Prediction in dynamic models with time-dependent conditional variances

This paper considers forecasting the conditional mean and variance from a single-equation dynamic model with autocorrelated disturbances following an ARMA process, and innovations with time-dependent conditional heteroskedasticity as represented by a linear GARCH process. Expressions for the minimum MSE predictor and the conditional MSE are presented. We also derive the formula for all the theoretical moments of the prediction error distribution from a general dynamic model with GARCH(1, 1) innovations. These results are then used in the construction of ex ante prediction confidence intervals by means of the Cornish-Fisher asymptotic expansion. An empirical example relating to the uncertainty of the expected depreciation of foreign exchange rates illustrates the usefulness of the results. © 1992.

From offshore to onshore: multiple origins of shallow-water corals from deep-sea ancestors.

Shallow-water tropical reefs and the deep sea represent the two most diverse marine environments. Understanding the origin and diversification of this biodiversity is a major quest in ecology and evolution. The most prominent and well-supported explanation, articulated since the first explorations of the deep sea, holds that benthic marine fauna originated in shallow, onshore environments, and diversified into deeper waters. In contrast, evidence that groups of marine organisms originated in the deep sea is limited, and the possibility that deep-water taxa have contributed to the formation of shallow-water communities remains untested with phylogenetic methods. Here we show that stylasterid corals (Cnidaria: Hydrozoa: Stylasteridae)--the second most diverse group of hard corals--originated and diversified extensively in the deep sea, and subsequently invaded shallow waters. Our phylogenetic results show that deep-water stylasterid corals have invaded the shallow-water tropics three times, with one additional invasion of the shallow-water temperate zone. Our results also show that anti-predatory innovations arose in the deep sea, but were not involved in the shallow-water invasions. These findings are the first robust evidence that an important group of tropical shallow-water marine animals evolved from deep-water ancestors.

R Markdown: Integrating A Reproducible Analysis Tool into Introductory Statistics

Nolan and Temple Lang argue that “the ability to express statistical computations is an es- sential skill.” A key related capacity is the ability to conduct and present data analysis in a way that another person can understand and replicate. The copy-and-paste workflow that is an artifact of antiquated user-interface design makes reproducibility of statistical analysis more difficult, especially as data become increasingly complex and statistical methods become increasingly sophisticated. R Markdown is a new technology that makes creating fully-reproducible statistical analysis simple and painless. It provides a solution suitable not only for cutting edge research, but also for use in an introductory statistics course. We present experiential and statistical evidence that R Markdown can be used effectively in introductory statistics courses, and discuss its role in the rapidly-changing world of statistical computation.

Natural hybridization between genera that diverged from each other approximately 60 million years ago.

A fern from the French Pyrenees-×Cystocarpium roskamianum-is a recently formed intergeneric hybrid between parental lineages that diverged from each other approximately 60 million years ago (mya; 95% highest posterior density: 40.2-76.2 mya). This is an extraordinarily deep hybridization event, roughly akin to an elephant hybridizing with a manatee or a human with a lemur. In the context of other reported deep hybrids, this finding suggests that populations of ferns, and other plants with abiotically mediated fertilization, may evolve reproductive incompatibilities more slowly, perhaps because they lack many of the premating isolation mechanisms that characterize most other groups of organisms. This conclusion implies that major features of Earth's biodiversity-such as the relatively small number of species of ferns compared to those of angiosperms-may be, in part, an indirect by-product of this slower "speciation clock" rather than a direct consequence of adaptive innovations by the more diverse lineages.

Olfactory Receptor Subgenomes Linked with Broad Ecological Adaptations in Sauropsida.

Olfactory receptors (ORs) govern a prime sensory function. Extant birds have distinct olfactory abilities, but the molecular mechanisms underlining diversification and specialization remain mostly unknown. We explored OR diversity in 48 phylogenetic and ecologically diverse birds and 2 reptiles (alligator and green sea turtle). OR subgenomes showed species- and lineage-specific variation related with ecological requirements. Overall 1,953 OR genes were identified in reptiles and 16,503 in birds. The two reptiles had larger OR gene repertoires (989 and 964 genes, respectively) than birds (182-688 genes). Overall, birds had more pseudogenes (7,855) than intact genes (1,944). The alligator had significantly more functional genes than sea turtle, likely because of distinct foraging habits. We found rapid species-specific expansion and positive selection in OR14 (detects hydrophobic compounds) in birds and in OR51 and OR52 (detect hydrophilic compounds) in sea turtle, suggestive of terrestrial and aquatic adaptations, respectively. Ecological partitioning among birds of prey, water birds, land birds, and vocal learners showed that diverse ecological factors determined olfactory ability and influenced corresponding olfactory-receptor subgenome. OR5/8/9 was expanded in predatory birds and alligator, suggesting adaptive specialization for carnivory. OR families 2/13, 51, and 52 were correlated with aquatic adaptations (water birds), OR families 6 and 10 were more pronounced in vocal-learning birds, whereas most specialized land birds had an expanded OR family 14. Olfactory bulb ratio (OBR) and OR gene repertoire were correlated. Birds that forage for prey (carnivores/piscivores) had relatively complex OBR and OR gene repertoires compared with modern birds, including passerines, perhaps due to highly developed cognitive capacities facilitating foraging innovations.