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 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 The quest for absolute abundance: the use of internal standards for DNA-based microbial and community ecology

2020 ◽  
Author(s):  
Joshua Harrison ◽  
W. John Calder ◽  
Bryan N. Shuman ◽  
C. Alex Buerkle
Keyword(s):  
Community Ecology ◽  
Relative Abundance ◽  
Compositional Data ◽  
Direct Measure ◽  
Absolute Abundance ◽  
Internal Standards ◽  
Integral Component ◽  
Dna Pools ◽  
Relative Abundances ◽  
Sequencing Process

To characterize microbiomes and other ecological assemblages, ecologists routinely sequence and compare loci that differ among focal taxa. Counts of these sequences convey information regarding the occurrence and relative abundances of taxa, but provide no direct measure of their absolute abundances, due to the technical limitations of the sequencing process. The relative abundances in compositional data are inherently constrained and difficult to interpret. The incorporation of internal standards (ISDs; colloquially referred to as ``spike-ins'') into DNA pools can ameliorate the problems posed by relative abundance data and allow absolute abundances to be approximated. Unfortunately, many laboratory and sampling biases cause ISDs to underperform or fail. Here, we discuss how careful deployment of ISDs can avoid these complications and be an integral component of well-designed studies seeking to characterize ecological assemblages via sequencing of DNA.

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.

scholarly journals A multi-view model for relative and absolute microbial abundances

2019 ◽  
Author(s):  
Brian D. Williamson ◽  
James P. Hughes ◽  
Amy D. Willis
Keyword(s):  
Relative Abundance ◽  
Estimation Error ◽  
Bacterial Species ◽  
Critical Role ◽  
Sensitivity Study ◽  
Universal Primers ◽  
Rrna Gene ◽  
Absolute Abundance ◽  
Abundance Data ◽  
The Absolute

AbstractThe absolute abundance of bacterial taxa in human host-associated environments play a critical role in reproductive and gastrointestinal health. However, obtaining the absolute abundance of many bacterial species is typically prohibitively expensive. In contrast, relative abundance data for many species is comparatively cheap and easy to collect (e.g., with universal primers for the 16S rRNA gene). In this paper, we propose a method to jointly model relative abundance data for many taxa and absolute abundance data for a subset of taxa. Our method provides point and interval estimates for the absolute abundance of all taxa. Crucially, our proposal accounts for differences in the efficiency of taxon detection in the relative and absolute abundance data. We show that modeling taxon-specific efficiencies substantially reduces the estimation error for absolute abundance, and controls the coverage of interval estimators. We demonstrate the performance of our proposed method via a simulation study, a sensitivity study where we jackknife the taxa with observed absolute abundances, and a study of women with bacterial vaginosis.

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

TEMPORAL LEONTIEF INVERSE

1998 ◽  
Vol 2 (1) ◽  
pp. 89-114 ◽  
Author(s):  
Michael Sonis ◽  
Geoffrey J.D. Hewings
Keyword(s):  
Time Series ◽  
Structural Change ◽  
Dynamic Models ◽  
Alternative Methods ◽  
Input Output ◽  
Accounting Systems ◽  
Alternative Approach ◽  
Leontief Inverse ◽  
Analytical Tools ◽  
Over Time

Interest in structural change over time has created a demand for analytical tools that can assist in exploiting trends and uncover tendencies in individual sectors or parts of sectors within the context of an economywide system of accounts. This paper offers an alternative approach and is designed to be used with annual input-output or social accounting systems. To date, analysts have been faced with the prospect of conducting simple comparative static approaches or the enormity of the task involved in constructing dynamic models with complex lead and lag structures. The temporal Leontief inverse, introduced in this paper, offers a less complex, more tractable method for examining structural change when a time series of input-output tables is available. The method draws upon some earlier work that proposed the notion of a field of influence of change and explored alternative methods of decomposition of change.

scholarly journals Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ICES Divisions VIIIc and IXa

2010 ◽  
Vol 67 (6) ◽  
pp. 1185-1197 ◽  
Author(s):  
C. Fernández ◽  
S. Cerviño ◽  
N. Pérez ◽  
E. Jardim
Keyword(s):  
Time Series ◽  
Stock Assessment ◽  
Reference Points ◽  
Assessment Model ◽  
Marine Science ◽  
Fishing Mortality ◽  
Change Over Time ◽  
Age Structured ◽  
Available Information ◽  
Over Time

Abstract Fernández, C., Cerviño, S., Pérez, N., and Jardim, E. 2010. Stock assessment and projections incorporating discard estimates in some years: an application to the hake stock in ICES Divisions VIIIc and IXa. – ICES Journal of Marine Science, 67: 1185–1197. A Bayesian age-structured stock assessment model is developed to take into account available information on discards and to handle gaps in the time-series of discard estimates. The model incorporates mortality attributable to discarding, and appropriate assumptions about how this mortality may change over time are made. The result is a stock assessment that accounts for information on discards while, at the same time, producing a complete time-series of discard estimates. The method is applied to the hake stock in ICES Divisions VIIIc and IXa, for which the available data indicate that some 60% of the individuals caught are discarded. The stock is fished by Spain and Portugal, and for each country, there are discard estimates for recent years only. Moreover, the years for which Portuguese estimates are available are only a subset of those with Spanish estimates. Two runs of the model are performed; one assuming zero discards and another incorporating discards. When discards are incorporated, estimated recruitment and fishing mortality for young (discarded) ages increase, resulting in lower values of the biological reference points Fmax and F0.1 and, generally, more optimistic future stock trajectories under F-reduction scenarios.

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.

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