Evolution on a Dancing Landscape: Organizations and Networks in Dynamic Blau Space

This article develops and tests an evolutionay model of the growth, decline, and demographic dynamics of voluntay organizations. The model demonstrates a strong analogy between the adaptive landscape of Sewall Wright (1931) and the exploitation surfaces generated by a model of member selection and retention for voluntay associations. The article connects the processes of membership recruitment and loss to the social networks connecting individuals. The model generates dynamic hypotheses about the time path of organizations in sociodemographic dimensions. A key idea in this model is that membership selection processes at the individual level produce adaptation in communities of organizations. The article concludes with an empirical example and some discussion of the implications of the model for a variety of research literatures. Predicting the behavior of empirical systems has proven to be an elusive goal for the social sciences. This article outlines a theory that predicts the growth, decline, and demographic changes of social groups. The theory posits a Darwinian mechanism of systematic variation, selection, and retention of members in groups. Social network theory provides a framework for understanding how social evolution (the transitions from hunting and gathering societies through the intervening stages to the contemporary industrial stage) has created the conditions for the Darwinian mechanism of the model. This study takes a brief tour through the macroevolutionary foundations of the theory to set the stage for the microevolutionary test of the model. The predictions tested in the article are in the short term over a period of less *Work on this article was supported by National ScienceFoundationgrants SES-8120666, SES8319899, and SES-8821365, Miller McPherson Principal Investigator. W e thank David Barron, Peter Blau, John Freeman, Michael Hannan, David Knoke, Peter Marsden, Susan Olzak, Pamela Popielarz, Lynn Smith-Lovin, and Jonathan Turner for comments on earlier versions of this article. Part of the analysis was conducted under a grant from the Cornell National Supercomputer Facility, a resource of the Cornell Theo y Center. Additional facilities were provided by the Cornell Institute for Social and Economic Research. Direct correspondence to J. Miller McPherson, the Department of Sociology, University of Arizona, Tucson, AZ 85721. O The University of North Carolina Press Social Forces, September 1991,70(1):19-42 20 / Social Forces 70:1, September 1991 than two decades. However, the mechanism of the model could in principle account for changes in the very long term. The core idea of the evolutionary model is that social groups exist in a multidimensional space of sociodemographic dimensions best identified with the work of Peter Blau, particularly his Inequality and Heterogeneity (1977). Since our interpretation of Blau is somewhat novel, we will try to distinguish clearly those occasions when we are adding to Blau from those when we are borrowing. We use voluntary associations (Knoke 1990; Smith & Freedman 1972) to illustrate the theory. These groups are a very interesting case for our theory because the entry and exit of the members are least constrained by macroinstitutional structures such as law and economy in late industrial societies. The Origins of Blau Space The received view1 of the early stages of human social evolution is that people existed in small hunter-gatherer social systems for tens of thousands of years (cf. Lenski & Lenski 1970). These groups were geographically mobile bands of ten to fifty individuals engaged in face-to-face everyday contact (cf. Sahlins 1972). The adult men appear to have hunted small game, while adult women and children gathered fruits, berries, and other vegetable material; the division of labor was based largely on age and sex. All social contact in such small systems was multiplex in that all connections among the people in the community had multiple components; they were simultaneously based on kinship, acquaintanceship, exchange, sustenance, sociality, and all other relations necessary to the survival of a small society (cf. Mauss 1966). As societies increased in scale, these small multiplex social networks differentiated into separate simplex networks spanning more people. In hunting and gathering societies, almost all social contacts had multiple facets; contacts were based on simultaneous multiple connections. Most people saw each other face to face, engaged in exchange relations, and were kin to one another. The increase in the size of society broke down the multiplex relations into their constituent (simplex) elements as they were spread over larger and larger numbers of contacts. As the division of labor became more developed, the bases of social relations became more diverse. The face-to-face power relationships of the band of twenty to fifty people who spent all their lives together slowly evolved into anonymous bureaucratic systems based on universalistic criteria. The day-to-day repetition of identical tasks involving the same communications with the same individuals were replaced by an ever increasing diversity of activities involving social networks of communication, exchange, migration, and acquaintanceship. Most of the major figures in sociological theory have a version of this transition. For instance, Durkheim (1933) spoke of the change in dynamic density because of the shift from mechanical to organic solidarity, while Toennies ([I887 1940) thought in terms of the transition from gemeinschaft to gesellschaft. Likewise, Simmel (1950) argued that increases in system size qualitatively changed the web of connections between individuals. Weber's interpretation (1947) of the growth of bureaucratic systems is sociological Organizations and Networks in Blau Space / 21 dogma. As Blau (1989) has indicated, the original objective of sociology was to understand the interdependence of these characteristics of society. The most important consequence of the change from the primal dense multiplex networks to sparse simplex nets based on increasingly specialized interactions is that the separation of the relations into their constituent parts produces dimensions of social life in which the management of social diversity becomes problematic for society. When power relations must span systems of millions of people, the bases of those relationships must become standardized and universalized. We no longer respond to each other as people with whom we share unique long-term experiences but as people with a given level of education, wealth, or occupational prestige. Thus, social order that depends on the unique history of interaction between small numbers of people in isolated bands is replaced by social order based on generalized dimensions of social esteem, rank, and sociodemographic characteristics.' Blau (1977,1989) used this idea to explore the proposition that the relations among individuals in modern industrial societies are shaped by properties of this space of sociodemographic dimensions. When the dimensions are strongly correlated, social relationships are constrained; one will not encounter women who are highly educated or grade school dropouts with large incomes. When the dimensions are less correlated, society is more diverse; one cannot predict one set of social characteristics from another. Thus, the correlations among the dimensions are essentially related to the number of them. When K dimensions are perfectly correlated, they operate as one. When K dimensions are uncorrelated, each dimension allows social differentiation along a new axis. What Blau leaves implicit in his theory is that the long run of history the transition from hunting and gathering to industrial modes of production is the transition from strong correlations in a limited number of dimensions to weaker and weaker correlations among an increasing number of these dimensions (but see Blau 1989). As multiplex relations based on small intensely focused groups give way to specialized relations spanning larger and larger systems, the proliferation of these specialized relations generates Blau space the dimensions in which social differentiation occurs (see also Redfield 1947, Schnore 1958, Smith [I7761 1971, and Spencer 1899). Organizations and Individuals in Blau Space A way of thinking about Blau's property space is that each individual occupies a point in a multidimensional coordinate system defined by the Blau variables such as education, age, and occupational prestige. The configuration of these points in Blau space determines the correlation of the dimensions at the system level. When the variables are strongly correlated, there are constraints on the distribution of points in the space; if occupational prestige and educational attainment are strongly related (cf. Blau & Duncan 1967), then most people in the system will be near the line of regression. When the variables are weakly correlated, the points are scattered in the space, and there is more room for social differentiation. As society increases in size and scale, multiple dimensions for ranking individuals come into being, and these multiple dimensions become 22 / Social Forces 70:1, September 1991 less and less correlated over time. The increasing number of outliers in the system (the individuals whose values on one Blau dimension are not consistent with their values on another) become identifiable social categories, with distinctive life chances and institutional structures. Social network researchers have long known that contacts between individuals in this space are not random. The probability of contact between two people is a declining function of distance in Blau space. This result occurs because the networks are homophilous; that is, the probability that two individuals are connected to each other in the network of social contacts (e.g. kinship, friendship, acquaintanceship) depends on their similarity (cf. McPherson & Smith-Louis 1982, 1987; Marsden 1987). Since similarity is an inverse function of the distance between the two individuals on any given Blau dimension (e.g., the farther apart two people are in years of education, the less similar they are), the distance between two points in Blau space determines the probability that the two points are ~onnected.~ Ilomophily vastly reduces the complexity of the network by translating the N individuals with R possible types of relationships into N individuals with K values on metric dimen~ions.~ The powerful idea in this model is that the connections that do not exist determine how the system behaves. These networks are always very sparse for communities larger than a few hundred. Given the finite capacity for human interaction, points in the network will be connected to only a very small proportion of the others in a large system; given homophily, most of the points connected will be close to each other in Blau space. Thus, processes such as the passage of information through large social networks are more determined by the absence of connections between individuals than by the presence of them.' Homophily becomes more important in determining transactions in the system as the size of the network increases. As we will see, the formation of voluntary groups depends on this fact. Since the networks are homophilous, activities that involve the mobilization of multiple individuals through the network will tend to be localized, since it is only locally that the network is dense enough to sustain the coordination of many individual^.^ This localization of activities explains why organizations formed through social networks develop distinctive niches in Blau space (McPherson 1983).' This effect is heightened because the internal processes of these organizations are often dependent upon "sociation," which is facilitated by similarity among the members and hindered by heterogeneity (McPherson & Smith-Lovin 1986,1987). Membership Growth and Decline as Natural Selection The recruitment of new members to organizations is conservative because the group replicates itself through homophilous connections. The group tends to stay in the same region of Blau space because the current members have connections primarily to people nearby in Blau space. If recruitment to a group depends on contact with more than one member, the conservative effect will be enhanced. When multiple contacts with members increase the probability of joining a group, then potential members nearer the center of the group niche are Organizations and Networks in Blau Space / 23 differentially selected; only in the interior of the group's niche are multiple contacts likely. Homophilous recruitment stabilizes the group in its current position in Blau space. This version of social dynamics is a classical Darwinian model of variation, selection, and retention parwin [I8591 1964). The population of individuals at risk for membership varies in the characteristics defined by the Blau dimensions. When potential members become actual members, their characteristics become the basis for the selection of further members. The stability of the membership pool in Blau space is shaped by homophily in the social network as an analogy to the genetic stability of populations of organisms in biotic communities. The fact that the replication of characteristics is not exact does not destroy the analogy. The stochastic nature of the selection process is balanced by the conservatism of the recruitment process. Each generation of members recruits similar new members through the constraints imposed by homophily in the social network. At the organizational level, the distribution of the individual characteristics is analogous to the distribution of genes in a biotic population. Organizations maintaining their niche recruit new members like themselves, just as stable biological populations produce the same distribution of genes from generation to generation. Normal processes of recruitment and attrition will result in stable niches through homophilous selection processes. When the population of members (the group) expands or contracts its niche space, it does so by recruiting or losing members at the edges of the niche. New members who are significantly different from the old are like mutations whose viability is being tested. If the new mutation survives (i.e., if the dissimilar member is retained), the group adapts in the direction of the new member whose connections to new potential members can generate more new members similar to the latest. If the new mutation dies (i.e., if the novel member leaves the group), the group maintains its old niche. Thus, selection of members produces adaptation (change in the position of the group) in Blau space. Competitive Dynamics The group replicates itself over time through the selection mechanism. When the systeni is in equilibrium, each group will stay in its niche, and the niches will be distributed regularly through Blau space by the competition of groups for the time and for other resources of the individuals. When two groups are located in the same niche, their attempts to consume the resources of the same people leads to competitive exclusion over time (Gause 1934). The resources of the individuals in the community are finite; when an increasing demand is made upon these resources by groups occupying the same niche, one or the other group will be excluded over time (Popielarz & McPherson 1991). As these forces equilibrate, the groups adjust to each other in the space. When a group is in a region not hotly contested by other groups, potential members in that region will join at a higher rate, and current members will stay longer. When a group is located in a densely occupied region, potential members will be less likely to join, and current members will be more likely to leave. The distribution 24 / Social Forces 70:1, September 1991 of group members across the Blau dimensions responds over time to the differential competitive pressures presented by other groups. The competitive pressures can vary in their effects on different parts of a group's niche. Groups facing increasing competitive pressure on all edges in Blau space will contract in Blau space as their peripheral members are lost to other groups. The one-to-one correspondence between volume in Blau space and membership diversity means that the group will grow less and less diverse as it shrinks in volume. If the group does not increase the density of its membership in the shrinking region of niche space, it will lose members. On the other hand, a group facing great competitive pressure in one direction of Blau space and less in the other direction will move through the space as it picks up members in one direction and loses them in the other. A group with reduced competitive pressures in all directions will expand its volume and become a generalist. Thus, differential competition can account for the location of groups in Blau space, their volume in that space, and their growth or decline in numbers. The next section explores circumstances leading to such differentials. The Carrying Capacity The potential of the pool of individuals in a given region of Blau space to support group activity is the carrying capacity. The system of organizations approximates the carrying capacity over time through the mechanisms of selection and competition. When a region of Blau space has few groups, it is underexploited, and the mechanism of the previous paragraph will lead to invasion by neighboring groups or the formation of new groups. When a region is overexploited, the carrying capacity will be exceeded, and groups will tend to move away from that region or decline in membership. The carrying capacity for groups is greater in some regions of Blau space than in others for several reasons. First, the number of individuals varies from region to region; Blau's Inequality and Heterogeneity (1977) explores the consequences of this fact. When dimensions are correlated, individuals are crowded into limited areas of the space, while other areas are vacant. For example, people will be clustered closely about the regression line relating education and occupational prestige when these dimensions are strongly related. This clustering reduces the available area in Blau space for organizations to exist; groups must be tightly packed around the regression line. Lower correlations allow groups to move farther and farther away from the line, as more people are dispersed. In the extreme case, two perfectly correlated dimensions are effectively reduced to one. On the other hand, when two dimensions are perfectly uncorrelated, people are maximally dispersed through the niche space, and group activity can occur at any location. Thus, the correlation between Blau dimensions affects the carrying capacity for groups in different areas of the space. A second reason for variation in the carrying capacity in Blau space is that the density of connections between people varies systematically. It is known that the number and range of social contacts varies with social class, age, and Organizations and Networks in Blau Space / 25 other sociodemographic characteristics (cf. Marsden 1987). Since these contacts form the channels through which the organization propagates itself, higher density of contacts in a local region facilitates group formation and persistence. When connections between people are sparse, groups recruiting through these links will have difficulty acquiring new members. At the limit, no matter how many people are in a region, organizations cannot form if there are no connections between individuals. Finally, other competitors for the time and other resources of the people in the region will set limits to the ability to sustain group activity. For instance, certain types of occupations (e.g., forest ranger) will interfere with voluntary group membership, while others will facilitate it (e.g., politician). Large families in low social status regions may consume more time that would otherwise be available for voluntary group activities than the smaller families of higher status individuals. The correlation between the average number of memberships and variables such as education, age, and income has been well established for decades (Babchuk & Edwards 1969, Bell & Force 1956; Lundberg, Komarovsky & McInery 1934; see review in Smith 1975). The carrying capacity of our model is a multidimensional interpretation of this well-known correlation? DYNAMICS OF EXPLOITATION The exploitation rate at any given time varies around the carrying capacity; perturbations and stochastic events produce short-term increases and decreases in the number of organizational memberships. Transient fluctuations above the carrying capacity will be brought back down by the greater competitive pressures in the overexploited region, while momentary dips below will be corrected by the increased rate of joining and retention of members in that region. These dynamics are illustrated in Figure 1. The carrying capacity, the dashed line, is the underlying rate at which the population of individuals can sustain organizational activity in the long term. The deviations from this underlying carrying capacity in the short term (the membership rate in cross section) produces effects on the gain and loss of members, effects that can be used to test the model. These deviations form an opportunity space for the organizations; their membership composition responds to a local excess of memberships as the rate of joining decreases and the rate of leaving increases. The net effect is for groups to move away from overexploited regions and to move toward underexploited regions. These dynamics are demonstrated in Figure 2, a hypothetical exploitation surface. The exploitation surface is the difference between the carrying capacity and the short-term rate of group membership the difference between the dashed and solid lines of Figure 1. This exploitation surface represents the gradient of high and low opportunity for the organizations in Blau space. Groups will move toward regions of underexploitation the valleys in the surface and away from regions of overexploitation the peaks in the surface. For instance, group A is located on a regular incline with greater opportunities located at higher levels of education. The group will lose more and gain fewer members in the low-education direction, while gaining more and losing fewer in the high-education direction. 26 / Social Forces 70:1, September 1991 FIGURE 1: Carrying Capacity and Membership Rate in One-Dimensional Blau Space