I use simple models to consider the short and long term responses of population density in a consumer species experiencing a selectively advantageous change in a single population growth parameter. This may be caused by a selective sweep by a beneficial mutation, or an advantageous environmental shift. In the context of a simple one-consumer - one-resource system, the consumer may evolve a more rapid rate of resource capture, greater efficiency of resource conversion, or decreased metabolic or mortality rates. This produces a short-term change in population size, which may be positive or negative. This and the resulting change in resource abundance in turn alter the selective pressure on other traits, producing 'trait-trait coevolution'. For example, decreased consumer mortality will always reduce resource abundance, which then reduces selection for greater resource capture rate and greater resource conversion efficiency. The subsequent evolution of these two traits alters population size in a way that may enhance or counteract the original change. I use simple ordinary differential equation models of food webs with two or more species to explore how this trait-trait co-evolution alters the original consumer population's response to an adaptive change. Particular attention will be given to whether different initial population responses to the selectively advantageous change are associated with different directions of modification due to trait-trait coevolution. After exploring several simple models of the one-consumer - one-resource system, I examine the effects of trait-trait coevolution in the top consumer species in a simple three-level food chain and in a 'diamond' web where a predator consumes two prey sharing a common resource.
In the Lotka-Volterra predator-prey system, there are 3 ecological parameters of the consumer: resource capture rate, conversion rate, and loss rate. The equilibrium (and mean) consumer population only changes in response to altered capture rate. The selectively favored higher capture rate reduces consumer population size. However, selectively favored changes in all parameters reduce the resource abundance, which in turn decreases the selective gradients for both the capture rate and the conversion efficiency. Thus, the coevolutionary decreases in mortality and/or increases in conversion efficiency are expected to counteract the initial decline in consumer population size due to greater consumption. The directions of the secondary responses in more complex models show that counter-intuitive population declines in response to selectively favored changes in mortality or conversion efficiency often lead to the same secondary responses as in cases with initial population increases.