Point 1: The ecological models of Alfred J. Lotka and Vito Volterra have had an enormous impact on ecology over the past century. Some of the earliest-and clearest-experimental tests of these models were famously conducted by Georgy Gause in the 1930s. Although well known, the data from these experiments are not widely available and are often difficult to analyze using standard statistical and computational tools. Point 2: Here, we introduce the gauseR package, a collection of tools for fitting Lotka-Volterra models to time series data of one or more species. The package includes several methods for parameter estimation and optimization, and includes 42 datasets from Gause's species interaction experiments and related work. Additionally, we include with this paper a short blog post discussing the historical importance of these data and models, and an R vignette with a walk-through introducing the package methods. The package is available for download at github.com/adamtclark/gauseR. Point 3: To demonstrate the package, we apply it to several classic experimental studies from Gause, as well as two other well-known datasets on multi-trophic dynamics on Isle Royale, and in spatially structured mite populations. In almost all cases, models fit observations closely and fitted parameter values make ecological sense. Point 4: Taken together, we hope that the methods, data, and analyses that we present here provide a simple and user-friendly way to interact with complex ecological data. We are optimistic that these methods will be especially useful to students and educators who are studying ecological dynamics, as well as researchers who would like a fast tool for basic analyses.
Download full-text PDF |
Source |
---|---|
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7713957 | PMC |
http://dx.doi.org/10.1002/ece3.6926 | DOI Listing |
iScience
December 2024
Division of Molecular Oncological Pharmacy, Faculty of Pharmacy, Keio University, 1-5-30, Shibakoen, Minato-ku, Tokyo 105-8512, Japan.
DNA double-strand breaks (DSBs) occurring within the genomic DNA of mammalian cells significantly impact cell survival, depending upon their repair capacity. This study presents a mathematical model to fit fibroblast survival rates with a sequence-specific DSB burden induced by the restriction enzyme AsiSI. When cells had a sporadic DSB burden under mixed culture, cell growth showed a good fit to the Lotka-Volterra competitive equation, predicting the presence of modifying factors acting as competitive cell-to-cell interactions compared to monocultures.
View Article and Find Full Text PDFChaos
May 2024
Departamento de Física, Universidade Estadual de Maringá, 87020-900 Maringá, PR, Brazil.
Quantification of chaos is a challenging issue in complex dynamical systems. In this paper, we discuss the chaotic properties of generalized Lotka-Volterra and May-Leonard models of biodiversity, via the Hamming distance density. We identified chaotic behavior for different scenarios via the specific features of the Hamming distance and the method of q-exponential fitting.
View Article and Find Full Text PDFWaste Manag
September 2023
School of Science, Wuhan University of Technology, Wuhan, 430070, PR China. Electronic address:
Aerobic compost is an effective method for the treatment of livestock manure, which is usually accompanied by complex interspecific competition. Describing these competitive relationships through mathematical models can help understand the interaction of microorganisms and analyze the effect of exogenous additive to regulate the composting process. The common model for analyzing competition problem is the Lotka-Volterra model.
View Article and Find Full Text PDFBull Math Biol
June 2023
Department of Mathematics, University of Pittsburgh, 301 Thackeray Avenue, Pittsburgh, PA, 15260, USA.
In this work, we describe mostly analytical work related to a novel approach to parameter identification for a two-variable Lotka-Volterra (LV) system. Specifically, this approach is qualitative, in that we aim not to determine precise values of model parameters but rather to establish relationships among these parameter values and properties of the trajectories that they generate, based on a small number of available data points. In this vein, we prove a variety of results about the existence, uniqueness, and signs of model parameters for which the trajectory of the system passes exactly through a set of three given data points, representing the smallest possible data set needed for identification of model parameter values.
View Article and Find Full Text PDFJ Theor Biol
February 2023
Department of Mathematics, University of Oxford, Oxford, UK.
The Lotka-Volterra model is widely used to model interactions between two species. Here, we generate synthetic data mimicking competitive, mutualistic and antagonistic interactions between two tumor cell lines, and then use the Lotka-Volterra model to infer the interaction type. Structural identifiability of the Lotka-Volterra model is confirmed, and practical identifiability is assessed for three experimental designs: (a) use of a single data set, with a mixture of both cell lines observed over time, (b) a sequential design where growth rates and carrying capacities are estimated using data from experiments in which each cell line is grown in isolation, and then interaction parameters are estimated from an experiment involving a mixture of both cell lines, and (c) a parallel experimental design where all model parameters are fitted to data from two mixtures (containing both cell lines but with different initial ratios) simultaneously.
View Article and Find Full Text PDFEnter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!