Interactions among multiple resources and consumers involve two indirect interactions: resource competition among consumers and apparent competition among resources. However, competition among multiple consumers is typically viewed through the lens of direct interactions embodied in the Lotka‐Volterra competition model, which fails to capture the mechanisms of these indirect interactions. In this paper, I analyze various elaborations of MacArthur's and Tilman's original consumer–resource models including more than two species per trophic level, saturating functional responses, and direct intraspecific density dependence within the consumers. First, the simplest model with two resources and two consumers with linear functional responses is analyzed via the structure of the resulting isoclines, and this is reconciled with Tilman's graphical ZNGI/consumption vector approach. With three species at each trophic level even in this simple model, each consumer is not required to have the largest impact on the resource that most limits its growth for multiple consumers to coexist. In fact, a consumer that is an inferior competitor on each resource in isolation may still coexist with superior competitors, and conversely a consumer that is an inferior competitor on each available resource may still be able to drive all other consumers extinct. However, the maximum number of coexisting consumers is set by the number of available resources. Saturating functional responses do not qualitatively alter the conditions for multiple consumers and resources to coexist at a stable point equilibrium but do increase the range of apparent competitive abilities for resources that can invade and coexist. Saturating functional responses also increase the range of dynamics that the community may display (i.e., limit cycles and chaos), which previous analyses have shown can permit more consumer species than resources to coexist. Adding direct intraspecific density dependence in the consumers, either in the form of feeding interference or density‐dependent demographic rates, permit more consumers to coexist than available resources, even at stable point equilibria. Understanding the indirect effects that cascade through a community is essential to predicting community changes and understanding how species at multiple trophic levels coexist, and these indirect effects should not be shrouded behind the curtain of Lotka‐Volterra competition.

中文翻译：

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影响多个消费者和多种资源共存的机制：资源和明显的竞争

多种资源和消费者之间的相互作用涉及两个间接相互作用：消费者之间的资源竞争和资源之间的表观竞争。但是，通常通过Lotka-Volterra竞争模型中体现的直接互动的视角来观察多个消费者之间的竞争，而该模型无法捕捉到这些间接互动的机制。在本文中，我分析了麦克阿瑟（MacArthur）和蒂尔曼（Tilman）的原始消费者资源模型的各种细节，其中包括每个营养级别有两种以上的物种，饱和的功能响应以及消费者内部直接的种内密度依赖性。首先，通过所得等值线的结构分析了具有两个资源和两个具有线性功能响应的消费者的最简单模型，并将其与Tilman's调和。图形化的ZNGI /消费向量方法。即使在此简单模型中，在每个营养级别都具有三个物种，因此，不需要每个消费者对资源产生最大影响的资源（最大限制了其增长），多个消费者可以共存。实际上，孤立地在每个资源上都是次要竞争者的消费者可能仍然与上级竞争者并存，相反，在每个可用资源上都是次要竞争者的消费者仍然可以使所有其他消费者灭绝。但是，共存使用者的最大数量由可用资源的数量设置。饱和的功能响应不会从质上改变多个消费者和资源在稳定点平衡下共存的条件，但会增加可入侵和共存的资源的明显竞争能力的范围。饱和的功能响应还增加了社区可能显示的动态范围（即，极限循环和混乱），先前的分析表明，这种变化可以允许比资源共存的消费者物种更多。以饲喂干扰或人口密度相关人口率的形式在消费者中直接增加种内密度依赖性，即使在稳定点均衡时，也比可用资源共存更多的消费者。