Department of Environmental Science, Policy and Management, University of California, Berkeley, California, United States of America.
PLoS One. 2011 Jan 20;6(1):e14539. doi: 10.1371/journal.pone.0014539.
The dominant paradigm for modeling the complexities of interacting populations and food webs is a system of coupled ordinary differential equations in which the state of each species, population, or functional trophic group is represented by an aggregated numbers-density or biomass-density variable. Here, using the metaphysiological approach to model consumer-resource interactions, we formulate a two-state paradigm that represents each population or group in a food web in terms of both its quantity and quality.
The formulation includes an allocation function controlling the relative proportion of extracted resources to increasing quantity versus elevating quality. Since lower quality individuals senescence more rapidly than higher quality individuals, an optimal allocation proportion exists and we derive an expression for how this proportion depends on population parameters that determine the senescence rate, the per-capita mortality rate, and the effects of these rates on the dynamics of the quality variable. We demonstrate that oscillations do not arise in our model from quantity-quality interactions alone, but require consumer-resource interactions across trophic levels that can be stabilized through judicious resource allocation strategies. Analysis and simulations provide compelling arguments for the necessity of populations to evolve quality-related dynamics in the form of maternal effects, storage or other appropriate structures. They also indicate that resource allocation switching between investments in abundance versus quality provide a powerful mechanism for promoting the stability of consumer-resource interactions in seasonally forcing environments.
CONCLUSIONS/SIGNIFICANCE: Our simulations show that physiological inefficiencies associated with this switching can be favored by selection due to the diminished exposure of inefficient consumers to strong oscillations associated with the well-known paradox of enrichment. Also our results demonstrate how allocation switching can explain observed growth patterns in experimental microbial cultures and discuss how our formulation can address questions that cannot be answered using the quantity-only paradigms that currently predominate.
用于模拟相互作用的种群和食物网复杂性的主流模型范式是一个耦合的常微分方程组系统，其中每个物种、种群或功能营养群的状态由聚合数量密度或生物量密度变量表示。在这里，我们使用代谢生理学方法来模拟消费者-资源相互作用，提出了一种两状态范式，根据数量和质量来表示食物网中的每个种群或群体。
该公式包括一个分配函数，用于控制从提取的资源中分配给数量增加和质量提高的相对比例。由于低质量个体比高质量个体衰老更快，因此存在最佳分配比例，我们推导出了一个表达式，说明这个比例如何取决于决定衰老率、个体死亡率和这些率对质量变量动态影响的种群参数。我们证明，我们的模型中的振荡不是仅由数量-质量相互作用引起的，而是需要跨营养级别的消费者-资源相互作用，可以通过明智的资源分配策略来稳定这些相互作用。分析和模拟为种群以母性效应、储存或其他适当结构的形式进化与质量相关的动态提供了有力的论据。它们还表明，在丰度与质量之间的资源分配转换为促进季节性强制环境中消费者-资源相互作用的稳定性提供了强大的机制。
结论/意义： 我们的模拟表明，由于低效消费者与著名的富化悖论相关的强烈振荡接触减少，与这种转换相关的生理效率低下可能会受到选择的青睐。此外，我们的结果还表明，分配转换如何解释实验微生物培养中观察到的生长模式，并讨论了我们的公式如何解决当前占主导地位的仅数量范式无法回答的问题。
