Climatic stability in the Brazilian Cerrado: implications for biogeographical connections of South American savannas, species richness and conservation in a biodiversity hotspot : Climatic stability and biodiversity in the Cerrado

A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.

A latitudinal gradient in biodiversity has existed since before the time of the dinosaurs, yet how and why this gradient arose remains unresolved. Here we review two major hypotheses for the origin of the latitudinal diversity gradient. The time and area hypothesis holds that tropical climates are older and historically larger, allowing more opportunity for diversification. This hypothesis is supported by observations that temperate taxa are often younger than, and nested within, tropical taxa, and that diversity is positively correlated with the age and area of geographical regions. The diversification rate hypothesis holds that tropical regions diversify faster due to higher rates of speciation (caused by increased opportunities for the evolution of reproductive isolation, or faster molecular evolution, or the increased importance of biotic interactions), or due to lower extinction rates. There is phylogenetic evidence for higher rates of diversification in tropical clades, and palaeontological data demonstrate higher rates of origination for tropical taxa, but mixed evidence for latitudinal differences in extinction rates. Studies of latitudinal variation in incipient speciation also suggest faster speciation in the tropics. Distinguishing the roles of history, speciation and extinction in the origin of the latitudinal gradient represents a major challenge to future research.