Published online by Cambridge University Press: 15 December 2009
Since Eldredge and Gould (1972) published their seminal paper on punctuated equilibrium, the field of evolutionary paleontology has been wracked by sometimes bitter disputes over the apparent reality or unreality of evolutionary stasis (Gould and Eldredge, 1977; Gingerich, 1985). Arguments have been advanced for stasis in lineages of protists (Wei and Kennett, 1988), invertebrates (Stanley and Yang, 1987), and vertebrates (Lich, 1990); see Barnosky (1987) and Levinton (1988) for additional references. Many, if not most, studies of morphological stasis in the fossil record have relied on qualitative and/or quantitative inferences about the behavior of location parameters (e.g., means and medians) as functions of geological time (usually estimated from stratigraphic and/or radiometric information). The simplicity and robustness of such tests cannot be gainsaid, but they do leave much unsaid. Figure 4.1 illustrates an artificial data set for which we would fail to reject the null hypothesis of evolutionary stasis when using such statistical tests as the nonparametric runs test (Sokal and Rohlf, 1981) or Lande's (1986) recommended test regarding the overlap of standard deviations about the means. Despite this conclusion we can see an “obvious” evolutionary trend in Z, the variable of interest. An alternative to such procedures is to examine the behavior of dispersion parameters. The purpose of this chapter is to introduce the geostatistical technique of variogram analysis to evolutionary paleontology as a way to supplement location inferences with dispersion inferences, specifically in the case of the Pliocene arvicoline rodent Cosomys primus (Lich, 1990; Anderson, Chapter 2, this volume).