Transfer entropy computation using the Perron-Frobenius operator

We propose a method for computing the transfer entropy between time series using Ulam's approximation of the Perron-Frobenius (transfer) operator associated with the map generating the dynamics. Our method differs from standard transfer entropy estimators in that the invariant measure is estimated not directly from the data points, but from the invariant distribution of the transfer operator approximated from the data points. For sparse time series and low embedding dimension, the transfer operator is approximated using a triangulation of the attractor, whereas for data-rich time series or higher embedding dimension, we use a faster grid approach. We compare the performance of our methods with existing estimators such as the k nearest neighbors method and kernel density estimation method, using coupled instances of well known chaotic systems: coupled logistic maps and a coupled Rössler-Lorenz system. We find that our estimators are robust against moderate levels of noise. For sparse time series with less than 100 observations and low embedding dimension, our triangulation estimator shows improved ability to detect coupling directionality, relative to standard transfer entropy estimators.publishedVersio

On how the power supply shapes microbial survival

Understanding how environmental factors affect microbial survival is an important open problem in microbial ecology. Patterns of microbial community structure have been characterized across a wide range of different environmental settings, but the mechanisms generating these patterns remain poorly understood. Here, we use mathematical modelling to investigate fundamental connections between chemical power supply to a system and patterns of microbial survival. We reveal a complex set of interdependences between power supply and distributions of survival probability across microbial habitats, in a case without interspecific resource competition. We also find that different properties determining power supply, such as substrate fluxes and Gibbs energies of reactions, affect microbial survival in fundamentally different ways. Moreover, we show how simple connections between power supply and growth can give rise to complex patterns of microbial survival across physicochemical gradients, such as pH gradients. Our findings show the importance of taking energy fluxes into account in order to reveal fundamental connections between microbial survival and environmental conditions, and to obtain a better understanding of microbial population dynamics in natural environments.publishedVersio

På vei mot mer studentorientert undervisning og læring i geostatistikk

Artikkelforfatterne har våren 2017 for første gang undervist emnet Geostatistikk (GEOV301) ved Institutt for geovitenskap ved Universitetet i Bergen. Emnet har, i likhet med resten av emneporteføljen ved universitetet, vært gjenstand for omfattende revisjon i 2016-17. I denne prosessen har pedagogiske begreper som «Scholarship of Teaching and Learning» (SoTL), samstemt undervisning («constructive alignment») og beregningsbasert læring («computational learning») vært viktige. Vi har gjort store endringer i GEOV301, i to omganger— i januar og i mai 2017. Det ble lagt mye større vekt på anvendelser med moderne datateknologi, og studentene tok i bruk programvaren RStudio/R på sine PCer. Vi var to likestilte lærere samtidig tilstede i undervisningssituasjonen og fikk med dette etablert en kontinuerlig fagfellevurdering av undervisningen gjennom semesteret. Endringene førte til mye merarbeid både for undervisere og studenter. Med bakgrunn i dette er emnet modifisert ytterligere og antall studiepoeng er økt fra 5 til 10. Vi ser at det er behov for bedre og mer effektiv kommunikasjon med studentenes veiledere. I tillegg til å hjelpe studentene vil dette kunne ha en positiv lagbyggingseffekt innenfor et institutt med en kompleks faglig sammensetting

Correlating microbial community profiles with geochemical data in highly stratified sediments from the Arctic Mid-Ocean Ridge

Microbial communities and their associated metabolic activity in marine sediments have a profound impact on global biogeochemical cycles. Their composition and structure are attributed to geochemical and physical factors, but finding direct correlations has remained a challenge. Here we show a significant statistical relationship between variation in geochemical composition and prokaryotic community structure within deep-sea sediments. We obtained comprehensive geochemical data from two gravity cores near the hydrothermal vent field Loki’s Castle at the Arctic Mid-Ocean Ridge, in the Norwegian- Greenland Sea. Geochemical properties in the rift valley sediments exhibited strong centimeter-scale stratigraphic variability. Microbial populations were profiled by pyrosequencing from 15 sediment horizons (59,364 16S rRNA gene tags), quantitatively assessed by qPCR, and phylogenetically analyzed. Although the same taxa were generally present in all samples, their relative abundances varied substantially among horizons and fluctuated between Bacteria- and Archaea-dominated communities. By independently summarizing covariance structures of the relative abundance data and geochemical data, using principal components analysis, we found a significant correlation between changes in geochemical composition and changes in community structure. Differences in organic carbon and mineralogy shaped the relative abundance of microbial taxa. We used correlations to build hypotheses about energy metabolisms, particularly of the Deep Sea Archaeal Group, specific Deltaproteobacteria, and sediment lineages of potentially anaerobic Marine Group I Archaea. We demonstrate that total prokaryotic community structure can be directly correlated to geochemistry within these sediments, thus enhancing our understanding of biogeochemical cycling and our ability to predict metabolisms of uncultured microbes in deep-sea sediments

Mapping Microbial Abundance and Prevalence to Changing Oxygen Concentration in Deep-Sea Sediments Using Machine Learning and Differential Abundance

Oxygen constitutes one of the strongest factors explaining microbial taxonomic variability in deep-sea sediments. However, deep-sea microbiome studies often lack the spatial resolution to study the oxygen gradient and transition zone beyond the oxic-anoxic dichotomy, thus leaving important questions regarding the microbial response to changing conditions unanswered. Here, we use machine learning and differential abundance analysis on 184 samples from 11 sediment cores retrieved along the Arctic Mid-Ocean Ridge to study how changing oxygen concentrations (1) are predicted by the relative abundance of higher taxa and (2) influence the distribution of individual Operational Taxonomic Units. We find that some of the most abundant classes of microorganisms can be used to classify samples according to oxygen concentration. At the level of Operational Taxonomic Units, however, representatives of common classes are not differentially abundant from high-oxic to low-oxic conditions. This weakened response to changing oxygen concentration suggests that the abundance and prevalence of highly abundant OTUs may be better explained by other variables than oxygen. Our results suggest that a relatively homogeneous microbiome is recruited to the benthos, and that the microbiome then becomes more heterogeneous as oxygen drops below 25 μM. Our analytical approach takes into account the oft-ignored compositional nature of relative abundance data, and provides a framework for extracting biologically meaningful associations from datasets spanning multiple sedimentary cores.publishedVersio

På vei mot mer studentorientert undervisning og læring i geostatistikk

Artikkelforfatterne har våren 2017 for første gang undervist emnet Geostatistikk (GEOV301) ved Institutt for geovitenskap ved Universitetet i Bergen. Emnet har, i likhet med resten av emneporteføljen ved universitetet, vært gjenstand for omfattende revisjon i 2016-17. I denne prosessen har pedagogiske begreper som «Scholarship of Teaching and Learning» (SoTL), samstemt undervisning («constructive alignment») og beregningsbasert læring («computational learning») vært viktige. Vi har gjort store endringer i GEOV301, i to omganger— i januar og i mai 2017. Det ble lagt mye større vekt på anvendelser med moderne datateknologi, og studentene tok i bruk programvaren RStudio/R på sine PCer. Vi var to likestilte lærere samtidig tilstede i undervisningssituasjonen og fikk med dette etablert en kontinuerlig fagfellevurdering av undervisningen gjennom semesteret. Endringene førte til mye merarbeid både for undervisere og studenter. Med bakgrunn i dette er emnet modifisert ytterligere og antall studiepoeng er økt fra 5 til 10. Vi ser at det er behov for bedre og mer effektiv kommunikasjon med studentenes veiledere. I tillegg til å hjelpe studentene vil dette kunne ha en positiv lagbyggingseffekt innenfor et institutt med en kompleks faglig sammensetting

Causality from palaeontological time series

As custodians of deep time, palaeontologists have an obligation to seek the causes and consequences of long‐term evolutionary trajectories and the processes of ecosystem assembly and collapse. Building explicit process models on the relevant scales can be fraught with difficulties, and causal inference is typically limited to patterns of association. In this review, we discuss some of the ways in which causal connections can be extracted from palaeontological time series and provide an overview of three recently developed analytical frameworks that have been applied to palaeontological questions, namely linear stochastic differential equations, convergent cross mapping and transfer entropy. We outline how these methods differ conceptually, and in practice, and point to available software and worked examples. We end by discussing why a paradigm of dynamical causality is needed to decipher the messages encrypted in palaeontological patterns

Causality from palaeontological time series

As custodians of deep time, palaeontologists have an obligation to seek the causes and consequences of long‐term evolutionary trajectories and the processes of ecosystem assembly and collapse. Building explicit process models on the relevant scales can be fraught with difficulties, and causal inference is typically limited to patterns of association. In this review, we discuss some of the ways in which causal connections can be extracted from palaeontological time series and provide an overview of three recently developed analytical frameworks that have been applied to palaeontological questions, namely linear stochastic differential equations, convergent cross mapping and transfer entropy. We outline how these methods differ conceptually, and in practice, and point to available software and worked examples. We end by discussing why a paradigm of dynamical causality is needed to decipher the messages encrypted in palaeontological patterns

On how the power supply shapes microbial survival

Understanding how environmental factors affect microbial survival is an important open problem in microbial ecology. Patterns of microbial community structure have been characterized across a wide range of different environmental settings, but the mechanisms generating these patterns remain poorly understood. Here, we use mathematical modelling to investigate fundamental connections between chemical power supply to a system and patterns of microbial survival. We reveal a complex set of interdependences between power supply and distributions of survival probability across microbial habitats, in a case without interspecific resource competition. We also find that different properties determining power supply, such as substrate fluxes and Gibbs energies of reactions, affect microbial survival in fundamentally different ways. Moreover, we show how simple connections between power supply and growth can give rise to complex patterns of microbial survival across physicochemical gradients, such as pH gradients. Our findings show the importance of taking energy fluxes into account in order to reveal fundamental connections between microbial survival and environmental conditions, and to obtain a better understanding of microbial population dynamics in natural environments