Modeling Historical Development: Fitting a Competing Practices ...

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 3, No. 1, 1999

Modeling Historical Development: Fitting a Competing Practices System to Coded Archival Data David K. Dirlam,1 Karen L. Gamble, and Heidi S. Lloyd

This project used curve fitting to refine an ecological model of historical development. Dirlam (1972, 1980, and 1996) constructed multidimensional classifiers for coding sociocultural practices by using theories of children's drawing, students' writing, and developmental researchers' methods. The last involved an eleven-dimensional classifier based mostly on Danziger's (1990) insights. An NDS analysis began with Van Geert's (1991) variant of the Lotka-Volterra two-species model, which was generalized by Dirlam (1997) to many competing species, each embodying an evolutionary strategy. Excellent fits to codings of research strategies in 599 articles from Child Development and Developmental Psychology, 1969-1992, revealed chaotic growth unless suppressed by new strategies. In this paper, coding was extended to 313 new articles published from 1930-1968. A refined model using Levins' (1969) "logistic weed" produced more meaningful parameter values and suggested dynamic differences between evolutionary strategies and sociocultural practices. Statistically adequate solutions with both low growth and high growth were found. To differentiate solutions, we proposed independent experimental testing and examining the scientific meaning of parameter values. The analysis identified two novel dynamic entities: default and polarized practices. Removing the person-practice link and coding many dimensions at once extends dynamic modeling to a greatly enriched variety of cultural and historical processes. KEY WORDS: developmental models; historical models; cultural practices; Lotka-Volterra models; developmental methodology.

'Correspondence should be directed to David K. Dirlam, 2016 Avenue of the Trees, Carlsbad, CA 92008; e-mail: [email protected].

93 1090-0578/99/0100-0093$16.IX)A> © 1999 Human Sciences Press, Inc.

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In the early nineteenth century, Adolphe Quetelet, the founder of social statistics, dreamed of an astronomy of society. By restricting Malthus' "J-curve" of population growth near a carrying capacity, Quetelet's student, Pierre-Francois Verhulst, invented a primordial application to social data of what is now called chaos theory. Nearly a century later, Lotka (1925) and Volterra (1926) enriched this application to include the competition between populations of different species. Yet another half-century remained before Schelling (1969) and Forrester (1969) returned to applying dynamic ecological models to such social problems as segregation, the role of jobs and housing quality in determining the movement of people in cities, and the limits of birth control in staving off humanity-created world disaster. Recently, the field of artificial societies has grown rapidly (see Epstein & Axtell, 1996) and social science applications have been extended to such interesting problems as the growth of virtual groups (Guastello & Phillippe, 1997). In the historical progression just outlined, the core concept has remained population growth. This article carries the argument into the realm of human practices by undertaking a dynamic analysis of competing scientific practices in developmental psychology research. Though practices are not agents in the sense that people are agents, they can "grow" in frequency of usage and "compete" for available time and other resources. The analogy from frequencies of agents to frequencies of practices was mediated by the use of multidimensional classifiers, generalized systems for coding complex, naturally occurring activities described by Dirlam (1972, 1980). Each dimension in a classifier partitions all possible records of the activity being studied. Consequently, when the frequency of one element in the partition increases, the total frequency of the others must decline. In this sense, the elements of a dimension can be said to "compete" with each other. Dirlam (1980,1996) constructed multidimensional classifiers for coding sociocultural practices using theories of children's drawing, students' writing, and developmental researchers' methods. The latter paper included an eleven dimensional classifier of developmental research that had three to four practices per dimension (see the Method section). Seven of the eleven dimensions were defined from Danziger's (1990) penetrating sociohistorical analysis of the early decades of psychological research. This classifier was used to code 599 articles from Child Development and Developmental Psychology, 1969-1992. In Dirlam (1997) each dimension was characterized as a microsystem of competing strategies—basically, a sociocultural analogy to evolutionarily stable strategies (the transition from a system of strategies to a system of practices depended on a further refinement of the model that will be described, below). Dirlam (1997) analyzed the results using a

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generalization of Van Geert's (1991) variant of the Lotka-Volterra model of competition between two strategies:

Here, x' is the next frequency of a strategy currently numbering x; r is its potential growth rate, y the current frequency of a competing strategy, k the carrying capacity of x, and c the competitive strength of y. The difference from the Lotka-Volterra model is that Van Geert placed the competition term outside of the term that multiplies growth rate. This is preferable because zero growth rates still result in decline. Though zero growth does not occur among species, it does characterize the default practices found in the present study. The generalization from two to any number of strategies used a common carrying capacity, as Clayton and Frey (1996) did, and summed both the current frequencies and the competition terms (the index, j, indicated unidirectional competition—later strategies reduced earlier ones but not the reverse):

Despite statistically excellent fits to both the drawing and developmental research data, some of the parameter values in Dirlam (1997) were not clearly meaningful. As Danziger and Dzinas (1997) showed for the use of the term variable, it is tempting to reify mathematical terms or results (as in "personality variables" or "negative growth") without having clear avenues for testing their usage. Three problems with the earlier analysis exist: (1) allowing negative growth rates introduced unnecessary complexity; (2) the units for competitive strengths were vague; (3) some factor analogous to carrying capacity appears essential. Problems with these three parameters exemplified fundamental issues in applying chaos models to psychology. Any adequate model must generate negative growth, since primitive strategies decline in usage. Emergence of a competing strategy qualifies as one such event. Any other would require accounting for initial positive growth changing to negative and then if above the carrying capacity, suddenly turning positive again. Thus, nonnegative potential growth rates are simpler. Therefore, the generalized growth rate used earlier was replaced by a more testable, nonnegative potential growth rate. Competitive strength was replaced by competitive success rate—a positive fraction, such that the rates for a microsystem sum to one. Removing negative competitive strengths necessitated making competition bidirectional (the growth of each strategy was reduced by all others). Independent validation of competitive success rates could be obtained from article rejection rates.

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To obtain good fits, the present data required variable carrying capacities. Obviously journals have environmental limits on numbers of articles published, but how this relates to carrying capacity is not obvious. In ecological theory, carrying capacity refers to the level where resource limitations produce zero population growth—births equal deaths within a time step. But how do births and deaths translate into research practices? The analogy becomes more transparent with the aid of Levins' (1969) "logistic weed." Using Roughgarden's (1998) notation, potential habitats, N, get colonized from x habitats containing a weed, at the rate of m per existing habitat, while the existing habitats go extinct at rate u. Analogously, we have N potential articles per time step. If x articles used the strategy in question, m is the probability that one of these articles will stimulate a prospective author to switch to the strategy. Since there are TV—x potential articles not using the strategy, the number of changes stimulated by each article is m(N—x) and the total number of such changes is m(N—x)x. But we also need to consider the rate, «, that current users drop the strategy, producing we drops in all. Thus, the overall change from one time step to the next, designated Ax is

Recall that the noncompetitive change portion (or Verhulst growth portion) of (1) gives

Factoring out first x and then mN—u in (3) and equating it with (4) reveals that

Anticipating cultural strategies, these results are converted to proportions of the total frequency for the first time step by letting N = 1, which gives

Adding the possibility of increases in the carrying capacity (i.e., the number of articles printed per time step in the journal), we have

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These results show that even without competition, strategies do not survive unless the new-user stimulation rate exceeds the current-user dropping rate by more than the growth in the journal. Furthermore, they clearly limit carrying capacity values to less than 1 + g. This formulation also gives meaning to carrying capacity by making its sociocultural contribution to strategy growth both transparent and essential. It took numerous repetitions of the preceding argument to make a habit of it, as if thinking of carrying capacity in the context of cultural strategy was itself a bad habit that needed to be replaced by a better one. In fact, the source of the habit may actually lie in our cultural tendency to equate practices with persons. Such difficulties implied that no matter how helpful, it was time to replace the evolutionary analogy with a terminology unique to the growth, dispersal, and competition of cultural strategies. Even "cultural strategy" is clumsy, since "logistic weed" is distinctly memorable, while "logistic cultural strategy" is a tongue twister. What is needed is a single word that will encompass culturally mediated actions ranging from simple habits to complex techniques. Scribner and Cole's (1981) concept of "practice" does the task elegantly: By a practice we mean a recurrent, goal-directed sequence of activities using a particular technology and particular systems of knowledge. We use the term "skills" to refer to the coordinated sets of actions involved in applying this knowledge in particular settings. A practice, then, consists of three components: technology, knowledge, and skills. We can apply this concept to spheres of activity that are predominantly conceptual (for example, the practice of law) as well as to those that are predominantly sensory-motor (for example, the practice of weaving). All practices involve interrelated tasks that share common tools, knowledge base, and skills. But we may construe them more or less broadly to refer to entire domains of activity around a common object (for example, law) or to more specific endeavors within such domains (cross-examination or legal research). Whether defined in broad or narrow terms, practice always refers to socially developed and patterned ways of using technology and knowledge to accomplish tasks. Conversely, tasks that individuals engage in constitute a social practice when they are directed to socially recognized goals and make use of a shared technology and knowledge system, (p. 236, by permission)

Logistic practice, therefore, refers to growth in the frequency of usage of a practice (in the narrow sense) that is limited by the level at which a community of practice (in the broad sense) reaches an equilibrium of dropping and adopting the particular practice. This level may be affected by resources. For example, computers engendered more elaborate statistical analyses and many researchers lack the resources for longitudinal studies. But the level is also limited by other factors. Social forces, not journal space, stimulated using significance values as publication criteria and lim-

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ited interdisciplinary or applied discussions. Therefore, instead of environmental carrying capacity, the growth of practices is limited by their acceptance level Though weeds cannot survive without resources, we all know of practices, especially primitive ones, that survive without social acceptance. The preceding considerations led to the following competing practices system (CPS) model of the historical survival of common practices:

METHOD The present study added codings of 313 more articles randomly selected from Child Development 1930-1968. These were combined with the 599 ratings reported in Dirlam (1996) to make a total of 912 articles from Child Development, 1930-1992 and Developmental Psychology, 1969-1992. Since, as reported in Dirlam (1996), there were no significant differences between practices used in the two journals, they were treated as one source. Coding and Rating Procedures As in the earlier study, two raters rated each article and resolved discrepancies by discussion. Potential rater drift was controlled by discussing ratings with a third, experienced rater after each 100 articles. The original 11-category classifier system is described below. The DEPENDENT VARIABLES dimension included (a) summed scores (standardized tests or sums of Likert-scale ratings of loosely connected items), (b) limited behaviors (possible responses restricted to a small, easily counted number), or (c) categorized free behavior. The origin and some of the serious problems with summed scores and limited behaviors were discussed at length by Danziger (cf., ANALYSIS). At the opposite end, this study, for one, categorizes the free behavior of journal article writing. The ANALYSIS dimension included (a) descriptive or correlational, (b) differences alone, (c) difference statistics and correlations, (d) anything new. Danziger argued that since significant differences are paltry minima to base findings upon, the notion has contributed nothing of value to the science. Nevertheless, physics has done well with paltry minimums like photons or

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subatomic particles and differences, at least, do not require normalized sums of loosely related scores (cf., DEPENDENT VARIABLES). The DESIGN dimension included (a) longitudinal, (b) single session, (c) microbngitudinal. Miller (1977) first revealed the power of microlongitudinal measurement, not just to make measures of reliability, but to undermine the whole notion of stages of linguistic development. Longitudinal designs assume a "developmental force," perfectly correlated with age, that produces their differences (cf., AGE). The AGE dimension included (a) more than one age group, (b) one narrow age group, (c) one broad age group, (d) age as a dependent variable. Wohlwill (1970) wrote a deeply insightful paper arguing that time, including age, is a measure of something. Instead of sampling from an assumed stream of development, supposed to be perfectly correlated with age, we should begin with a known result and use age as a measure of how long it takes to develop. The "one age group" study is progress in that direction. Dynamic modeling of development, like that done in this article, requires the use of age as a dependent variable. The ASSESSOR dimension included (a) objective test, experimenter or aide, (b) significant adult, (c) self, (d) mixed. Danziger (1990) argued that depriving the subject of his or her historical identity is one way to create an illusion of generality (see also LOCATION and SUBJECT). The SOCIAL CONTROL dimension included (a) child, (b) child plus experimenter, (c) child plus significant other. Another way to remove situational contexts and add to the illusion of generality is to isolate subjects. The LOCATION dimension included (a) unspecified, (b) lab, (c) school, (d) home or other. A third way of creating an illusion of generality for psychological research is to omit discussion of situational context and remove situational markers. The GROUPS dimension included (a) psychometric, (b) natural, (c) single (ages were considered under AGE), (d) randomized. Psychometric and natural groups were discussed at length by Danziger. Psychometric designs use tests based on summed scores to divide groups up and then measure the groups on another test. Since individual items are obscured in the totals, the results often merely demonstrate what was assumed. The power of randomized groups for statistical generalization is well known. The INTRODUCTION CONTEXT dimension included (a) background and topic from the same chapter of a developmental text, (b) some background from a different chapter, (c) some from another discipline, (d) some from both. Extending the "converging operations" argument to a grand scale, Danziger suggested that interdisciplinary analyses are a primary way of overcoming self-fulfilling prophecies. This dimension applied to the introduction of the article.

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Table 1. The Final Eight Dimensional Classifier of Developmental Research Practices Dimension

Practice 1

Practice 2

Practice 3

DEPENDENT VARIABLES

Limited only/ Categorized free only

Summed/Enumerated (maybe with limited)

DATA ANALYSIS

Descriptive or correlational

Differences

DESIGNS

Microlongitudinal

Single session per task

Longitudinal

AGE VARIABLE

Age as a dependent variable

Two or more age groups

Single age group

SOCIAL CONTEXT

Significant other or experimenter but no test

Test & significant other (maybe plus Experimenter)

Test alone

LOCATION

School/home/ other

Unspecified

Laboratory or multiple

BACKGROUND

Interdisciplinary

Disciplinary

APPLICATIONS

Researchers only Other

Practice 4

Categorized free + other

Test & Experimenter

The DISCUSSION CONTEXT dimension included INTRODUCTION categories applied to the discussion section. The APPLICATION dimension included (a) administrator or other professional, (b) researcher, (c) individuals. Danziger (1990) showed that serving the rich and powerful, even if they only use it to justify their own decisions, is a good way to sell a science. Worthwhile knowledge, in contrast, seeks to emancipate individuals from the prisons of their assumptions. Preliminary analysis collapsed theoretical distinctions that did not result in different mean times of appearance. The GROUPS dimension was dropped due to problems with rating reliability in the first sample of 299 studies; ASSESSOR and SOCIAL CONTROL were combined to make a single SOCIAL CONTEXT dimension and INTRODUCTION and DISCUSSION CONTEXTS were combined to make a BACKGROUNDS dimension. Table 1 gives the resulting eight-dimensional classifier. Analysis Time steps were set to eight-year periods. The 1930-1992 growth rate of articles per time step for Child Development was 0.27, so the maximum

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acceptance level was 1.27. Tb avoid reifying a particular outcome (i.e., treating the first solution that works as the "way the world is"), two solutions were constructed for most dimensions. The first, called the "low growth solution," used a standard approach with initial usage rates (the *,-) set to the observed values for the first time step (1930-1937), growth rates to .27, acceptance levels to 1.27, and competitive success rates to the observed values for the final time step (1986-1992). A program (written in Visual Basic as an Excel macro) adjusted parameters in Eq. 11 to minimize the least squared differences between observed proportions and those based on Eq. 11. Proportions were then converted back to frequencies and the chi-square calculated. A significant difference (p < .05) between observed values and those calculated from the model (based on the chi-square) indicated that a good fit between the data and the model had not been found. When the chi-square was not significant, the set of parameter values resulting in the least squared difference was called the "low growth solution." After obtaining the low growth solution, one with high growth rates (above 300%) was sought. In this case, the initial parameter values were found by trial and error with the restriction that there was high growth for at least one practice in the dimension and the system did not collapse. The program was then used to refine the fit. Although it is rarely possible to find all "high growth solutions," in most cases the ones found had "numerically" lower least-squares and chi-square values than the low growth solutions. Nevertheless, since in most cases the latter had not resulted in significant differences between actual and expected frequencies, the high growth solutions cannot be said to be "statistically" better.

RESULTS

Table 2 gives the chi-square, degrees of freedom, and probabilities for both solutions for each dimension. All low growth solutions for background were significantly different from the data (the least significant was p < 10~7). For the other 15 low and high growth solutions, the probability values were far above significance, making it impossible to decide between the solutions on statistical grounds. Therefore, scientific meaning and converging evidence became more important for deciding between the solutions than statistical significance. Both low and high growth solutions are shown in Figures 1 to 8 along with projections for several future decades. The data for DEPENDENT VARIABLES (Figure 1) showed erratic oscillations with (a) a jump in the use of summed or enumerated scores during the postwar period, (b) a mirror-image decline in studies using experimenter con-

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Table 2. Statistics of Curve-Fitting Solutions that Used Low and High Potential Growth Rates Low Growth Dimension Dependent variables Data analysis Designs Age variable Social context Location Background Applications

X2

df

26.7

23 15 23 23 28 23 15 15

9.9 22.7 11.6 16.4 18.6 61.5 19.4

High Growth

P 0.27 0.83 0.48 0.98 0.96 0.72 7

io-

0.20

x2

df

P

7.43 4.75 7.44 4.48 15.3 12.2 12.8 11.9

23 15 23 23 27 23 15 15

0.999 0.994 0.999 0.9995 0.97 0.97 0.62 0.69

trolled observational techniques like limited or categorized free behaviors, and (c) accelerating growth in the last two decades of studies that combined categorized free behavior with other observations. The low growth solution did not track the large postwar changes but the high growth solution did. The frequency of the two major DATA ANALYSIS methods showed two hallmarks of dynamic systems: exponential growth and regular oscillation (see Figure 2). Since the latter is characteristic of fast growth, it is not surprising that the high growth solution produced an extremely close fit. For the high growth model, the potential growth rate for difference statistics was high enough to cause the regular oscillations which became more prominent as descriptive and correlational analyses were driven out.

Fig. 1. Best fitting low and high growth CPS models for DEPENDENT VARIABLES.

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Fig. 2. Best fitting low and high growth CPS models for DATA ANALYSIS. There was relatively little net change in designs during the period studied, but the 1950s showed a sharp adjustment downward in longitudinal studies that was slowly recovered up to the current decade (see Figure 3). For both solutions, microlongitudinal studies had second place growth and no competitive success while single session studies had the slowest growth. The zero growth of single session per task revealed this to be the default practice for the microsystem.

Fig. 3. Best fitting low and high growth CPS models for DESIGN.

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Fig. 4. Best low and high growth fit of the CPS models for AGE VARIABLES.

The "Wohlwill practice," age as a dependent variable, appeared in the early studies of physical growth, but declined rapidly in the absence of applications to more complex psychological processes (see Figure 4). There was oscillating, symmetrical growth (as for analysis of differences) of single age groups at the expense of multiple age groups. The oscillations were temporarily reversed in the early 1970s. Both the low growth and the high

Fig. 5. Best fitting low growth CPS models for SOCIAL CONTEXT.

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Fig. 6. Best fitting low and high growth CPS models for LOCATION. growth solutions for the AGE dimension produced excellent fits. The two solutions were, however, dynamically different. The low growth solution was produced with single age groups as a default practice, while the high growth solution produced an almost perfect match to the data by repeatedly overshooting the acceptance level. The most prominent event for SOCIAL CONTEXT was the decline of practices involving observation in normal social situations (see Figure 5). Using

Fig. 7. Best fitting CPS model for BACKGROUND.

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Fig. 8. Best fitting CPS model for APPLICATIONS. group tests (test alone) reached a peak in the 1970s and then declined. Combining a test with a significant other hovered steadily around 10% usage and individual testing by an experimenter showed a steady rise from almost no usage in the 1930s to a fourth of all the studies in the last eight-year time step studied. The low and high growth solutions were very similar with the low growth solution being produced by coding the curve-fitting program to cease adjusting growth levels when they met or exceeded 3.0. The three LOCATIONS practices were fairly evenly distributed (see Figure 6). Unspecified locations reached a peak of half of the studies in the early 1970s and then declined, but still accounted for more than a fourth of the studies published in the most recent time step. The use of natural settings without adding a laboratory component declined up through World War II and recovered slightly thereafter while laboratory or multiple settings showed modest growth in recent decades. With the low growth solution, unspecified locations became a default practice, which was maintained only by its competitive success rate. There was a surge in interdisciplinary BACKGROUNDS during World War II, followed by a steep decline in the late 1950s (see Figure 7). There was no low growth solution but a reasonably good high growth solution was found. This results in the choice of background being unusually volatile. In the early decades of Child Development, APPLICATIONS for researchers only dominated the articles (see Figure 8). There was a small postwar surge in applied articles and then a much larger surge in the sixties and seventies resulting in an even split in the two journals in recent decades. The two solutions generate interestingly different future scenarios. For the low growth solution, researchers only was the default practice and

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considering applications for others was dominant. With this solution, maintaining the current balance of the two practices would require every competitive encounter to be won by non-applied articles. If the high growth solution is correct, the field is in the midst of a crisis already—non-applie research will vanish from the journals within a few years.

DISCUSSION Major trends for the eight dimensions were nonlinear. Collectively, the high growth solutions tracked the data better than the low growth solutions, but only in the backgrounds case was the low growth solution significantly different from the data. This implies that corroborative evidence other than statistical significance are needed to decide on the correct parameter values. Trends, solutions, and known or needed corroborative evidence for individual dimensions are given below, with a collective summary afterwards. Dependent Variables There were dramatic changes during the 1950s in the use of summed or enumerated scores and limited or categorized free behaviors. During recent decades, as a result of accelerating growth in categorized free behavior, frequencies of all three practices converged. The low and high growth CPS solutions showed that random variation (low growth) or chaotic dynamics (high) can explain the effects. Since both solutions involve non-changing "state" variables, these findings present a challenge to historians who would argue that such changes are due to influences from idiosyncratic events like World War II or the baby boom. Data Analysis The use of difference statistics grew from a minority to 90% of the studies in oscillating steps. Though both solutions were very good, only the high growth solution tracked the regular oscillations in the data. Corroboration of a high growth rate for difference statistics is the well-documented pressure by editors for researchers to report "statistically significant" results (Gigerenzer et al., 1989). The CPS fit showed the danger of such prodding, since the high growth solution projects a crash for difference statistics within a few decades. This situation could be stabilized by developing a new data analysis practice—why not curve fitting using NDS?

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Designs Research DESIGNS were dominated by studies involving a single session per task, which peaked in the late 1950s. The low growth solution for designs had zero growth for this practice. Such default practices appear regardless of their acceptance levels and may even grow in usage until a more competitive practice that has not reached its acceptance level is established. Microlongitudinal designs appeared in early studies of body growth. They are rare but reappearing along with categorized free behavior and age as a dependent variable in the "microgenetic" studies of Kuhn (1995) and Siegler (1996).

Age Variable

Using the AGE VARIABLE as a dependent variable declined to near zero early in the period, while studies with single age groups increased in oscillating steps at the expense of multiple age groups in recent years. As for microlongitudinal designs, age as a dependent variable appeared in the early studies of physical growth but declined rapidly. Though both solutions produced excellent fits, the dynamics were so different that different editorial policies would be needed to support age as a dependent variable. The low growth solution implies that the potential growth of that practice must be increased; the high growth solution implies the reverse. Because dynamic modeling requires age as a dependent variable, the growth of developmental articles in this journal would be an index of which potential growth rate prevails.

Social Context The major SOCIAL CONTEXT trend involved an increase in the use of tests at the expense of practices involving observation in normal social situations, but tests unaccompanied by any other observation peaked in the early 1970s. For both solutions, the results show that developmental researchers interested in sociocultural issues may need to include some laboratory testing to be competitively successful. Moreover, the ability to make reliable observations of social practice seems to be a threatened skill. Dynamic modeling implied that editors could choose to support this skill by increasing its competitive success rate merely to 10%.

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Locations The three LOCATIONS practices were fairly evenly distributed throughout the period, even including unspecified locations, which peaked to a majority of studies in the early 1970s. Although there was also an excellent high growth solutions, with the good low growth solution, unspecified locations became a default practice that was maintained only by its competitive success rate. This outcome is quite meaningful, especially considering that for the latter half of the study period, Dirlam (1996) showed that this practice was more common among the eight most prolific authors than among other authors. Editors may be too familiar with these authors' settings to notice the missing descriptions. Failure to specify locations does not need acceptance to survive. Thus, there are good reasons to accept the low growth solution, even if it is not numerically superior. Backgrounds Other than a surge to nearly half the articles during World War II, interdisciplinary BACKGROUNDS represented between 10% and 25% of the studies. The large surge could not be fit with the low growth solution. Consequently, it might reflect an extra-system factor, like post-war consolidation of the field. However, if fast growth for disciplinary research appeared in a random sample of all developmental articles indexed in Psyclnfo in say, the 1970s, high growth would be corroborated. In that case, interdisciplinary work is projected to decline. It could be supported by increasing its competitive success rate from the 1% of the current fit to 33%. Because of the high potential growth, increasing it above 33% would threaten the microsystem with chaotic changes. Applications After hovering around 80% of studies for decades, APPLICATIONS for researchers only declined rapidly to half the studies by the early 1970s and remained there. The low growth solution required basic research to be a default practice. This is refuted by Danziger's (1990) evidence from several decades before the period of this study that applied research came first. The high growth solution, on the other hand, suggests that basic research articles will disappear in the journals studied by the next decade. There is external evidence for such an outcome. Near the end of the final time step studied, the American Psychological Society split from the American Psychological Association in 1988, in order to generate better support for sci-

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entific psychology (presumably including more emphasis on basic research). For both low and high growth solutions, there is stability only if one of the two practices is very dominant. Thus, the preservation of both practices requires either separating them into distinct systems (as accomplished by APS) or suppressing their growth rates. To distinguish them as a special type of competition, such dynamics might best be characterized as polarized practices. CONCLUSIONS: CPS MODELING OF CULTURAL AND HISTORICAL CHANGE

In general, curve fitting with the CPS model revealed several conclusions possible from multidimensional codings of approximately 1,000 samples. First, it refuted some models, such as the single carrying capacity model and the low growth model of backgrounds. Secondly, it revealed complex outcomes of small microsystems that were based solely on dynamic processes involving just four constants per practice. Third, it led to designing empirical tests of parameters, like Psyclnfo searches or looking for external events implied by the model (like the birth of APS or the existence of basic before applied research). Fourth, it identified unanticipated types of microsystem dynamics—default and polarized practices. Finally, the modeling process can help to prepare developmental researchers for the time, just a few decades from now, when computers can code human practices. The rewards for curve fitting with dynamic models derived from ecology are potentially great. Thus, in addition to the historical movement of people or organisms, this paper generalizes the scope of dynamic analysis to include the historical changes of sociocultural practices. Modeling consumer practices, voting behavior, practices of youth gangs, and risk taking (from driving behavior to building maintenance) are all areas of considerable social and economic consequence. Removing the agent-practice link is fundamental to seeing that individuals adopt different practices from one occurrence to another of a particular type of situation. Separating the person from the practice not only broadens the scope of dynamic modeling, it also opens up potential for creating healthy change. Perhaps, Quetelet and Verhulst came closer than many of their successors imagined to their dream of an astronomy of society. ACKNOWLEDGMENTS

The Mellon Foundation and Appalachian College Association funded all the developmental research coding. Final revisions were made while the

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senior author was a James McKeen Cattell Fellow at the Laboratory of Comparative Human Cognition of the University of California San Diego. Kurt Danziger commented on every step of the developmental research project, even suggesting a chaos theory analysis. Michael Cole provided much encour agement and significant commentary. Carla Overbay and Crystal Coe coded one-third of the developmental research articles. Daniel Fetters provided helpful mathematical input and Daniel Bowell located obsecure materials.

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