Palaeontologists characterize mass extinctions as times when the Earth loses more than three-quarters of its species in a geologically short interval, as has happened only five times in the past 540 million years or so. Biologists now suggest that a sixth mass extinction may be under way, given the known species losses over the past few centuries and millennia. Here we review how differences between fossil and modern data and the addition of recently available palaeontological information influence our understanding of the current extinction crisis. Our results confirm that current extinction rates are higher than would be expected from the fossil record, highlighting the need for effective conservation measures.

Founder-event speciation, where a rare jump dispersal event founds a new genetically isolated lineage, has long been considered crucial by many historical biogeographers, but its importance is disputed within the vicariance school. Probabilistic modeling of geographic range evolution creates the potential to test different biogeographical models against data using standard statistical model choice procedures, as long as multiple models are available. I re-implement the Dispersal-Extinction-Cladogenesis (DEC) model of LAGRANGE in the R package BioGeoBEARS, and modify it to create a new model, DEC + J, which adds founder-event speciation, the importance of which is governed by a new free parameter, [Formula: see text]. The identifiability of DEC and DEC + J is tested on data sets simulated under a wide range of macroevolutionary models where geography evolves jointly with lineage birth/death events. The results confirm that DEC and DEC + J are identifiable even though these models ignore the fact that molecular phylogenies are missing many cladogenesis and extinction events. The simulations also indicate that DEC will have substantially increased errors in ancestral range estimation and parameter inference when the true model includes + J. DEC and DEC + J are compared on 13 empirical data sets drawn from studies of island clades. Likelihood-ratio tests indicate that all clades reject DEC, and AICc model weights show large to overwhelming support for DEC + J, for the first time verifying the importance of founder-event speciation in island clades via statistical model choice. Under DEC + J, ancestral nodes are usually estimated to have ranges occupying only one island, rather than the widespread ancestors often favored by DEC. These results indicate that the assumptions of historical biogeography models can have large impacts on inference and require testing and comparison with statistical methods.

Localized ecological systems are known to shift abruptly and irreversibly from one state to another when they are forced across critical thresholds. Here we review evidence that the global ecosystem as a whole can react in the same way and is approaching a planetary-scale critical transition as a result of human influence. The plausibility of a planetary-scale 'tipping point' highlights the need to improve biological forecasting by detecting early warning signs of critical transitions on global as well as local scales, and by detecting feedbacks that promote such transitions. It is also necessary to address root causes of how humans are forcing biological changes.

The methods employed in historical biogeography are very diverse and include historical narrative, panbiogeography (Heads 2012, Waters et al. 2013), cladistic biogeography, multistate character methods, and ancestral state methods specialized for biogeography. The latter methods, which have become very popular, and been used and cited in hundreds of published analyses, include the parsimony-based Dispersal-Vicariance Analysis (DIVA; Ronquist 1997), and the likelihood-based Dispersal-Extinction Cladogenesis (DEC) model of the LAGRANGE program (Ree 2005, Ree and Smith 2008). A variety of new methods have also recently been proposed, including pseudo-Bayesian versions of DIVA and LAGRANGE (e.g., Wood et al. 2013). Another new method is BayArea, a Bayesian technique which samples geographical histories along phylogenetic branches jointly with the sampling of parameter values (Landis et al. 2013). Each method described above relies on some model of geographic range evolution, explicitly or implicitly, and therefore makes some assumption about the processes that have produced the geographic ranges of observed taxa. These assumptions about process typically have a much larger impact on conclusions about biogeographical history than differences in statistical procedure (e.g., parsimony, likelihood, or Bayesian inference). However, thus far there has been no method to determine which processes are most important, nor to determine which available model best fits the geographical and phylogenetic data for any particular clade. This was the problem I addressed in my thesis (Matzke 2013a).

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a "data-augmentation" approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea.

The methods employed in historical biogeography are very diverse and include historical narrative, panbiogeography (Heads 2012, Waters et al. 2013), cladistic biogeography, multistate character methods, and ancestral state methods specialized for biogeography. The latter methods, which have become very popular, and been used and cited in hundreds of published analyses, include the parsimony-based Dispersal-Vicariance Analysis (DIVA; Ronquist 1997), and the likelihood-based Dispersal-Extinction Cladogenesis (DEC) model of the LAGRANGE program (Ree 2005, Ree and Smith 2008). A variety of new methods have also recently been proposed, including pseudo-Bayesian versions of DIVA and LAGRANGE (e.g., Wood et al. 2013). Another new method is BayArea, a Bayesian technique which samples geographical histories along phylogenetic branches jointly with the sampling of parameter values (Landis et al. 2013). Each method described above relies on some model of geographic range evolution, explicitly or implicitly, and therefore makes some assumption about the processes that have produced the geographic ranges of observed taxa. These assumptions about process typically have a much larger impact on conclusions about biogeographical history than differences in statistical procedure (e.g., parsimony, likelihood, or Bayesian inference). However, thus far there has been no method to determine which processes are most important, nor to determine which available model best fits the geographical and phylogenetic data for any particular clade. This was the problem I addressed in my thesis (Matzke 2013a).

Contents 38I.38II.Approaches for reconstructing refugia: strengths, limitations and recent advances39III.46IV.47V.48VI.4949References49 Summary Climate refugia, locations where taxa survive periods of regionally adverse climate, are thought to be critical for maintaining biodiversity through the glacial–interglacial climate changes of the Quaternary. A critical research need is to better integrate and reconcile the three major lines of evidence used to infer the existence of past refugia – fossil records, species distribution models and phylogeographic surveys – in order to characterize the complex spatiotemporal trajectories of species and populations in and out of refugia. Here we review the complementary strengths, limitations and new advances for these three approaches. We provide case studies to illustrate their combined application, and point the way towards new opportunities for synthesizing these disparate lines of evidence. Case studies with European beech, Qinghai spruce and Douglas‐fir illustrate how the combination of these three approaches successfully resolves complex species histories not attainable from any one approach. Promising new statistical techniques can capitalize on the strengths of each method and provide a robust quantitative reconstruction of species history. Studying past refugia can help identify contemporary refugia and clarify their conservation significance, in particular by elucidating the fine‐scale processes and the particular geographic locations that buffer species against rapidly changing climate.

Aim The tomato family Solanaceae is distributed on all major continents except Antarctica and has its centre of diversity in South America. Its worldwide distribution suggests multiple long-distance dispersals within and between the New and Old Worlds. Here, we apply maximum likelihood (ML) methods and newly developed biogeographical stochastic mapping (BSM) to infer the ancestral range of the family and to estimate the frequency of dispersal and vicariance events resulting in its present-day distribution.Location Worldwide.Methods Building on a recently inferred megaphylogeny of Solanaceae, we conducted ML model fitting of a range of biogeographical models with the program 'BioGeoBEARS'. We used the parameters from the best fitting model to estimate ancestral range probabilities and conduct stochastic mapping, from which we estimated the number and type of biogeographical events. ResultsOur best model supported South America as the ancestral area for the Solanaceae and its major clades. The BSM analyses showed that dispersal events, particularly range expansions, are the principal mode by which members of the family have spread beyond South America.Main conclusions For Solanaceae, South America is not only the family's current centre of diversity but also its ancestral range, and dispersal was the principal driver of range evolution. The most common dispersal patterns involved range expansions from South America into North and Central America, while dispersal in the reverse direction was less common. This directionality may be due to the early build-up of species richness in South America, resulting in large pool of potential migrants. These results demonstrate the utility of BSM not only for estimating ancestral ranges but also in inferring the frequency, direction and timing of biogeographical events in a statistically rigorous framework.