scholarly journals Structural identifiability of the generalized Lotka–Volterra model for microbiome studies

2021 ◽  
Vol 8 (7) ◽  
pp. 201378
Author(s):  
Christopher H. Remien ◽  
Mariah J. Eckwright ◽  
Benjamin J. Ridenhour
Keyword(s):  
Time Series ◽  
Relative Abundance ◽  
Population Dynamic ◽  
Dynamic Models ◽  
Microbial Interactions ◽  
Volterra Model ◽  
Underlying Structure ◽  
Structural Identifiability ◽  
Abundance Data ◽  
Relative Abundances

Population dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research, including predicting how populations change over time, determining how manipulations of microbiomes affect dynamics and designing synthetic microbiomes to perform tasks. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka–Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka–Volterra model. We used structural identifiability analyses to determine the extent to which a time series of relative abundances can be used to parametrize the generalized Lotka–Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Using synthetic data of a simple community for which we know the underlying structure, local practical identifiability analysis showed that modest amounts of both process and measurement error do not fundamentally affect these identifiability properties.

scholarly journals Parameter Identifiability of the Generalized Lotka-Volterra Model for Microbiome Studies

2018 ◽  
Author(s):  
Christopher H Remien ◽  
Mariah J Eckwright ◽  
Benjamin J Ridenhour
Keyword(s):  
Time Series ◽  
Relative Abundance ◽  
Population Dynamic ◽  
Dynamic Models ◽  
Volterra Model ◽  
Sufficient Information ◽  
Absolute Abundance ◽  
Abundance Data ◽  
Relative Abundances ◽  
Over Time

AbstractBackgroundPopulation dynamic models can be used in conjunction with time series of species abundances to infer interactions. Understanding microbial interactions is a prerequisite for numerous goals in microbiome research; predicting how populations change over time, determining how manipulations of microbiomes affect dynamics, and designing synthetic microbiomes to perform tasks are just a few examples. As such, there is great interest in adapting population dynamic theory for microbial systems. Despite the appeal, numerous hurdles exist. One hurdle is that the data commonly obtained from DNA sequencing yield estimates of relative abundances, while population dynamic models such as the generalized Lotka-Volterra model track absolute abundances or densities. It is not clear whether relative abundance data alone can be used to infer parameters of population dynamic models such as the Lotka-Volterra model.ResultsWe used structural identifiability analyses to determine the extent to which time series of relative abundances can be used to parameterize the generalized Lotka-Volterra model. We found that only with absolute abundance data to accompany relative abundance estimates from sequencing can all parameters be uniquely identified. However, relative abundance data alone do contain information on relative interaction strengths, which is sufficient for many studies where the goal is to estimate key interactions and their effects on dynamics. Our results also indicate that the relative interaction rates that can be estimated using relative abundance data provide ample information to estimate relative changes of absolute abundance over time. Using synthetic data for which we know the underlying structure, we found our results to be robust to modest amounts of both process and measurement error.ConclusionsFitting the generalized Lotka-Volterra model to time-series sequencing data typically requires either assuming a constant population size or performing additional measurements to obtain absolute abundances. We have found that these assumptions are not strictly necessary because relative abundance data alone contain sufficient information to estimate relative rates of interaction, and thus to infer key drivers of microbial population dynamics.

scholarly journals propr: An R-package for Identifying Proportionally Abundant Features Using Compositional Data Analysis

2017 ◽  
Author(s):  
Thomas Quinn ◽  
Mark F. Richardson ◽  
David Lovell ◽  
Tamsyn Crowley
Keyword(s):  
Data Analysis ◽  
Relative Abundance ◽  
Compositional Data ◽  
Life Sciences ◽  
Genomic Data ◽  
R Package ◽  
Compositional Data Analysis ◽  
Computationally Efficient ◽  
Abundance Data ◽  
Relative Abundances

AbstractIn the life sciences, many assays measure only the relative abundances of components for each sample. These data, called compositional data, require special handling in order to avoid misleading conclusions. For example, in the case of correlation, treating relative data like absolute data can lead to the discovery of falsely positive associations. Recently, researchers have proposed proportionality as a valid alternative to correlation for calculating pairwise association in relative data. Although the question of how to best measure proportionality remains open, we present here a computationally efficient R package that implements two proposed measures of proportionality. In an effort to advance the understanding and application of proportionality analysis, we review the mathematics behind proportionality, demonstrate its application to genomic data, and discuss some ongoing challenges in the analysis of relative abundance data.

FITTING POPULATION DYNAMIC MODELS TO TIME-SERIES DATA BY GRADIENT MATCHING

Ecology ◽  
2002 ◽  
Vol 83 (8) ◽  
pp. 2256-2270 ◽  
Author(s):  
Stephen P. Ellner ◽  
Yodit Seifu ◽  
Robert H. Smith
Keyword(s):  
Time Series ◽  
Population Dynamic ◽  
Dynamic Models ◽  
Time Series Data ◽  
Series Data

Prediction of Surge Motion Response of Floating Structure Using Kalman Smoother Adaptive Filters Based Time-Domain Volterra Model

2014 ◽  
Vol 660 ◽  
pp. 799-803
Author(s):  
Edwar Yazid ◽  
M.S. Liew ◽  
Setyamartana Parman ◽  
V.J. Kurian ◽  
C.Y. Ng
Keyword(s):  
Time Series ◽  
Transfer Function ◽  
Time Domain ◽  
Adaptive Filters ◽  
Low Frequency ◽  
Volterra Model ◽  
Floating Structure ◽  
Frequency Responses ◽  
Kalman Smoother ◽  
System Output

This work presents an approachto predict the low frequency and wave frequency responses (LFR and WFR) of afloating structure using Kalman smoother adaptive filters based time domain Volterramodel. This method utilized time series of a measured wave height as systeminput and surge motion as system output and used to generate the linear andnonlinear transfer function (TFs). Based on those TFs, predictions of surgemotion in terms of LFR and WFR were carried out in certain frequency ranges ofwave heights. The applicability of the proposed method is then applied in ascaled 1:100 model of a semisubmersible prototype.

An Enquiry Into Linear Conflict Models

2021 ◽  
Author(s):  
Klaus B. Beckmann ◽  
Lennart Reimer
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Bounded Rationality ◽  
Dynamic Models ◽  
Conflict Analysis ◽  
Monte Carlo Techniques ◽  
Linear Dynamic ◽  
Rich Variety ◽  
Time Series Analyses ◽  
Linear Dynamic Models

This monograph generalises, and extends, the classic dynamic models in conflict analysis (Lanchester 1916, Richardson 1919, Boulding 1962). Restrictions on parameters are relaxed to account for alliances and for peacekeeping. Incrementalist as well as stochastic versions of the model are reviewed. These extensions allow for a rich variety of patterns of dynamic conflict. Using Monte Carlo techniques as well as time series analyses based on GDELT data (for the Ethiopian-Eritreian war, 1998–2000), we also assess the empirical usefulness of the model. It turns out that linear dynamic models capture selected phases of the conflict quite well, offering a potential taxonomy for conflict dynamics. We also discuss a method for introducing a modicum of (bounded) rationality into models from this tradition.

Using Time Series to Estimate Rates of Population Change from Abundance Data

2007 ◽  
Vol 71 (1) ◽  
pp. 202-207 ◽  
Author(s):  
KRISTEN E. RYDING ◽  
JOSHUA J. MILLSPAUGH ◽  
JOHN R. SKALSKI
Keyword(s):  
Time Series ◽  
Population Change ◽  
Abundance Data

Time Series and Dynamic Models

Technometrics ◽  
1998 ◽  
Vol 40 (2) ◽  
pp. 158-158
Author(s):  
Errol Caby
Keyword(s):  
Time Series ◽  
Dynamic Models

scholarly journals A phylogenetic transform enhances analysis of compositional microbiota data

2016 ◽  
Author(s):  
Justin D Silverman ◽  
Alex Washburne ◽  
Sayan Mukherjee ◽  
Lawrence A David
Keyword(s):  
Microbial Communities ◽  
Relative Abundance ◽  
Dominant Role ◽  
Phylogenetic Information ◽  
Abundance Data ◽  
Sequencing Technologies ◽  
Environmental Selection ◽  
Health And Disease ◽  
High Throughput Dna Sequencing ◽  
Spurious Results

ABSTRACTHigh-throughput DNA sequencing technologies have revolutionized the study of microbial communities (microbiota) and have revealed their importance in both human health and disease. However, due to technical limitations, data from microbiota surveys reflect the relative abundance of bacterial taxa and not their absolute levels. It is well known that applying common statistical methods, such as correlation or hypothesis testing, to relative abundance data can lead to spurious results. Here, we introduce the PhILR transform, a data transform that utilizes microbial phylogenetic information. This transform enables off-the-shelf statistical tools to be applied to microbiota surveys free from artifacts usually associated with analysis of relative abundance data. Using environmental and human-associated microbial community datasets as benchmarks, we find that the PhILR transform significantly improves the performance of distance-based and machine learning-based statistics, boosting the accuracy of widely used algorithms on reference benchmarks by 90%. Because the PhILR transform relies on bacterial phylogenies, statistics applied in the PhILR coordinate system are also framed within an evolutionary perspective. Regression on PhILR transformed human microbiota data identified evolutionarily neighboring bacterial clades that may have differentiated to adapt to distinct body sites. Variance statistics showed that the degree of covariation of bacterial clades across human body sites tended to increase with phylogenetic relatedness between clades. These findings support the hypothesis that environmental selection, not competition between bacteria, plays a dominant role in structuring human-associated microbial communities.

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