Constructing knowledge landscapes within the framework of geometrically oriented evolutionary theories more

Integrative Systems Approaches to Natural and Social Dynamics Systems Science 2000 Contributors P. M. Allen, H. E Alroe, E. G. D'Ambrogio, A. Barbieri, G. Bechmann, F. Beckenbach, V. Berding, J. Berlekamp, A. Bobyrev, A. Bockermann, R. Briiggemann, V. Burmensky, R. Daccd, N. Dioguardi, W. Ebeling, I. Fernandez, St. Fuest, G. Geiger, St. Giljum, E Grizzi, J.-D. Haynes, E Hinterberger, M. Jenssen, S.E. Jorgensen, J. Kohn, J.L. de Kok, E. Kriksunov, E. St. Kristensen, J. Kriz, Th. Leiber, B.-L. Li, Z.-S. Lin, H, Lieth, C. E Mahler, H. Malchow, M. Matthies, B. Meyer, H.-J. Mosler, A. Nasrulin, L. C. D. de Oliveira, I. Omann, J. M. Pacheco, E Pfafflin, M. Ruth, A. Scharnhorst, Ch. Scheier, A. Schierwagen, St. Schwartz, E Schweitzer, R. Seppelt, W. Silvert, J. H. Spangenberg, M. A. Stadler, N. Stehr, N. Stollenwerk, M.-M. Temme, W. Tschacher, I. Tulbure, E. Umbach, J. Wesseler, Th. Wilhelm, H. G. Wind Editors M. Matthies, H. Malchow and J. Kriz M Springer 500.1 Constructing Knowledge Landscapes Within the Framework of Geometrically Oriented Evolutionary Theories Andrea Scharnhorst Virtual knowledge landscapes are constructed from empirical data to visualize and to understand search and innovation processes in science and technology. In this paper we discuss how geometrically oriented evolution theories (G_0_E_THE) may represent an appropriate framework for the empirical design of such knowledge landscapes as well as for theoretical explanations of observ- able, dynamic processes therein. G_0_E_THE describes evolution as a com- petitive hill-climbing process of different searchers or searching groups in an unknown adaptive landscape over a continuous characteristics space. In this chapter we discuss the application of this framework to the dynamics of na- tional science systems in the international scientific communication system. Keywords. Knowledge landscapes, Fitness landscape, Evolutionary models, Biblio- metrics, Research profiles of countries 1 Introduction The information society is confronted with increasing problems of information retrieval and knowledge management. Considering science and technology, we find tremendous data mountains of scientific publications, patents, and techni- cal manuals. The visualization of this information in virtual spaces and the de- velopment of corresponding navigation tools has become a main part of infor- mation science. In this chapter, the location of national science systems in a space of disci- plines and the changing occupation of research areas in this space by the inter- national scientific community as a whole is shown. Concepts and models taken from physical theories of complex systems are used for the construction and in- terpretation of such a knowledge landscape. In particular we consider geomet- rically oriented evolution theories (G_OJB_THE). The term "landscape" func- tions as linking element between natural and social sciences theoretical ap- proaches. The landscape concept is one key concept in the analysis of the dynamics of complex non-linear systems. The emergence of self-organized structures can be understood as the result of a search for optimal solutions of a certain problem, and the corresponding models (conceptual and mathematical) describe charac- teristics of search processes in unknown landscapes. 506 A. Scharnhorst National science systems can be considered as searchers for optimal research strategies. In the arena of international scientific communication they compete for scientific reward. The efforts of countries become measurable - for instance in terms of number of publications. Their research strategies - at a very high level of aggregation - are represented in the distribution of publications over scientific disciplines. In a space of scientific disciplines countries occupy differ- ent locations. Similar research profiles lead to an agglomeration of occupied lo- cations in this space. Changes in the research profile of single countries form trajectories. The intention of the methodological approach introduced in this chapter is to ask for possible relations between spatial knowledge representations in science and geometrically oriented models of search and evolution in complex systems. 2 G_0„E_THE as a Framework to Construct Knowledge Landscapes The idea of geometrically oriented evolutionary theories goes back to Wright's description of biological evolution. Wright introduced the picture of a hypo- thetical fitness or adaptive function over a space of gene combinations (Wright 1932,1988). This representation can be used to visualize the position of a popu- lation and to visualize the influence of selection and mutation on the evolution of populations. Evolution can be considered as hill-climbing in such a fitness landscape. Meanwhile, the idea of evolution as hill-climbing in an adaptive fit- ness landscape has been applied in various problem areas and using different mathematical approaches (Allen and McGlade 1987; Allen and Lesser 1991; Allen 1994; Kauffman 1983, 1996; Rechenberg 1994; Schuster 1999; Schwefel 1995). In this chapter, a special approach developed by the Ebeling group in Berlin is referred to which employs a continuous description of evolution (Feistel and Ebeling 1982,1989; Ebeling et al. 1984,1990). Key elements of the concept are: - The characteristics space. - The occupation landscape. - The valuation landscape. In the following we will illustrate these elements by means of examples from sci- ence and technology. We start with the idea that the elements can be described by certain charac- teristics which are quantitatively measurable. In the case of technological evolution, for instance, products (e.g., cars, air- craft) are considered as elements (Fig. 1). Each product can be described by a set of variables. In a characteristics space of technological output indicators (tech- nical and service parameters), product models like airplanes have a certain po- sition. Such a spatial representation was introduced by Saviotti and Metcalfe (Saviotti and Metcalfe 1984; Saviotti 1996). In this way, technological trajectories can be made visible. The technological trajectory represents the search process of engineers for improvements and innovations. The realized products mirror Constructing Knowledge Landscapes 507 Fig. 1. Aircrafts in a space of technological output indicators Speed Engine type the technological knowledge. In this sense, the characteristics space is a knowl- edge space (Ebeling et al. 1999). Another knowledge space emerges when scientific publications are consid- ered. We choose an example in which countries are compared by the way their publications are distributed over the main scientific disciplines in the natural sciences. Then, each country has a position in the space of publication shares (Fig. 2). Now, we can ask, how the research profiles (measured in terms of publi- cations) of countries change. If the characteristics space is constructed, the next idea is to count the ele- ments which are occupying locations in the characteristics space and to con- struct an occupation landscape (Fig. 3). The temporal change of this occupation landscape will be described by cer- tain mathematical models. The approach of continuous evolutionary models employs an equation of the following type (Fig. 4) to describe the interplay be- tween the basic elements of the concept introduced so far (Feistel and Ebeling 1989). Without going into the mathematical details, the idea is that selection leads to a concentration of the occupation around the maxima of the fitness landscape. Mutation describes the spreading of occupation into the space and ensures the variety necessary for changes. Further, the expression allows one to model evo- Fig. 2. Countries in a space of research profiles Publications in Mathematics Publications in Physics (Number, Share) + 1*1 Publications in Life Sciences 508 A.Scharnhorst Number, Frequency, Density Function X 1 Individual 1 Product 1 Country Area which can be occupied Population Type Group Characteristics 2: q2 Fig. 3. Occupied locations in a characteristics space form an occupation landscape lution in changing environments (with a time-dependent fitness landscape) and under uncertainty. In general, evolution will be described as hill-climbing in an adaptive landscape. What we can observe empirically are mainly occupation landscapes. The change in occupation may be the result of a competition process between ele- ments or groups in the characteristics space. In biology, populations compete for resources. Technological products compete for the market. National science sys- tems compete for successful research strategies. Competition requires a com- parison, and this means a valuation of the occupied areas with respect to an adaptation in a generalized sense. The adaptive landscape might be a fitness in the case of biological evolution, an efficiency criterion in the case of technolog- ical evolution, or a scientific reward in the case of national science systems. In general, the valuation function will be unknown, or known only in a local region around the searching individuals and groups. Nevertheless, from features of empirically observable search and evolution processes, by means of natural science theories we can deduce certain characteristics of the hidden valuation landscape. For instance, the coexistence of different types, groups, or popula- tions indicates the multimodality of the fitness landscape. Further, the search processes take place under uncertainty. One approach to model this uncertainty Occupation Function Valuation Function Mutation Operator ; Fitness Landscape / _ 1 - M 1 - dtx(q, t) ~ x(q, t)w(q; \xj) + Mx(q,t) Characteristics Y Y Comparison Spreading Selection Mutation Fig. 4. The mathematical model Constructing Knowledge Landscapes 509 consists in describing the fitness landscape as a stochastic function with certain statistical properties. The existence of correlation of this stochastic function is necessary to ensure that the evolution can proceed. This indicates a certain smoothness in the geometry of the valuation function (Conrad and Ebeling 1992). In Fig. 5 the course of a search process in such a landscape is illustrated. We start with a small population in a restricted area of the space. Then, according to the model (see Fig. 4) sequences of growth and decline at certain occupied points on the one hand and spreading into unknown territory on the other leads to a situation in which the shape of the occupation landscape mirrors the shape of the valuation landscape. The model framework (G_0_E_THE) entails pro- posals about the interaction of mutation and selection responsible for the shap- ing of the occupation landscape and allows one to test scenarios of search processes under varying conditions. 3 Trends in National Research Profiles Visible in a Disciplinary Knowledge Space In the following, the heuristic power of geometrically oriented evolutionary the- ories for the construction of knowledge landscapes from empirical data will be demonstrated. We consider the development of national science systems in terms of bibliometric indicators. There are different ways to compare countries, e.g., by comparing their publication shares in a certain field or by making refer- ence to the share in the world-wide production in this field. Using the example of national science systems, we will show how the landscape concept can be ap- 510 A. Scharnhorst plied to structure the collection, presentation, and interpretation of empirical data in an alternative way (Scharnhorst 1998,2000). For this purpose, we com- pare the publication profiles of countries in natural sciences (Bonitz et al. 1993). At a certain point in time each country has a special pattern or distribution of its publications over scientific disciplines like Life Sciences, Physics, Chemistry, Engineering, Mathematics. The shares of a country's publications in these main fields build the components of a vector q - {qLi q?, qc, gE> qM}. Typically, the largest shares are qh {Life Sciences) and q? (Physics). The simplest way is to plot the location of countries according to two variables {qv q?} (shares in Life Sciences and Physics in our case). What we will see is a scattering of countries in this two-dimensional space. We find countries with a high share in Life Sciences and countries with a high share in Physics. In the following, we use data drawn from the Science Citation Index (SCI), the bibliometric indicators (publication per field and country) being constructed by the ISSRU group and RASCI e.V.l~We consider 44 countries (the largest countries in the database used in terms of publications); most of them are OECD coun- tries. Considering the period 1980-1994, we look at what changes can be made visible by means of the proposed framework. During this period, the importance of biologically oriented research obviously increased. The question is to which extent these changes can be made visible and how different countries adapt to these changes. A second interesting point concerns the question to which extent new media and processes of globalization affect the structure of the interna- tional scientific community and the role of national science systems therein. To obtain a clearer picture of the structure of the international scientific com- munity as a whole we look at the distribution of the different research profiles. Obviously, some of the countries have similar profiles. We construct an "occu- pation landscape" in the following way: each country is represented by a Gaussian hill, and the superposition of these Gaussian functions produces the landscape. First, we consider only the change of the shape of this occupation landscape in time (Fig. 6). There is a certain trend to approaching national publication pro- files for a part of the country group analyzed. This trend becomes clearer when we consider the contour plot of the occupation landscape (Fig. 7). The following comment is included for readers not familiar with this database. The Science Citation Index produced by the Institute of Scientific Information in Philadelphia covers yearly about 3500 journals (and some monographic series titles) across all fields (Garfield 1977). Articles, notes, letters, editorials, reviews, etc., are the source items taken from these journals. Each record includes the authors names, their addresses, the title, the journal name (volume, number, pages), the abstract, the full bibliographic list of references of the docu- ment, and some further information. To construct the country-specific bibliometric indica- tors from this material one has to classify the documents with respect to the countries of ori- gin (here according to the first author) and by fields (via the affiliation of journals by fields). Of course, the selection of journals covered by the database determines the meaning of pub- lication and citation indicators on a national level. For the SCI, the resulting publication pro- file does not directly represent the output or performance of a certain country. Rather, it re- flects how the performance of a certain national science system is perceived by the interna- tional scientific community. Constructing Knowledge Landscapes 511 Publication Profiles 1980-1984 Publication Profiles 1985-1989 Publication Profiles 1990-1994 Publication Profiles 1994-1998 Fig. 6. The occupation of Life Sciences (L) and Physics (P) in the international scientific com- munity in the time period from 1980 to 1998 Globalization in science seems to entail two processes: for a group of coun- tries we observe an approaching of their publication profiles. On the other hand, countries located at the periphery of the centers are driven away. For these coun- tries the stratification increases. If we look at the concrete countries2 whose scientific performance generates the landscape we find certain regularities (Fig. 8). Most of the OECD countries are grouped together, independent of size in terms of absolute publication num- bers or geographical location. Inside the main group, one main peak is located around the USA, whereby another peak is formed by a "Scandinavian group" and 2 Abbreviations used: ARG - Argentina; AUS - Australia; AUT - Austria; BEL - Belgium; BGR - Bulgaria; BRA - Brazil; CAN - Canada; CHE - Switzerland; CSK - Czechoslovakia; DEU - Germany FR; DNK - Denmark; EGY - Egypt; ESP - Spain; FIN - Finland; FRA - France; GRC - Greece; HKG - Hong Kong; HUN - Hungary; IND - India; IRL - Ireland; ISR - Israel; ITA - Italy; JPN - Japan; KOR - South Korea; MEX - Mexico; NIG - Nigeria; NDL - Netherlands; NOR - Norway; NZL - New Zealand; POL - Poland; PRC - PR China; PRT - Portugal; ROM - Romania; SAU - Saudi Arabia; SGP - Singapore; SUN - USSR; SWE - Sweden; TUR - Turkey; TWN - Taiwan; UKD - UK; USA - USA; VEN - Venezuela; YUG - Yugoslavia; ZAF - South African R. 512 A. Scharnhorst Pifclicaticn Profiles 1980 - 1984 PuWiraticn Profiles 1985 - 1969 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0. PcblicaUiai Profiles 1990 - 1994 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 Publication Profiles 1994 - 1998 0.5 0.4 I 0.3 . © ^) 0.2 0 0.1 0 0.1 0.2 0.3 0.4 0.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.£ Fig. 7. Contour plots of the occupation landscape in the space of Life Sciences and Physics in the international scientific community in the time period from 1980 to 1998 0.5 0.4 0.3 0.2 0.1 1990-1994 ROM KOR ISR USA, CAN, BEL AUT, NDL, AUS, NOR IRE, ZAF, UKD HGK DNK NZL.SWE .FIN VEN, DEU ARG JPN 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Fig. 8. Contour plot and country points for the time period from 1990 to 1994 Constructing Knowledge Landscapes 513 some African/Pacific countries. Most of the West European countries are located in the foothills of this group, and most of the former socialist countries appear in the periphery as more or less isolated points. So far, we have considered the occupation landscape. Which valuation land- scape generates it remains open. In physics or mathematics, conclusions can (under certain assumptions) be drawn about the shape of the underlying po- tential function from a vector field. Therefore, by using a vector field represen- tation of the temporal changes we can speculate about the form of the underly- ing valuation landscape. For this purpose, the locations in each two subsequent periods are linked by arrows (Fig. 9). Obviously, some coherent movements can be observed. Further, we see that the fluctuations in the movement increase for countries with small total publication output. What the character of this potential or valuation function could be remains hidden. It seems to be very difficult to formulate an objective evaluation of a cer- tain publication profile. However, within the framework used we can discuss variants. The search for a criterion is determined by the level of selection and competition to which we are referring. One possible approach might be to con- sider competition between countries in the economic sphere, selection being in- fluenced by the national innovation system and, finally, also by research strate- gies and the corresponding change in the publication structure. One would then search for indicators of economic growth and wealth as an expression of a se- lective valuation landscape over the bibliometric space of publication struc- tures. However, the influence of research strategies on economic performance is mediated through different levels, and while the economic wealth of nations will determine research conditions, it is unlikely to determine publication output in different fields directly. An alternative approach consists in describing changes in national publication profiles as the outcome of a selection process within the world scientific system. nc Vector Field (1980-84,1985-89,1990-94,1994-98) 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Fig. 9. Trajectories of the movements of countries shown in terms of a vector field represen- tation 514 A. Scharnhorst Countries compete for excellent scientists, for research results, and, in biblio- metric terms, for visibility in international journals. Visibility measured by cita- tions could then serve as selection criterion (Leydesdorff and Wouters 1999). According to such an approach, countries would compete for citations on the ba- sis of (possibly implicit) national research strategies. In a forthcoming paper we will investigate in more detail what kind of citation indicator might serve as an expression of a valuation landscape. 4 Summary Virtually constructed science or knowledge landscapes make hidden or distrib- uted information visible. They can facilitate orientation and navigation in exis- tent knowledge landscapes and the comparison of different institutional struc- tures. Links to theories of evolutionary search in complex adaptive landscapes and to evolutionary strategies can provide some insight into the mechanisms for the formation and re-shaping of such landscapes. They can help to understand better the conditions for successful and effective searches for innovations and supporting institutional frameworks. In this chapter, a special framework of continuous evolutionary models (geo- metrically oriented evolution theory - G_0_E_THE) is presented. G_0_E_THE may serve as: - A guideline for empirical investigations and their interpretation (search and innovation processes can be made visible). - A framework for theory building (measurement of qualitative changes and design of a corresponding characteristics space, search process is understood as part of an evolutionary process including competition and selection). - A tool for computer-animated search processes in which conditions for search and innovation processes can be tested (as, e. g., the role of diversity, of the population size and of the initial conditions for the success of the search process). In this chapter, in the case of the development of national science structures, the approach has been used as a framework to establish questions, from a novel per- spective, for empirical research. In particular, the focus is on dynamical changes and their possible interpretations. References Allen PM, McGlade JM (1987) Modelling complex human systems: a fisheries example. 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