Density delay in the evolution of organizational populations: a model and five empirical tests

Administrative Science Quarterly,  Sept, 1989  by Glenn R. Carroll,  Michael T. Hannan

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Our interest in the delayed effects of density stems partly from an interest in learning why density typically declines from its peak rather than fluctuating in a narrow range around the peak. One type of answer focuses on the effects of environmental change and the obsolescence of organization forms.

If strong inertial forces hamper organizations' capacities to reorganize rapidly, then populations of organizations existing in uncertain and changing environments eventually become obsolete. Organizations with strategies and structures fashioned in distant eras presumably fare badly in competition for members and resources. Eventually such diminished competitiveness leads to heightened mortality and perhaps to the disappearance of the population and the organizational form. Obsolescence processes undoubtedly have played a major role in shaping the world of organizations, and it is tempting to attribute the observed demographic pattern to them. In any concrete application, however, this type of explanation does little more than restate what can be observed in a historical trajectory of density. It does not account for the dynamics of the trajectories, the actual timing of the rise and fall in numbers. As an alternative to ad hoc explanations based on obsolescence, we suggest that ecological dynamics might also explain the observed pattern. The relevant dynamics involve density dependence in mortality rates in a slightly broadened model, one with delayed as well as contemporaneous effects of density on mortality rates. The model of density dependence described above assumes that the mortality of all organizations in a population responds to variations in density in the same way. An increase in density beyond a certain threshold (determined by the parameters of the model) increases the mortality rates of all organizations proportionately. That is, the mortality rate of any particular organization at a specific historical time is found by taking the rate implied by its age and other characteristics and multiplying it by the effect of the level of density that obtains at that time--the effect of density is contemporaneous. Another possibility is that organizations may be particularly sensitive to density at the time of founding. This would be consistent with Stinchcombe's (1965) well-known argument about imprinting of conditions of founding; below, we discuss a number of reasons why the argument might hold for effects of density at time of founding. Assuming for the moment that density at time of founding does affect later mortality, there are several implications. If the effect of density at time of founding persists, then organizations entering a population at high density have elevated rates of mortality for some time. As a consequence, the size of the population falls from the peak, unless the founding rate rises in compensation.(1) A similar scenario has received attention in the literature on mathematical population biology. Leslie (1959) proposed a model in which the mortality rate depends on contemporaneous density and conditions at time of birth. Citing research on human mortality, Leslie (1959: 152) observed that "It appears that each generation of young tends to carry throughout life a relative degree of mortality peculiar to itself, and it is supposed that this characteristic mortality ... represents the effect of environmental conditions experienced by each generation during the early years of its life in the population." For present purposes, what is important is that Leslie showed that adding delayed density dependence (with an implicit interaction with age structure) produced dampened cycles in trajectories of growth even when the environment does not vary.(2) This kind of process can generate the type of trajectory commonly observed for organizational populations. The appeal of Leslie's model leads us to ask whether density at time of founding might affect the mortality rate of "mature" organizations. We suggest that there are two related affirmative answers. The first concerns a "liability of resource scarcity." Intense competition at time of founding (due to high density) creates conditions of resource scarcity. When resources are scarce, new organizations that cannot move quickly from organizing to full-scale operation face very strong selection pressures. Those that survive the initial period of organizing presumably do not have the luxury of devoting time, attention, and resources to creating formal structures and perfecting stable, reproducible routines for making decisions and taking collective action. In cohorts of organizations facing such circumstances, staff members have little motivation for investing heavily in acquiring organization-specific skills, which is an essential part of developing reproducible routines. It might be difficult to recover fully from such deprived initial organizing. Inertial forces presumably operate in this context as well as others. That is, attempts at redesigning poorly fashioned structures may well encounter the risks identified by Hannan and Freeman (1984). If so, cohorts of organizations that experience high density at founding will tend to be inferior competitors at every age. A second consequence of high density at time of founding concerns "tight niche packing." When density is high, resources are subject to intense exploitation and few resources go unexploited. Since newly founded organizations can seldom compete head-to-head with established organizations, the new entrants tend to be pushed to the margins of resource distributions. Tight niche packing thus causes new organizations to attempt to exploit thinly spread and ephemeral resources. Even if they succeed at creating structures and routines for adapting successfully to the inferior regions of the resource space, in the course of doing so they commit themselves to persisting at the margins. The specialized learning of staff, the collective experience of the organization, and the organization's connections with the environment all become specialized to exploiting the inferior regions of the environment. Attempting to shift toward the richer center at some later time entails high risks of mortality during periods of protracted reorganization. If reorganization is successful, it brings the organization into competition with others specialized in exploiting the center. In either case, these marginal organizations have higher than average mortality rates. A reviewer has proposed a third possibility, namely that there is a "trial by fire." Suppose that each cohort of organizations has a distribution of unobserved frailty (to follow the terminology of Vaupel, Manton, and Stallard, 1979). Presumably, the most frail organizations are likely to fail early in their histories under almost any circumstance. Those with slightly less frailty may persist if founded in favorable environmental circumstances, but they will fail otherwise. Those with moderate frailty will tend to persist unless founding conditions are highly unfavorable, and so forth. Founding conditions affect population dynamics by altering the "post-trial" distributions of frailty by cohort rather than by elevating the mortality rates of individual organizations. In particular, cohorts founded in periods of high environmental stress, e.g., high density, have a lower mean frailty after the initial year than cohorts founded in favorable circumstances. As a consequence, they have lower mortality rates after the period of initial selection (Vaupel, Manton, and Stallard, 1979). In the imagery proposed by the reviewer, cohorts of organizations that survived the trial by fire have lower mortality rates than those that did not face the trial. The trial-by-fire hypothesis leads to a different prediction than the arguments about liability of scarcity and tight niche packing. A trial by fire affects the post-selection distribution of mortality rates in a population but does not elevate the rates for particular organizations. In other words, an organization that passes the trial has the same mortality rate it had before the trial. The arguments involving liability of scarcity and tight niche packing imply that mortality rates are elevated for all members of cohorts founded in periods of high density and that this increase persists over time. In order to learn whether density at time of founding has persistent effects on mortality rates, we pursue a variant of Leslie's model. Our model holds that density at time of founding matters--not time of founding per se. The difference is that two cohorts founded in different periods when density happened to be at the same level have the same rate according to our argument but not according to Leslie's. The arguments about the liability of scarcity and tight niche packing suggest that the effect of density at founding is monotonic and positive. It seems likely to us that such an effect has the same relative effect at all ages, which means that the absolute effect is largest at young ages, since the rate is highest at those ages. So we propose a model of mortality with the form: (6a) [Mathematical Expression Omitted] where [n.sub.a] denotes density at age a, and [n.sub.fi] denotes density at time of founding of the ith organization. We continue to assume that contemporaneous density has the nonmonotonic pattern of effects (at all ages) discussed above. We hypothesize that density at time of founding has a positive effect on the age-specific mortality rate and that this effect persists over time. In terms of the model above, the hypotheses are that (6b) [Theta.sub.1] [is less than] 0; [Theta.sub.2] [is greater than] 0; [Phi] [is greater than] 0. The trial-by-fire hypothesis leads to a different prediction. In this view, high density at time of founding increases the mortality rate of new organizations (this is an effect of contemporaneous density) but does not affect mortality rates of individual organizations conditional on their level of frailty. However, we do not observe frailty. What does this hypothesis imply about the relationship between density and the unconditional mortality rate after the founding period? The claim that density at time of founding affects mortality rates at that time is an instance of an effect of contemporaneous density. Net of the effect of contemporaneous density, would founding density affect later mortality? The answer seems to depend on one's conception of the length of the period of a trial by fire. We presume here that this trial occurs during the year of founding. Since the trial-by-fire hypothesis assumes that high founding density causes mortalities over a broader range of frailty, one interpretation is that the unconditional mortality rate is lower after the founding year for cohorts founded in periods of high density. In terms of the model in (6), this means that the persisting effect of founding density on the mortality rate is negative: [Phi] [is less than] 0.