The dominant differential equation paradigm for modeling the population dynamics of species interacting in the framework of a food web retains at its core the basic prey-predator and competition models formulation by Alfred J. Lotka (1880-1945) and Vito Volterra (1860-1940) nearly nine decades ago. This paradigm lacks a trophic-level-independent formulation of population growth leading to ambiguities in how to treat populations that are simultaneously both prey and predator. Also, this paradigm does not fundamentally include inertial (i.e. change resisting) processes needed to account for the response of populations to fluctuating resource environments. Here I present an approach that corrects both these deficits and provides a unified framework for accounting for biomass transformation in food webs that include both live and dead components of all species in the system. This biomass transformation formulation (BTW) allows for a unified treatment of webs that include consumers of both live and dead material-both carnivores and carcasivores, herbivores and detritivores-and incorporates scavengers, parasites, and other neglected food web consumption categories in a coherent manner. I trace how BTW is an outgrowth of the metaphysiological growth modeling paradigm and I provide a general compact formulation of BTW in terms of a three-variable differential equation formulation for each species in the food web: viz. live biomass, dead biomass, and a food-intake-related measure called deficit-stress. I then illustrate the application of this new paradigm to provide insights into two-species competition in variable environments and discuss application of BTW to food webs that incorporate parasites and pathogens.

中文翻译：

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人口模型和食物网的生物质流方法

在食物网框架内对物种相互作用的种群动态进行建模的主要微分方程范式的核心保留了由 Alfred J. Lotka (1880-1945) 和 Vito Volterra (1860-1940) 制定的基本猎物-捕食者和竞争模型）将近九年前。这种范式缺乏与营养水平无关的人口增长公式，导致在如何处理同时是猎物和捕食者的种群方面存在歧义。此外，这种范式从根本上不包括解释人口对波动的资源环境的反应所需的惯性（即抵制变化）过程。在这里，我提出了一种纠正这些缺陷的方法，并提供了一个统一的框架来解释食物网中的生物量转化，其中包括系统中所有物种的活体和死体成分。这种生物质转化公式 (BTW) 允许对包括活的和死的物质（食肉动物和食肉动物、食草动物和碎屑动物）的消费者在内的网络进行统一处理，并以连贯的方式包含清道夫、寄生虫和其他被忽视的食物网络消费类别. 我追溯了 BTW 如何是形而上学生长建模范式的产物，并且我根据食物网中每个物种的三变量微分方程公式提供了 BTW 的一般紧凑公式：即。活生物量、死生物量和一种与食物摄入相关的措施，称为赤字压力。