Computing ancestral ranges via the Dispersion Extinction and Cladogensis (DEC) model of biogeography is characterized by an exponential number of states relative to the number of regions considered. This is because the DEC model requires computing a large matrix exponential, which typically accounts for up to 80% of overall runtime. Therefore, the kinds of biogeographical analyses that can be conducted under the DEC model are limited by the number of regions under consideration. In this work, we present a completely redesigned efficient version of the popular tool Lagrange which is up to 49 times faster with multi-threading enabled, and is also 26 times faster when using only one thread. We call this new version Lagrange-NG (Lagrange-Next Generation). The increased computational efficiency allows Lagrange-NG to analyze datasets with a large number of regions in a reasonable amount of time, up to 12 regions in approximately 18 minutes. We achieve these speedups using a relatively new method of computing the matrix exponential based on Krylov subspaces. In order to validate the correctness of Lagrange-NG, we also introduce a novel metric on range distributions for trees so that researchers can assess the difference between any two range inferences. Finally, Lagrange-NG exhibits substantially higher adherence to coding quality standards. It improves a respective software quality indicator as implemented in the SoftWipe tool from average (5.5; Lagrange) to high (7.8; Lagrange-NG). Lagrange-NG is freely available under GPL2.

Retrophylogenomics makes use of genome-wide retrotransposon presence/absence insertion patterns to resolve questions in phylogeny and population genetics. In the genomics era, evaluating high-throughput data requires the associated development of appropriately powerful statistical tools. The currently used KKSC 3-lineage statistical test for estimating the significance of retrophylogenomic data is limited by the number of possible tree topologies it can assess in one step. To improve on this, we have extended the analysis to simultaneously compare 4-lineages, enabling us to evaluate ten distinct presence/absence insertion patterns for 26 possible tree topologies plus 129 trees with different incidences of hybridization or introgression. The new tool provides statistics for cases involving multiple ancestral hybridizations/introgressions, ancestral incomplete lineage sorting, bifurcation, and polytomy. The test is embedded in a user-friendly web R-application (http : // retrogenomics.uni-muenster.de:3838/hammlet/) and is available for use by the scientific community.

Understanding the origins of diversity and the factors that drive some clades to be more diverse than others are important issues in evolutionary biology. Sophisticated SSE (state-dependent speciation and extinction) models provide insights into the association between diversification rates and the evolution of a trait. The empirical data used in SSE models and other methods is normally imperfect, yet little is known about how this can affect these models. Here, we evaluate the impact of common phylogenetic issues on inferences drawn from SSE models. Using simulated phylogenetic trees and trait information, we fitted SSE models to determine the effects of sampling fraction (phylogenetic tree completeness) and sampling fraction misspecification on model selection and parameter estimation (speciation, extinction, and transition rates) under two sampling regimes (random and taxonomically biased). As expected, we found that both model selection and parameter estimate accuracies are reduced at lower sampling fractions (i.e., low tree completeness). Furthermore, when sampling of the tree is imbalanced across subclades and tree completeness is ≤ 60%, rates of false positives increase and parameter estimates are less accurate, compared to when sampling is random. Thus, when applying SSE methods to empirical datasets, there are increased risks of false inferences of trait dependent diversification when some sub-clades are heavily under-sampled. Mis-specifying the sampling fraction severely affected the accuracy of parameter estimates: parameter values were over-estimated when the sampling fraction was specified as lower than its true value, and under-estimated when the sampling fraction was specified as higher than its true value. Our results suggest that it is better to cautiously under-estimate sampling efforts, as false positives increased when the sampling fraction was over-estimated. We encourage SSE studies where the sampling fraction can be reasonably estimated and provide recommended best practices for SSE modelling.