Rugged Fitness Landscapes Research Articles

EPISTATIC INTERACTIONS DETERMINE THE MUTATIONAL PATHWAYS AND COEXISTENCE OF LINEAGES IN CLONALESCHERICHIA COLIPOPULATIONS

Understanding how diversity emerges in a single niche is not fully understood. Rugged fitness landscapes and epistasis between beneficial mutations could explain coexistence among emerging lineages. To provide an experimental test of this notion, we investigated epistasis among four pleiotropic mutations in rpoS, mglD, malT, and hfq present in two coexisting lineages that repeatedly fixed in experimental populations of Escherichia coli. The mutations were transferred into the ancestral background individually or in combination of double or triple alleles. The combined competitive fitness of two or three beneficial mutations from the same lineage was consistently lower than the sum of the competitive fitness of single mutants--a clear indication of negative epistasis within lineages. We also found sign epistasis (i.e., the combined fitness of two beneficial mutations lower than the ancestor), not only from two different lineages (i.e., hfq and rpoS) but also from the same lineage (i.e., mglD and malT). The sign epistasis between loci of different lineages indeed indicated a rugged fitness landscape, providing an epistatic explanation for the coexistence of distinct rpoS and hfq lineages in evolving populations. The negative and sign epistasis between beneficial mutations within the same lineage can further explain the order of mutation acquisition.

HIV-1 Env C2-V4 diversification in a slow-progressor infant reveals a flat but rugged fitness landscape.

Human immunodeficiency virus type-1 (HIV-1) fitness has been associated with virus entry, a process mediated by the envelope glycoprotein (Env). We previously described Env genetic diversification in a Zambian, subtype C infected, slow-progressor child (1157i) in parallel with an evolving neutralizing antibody response. Because of the role the Variable-3 loop (V3) plays in transmission, cell tropism, neutralization sensitivity, and fitness, longitudinally isolated 1157i C2-V4 alleles were cloned into HIV-1NL4-3-eGFP and -DsRed2 infectious molecular clones. The fluorescent reporters allowed for dual-infection competitions between all patient-derived C2-V4 chimeras to quantify the effect of V3 diversification and selection on fitness. ‘Winners’ and ‘losers’ were readily discriminated among the C2-V4 alleles. Exceptional sensitivity for detection of subtle fitness differences was revealed through analysis of two alleles differing in a single synonymous amino acid. However, when the outcomes of N = 33 competitions were averaged for each chimera, the aggregate analysis showed that despite increasing diversification and divergence with time, natural selection of C2-V4 sequences in this individual did not appear to be producing a ‘survival of the fittest’ evolutionary pattern. Rather, we detected a relatively flat fitness landscape consistent with mutational robustness. Fitness outcomes were then correlated with individual components of the entry process. Env incorporation into particles correlated best with fitness, suggesting a role for Env avidity, as opposed to receptor/coreceptor affinity, in defining fitness. Nevertheless, biochemical analyses did not identify any step in HIV-1 entry as a dominant determinant of fitness. Our results lead us to conclude that multiple aspects of entry contribute to maintaining adequate HIV-1 fitness, and there is no surrogate analysis for determining fitness. The capacity for subtle polymorphisms in Env to nevertheless significantly impact viral fitness suggests fitness is best defined by head-to-head competition.

Statistical Mechanics of Modularity and Horizontal Gene Transfer

Biological structure organizes over evolutionary timescales. This review discusses the spontaneous emergence of hierarchical structure in biology as a result of environmental change. A body of theoretical and experimental work on evolutionary dynamics is reviewed, and a theory for these results based on a principle of least action is discussed. The structure that has emerged in biology is complementary to a type of evolutionary dynamics known as horizontal gene transfer. How horizontal gene transfer ameliorates the difficulty that finite populations would otherwise have to evolve on rugged fitness landscapes is also discussed.

Navigating Challenging Fitness Landscapes: Social Entrepreneurship and the Competing Dimensions of Sustainability

This paper uses the concepts of organizational fitness and fitness landscapes to examine management challenges that arise from social entrepreneurship efforts. Organizations pursuing social entrepreneurship must manage based on the need to ‘do no harm’ across all three tenets of sustainability: social equity, economic prosperity, and environmental integrity. These three tenets may be in conflict with each other, but organizations that pursue social entrepreneurship must manage with all three of them in mind across a wide range of stakeholders. Extending research on managing organizational fitness in rugged fitness landscapes, this paper argues that social entrepreneurship organizations will need to engage in substantial search processes, will face particularly difficult challenges in managing goals and initiatives, and will need to move into environmental search and adaptive modes early in their maturation process.

Evolution at increased error rate leads to the coexistence of multiple adaptive pathways in an RNA virus

BackgroundWhen beneficial mutations present in different genomes spread simultaneously in an asexual population, their fixation can be delayed due to competition among them. This interference among mutations is mainly determined by the rate of beneficial mutations, which in turn depends on the population size, the total error rate, and the degree of adaptation of the population. RNA viruses, with their large population sizes and high error rates, are good candidates to present a great extent of interference. To test this hypothesis, in the current study we have investigated whether competition among beneficial mutations was responsible for the prolonged presence of polymorphisms in the mutant spectrum of an RNA virus, the bacteriophage Qβ, evolved during a large number of generations in the presence of the mutagenic nucleoside analogue 5-azacytidine.ResultsThe analysis of the mutant spectra of bacteriophage Qβ populations evolved at artificially increased error rate shows a large number of polymorphic mutations, some of them with demonstrated selective value. Polymorphisms distributed into several evolutionary lines that can compete among them, making it difficult the emergence of a defined consensus sequence. The presence of accompanying deleterious mutations, the high degree of recurrence of the polymorphic mutations, and the occurrence of epistatic interactions generate a highly complex interference dynamics.ConclusionsInterference among beneficial mutations in bacteriophage Qβ evolved at increased error rate permits the coexistence of multiple adaptive pathways that can provide selective advantages by different molecular mechanisms. In this way, interference can be seen as a positive factor that allows the exploration of the different local maxima that exist in rugged fitness landscapes.

Quantifying the similarity of monotonic trajectories in rough and smooth fitness landscapes

When selection is strong and mutations are rare, evolution can be thought of as an uphill trajectory in a rugged fitness landscape. In this context the fitness landscape is a directed acyclic graph in which nodes are genotypes and edges lead from lower to higher fitness genotypes that differ by a single mutation. Because the space of genotypes is vastly multi-dimensional, classification of fitness landscapes is challenging. Many proposed summary characteristics of fitness landscapes attempt to quantify biologically relevant and intuitive notions such as roughness or peak accessibility in alternative ways. Here we explore, in different types of landscapes, the behavior of the recently introduced mean path divergence which quantifies the degree of similarity among evolutionary trajectories with the same endpoints. We find that monotonic trajectories in empirical and model fitness landscapes are significantly more constrained, with low median path divergence, than those in purely additive landscapes. By contrast, transcription factor sequence specificity (aptamer binding affinity) landscapes are markedly smoother and allow substantial variability in monotonic paths that can be greater than that in fully additive landscapes. We propose that the smoothness of the specificity landscapes is a consequence of the simple dependence of the transcription factor binding affinity on the aptamer sequence in contrast to the complex sequence-fitness mapping in folding landscapes.

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

The adaptive evolution of a population under the influence of mutation and selection is strongly influenced by the structure of the underlying fitness landscape, which encodes the interactions between mutations at different genetic loci. Theoretical studies of such landscapes have been carried out for several decades, but only recently experimental fitness measurements encompassing all possible combinations of small sets of mutations have become available. The empirical studies have spawned new questions about the accessibility of optimal genotypes under natural selection. Depending on population dynamic parameters such as mutation rate and population size, evolutionary accessibility can be quantified through the statistics of accessible mutational pathways (along which fitness increases monotoncially), or through the study of the basin of attraction of the optimal genotype under greedy (steepest ascent) dynamics. Here we investigate these two measures of accessibility in the framework of Kauffman's $LK$-model, a paradigmatic family of random fitness landscapes with tunable ruggedness. The key parameter governing the strength of genetic interactions is the number $K$ of interaction partners of each of the $L$ sites in the genotype sequence. In general, accessibility increases with increasing genotype dimensionality $L$ and decreases with increasing number of interactions $K$. Remarkably, however, we find that some measures of accessibility behave non-monotonically as a function of $K$, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2. The relation between models for fitness landscapes and spin glasses is also addressed.

Fast stochastic algorithm for simulating evolutionary population dynamics

Many important aspects of evolutionary dynamics can only be addressed through simulations. However, accurate simulations of realistically large populations over long periods of time needed for evolution to proceed are computationally expensive. Mutants can be present in very small numbers and yet (if they are more fit than others) be the key part of the evolutionary process. This leads to significant stochasticity that needs to be accounted for. Different evolutionary events occur at very different time scales: mutations are typically much rarer than reproduction and deaths. We introduce a new exact algorithm for fast fully stochastic simulations of evolutionary dynamics that include birth, death and mutation events. It produces a significant speedup compared to direct stochastic simulations in a typical case when the population size is large and the mutation rates are much smaller than birth and death rates. The algorithm performance is illustrated by several examples that include evolution on a smooth and rugged fitness landscape. We also show how this algorithm can be adapted for approximate simulations of more complex evolutionary problems and illustrate it by simulations of a stochastic competitive growth model.

Thinking through the Middle Stone Age of sub-Saharan Africa

Together with the disciplines of palaeoanthropology and genetics, archaeological finds and studies on material dating to the Middle Stone Age of sub-Saharan Africa have changed the way scholars think about ancient Africans and the later stages of human evolution. In general, it shows that anatomically modern humans have evolved by ∼200 ka in the region, and that relatively high levels of symbolic behaviour, and behavioural and cognitive complexity were achieved long before the previous 40–50 ka benchmark. The main focus of the paper is on aspects of post-100 ka archaeological material and how it can assist in the reconstruction of hypotheses and models regarding human cognitive and behavioural evolution. Some of the explored topics include fire as engineering tool, the manufacture and use of technologies such as compound adhesives, composite tools, bow-and-arrow sets and snares, and Middle Stone Age housekeeping. Although not central to the paper, an updated list of most Middle Stone Age stone tool assemblages is presented in Appendix A as context for sites, regions and topics mentioned throughout the text. On a theoretical level, the ratchet analogy as blanket explanation for behavioural and cognitive evolution is critiqued. Instead, the rugged fitness landscape model is brought to mind and combined with a mountaineering analogy to better explain human cognitive and behavioural flexibility as reflected in the Middle Stone Age record of sub-Saharan Africa.

Evolutionary Origins of Transcription Factor Binding Site Clusters

Empirical studies have revealed that regulatory DNA sequences such as enhancers or promoters often harbor multiple binding sites for the same transcription factor. Such "homotypic site clustering" has been hypothesized as arising out of functional requirements of the sequences. Here, we propose an alternative explanation of this phenomenon that multisite enhancers are common because they are favored by evolutionary sampling of the genotype-phenotype landscape. To test this hypothesis, we developed a new computational framework specialized for population genetic simulations of enhancer evolution. It uses a thermodynamics-based model of enhancer function, integrating information from strong as well as weak binding sites, to determine the strength of selection. Using this framework, we found that even when simpler genotypes exist for a desired strength of regulation, relatively complex genotypes (enhancers with more sites) are more readily reached by the simulated evolutionary process. We show that there are more ways to "build" a fit genotype with many weak sites than with a few strong sites, and this is why evolution finds complex genotypes more often. Our claims are consistent with an empirical analysis of binding site content in enhancers characterized in Drosophila melanogaster and their orthologs in other Drosophila species. We also characterized a subtle but significant difference between genotypes likely to be sampled by evolution and equally fit genotypes one would obtain by uniform sampling of the fitness landscape, that is, an "evolutionary signature" in enhancer sequences. Finally, we investigated potential effects of other factors, such as rugged fitness landscapes, short local duplications, and noise characteristics of enhancers, on the emergence of homotypic site clustering. Homotypic site clustering is an important contributor to the complexity and function of cis-regulatory sequences. This work provides a simple null hypothesis for its origin, against which alternative adaptationist explanations may be evaluated, and cautions against "evolutionary mirages" present in common features of genomic sequence. The quantitative framework we develop here can be used more generally to understand how mechanisms of enhancer action influence their composition and evolution.

Multiple Adaptive Substitutions During Evolution in Novel Environments

We consider an asexual population under strong selection-weak mutation conditions evolving on rugged fitness landscapes with many local fitness peaks. Unlike the previous studies in which the initial fitness of the population is assumed to be high, here we start the adaptation process with a low fitness corresponding to a population in a stressful novel environment. For generic fitness distributions, using an analytic argument we find that the average number of steps to a local optimum varies logarithmically with the genotype sequence length and increases as the correlations among genotypic fitnesses increase. When the fitnesses are exponentially or uniformly distributed, using an evolution equation for the distribution of population fitness, we analytically calculate the fitness distribution of fixed beneficial mutations and the walk length distribution.

Network Models of TEM β-Lactamase Mutations Coevolving under Antibiotic Selection Show Modular Structure and Anticipate Evolutionary Trajectories

Understanding how novel functions evolve (genetic adaptation) is a critical goal of evolutionary biology. Among asexual organisms, genetic adaptation involves multiple mutations that frequently interact in a non-linear fashion (epistasis). Non-linear interactions pose a formidable challenge for the computational prediction of mutation effects. Here we use the recent evolution of β-lactamase under antibiotic selection as a model for genetic adaptation. We build a network of coevolving residues (possible functional interactions), in which nodes are mutant residue positions and links represent two positions found mutated together in the same sequence. Most often these pairs occur in the setting of more complex mutants. Focusing on extended-spectrum resistant sequences, we use network-theoretical tools to identify triple mutant trajectories of likely special significance for adaptation. We extrapolate evolutionary paths (n = 3) that increase resistance and that are longer than the units used to build the network (n = 2). These paths consist of a limited number of residue positions and are enriched for known triple mutant combinations that increase cefotaxime resistance. We find that the pairs of residues used to build the network frequently decrease resistance compared to their corresponding singlets. This is a surprising result, given that their coevolution suggests a selective advantage. Thus, β-lactamase adaptation is highly epistatic. Our method can identify triplets that increase resistance despite the underlying rugged fitness landscape and has the unique ability to make predictions by placing each mutant residue position in its functional context. Our approach requires only sequence information, sufficient genetic diversity, and discrete selective pressures. Thus, it can be used to analyze recent evolutionary events, where coevolution analysis methods that use phylogeny or statistical coupling are not possible. Improving our ability to assess evolutionary trajectories will help predict the evolution of clinically relevant genes and aid in protein design.

Phi-array: A novel method for fitness visualization and decision making in evolutionary design optimization

There is a growing interest in integrating model based evolutionary optimization in engineering design decision making for effective search of the solution space. Most applications of evolutionary optimization are concerned with the search for optimal solutions satisfying pre-defined constraints while minimizing or maximizing desired goals. A few have explored post-optimization decision making using concepts such as Pareto optimality, but mostly in multi-objective problems. Sub-optimal solutions are usually discarded and do not contribute to decision making after optimization runs. However, the discarded ‘inferior’ solutions and their fitness contain useful information about underlying sensitivities of the system and can play an important role in creative decision making. The need for understanding the underlying system behavior is more pronounced in cases where variations in the genotype space can cause non-deterministic changes in either the fitness or phenotype space and where fitness evaluations are computationally expensive. The optimized design of an artificial lighting environment of a senior living room is used as a test case to demonstrate the need for and application of fitness visualization in genotype and phenotype spaces for effective decision making. Sub-optimal solutions are retained during optimization and visualized along with the optimum solution in a fitness array visualization system called phi-array, developed as part of this research. The optimization environment is based on genetic algorithm (GA) in which a compute-intensive raytracing rendering engine, RADIANCE, is used to evaluate the fitness of prospective design solutions. Apart from describing the development of the optimization system and demonstrating the utility of phi-array in effective decision making, this article explores optimization parameters and their effectiveness for artificial lighting design problems and the nature of their rugged fitness and constraint landscapes.

Reciprocal Sign Epistasis between Frequently Experimentally Evolved Adaptive Mutations Causes a Rugged Fitness Landscape

The fitness landscape captures the relationship between genotype and evolutionary fitness and is a pervasive metaphor used to describe the possible evolutionary trajectories of adaptation. However, little is known about the actual shape of fitness landscapes, including whether valleys of low fitness create local fitness optima, acting as barriers to adaptive change. Here we provide evidence of a rugged molecular fitness landscape arising during an evolution experiment in an asexual population of Saccharomyces cerevisiae. We identify the mutations that arose during the evolution using whole-genome sequencing and use competitive fitness assays to describe the mutations individually responsible for adaptation. In addition, we find that a fitness valley between two adaptive mutations in the genes MTH1 and HXT6/HXT7 is caused by reciprocal sign epistasis, where the fitness cost of the double mutant prohibits the two mutations from being selected in the same genetic background. The constraint enforced by reciprocal sign epistasis causes the mutations to remain mutually exclusive during the experiment, even though adaptive mutations in these two genes occur several times in independent lineages during the experiment. Our results show that epistasis plays a key role during adaptation and that inter-genic interactions can act as barriers between adaptive solutions. These results also provide a new interpretation on the classic Dobzhansky-Muller model of reproductive isolation and display some surprising parallels with mutations in genes often associated with tumors.

Evolution combined with genomic study elucidates genetic bases of isobutanol tolerance in Escherichia coli

BackgroundIsobutanol is a promising next-generation biofuel with demonstrated high yield microbial production, but the toxicity of this molecule reduces fermentation volumetric productivity and final titer. Organic solvent tolerance is a complex, multigenic phenotype that has been recalcitrant to rational engineering approaches. We apply experimental evolution followed by genome resequencing and a gene expression study to elucidate genetic bases of adaptation to exogenous isobutanol stress.ResultsThe adaptations acquired in our evolved lineages exhibit antagonistic pleiotropy between minimal and rich medium, and appear to be specific to the effects of longer chain alcohols. By examining genotypic adaptation in multiple independent lineages, we find evidence of parallel evolution in marC, hfq, mdh, acrAB, gatYZABCD, and rph genes. Many isobutanol tolerant lineages show reduced RpoS activity, perhaps related to mutations in hfq or acrAB. Consistent with the complex, multigenic nature of solvent tolerance, we observe adaptations in a diversity of cellular processes. Many adaptations appear to involve epistasis between different mutations, implying a rugged fitness landscape for isobutanol tolerance. We observe a trend of evolution targeting post-transcriptional regulation and high centrality nodes of biochemical networks. Collectively, the genotypic adaptations we observe suggest mechanisms of adaptation to isobutanol stress based on remodeling the cell envelope and surprisingly, stress response attenuation.ConclusionsWe have discovered a set of genotypic adaptations that confer increased tolerance to exogenous isobutanol stress. Our results are immediately useful to further efforts to engineer more isobutanol tolerant host strains of E. coli for isobutanol production. We suggest that rpoS and post-transcriptional regulators, such as hfq, RNA helicases, and sRNAs may be interesting mutagenesis targets for future global phenotype engineering.

Bose-Einstein distribution, condensation transition, and multiple stationary states in multiloci evolution of diploid populations

The mapping between genotype and phenotype is encoded in the complex web of epistatic interaction between genetic loci. In this rugged fitness landscape, recombination processes, which tend to increase variation in the population, compete with selection processes that tend to reduce genetic variation. Here, we show that the Bose-Einstein distribution describe the multiple stationary states of a diploid population under this multiloci evolutionary dynamics. Moreover, the evolutionary process might undergo an interesting condensation phase transition in the universality class of a Bose-Einstein condensation when a finite fraction of pairs of linked loci is fixed into given allelic states. Below this phase transition the genetic variation within a species is significantly reduced and only maintained by the remaining polymorphic loci.

Regulated superinfection may help HIV adaptation on rugged landscape

Human immunodeficiency virus (HIV) is highly adaptable to a, changing environment, including host immune response and antiviral drugs. Superinfection occurs when several HIV proviruses share the same host cell. We previously proposed that HIV may regulate the rate of its superinfection, which would help the virus to adapt (Leontiev et al., 2008). In this paper we, investigate the effect of regulated superinfection in HIV on complex, adaptation on rugged fitness landscapes. We present the results of our in silico experiments that suggest that regulated superinfection facilitates HIV, adaptation on rugged fitness landscapes and that the advantage of regulated, superinfection increases with the ruggedness of the landscape.

A Tale of Three Classes: Case Studies in Course Complexity

Introduction Pedagogical research is unusual within academic research in that nearly all the researchers in the area are also practitioners, which is to say they teach as well as research teaching. For this reason, interest in the answers to the research questions is personal as well as professional. Will distance learning teaching be as effective as face-to-face techniques? Is the case method really more effective than lecture? Should laptops be allowed in the classroom? The number of questions that might be posed is essentially unbounded. No one would dispute that research on teaching and learning can be challenging. After all, there are many variables that must be considered. Who could plausibly argue, for example, that factors such as the experience of the instructor, the characteristics of the students, the form of content being presented, the method of delivery, and the setting of the class are irrelevant to learning? Nonetheless, often for causal relationships that involve many variables, the individual effects of specific factors can be teased out using techniques such as regression or structural equation modeling (SEM). In such cases, the underlying process can be described as nearly decomposable (Simon, 1981). Additionally, sometimes the interrelationship between variables is so great that such decomposition is impossible. In such cases, the relationship is complex. Where such complexity exists, the research strategy needs to be reevaluated, since an individual variable's impact on overall effectiveness can be highly dependent upon the values of other variables. A particularly significant implication of complexity relates to the value of quantitative analytical techniques, such as those just mentioned. Recent research has demonstrated that, under the reasonable assumption that individuals continuously attempt to improve fitness, complex underlying relationships can produce statistically significant yet entirely misleading results (Gill & Sincich, 2008). Thus, the assumption of decomposability needs to be carefully tested prior to applying these techniques. At the present time, such tests require qualitative analysis of the process; quantitative tests for this form of complexity have yet to be devised (Gill, 2008). The present paper considers the question of the decomposability of teaching situations by presenting a qualitative analysis of three case studies of MIS courses. The cases themselves are intrinsically interesting--all three illustrate innovative teaching techniques, 2 of the 3 were winners of the Decision Science Institute's (DSI) Innovative Curriculum Competition, and all demonstrated substantial evidence of learning and student satisfaction. The research also finds that by comparing the three cases side-by-side considerable insight is gained into the complexity of the relationship between teaching approach, course setting, and outcome. The paper begins by introducing the concept of a rugged fitness landscape, taken directly from a model proposed in evolutionary biology (Kauffman, 1993). Then the research design is presented, which involves a qualitative search for interactions across four key areas of the course context: instructor characteristics, content characteristics, design/delivery characteristics, and student characteristics. Each class is presented, with details provided in two appendices, and the key interactions that were observed are identified. Because the first of these courses--referred to as Ism3232.A--evolved dramatically over time, it is presented in both longitudinal and cross sectional terms. The remaining two courses--Ism3232.B and Ism6155.A--experienced relatively few design changes from the time they were first offered. Both are therefore presented only in cross sectional terms. By comparing time slices and cross sectional observations, observational evidence of high levels of interaction between areas is acquired. The paper concludes by considering how this evidence might change the conduct of future research into IT education. …

Evolutionary dynamics on rugged fitness landscapes: Exact dynamics and information theoretical aspects

The parallel mutation-selection evolutionary dynamics, in which mutation and replication are independent events, is solved exactly in the case that the Malthusian fitnesses associated to the genomes are described by the random energy model (REM) and by a ferromagnetic version of the REM. The solution method uses the mapping of the evolutionary dynamics into a quantum Ising chain in a transverse field and the Suzuki-Trotter formalism to calculate the transition probabilities between configurations at different times. We find that in the case of the REM landscape the dynamics can exhibit three distinct regimes: pure diffusion or stasis for short times, depending on the fitness of the initial configuration, and a spin-glass regime for large times. The dynamic transition between these dynamical regimes is marked by discontinuities in the mean-fitness as well as in the overlap with the initial reference sequence. The relaxation to equilibrium is described by an inverse time decay. In the ferromagnetic REM, we find in addition to these three regimes, a ferromagnetic regime where the overlap and the mean-fitness are frozen. In this case, the system relaxes to equilibrium in a finite time. The relevance of our results to information processing aspects of evolution is discussed.

A complex systems methodology to transition management

There is a general sense of urgency that major technological transitions are required for sustainable development. Such transitions are best perceived as involving multiple transition steps along a transition path. Due to the path dependent and irreversible nature of innovation in complex technologies, an initial transition step along some preferred path may cut off paths that later may turn out to be more desirable. For these reasons, initial transition steps should allow for future flexibility, where we define flexibility as robustness regarding changing evidence and changing preferences. We propose a technology assessment methodology based on rugged fitness landscapes, which identifies the flexibility of initial transition steps in complex technologies. We illustrate our methodology by an empirical application to 2,646 possible future car systems.