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Knowledge of DNA evolution is central to our understanding of biological history, but how fast does DNA change? Previously, pedigree and ancient DNA studies--focusing on evolution in the short term--have yielded molecular rate estimates substantially faster than those based on deeper phylogenies. It has recently been suggested that short-term, elevated molecular rates decay exponentially over 1-2 Myr to long-term, phylogenetic rates, termed "time dependency of molecular rates." This transition has potential to confound molecular inferences of demographic parameters and dating of many important evolutionary events. Here, we employ a novel approach--geologically dated changes in river drainages and isolation of fish populations--to document rates of mitochondrial DNA change over a range of temporal scales. This method utilizes precise spatiotemporal disruptions of linear freshwater systems and hence avoids many of the limitations associated with typical DNA calibration methods involving fossil data or island formation. Studies of freshwater-limited fishes across the South Island of New Zealand have revealed that genetic relationships reflect past, rather than present, drainage connections. Here, we use this link between drainage geology and genetics to calibrate rates of molecular evolution across nine events ranging in age from 0.007 Myr (Holocene) to 5.0 Myr (Pliocene). Molecular rates of change in galaxiid fishes from calibration points younger than 200 kyr were faster than those based on older calibration points. This study provides conclusive evidence of time dependency in molecular rates as it is based on a robust calibration system that was applied to closely related taxa, and analyzed using a consistent and rigorous methodology. The time dependency observed here appears short-lived relative to previous suggestions (1-2 Myr), which has bearing on the accuracy of molecular inferences drawn from processes operating within the Quaternary and mechanisms invoked to explain the decay of rates with time.

We discuss a method for analyzing data that are positively skewed and contain a substantial proportion of zeros. Such data commonly arise in ecological applications, when the focus is on the abundance of a species. The form of the distribution is then due to the patchy nature of the environment and/or the inherent heterogeneity of the species. The method can be used whenever we wish to model the data as a response variable in terms of one or more explanatory variables. The analysis consists of three stages. The first involves creating two sets of data from the original: one shows whether or not the species is present; the other indicates the logarithm of the abundance when it is present. These are referred to as the 'presence data' and the 'log-abundance' data, respectively. The second stage involves modelling the presence data using logistic regression, and separately modelling the log-abundance data using ordinary regression. Finally, the third stage involves combining the two models in order to estimate the expected abundance for a specific set of values of the explanatory variables. A common approach to analyzing this sort of data is to use a ln (y+c) transformation, where c is some constant (usually one). The method we use here avoids the need for an arbitrary choice of the value of c, and allows the modelling to be carried out in a natural and straightforward manner, using well-known regression techniques. The approach we put forward is not original, having been used in both conservation biology and fisheries. Our objectives in this paper are to (a) promote the application of this approach in a wide range of settings and (b) suggest that parametric bootstrapping be used to provide confidence limits for the estimate of expected abundance.

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