Pick your trade-offs wisely: Predator-prey eco-evo dynamics are qualitatively different under different trade-offs

In recent decades, myriad studies have explored the population dynamics of coevolving populations of predator and prey. A variety of choices are made in these models: exponential or logistic prey growth in the absence of a predator, various forms of predator functional response, and uni- or bi-directional trait axes. In addition, some form of trade-offs are assumed in order to prevent run-away evolution of the prey and predator traits. While there is a considerable amount of theory regarding various forms of prey growth rates and predator functional responses, only a few studies have explored how different types of trade-offs affect predator-prey dynamics. Here, we compared two ditrophic coevolution models incorporating different trade-offs via dual effects of the prey trait on attack rate and either prey carrying capacity or intrinsic growth rate. We employed a standard dynamical systems approach to analyze the equilibrium conditions of each model and find conditions for non-equilibrium oscillatory coexistence. The exact effect of various parameters on the outcome of predator-prey interactions depends on whether the trade-offs affect the intrinsic growth rate or carrying capacity. In particular, coexistence is more likely when prey growth rate is affected by the evolving trait. In addition, in parameter regimes where cycles occur in both models, oscillations typically have larger periods and amplitudes when prey growth rate is affected by the evolving trait.