Cumulative Advantage and Success-Breeds-Success: The Value of Time Pattern Analysis

Many different theoretical models can be made to fit model implies that the shape of the distribution of producempirical informetric data. For the case of the distribution across a population arises from the distribution of tion of papers across authors, the Success-Breeds-Sucproduction within each individual’s career. It is this applicess or Cumulative Advantage model is a popular candication which will be investigated in this article. In the date. This article shows that examination of the time general case, the Simon-Yule framework is expressed as pattern of production allows independent evaluation of the component processes that generate the distribution sources which produce items. For clarity, we will express of papers across authors. Specifically for inventors, the it as authors who produce publications in keeping with Cumulative Advantage model for increasing rate of prothe application chosen here. duction with experience is not confirmed. Furthermore, Burrell and Fenton (1993) clearly described the two the distribution of individual production is Poisson and the distribution of the rate of production across the popcomponent processes that must be present to generate data ulation fits the Gamma distribution. Thus, the non-unithat fits the distribution of publications across authors. form giftedness model is more appropriate for inventors. Readers who are unfamiliar with the typical distribution of publications across authors may wish to examine Figure 1. One of the component processes is the time pattern Introduction of individual production (publications counted over the years of a career) . The other is the distribution of producThe principle of Cumulative Advantage or Successtivity over the population of authors, analogous to the Breeds-Success has a long tradition in informetrics. Sidistribution of IQ over the general population. mon (1957) first proposed such a model, later named the However, there are models other than Cumulative AdSimon-Yule process. Many other authors (Chen, 1989; vantage which also fit the empirical laws. One popular Chen, Chong, & Tong, 1994; Fedorowicz, 1982; Price, 1976) added to this tradition. This process produces mathmodel (Allison, 1980a; Burrell & Fenton, 1993) assumes ematical functions showing that the primary informetric that the rate of publication for an individual is stable over laws (Lotka, Price, Pareto, Zipf, etc.) are related his or her career and that the distribution of the rate of (Bookstein, 1990; Fedorowicz, 1982; Tague, 1981). Most publication over the population determines the distriburecently Egghe and Rousseau (1995) and Glanzel and tion of publications over authors. This model generally Schubert (1995) have developed more generalized Suchas been nameless; here it will be denoted ‘‘non-uniform cess-Breeds-Success models. Clearly the principle of Sucgiftedness.’’ Thus, the Cumulative Advantage and noncess-Breeds-Success and Cumulative Advantage is alive uniform giftedness models reflect nearly opposite views and well as a model for general studies in informetrics. or opposite ends of a continuum. One objective of this The Simon-Yule framework is often expressed in such article is to demonstrate a method of determining which a way as to model the growth of the population of authors model is a better fit for a given set of empirical data, or publishing in a field. However, Schubert and Glanzel if a mixture of the models is appropriate. (1984), Allison, Long, and Krauze (1982), and Rao Lotka (1926) established the field of investigating the (1980) have expressed it explicitly as a model for the distribution of production of scientific publications over increasing rate of publication for individual authors. This authors. Lotka found that the number of authors fell as the square of the number of papers produced, since known as Lotka’s Law. It has since been generalized to be an Received April 29, 1997; revised July 18, 1997; accepted July 18, 1997. inverse power function with exponent ranging from about 1.8 to 3.8 (Pao, 1986). Since then, there has been considq 1998 John Wiley & Sons, Inc.