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.

The scale of population structure in Arabidopsis thaliana.

The population structure of an organism reflects its evolutionary history and influences its evolutionary trajectory. It constrains the combination of genetic diversity and reveals patterns of past gene flow. Understanding it is a prerequisite for detecting genomic regions under selection, predicting the effect of population disturbances, or modeling gene flow. This paper examines the detailed global population structure of Arabidopsis thaliana. Using a set of 5,707 plants collected from around the globe and genotyped at 149 SNPs, we show that while A. thaliana as a species self-fertilizes 97% of the time, there is considerable variation among local groups. This level of outcrossing greatly limits observed heterozygosity but is sufficient to generate considerable local haplotypic diversity. We also find that in its native Eurasian range A. thaliana exhibits continuous isolation by distance at every geographic scale without natural breaks corresponding to classical notions of populations. By contrast, in North America, where it exists as an exotic species, A. thaliana exhibits little or no population structure at a continental scale but local isolation by distance that extends hundreds of km. This suggests a pattern for the development of isolation by distance that can establish itself shortly after an organism fills a new habitat range. It also raises questions about the general applicability of many standard population genetics models. Any model based on discrete clusters of interchangeable individuals will be an uneasy fit to organisms like A. thaliana which exhibit continuous isolation by distance on many scales.

Disturbance, response, and persistence in self-organized forested communities: Analysis of robustness and resilience in five communities in Southern Indiana

We develop an analytic framework for the analysis of robustness in social-ecological systems (SESs) over time. We argue that social robustness is affected by the disturbances that communities face and the way they respond to them. Using Ostrom's ontological framework for SESs, we classify the major factors influencing the disturbances and responses faced by five Indiana intentional communities over a 15-year time frame. Our empirical results indicate that operational and collective-choice rules, leadership and entrepreneurship, monitoring and sanctioning, economic values, number of users, and norms/social capital are key variables that need to be at the core of future theoretical work on robustness of self-organized systems. © 2010 by the author(s).

On the multiple ecological roles of water in river networks

The distribution and movement of water can influence the state and dynamics of terrestrial and aquatic ecosystems through a diversity of mechanisms. These mechanisms can be organized into three general categories wherein water acts as (1) a resource or habitat for biota, (2) a vector for connectivity and exchange of energy, materials, and organisms, and (3) as an agent of geomorphic change and disturbance. These latter two roles are highlighted in current models, which emphasize hydrologic connectivity and geomorphic change as determinants of the spatial and temporal distributions of species and processes in river systems. Water availability, on the other hand, has received less attention as a driver of ecological pattern, despite the prevalence of intermittent streams, and strong potential for environmental change to alter the spatial extent of drying in many regions. Here we summarize long-term research from a Sonoran Desert watershed to illustrate how spatial patterns of ecosystem structure and functioning reflect shifts in the relative importance of different 'roles of water' across scales of drainage size. These roles are distributed and interact hierarchically in the landscape, and for the bulk of the drainage network it is the duration of water availability that represents the primary determinant of ecological processes. Only for the largest catchments, with the most permanent flow regimes, do flood-associated disturbances and hydrologic exchange emerge as important drivers of local dynamics. While desert basins represent an extreme case, the diversity of mechanisms by which the availability and flow of water influence ecosystem structure and functioning are general. Predicting how river ecosystems may respond to future environmental pressures will require clear understanding of how changes in the spatial extent and relative overlap of these different roles of water shape ecological patterns. © 2013 Sponseller et al.