Hirsch's (1982) maintenance of variance extension technique for filling in missing observations or producing a unique extended streamflow sequence with a specified mean and variance is generalized to reproduce also the correlation between the variate of interest and other variables. The technique is used to extend several seasonal streamflow forecast series so that the generated forecasts have the appropriate mean, variance, and forecasting power. A multivariate model is developed which can extend several series simultaneously.

The sampling error variances

No abstract

Ecological communities are inherently dynamic: species constantly turn over within years, months, weeks, or even days. These temporal shifts in community composition determine species interactions, energy flow, nutrients, information, diseases, and how perturbations cascade through the system. Yet, our understanding of community structure has relied heavily on static approaches that do not capture key features of this dynamic temporal dimension of communities. Here we propose a conceptual and methodological framework to quantify and analyze this temporal dimension. Conceptually, we split the temporal structure into two definitive features, sequence, and duration, and discuss how they are linked to key concepts in ecology. We then outline how to capture these definitive features using perspectives from temporal graph theory. While we focus on how ongoing research in phenology and species interactions easily integrates into our proposed framework, we also describe how this framework applies to other outstanding questions in community ecology. As climate change reshuffles ecological communities worldwide, integrating the temporal dimensions of communities is not only imperative to resolve the fundamental processes that shape natural ecosystems, but also essential to predict how these systems may change in the future.