The incorporation of the random walk model into stratophenetic analysis marked a turning point by presenting a potential null model for microevolutionary patterns. Random walks are derived from a family of statistical fractals, and their statistics can be reconstructed using appropriate techniques. This paper lays the foundation for the explicit and uniform description of evolutionary mode in stratophenetic series using random walk null models and the information contained within incompletely preserved time series.
The method relies upon the iterative analysis of subseries of an original stratophenetic series by measuring the presence of deviations from statistical randomness as the lineage evolves. This measure, and its probability of significance (evaluated using a randomization test), forms the dimensions of a descriptive space for microevolutionary modes. Each stratophenetic series can then be viewed as a journey through this space. Computer simulation of various evolutionary modes demonstrates that different modes, for example stasis and gradualism, have differing trajectories and occupy different regions of the microevolutionary space. The method is applied to two published foraminiferal stratophenetic series, the Mio-Pliocene Globorotalia plesiotumida-tumida punctuated transition and an anagenetic trend in the Late Cretaceous Contusotruncana fornicata-contusa lineage. An anagenetic trend is strongly supported in the latter example, whereas transformation of the Globorotalia species seems to result from the fluctuating effectiveness of constraining processes.