Trond Reitan

Measuring system normality

A comparative analysis of transaction time-series is made, for light to moderately loaded hosts, motivated by the problem of anomaly detection in computers. Criteria for measuring the statistical state of hosts are examined. Applying a scaling transformation to the measured data, it is found that the distribution of fluctuations about the mean is closely approximated by a steady-state, maximum-entropy distribution, modulated by a periodic variation. The shape of the distribution, under these conditions, depends on the dimensionless ratio of the daily/weekly periodicity and the correlation length of the data. These values are persistent or even invariant. We investigate the limits of these conclusions, and how they might be applied in anomaly detection.

Ecological interactions on macroevolutionary time scales: clams and brachiopods are more than ships that pass in the night

Competition among organisms has ecological and evolutionary consequences. However, whether the consequences of competition are manifested and measureable on macroevolutionary time scales is equivocal. Marine bivalves and brachiopods have overlapping niches such that competition for food and space may occur. Moreover, there is a long-standing debate over whether bivalves outcompeted brachiopods evolutionarily, because brachiopod diversity declined through time while bivalve diversity increased. To answer this question, we estimate the origination and extinction dynamics of fossil marine bivalve and brachiopod genera from the Ordovician through to the Recent while simultaneously accounting for incomplete sampling. Then, using stochastic differential equations, we assess statistical relationships among diversification and sampling dynamics of brachiopods and bivalves and five paleoenvironmental proxies. None of these potential environmental drivers had any detectable influence on brachiopod or bivalve diversification. In contrast, elevated bivalve extinction rates causally increased brachiopod origination rates, suggesting that bivalves have suppressed brachiopod evolution.

Phenotypic evolution studied by layered stochastic differential equations

Time series of cell size evolution in unicellular marine algae (division Haptophyta; Coccolithus lineage), covering 57 million years, are studied by a system of linear stochastic differential equations of hierarchical structure.The data consists of size measurements of fossilized calcite platelets (coccoliths) that cover the living cell, found in deep-sea sediment cores from six sites in the world oceans and dated to irregularly points in time. To accommodate biological theory of populations tracking their fitness optima, and to allow potentially interpretable correlations in time and space, the model framework allows for an upper layer of partially observed site-specific population means, a layer of site-specific theoretical fitness optima and a bottom layer representing environmental and ecological processes. While the modeled process has many components, it is Gaussian and analytically tractable. A total of 710 model specifications within this framework are compared and inference is drawn with respect to model structure, evolutionary speed and the effect of global temperature.

Common species link global ecosystems to climate change: dynamical evidence in the planktonic fossil record

Common species shape the world around us, and changes in their commonness signify large-scale shifts in ecosystem structure and function. However, our understanding of long-term ecosystem response to environmental forcing in the deep past is centred on species richness, neglecting the disproportional impact of common species. Here, we use common and widespread species of planktonic foraminifera in deep-sea sediments to track changes in observed global occupancy (proportion of sampled sites at which a species is present and observed) through the turbulent climatic history of the last 65 Myr. Our approach is sensitive to relative changes in global abundance of the species set and robust to factors that bias richness estimators. Using three independent methods for detecting causality, we show that the observed global occupancy of planktonic foraminifera has been dynamically coupled to past oceanographic changes captured in deep-ocean temperature reconstructions. The causal inference does not imply a direct mechanism, but is consistent with an indirect, time-delayed causal linkage. Given the strong quantitative evidence that a dynamical coupling exists, we hypothesize that mixotrophy (symbiont hosting) may be an ecological factor linking the global abundance of planktonic foraminifera to long-term climate changes via the relative extent of oligotrophic oceans.

Generalized extreme value shape parameter and its nature for extreme precipitation using long time series and the Bayesian approach

ABSTRACT Assessing the probability of extreme precipitation events is consequential in civil planning. This requires an understanding of how return values change with return periods, which is essentially described by the generalized extreme value (GEV) shape parameter. Some works in the field suggest a constant shape parameter, while our analysis indicates a non-universal value. We re-analysed an older precipitation dataset (169 stations) extended by Norwegian data (71 stations). We showed that while each set seems to have a constant shape parameter, it differs between the two datasets, indicating regional differences. For a more comprehensive analysis of spatial effects, we examined a global dataset (1495 stations). We provided shape parameter maps for two models and found clear evidence that the shape parameter depends on elevation, while the effect of latitude remains uncertain. Our results confirm an explanation in terms of dominating precipitation systems based on a proxy derived from the Köppen-Geiger climate classification. EDITOR D. Koutsoyiannis ASSOCIATE EDITOR not assigned

Propagation of rating curve uncertainty in design flood estimation

Statistical flood frequency analysis is commonly performed based on a set of annual maximum discharge values which are derived from stage measurements via a stage-discharge rating curve model. Such design flood estimation techniques often ignore the uncertainty in the underlying rating curve model. Using data from eight gauging stations in Norway, we investigate the effect of curve and sample uncertainty on design flood estimation by combining results from a Bayesian multi-segment rating curve model and a Bayesian flood frequency analysis. We find that sample uncertainty is the main contributor to the design flood estimation uncertainty. However, under extrapolation of the rating curve, the uncertainty bounds for both the rating curve model and the flood frequency analysis are highly skewed and ignoring these features may underestimate the potential risk of flooding. We expect this effect to be even more pronounced in arid and semi-arid climates with a higher variability in floods. This article is protected by copyright. All rights reserved.

A risk analysis of disk backup or repository maintenance

We discuss a simple model of disk backups and other maintenance processes that include change to computer data. We determine optimal strategies for scheduling such processes. A maximum entropy model of random change provides a simple and intuitive guide to the process of sector based disk change and leads to an easily computable optimum time for backup that is robust to changes in the model. We conclude with some theoretical considerations about strategies for organizing backup information.

An unknown phanerozoic driver of brachiopod extinction rates unveiled by multivariate linear stochastic differential equations

Abstract. Whether the evolutionary dynamics of one group of organisms influence that of another group of organisms over the vast timescale of the geological record is a difficult question to tackle. This is not least because multiple factors can influence or mask the effects of potential driving forces on evolutionary dynamics of the focal group. Here, we show how an approach amenable to causality inference for time series, linear stochastic differential equations (SDEs), can be used in a multivariate fashion to shed light on driving forces of diversification dynamics across the Phanerozoic. Using a new, enhanced stepwise search algorithm, we searched through hundreds of models to converge on a model that best describes the dynamic relationships that drove brachiopod and bivalve diversification rates. Using this multivariate framework, we characterized a slow process (half-life of c. 42 Myr) that drove brachiopod extinction. This slow process has yet to be identified from the geological record. Using our new framework for analyzing multiple linear SDEs, we also corroborate our previous findings that bivalve extinction drove brachiopod origination in the sense that brachiopods tended to diversify at a greater rate when bivalves were removed from the system. It is also very likely that bivalves “self-regulate” in the sense that bivalve extinctions also paved the way for higher bivalve origination rates. Multivariate linear SDEs as we presented them here are likely useful for studying other dynamic systems whose signatures are preserved in the paleontological record.

Common species link global ecosystems to climate change

Common species shape the world around us, and changes in their commonness signify large-scale shifts in ecosystem structure and function1-4. Dominant taxa drive productivity and biogeochemical cycling, in direct interaction with abiotic components of the Earth system3,4. However, our understanding of the dynamic response of ecosystems to global environmental changes in the past is limited by our ability to robustly estimate fossil taxonomic richness5,6, and by our neglect of the importance of common species. To rectify this, we use observations of the most common and widespread species to track global changes in their distribution in the deep geological past. Our simple approach is robust to factors that bias richness estimators, including widely used sampling-standardization methods5, which we show are highly sensitive to variability in the species-abundance distribution. Causal analyses of common species frequency in the deep-sea sedimentary record detect a lagged response in the ecological prominence of planktonic foraminifera to oceanographic changes captured by deep-ocean temperature records over the last 65 million years, encompassing one of Earths major climate transitions. Our results demonstrate that common species can act as tracers of a past global ecosystem and its response to physical changes in Earths dynamic history.

Do not divide count data with count data; a story from pollination ecology with implications beyond

Studies in ecology are often describing observed variations in a certain ecological phenomenon by use of environmental explanatory variables. A common problem is that the numerical nature of the ecological phenomenon does not always fit the assumptions underlying traditional statistical tests. A text book example comes from pollination ecology where flower visits are normally reported as frequencies; number of visits per flower per unit time. Using visitation frequencies in statistical analyses comes with two major caveats: the lack of knowledge on its error distribution and that it does not include all information found in the data; 10 flower visits in 20 flowers is treated the same as recording 100 visits in 200 flowers. We simulated datasets with various “flower visitation distributions” over various numbers of flowers observed (exposure) and with different types of effects inducing variation in the data. The different datasets were then analyzed first with the traditional approach using number of visits per flower and then by using count data models. The analysis of count data gave a much better chance of detecting effects than the traditionally used frequency approach. We conclude that if the data structure, statistical analyses and interpretations of results are mixed up, valuable information can be lost.