A trait-based approach to understand the evolution of complex coalitions in male mammals

Numerous rules-of-thumb have been suggested for determining the minimum number of subjects required to conduct multiple regression analyses. These rules-of-thumb are evaluated by comparing their results against those based on power analyses for tests of hypotheses of multiple and partial correlations. The results did not support the use of rules-of-thumb that simply specify some constant (e.g., 100 subjects) as the minimum number of subjects or a minimum ratio of number of subjects (N) to number of predictors (m). Some support was obtained for a rule-of-thumb that N ≥ 50 + 8 m for the multiple correlation and N ≥104 + m for the partial correlation. However, the rule-of-thumb for the multiple correlation yields values too large for N when m ≥ 7, and both rules-of-thumb assume all studies have a medium-size relationship between criterion and predictors. Accordingly, a slightly more complex rule-of thumb is introduced that estimates minimum sample size as function of effect size as well as the number of predictors. It is argued that researchers should use methods to determine sample size that incorporate effect size.

Molecular phylogenetic studies have resolved placental mammals into four major groups, but have not established the full hierarchy of interordinal relationships, including the position of the root. The latter is critical for understanding the early biogeographic history of placentals. We investigated placental phylogeny using Bayesian and maximum-likelihood methods and a 16.4-kilobase molecular data set. Interordinal relationships are almost entirely resolved. The basal split is between Afrotheria and other placentals, at about 103 million years, and may be accounted for by the separation of South America and Africa in the Cretaceous. Crown-group Eutheria may have their most recent common ancestry in the Southern Hemisphere (Gondwana).