  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.
