A note on synchronous egg laying in a seabird behaviour model

ABSTRACT

During years when sea surface temperature (SST) is high, gulls in a colony on Protection Island, Washington, USA typically experience low food availability. As SST rises, feeder fish follow plankton to cooler temperatures in deeper water levels. Since gulls are surface-feeding birds, they face a food shortage. A tactic male gulls employ to deal with this food shortage is to cannibalize their neighbours' eggs. Gulls in this colony exhibit an adaptive tactic of every-other-day egg-laying synchrony in response to egg cannibalism, and the level of synchrony increases with colony density. Here we analyze the dynamics of an animal behaviour model for egg laying as a function of colony density. As colony density increases, the equilibrium loses stability in a 2-cycle bifurcation. The 2-cycle becomes increasingly synchronous as the colony density continues to increase. We show that egg-laying synchrony benefits the colony in the presence of cannibalism.

KEYWORDS:

• Egg cannibalism
• egg-laying synchrony
• glaucous-winged gulls
• mathematical model
• sea surface temperature

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 39A28
• 92D25
• 92D50

Acknowledgments

This paper was written by members of a Research Experience for Undergraduates (REU) team funded by the US National Science Foundation (NSF). We thank James L. Hayward and J. M. Cushing, and as well as fellow REU team members Mykhaylo Malakhov and Benjamin MacDonald, for discussions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

ORCID

Shandelle M. Henson  http://orcid.org/0000-0001-8439-7532

Additional information

Funding

This project was funded by NSF grant DMS- 1407040 to S. M. Henson and J. L. Hayward; Division of Mathematical Sciences.