When is evolutionary branching in predator-prey systems possible with an explicit carrying capacity?

Area of Science:

• Ecology
• Evolutionary Biology
• Mathematical Biology

Background:

• Predator-prey dynamics are fundamental to ecological systems.
• Adaptive dynamics provides a framework for studying evolutionary processes.
• Understanding speciation mechanisms is crucial in evolutionary biology.

Purpose of the Study:

• To investigate evolutionary branching in a predator-prey model using adaptive dynamics.
• To compare the impact of emergent versus explicit carrying capacity on evolutionary outcomes.
• To identify conditions that permit or prevent evolutionary branching.

Main Methods:

• Utilized the theory of adaptive dynamics.
• Modeled a generalist predator with a Holling Type II functional response.
• Compared two formulations of carrying capacity: emergent and explicit.
• Analyzed the effects of different trade-offs on evolutionary branching.
• Investigated a generalized functional response to derive branching conditions.

Main Results:

• Evolutionary branching was only possible when carrying capacity was an emergent property.
• With an explicit carrying capacity, branching occurred under specific trade-off conditions.
• A condition was derived where branching cannot occur if the functional response is separable.

Conclusions:

• The formulation of carrying capacity significantly influences evolutionary branching in predator-prey models.
• Adaptive dynamics can reveal conditions conducive to speciation through evolutionary branching.
• The separability of the functional response is a key factor determining the possibility of branching.