Methods of quantifying interactions among populations using Lotka-Volterra models

Jacob D. Davis, Daniel V. Olivença, S. Brown, E. Voit
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引用次数: 6

Abstract

The Lotka-Volterra (LV) model was introduced in the early 20th Century to describe predator-prey systems. Since then, the model has been expanded to capture the dynamics of numerous types of interacting populations and to include the effects of external factors from the environment. Despite many simplifying assumptions, the LV approach has proven to be a very valuable tool for gaining insights into the dynamics of diverse biological interaction systems. In particular, recognizing the critical importance of microbiomes for human and environmental heath, LV systems have become effective tools of analysis and, indeed, the default for quantitatively assessing interactions within these large microbial communities. Here we present an overview of parameter inference methods for LV systems, specifically addressing individuals entering the field of biomathematical modeling, who have a modest background in linear algebra and calculus. The methods include traditional local and global strategies, as well as a recently developed inference method based strictly on linear algebra. We compare the different strategies using both lab-acquired and synthetic time series data. We also address a recent debate within the scientific community of whether it is legitimate to compose large models from information inferred for the dynamics of subpopulations. In addition to parameter estimation methods, the overview includes preparatory aspects of the inference process, including data cleaning, smoothing, and the choice of an adequate loss function. Our comparisons demonstrate that traditional fitting strategies, such as gradient descent optimization and differential evolution, tend to yield low residuals but sometimes overfit noisy data and incur high computation costs. The linear-algebra-based method produces a satisfactory solution much faster, generally without overfitting, but requires the user to estimate slopes from the time series, which can introduce undue error. The results also suggest that composing large models from information regarding sub-models can be problematic. Overall, there is no clear “always-best method” for inferring parameters from data, and prudent combinations may be the best strategy.
利用Lotka-Volterra模型量化种群间相互作用的方法
Lotka-Volterra (LV)模型是在20世纪初引入的,用于描述捕食者-猎物系统。从那时起,该模型得到了扩展,以捕捉各种相互作用的种群的动态,并包括来自环境的外部因素的影响。尽管有许多简化的假设,LV方法已被证明是一种非常有价值的工具,可以深入了解各种生物相互作用系统的动力学。特别是,认识到微生物组对人类和环境健康的关键重要性,LV系统已经成为有效的分析工具,实际上,是定量评估这些大型微生物群落内部相互作用的默认工具。在这里,我们概述了LV系统的参数推理方法,特别是针对进入生物数学建模领域的个人,他们在线性代数和微积分方面有一定的背景。这些方法包括传统的局部策略和全局策略,以及最近发展起来的严格基于线性代数的推理方法。我们使用实验室获得的和合成的时间序列数据来比较不同的策略。我们还讨论了科学界最近的一个争论,即从亚种群动态推断的信息组成大型模型是否合理。除了参数估计方法外,概述还包括推理过程的准备方面,包括数据清理,平滑和选择适当的损失函数。我们的比较表明,传统的拟合策略,如梯度下降优化和差分进化,往往产生较低的残差,但有时会过度拟合噪声数据,并产生较高的计算成本。基于线性代数的方法可以更快地产生满意的解,通常没有过拟合,但需要用户从时间序列中估计斜率,这可能会引入不适当的误差。结果还表明,从有关子模型的信息组成大型模型可能会有问题。总的来说,从数据中推断参数没有明确的“永远最好的方法”,谨慎的组合可能是最好的策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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