POWER OF STATISTICAL TESTS TO SUPPORT OR REFUTE THE PRESENCE OF MULTIPLE SPECIES OF THE SAME GENUS WHEN SAMPLE SIZES ARE SMALL

Among fossil rodents, specimens often consist of isolated teeth and many species have been erected based on the possession, or degree of development, of accessory structures of the tooth crown. Such characters have often been used to propose the presence of multiple closely related species within samples consisting of no more than a few dozen specimens. Recent studies have shown that significant changes in tooth form can result from relatively minor alterations in the timing of certain gene activations during development. These studies, combined with others on morphological variation in modern rodent populations, cast doubt on the validity of using accessory tooth structures to define and differentiate species of fossil rodents. This suggests that many of the characters historically used to identify species simply represent variation within populations. With this in mind, how does one argue for the presence of multiple species when dealing with isolated teeth and small sample sizes?

Under a null hypothesis of a single normally distributed species I tested the power of several statistical tests (Shapiro-Wilk Test of Normality, Hartigans’ Dip Test, and Cope and Lacy’s coefficient of variation method) to detect the presence of two species in a sample. I constructed a two-species model dataset with randomly generated tooth lengths and character states for two morphological characters. In the model, tooth length is normally distributed for each species; character states were generated under predefined ratios. I varied the difference between species means by increments of ¼ standard deviation, the frequency of each species within the population, and sample size for a total of 1734 possible scenarios. Under each scenario I performed 700 replicates of each test to determine how statistical power changed as conditions were altered. My model suggests that even with as much as 4 standard deviations between means these tests do not regularly exceed a statistical power of 0.80 until sample size reaches 40 or more total specimens. Species groups can be recognized in smaller samples when there is a significant correlation between size class and character state. However it is not possible to assign a single specimen to a species a priori based on the possession of a particular character state when variation exists within a population.