We study how the complexity of evolutionary dynamics in the classic MacArthur consumer-resource model depends on resource uptake and utilization rates. The traditional assumption in such models is that the utilization rate of the consumer is proportional to the uptake rate. More generally, we show that if these two rates are related through a power law (which includes the traditional assumption as a special case), then the resulting evolutionary dynamics in the consumer is necessarily a simple hill-climbing process leading to an evolutionary equilibrium, regardless of the dimension of phenotype space. When utilization and uptake rates are not related by a power law, more complex evolutionary trajectories can occur, including the chaotic dynamics observed in previous studies for high-dimensional phenotype spaces. These results draw attention to the importance of distinguishing between utilization and uptake rates in consumer-resource models.

中文翻译：

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关于经典消费者资源模型中演化动力学的复杂性的注释

我们研究了经典麦克阿瑟消费者资源模型中进化动力学的复杂性如何取决于资源吸收和利用率。这种模型中的传统假设是，消费者的利用率与吸收率成正比。更笼统地说，我们表明，如果这两个比率通过幂定律相关联（包括作为特殊情况的传统假设），那么消费者中产生的演化动态必然是导致演化均衡的简单爬坡过程，无论表型空间的大小如何。当利用率和吸收率与幂律不相关时，可能会出现更复杂的进化轨迹，包括先前在高维表型空间研究中观察到的混沌动力学。