better than a random selection, and (ii) highly favorable configurations simply do not exist. The complexity of the interactions ensures a catastrophic loss of the potential to improve beyond mediocrity. Despite their best efforts to distinguish themselves, perhaps Mr. Bush and Mr. Gore appear similar because large-scale communication, transportation, and economic networks have resulted in a globally integrated political economy, with many conflicting interactions. Globalization is equivalent to increasing the “K parameter” of economic networks, resulting in an uncorrelated landscape of mediocre compromises among political, environmental, and cultural systems. Differences in principle and means become irrelevant as each candidate faces the fact that acceptable solutions to large-scale political problems are, at best, hard to find, and, at worst, nonexistent. Although the platforms of Bush and Gore differ in detail, any policy decision concerning large domestic or foreign programs, such as urban housing ([4][4]) or free trade agreements ([5][5]), will necessarily result in as much harm or risk as benefit ([6][6]). Their platforms seem similar because a highly integrated political economy ensures that any policy will have mediocre outcomes. A Kauffmanian complexity catastrophe also implies that a random casting of votes would, paradoxically, do as well as costly lobbying and political analysis in directing national affairs. 1. [↵][7]1. D. McGregor , “U.S. voters hard-pressed to tell the difference,” Financial Times, London 6 (13 September 2000). 2. [↵][8]1. S. Mallaby , The Irrelevant Election. Foreign Policy (Carnegie Endowment for International Peace, Washington, DC, Sept./Oct. 2000), p. 74, 80. 3. [↵][9]1. S. A. Kauffman , Origins of Order: Self-organization and Selection in Evolution (Oxford Univ. Press, London, 1993), pp. 33-67. 4. [↵][10]1. H. Cisneros , Nat. Press Club Speaker Ser., 7 January 1997 (Wave Communications, Alexandria, VA, 1997), p. 12, 13. 5. [↵][11]1. J. Mazur , Foreign Aff. 79, 79 (2000). [OpenUrl][12][CrossRef][13][Web of Science][14] 6. [↵][15]1. J. E. Harrison 1. H. C. Binswanger , J. E. Harrison, Money and Magic: A Critique of the Modern Economy in Light of Goethe's Faust (Univ. of Chicago Press, Chicago, 1994). [1]: #ref-1 [2]: #ref-2 [3]: #ref-3 [4]: #ref-4 [5]: #ref-5 [6]: #ref-6 [7]: #xref-ref-1-1 View reference 1 in text [8]: #xref-ref-2-1 View reference 2 in text [9]: #xref-ref-3-1 View reference 3 in text [10]: #xref-ref-4-1 View reference 4 in text [11]: #xref-ref-5-1 View reference 5 in text [12]: {openurl}?query=rft.jtitle%253DForeign%2BAff.%26rft.volume%253D79%26rft.spage%253D79%26rft.atitle%253DFOREIGN%2BAFF%26rft_id%253Dinfo%253Adoi%252F10.2307%252F20049615%26rft.genre%253Darticle%26rft_val_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Ajournal%26ctx_ver%253DZ39.88-2004%26url_ver%253DZ39.88-2004%26url_ctx_fmt%253Dinfo%253Aofi%252Ffmt%253Akev%253Amtx%253Actx [13]: /lookup/external-ref?access_num=10.2307/20049615&link_type=DOI [14]: /lookup/external-ref?access_num=000084465900007&link_type=ISI [15]: #xref-ref-6-1 View reference 6 in text