Wim Hordijk

University of Lausanne, Lausanne, VD, Switzerland

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Publications (39)58.85 Total impact

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    Italian Workshop on Artificial Life and Evolutionary Computation, Vietri sul Mare; 05/2014
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    Wim Hordijk, Nilesh Vaidya, Niles Lehman
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    ABSTRACT: The concept of an autocatalytic set of molecules has been posited theoretically and demonstrated empirically with catalytic RNA molecules. For this concept to have significance in a realistic origins-of-life scenario, it will be important to demonstrate the evolvability of such sets. Here, we employ a Gillespie algorithm to improve and expand on previous simulations of an empirical system of self-assembling RNA fragments that has the ability to spontaneously form autocatalytic networks. We specifically examine the role of serial transfer as a plausible means to allow time-dependent changes in set composition, and compare the results to equilibrium, or "batch" scenarios.
    Journal of systems chemistry. 01/2014; 5:4.
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    Wim Hordijk, Peter R Wills, Mike Steel
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    ABSTRACT: A universal feature of the biochemistry of any living system is that all the molecules and catalysts that are required for reactions of the system can be built up from an available food source by repeated application of reactions from within that system. RAF (reflexively autocatalytic and food-generated) theory provides a formal way to study such processes. Beginning with Kauffman's notion of "collectively autocatalytic sets," this theory has been further developed over the last decade with the discovery of efficient algorithms and new mathematical analysis. In this paper, we study how the behaviour of a simple binary polymer model can be extended to models where the pattern of catalysis more precisely reflects the ligation and cleavage reactions involved. We find that certain properties of these models are similar to, and can be accurately predicted from, the simple binary polymer model; however, other properties lead to slightly different estimates. We also establish a number of new results concerning the structure of RAFs in these systems.
    Bulletin of Mathematical Biology 11/2013; · 2.02 Impact Factor
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    Joshua I Smith, Mike Steel, Wim Hordijk
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    ABSTRACT: In previous work, RAF theory has been developed as a tool for making theoretical progress on the origin of life question, providing insight into the structure and occurrence of self-sustaining and collectively autocatalytic sets within catalytic polymer networks. We present here an extension in which there are two "independent" polymer sets, where catalysis occurs within and between the sets, but there are no reactions combining polymers from both sets. Such an extension reflects the interaction between nucleic acids and peptides observed in modern cells and proposed forms of early life.
    Journal of systems chemistry. 10/2013; 5.
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    Mike Steel, Wim Hordijk, Joshua Smith
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    ABSTRACT: Self-sustaining autocatalytic chemical networks represent a necessary, though not sufficient condition for the emergence of early living systems. These networks have been formalised and investigated within the framework of RAF theory, which has led to a number of insights and results concerning the likelihood of such networks forming. In this paper, we extend this analysis by focussing on how small autocatalytic networks are likely to be when they first emerge. First we show that simulations are unlikely to settle this question, by establishing that the problem of finding a smallest RAF within a catalytic reaction system is NP-hard. However, irreducible RAFs (irrRAFs) can be constructed in polynomial time, and we show it is possible to determine in polynomial time whether a bounded size set of these irrRAFs contain the smallest RAFs within a system. Moreover, we derive rigorous bounds on the sizes of small RAFs and use simulations to sample irrRAFs under the binary polymer model. We then apply mathematical arguments to prove a new result suggested by those simulations: at the transition catalysis level at which RAFs first form in this model, small RAFs are unlikely to be present. We also investigate further the relationship between RAFs and another formal approach to self-sustaining and closed chemical networks, namely chemical organisation theory (COT).
    Journal of Theoretical Biology 05/2013; · 2.35 Impact Factor
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    Daniel W. McShea, Wim Hordijk
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    ABSTRACT: The eye and brain: standard thinking is that these devices are both complex and functional. They are complex in the sense of having many different types of parts, and functional in the sense of having capacities that promote survival and reproduction. Standard thinking says that the evolution of complex functionality proceeds by the addition of new parts, and that this build-up of complexity is driven by selection, by the functional advantages of complex design. The standard thinking could be right, even in general. But alternatives have not been much discussed or investigated, and the possibility remains open that other routes may not only exist but may be the norm. Our purpose here is to introduce a new route to functional complexity, a route in which complexity starts high, rising perhaps on account of the spontaneous tendency for parts to differentiate. Then, driven by selection for effective and efficient function, complexity decreases over time. Eventually, the result is a system that is highly functional and retains considerable residual complexity, enough to impress us. We try to raise this alternative route to the level of plausibility as a general mechanism in evolution by describing two cases, one from a computational model and one from the history of life.
    Evolutionary Biology 01/2013; · 2.39 Impact Factor
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    Wim Hordijk, Mike Steel
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    ABSTRACT: Background: The idea that autocatalytic sets played an important role in the origin of life is not new. However, the likelihood of autocatalytic sets emerging spontaneously has long been debated. Recently, progress has been made along two different lines. Experimental results have shown that autocatalytic sets can indeed emerge in real chemical systems, and theoretical work has shown that the existence of such self-sustaining sets is highly likely in formal models of chemical systems. Here, we take a first step towards merging these two lines of work by constructing and investigating a formal model of a real chemical system of RNA replicators exhibiting autocatalytic sets. Results: We show that the formal model accurately reproduces recent experimental results on an RNA replicator system, in particular how the system goes through a sequence of larger and larger autocatalytic sets, and how a cooperative (autocatalytic) system can outcompete an equivalent selfish system. Moreover, the model provides additional insights that could not be obtained from experiments alone, and it suggests several experimentally testable hypotheses. Conclusions: Given these additional insights and predictions, the modeling framework provides a better and more detailed understanding of the nature of chemical systems in general and the emergence of autocatalytic sets in particular. This provides an important first step in combining experimental and theoretical work on autocatalytic sets in the context of the orgin of life.
    Journal of Systems Chemistry. 11/2012; 4(1).
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    Wim Hordijk, Mike Steel, Stuart Kauffman
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    ABSTRACT: This paper presents new results from a detailed study of the structure of autocatalytic sets. We show how autocatalytic sets can be decomposed into smaller autocatalytic subsets, and how these subsets can be identified and classified. We then argue how this has important consequences for the evolvability, enablement, and emergence of autocatalytic sets. We end with some speculation on how all this might lead to a generalized theory of autocatalytic sets, which could possibly be applied to entire ecologies or even economies.
    Acta Biotheoretica 09/2012; · 0.95 Impact Factor
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    ABSTRACT: The MIGCLIM R package is a function library for the open source R software that enables the implementation of species specific dispersal constraints into projections of species distribution models under environmental change and/or landscape fragmentation scenarios. The model is based on a cellular automaton and the basic modeling unit is a cell that is inhabited or not. Model parameters include dispersal distance and kernel, long distance dispersal, barriers to dispersal, propagule production potential and habitat invasibility. The MIGCLIM R package has been designed to be highly flexible in the parameter values it accepts, and to off er good compatibility with existing species distribution modeling software. Possible applications include the projection of future species distributions under environmental change conditions and modeling the spread of invasive species.
    Ecography 08/2012; 35(10):872 - 878. · 5.12 Impact Factor
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    Wim Hordijk, Olivier Broennimann
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    ABSTRACT: We show that the dispersal routes reconstruction problem can be stated as an instance of a graph theoretical problem known as the minimum cost arborescence problem, for which there exist efficient algorithms. Furthermore, we derive some theoretical results, in a simplified setting, on the possible optimal values that can be obtained for this problem. With this, we place the dispersal routes reconstruction problem on solid theoretical grounds, establishing it as a tractable problem that also lends itself to formal mathematical and computational analysis. Finally, we present an insightful example of how this framework can be applied to real data. We propose that our computational method can be used to define the most parsimonious dispersal (or invasion) scenarios, which can then be tested using complementary methods such as genetic analysis.
    Journal of Theoretical Biology 06/2012; 308:115-22. · 2.35 Impact Factor
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    Wim Hordijk, Mike Steel
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    ABSTRACT: Background: Autocatalytic sets are often considered a necessary (but not sufficient) condition for the origin and early evolution of life. Although the idea of autocatalytic sets was already conceived of many years ago, only recently have they gained more interest, following advances in creating them experimentally in the laboratory. In our own work, we have studied autocatalytic sets extensively from a computational and theoretical point of view. Results: We present results from an initial study of the dynamics of self-sustaining autocatalytic sets (RAFs). In particular, simulations of molecular flow on autocatalytic sets are performed, to illustrate the kinds of dynamics that can occur. Next, we present an extension of our (previously introduced) algorithm for finding autocatalytic sets in general reaction networks, which can also handle inhibition. We show that in this case detecting autocatalytic sets is fixed parameter tractable. Finally, we formulate a generalized version of the algorithm that can also be applied outside the context of chemistry and origin of life, which we illustrate with a toy example from economics. Conclusions: Having shown theoretically (in previous work) that autocatalytic sets are highly likely to exist, we conclude here that also in terms of dynamics such sets are viable and outcompete non-autocatalytic sets. Furthermore, our dynamical results confirm arguments made earlier about how autocatalytic subsets can enable their own growth or give rise to other such subsets coming into existence. Finally, our algorithmic extension and generalization show that more realistic scenarios (e.g., including inhibition) can also be dealt with within our framework, and that it can even be applied to areas outside of chemistry, such as economics.
    Journal of Systems Chemistry. 06/2012; 3(1).
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    ABSTRACT: Paleoclimatic reconstructions coupled with species distribution models and identification of extant spatial genetic structure have the potential to provide insights into the demographic events that shape the distribution of intra-specific genetic variation across time. Using the globeflower Trollius europaeus as a case-study, we combined (1) Amplified Fragment Length Polymorphisms, (2) suites of 1000-years stepwise hindcasted species distributions and (3) a model of diffusion through time over the last 24,000 years, to trace the spatial dynamics that most likely fits the species' current genetic structure. We show that the globeflower comprises four gene pools in Europe which, from the dry period preceding the Last Glacial Maximum, dispersed while tracking the conditions fitting its climatic niche. Among these four gene pools, two are predicted to experience drastic range retraction in the near future. Our interdisciplinary approach, applicable to virtually any taxon, is an advance in inferring how climate change impacts species' genetic structures.
    Ecology Letters 04/2012; 15(7):649-57. · 17.95 Impact Factor
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    Wim Hordijk, Mike Steel
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    ABSTRACT: We show that in a particular model of catalytic reaction systems, known as the binary polymer model, there is a mathematical concordance between two versions of the model: (1) random catalysis and (2) template-based catalysis. In particular, we derive an analytical calculation that allows us to accurately predict the (observed) required level of catalysis in one version of the model from that in the other version, for a given probability of having self-sustaining autocatalytic sets exist in instances of both model versions. This provides a tractable connection between two models that have been investigated in theoretical origin-of-life studies.
    Journal of Theoretical Biology 12/2011; 295:132-8. · 2.35 Impact Factor
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    ABSTRACT: The formation of a self-sustaining autocatalytic chemical network is a necessary but not sufficient condition for the origin of life. The question of whether such a network could form "by chance" within a sufficiently complex suite of molecules and reactions is one that we have investigated for a simple chemical reaction model based on polymer ligation and cleavage. In this paper, we extend this work in several further directions. In particular, we investigate in more detail the levels of catalysis required for a self-sustaining autocatalytic network to form. We study the size of chemical networks within which we might expect to find such an autocatalytic subset, and we extend the theoretical and computational analyses to models in which catalysis requires template matching.
    International Journal of Molecular Sciences 01/2011; 12(5):3085-101. · 2.46 Impact Factor
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    Luis M. Rocha, Wim Hordijk
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    ABSTRACT: Material Representations: From the Genetic Code to the Evolution of Cellular Automata try to bring together connectionist and symbolist approaches to cognition from the description of connectionist systems: -"Indeed, the emergent behavior of agents that are dynamically coherent with their environments (embodied agents) is as much a result of the production rules of the agent as of the laws of the environment [Beer ,1995] [Clark ,1996] [Rocha and Joslyn ,1998]." -Do current *intelligent* dynamical systems scale? "What needs to be stressed here is that evolutionary systems require both dynamic and [genetic] memory components for selection."
    Artificial Life 01/2005; · 1.59 Impact Factor
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    Luis Mateus Rocha, Wim Hordijk
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    ABSTRACT: We present a new definition of the concept of representation for cognitive science that is based on a study of the origin of structures that are used to store memory in evolving systems. This study consists of novel computer experiments in the evolution of cellular automata to perform nontrivial tasks as well as evidence from biology concerning genetic memory. Our key observation is that representations require inert structures to encode information used to construct appropriate dynamic configurations for the evolving system. We propose criteria to decide if a given structure is a representation by unpacking the idea of inert structures that can be used as memory for arbitrary dynamic configurations. Using a genetic algorithm, we evolved cellular automata rules that can perform nontrivial tasks related to the density task (or majority classification problem) commonly used in the literature. We present the particle catalogs of the new rules following the computational mechanics framework. We discuss if the evolved cellular automata particles may be seen as representations according to our criteria. We show that while they capture some of the essential characteristics of representations, they lack an essential one. Our goal is to show that artificial life can be used to shed new light on the computation-versus-dynamics debate in cognitive science, and indeed function as a constructive bridge between the two camps. Our definitions of representation and cellular automata experiments are proposed as a complementary approach, with both dynamics and informational modes of explanation.
    Artificial Life 01/2005; 11(1-2):189-214. · 1.59 Impact Factor
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    Wim Hordijk, Stuart A. Kauffman
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    ABSTRACT: The correlation structure of tness landscapes is a much used measure to characterize and classify various types of landscapes. However, analyzing the correlation structure of tness landscapes has so far been restricted to static landscapes only. Here, we investigate the correlation structure of coupled, or dynamic, tness landscapes. Using the NKC model of coevolution, we apply a correlation analysis on various instances of this model and present the results. One of the main goals of this paper is thus to show that a previously introduced correlation analysis can be successfully extended to coupled tness landscapes. Furthermore, our analysis shows that this provides meaningful and interesting results that can contribute to a better understanding of coevolution in general.
    Complexity 01/2005; 10:41-49. · 1.33 Impact Factor
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    ABSTRACT: Supertree methods have been often identified as a possible approach to the reconstruction of the 'Tree of Life'. However, a limitation of such methods is that, typically, they use just leaf-labelled phylogenetic trees to infer the resulting supertree. In this paper, we describe several new supertree algorithms that extend the allowable information that can be used for phylogenetic inference. These algorithms have been recently implemented and we describe here two illustrative applications. These new algorithms are freely available for application at http://darwin.zoology.gla.ac.uk/cgi-bin/build.pl.
    Bioinformatics 11/2004; 20(15):2355-60. · 5.32 Impact Factor
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    ABSTRACT: Eigenvectors of the Laplacian of a graph G have received increasing attention in the recent past. Here we investigate their so-called nodal domains, i.e., the connected components of the maximal induced subgraphs of G on which an eigenvector psi does not change sign. An analogue of Courant's nodal domain theorem provides upper bounds on the number of nodal domains depending on the location of psi in the spectrum. This bound, however, is not sharp in general. In this contribution we consider the problem of computing minimal and maximal numbers of nodal domains for a particular graph. The class of Boolean Hypercubes is discussed in detail. We find that, despite the simplicity of this graph class, for which complete spectral information is available, the computations are still non-trivial. Nevertheless, we obtained some new results and a number of conjectures.
    Linear Algebra and its Applications 09/2004; 390:155-174. · 0.97 Impact Factor

Publication Stats

529 Citations
58.85 Total Impact Points

Institutions

  • 2011
    • University of Lausanne
      • Department of Ecology and Evolution
      Lausanne, VD, Switzerland
  • 2005
    • Indiana University Bloomington
      Bloomington, Indiana, United States
  • 2002–2004
    • University of Canterbury
      • • Department of Mathematics and Statistics
      • • Biomathematics Research Centre
      Christchurch, Canterbury, New Zealand
  • 2003
    • University of São Paulo
      • Institute of Physics São Carlos (IFSC)
      San Paulo, São Paulo, Brazil
  • 1995–2001
    • Santa Fe Institute
      Santa Fe, New Mexico, United States