Long transients appear in predator-prey systems with group defense and nonreproductive stages

During recent years, the study of long transients has been expanded in ecological theory to account for shifts in long-term behavior of ecological systems. These long transients consist of long periods of time where a system is apparently in equilibrium; after which the system undergoes an abrupt change into qualitatively different dynamics. In this work, we analyze the potential for long transients in a model for a predator-prey system in which the prey present group defense, and their nonreproductive stages do not contribute to predator growth. This model has been previously used to analyze kelp-urchin dynamics, but it can be used in other systems such as colonial spider-wasp or honeybee-hornet systems. We have identified this system presents crawl-by transients near the extinction and carrying capacity states of prey. In addition, we identify a transcritical bifurcation in our system, under which a ghost limit cycle appears. We are able to estimate the escape time of our system from these transients using perturbation theory. This work advances an understanding of how systems shift between alternate stable states and their duration of staying in a given regime.