Follicular competition in cows: the selection of dominant follicles as a synergistic effect
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The reproductive cycle of mono-ovulatory species such as cows or humans is known to show two or more waves of follicular growth and decline between two successive ovulations. Within each wave, there is one dominant follicle escorted by subordinate follicles of varying number. Under the surge of the luteinizing hormone a growing dominant follicle ovulates. Rarely the number of ovulating follicles exceeds one. In the biological literature, the change of hormonal concentrations and individually varying numbers of follicular receptors are made responsible for the selection of exactly one dominant follicle, yet a clear cause has not been identified. In this paper, we suggest a synergistic explanation based on competition, formulated by a parsimoniously defined system of ordinary differential equations (ODEs) that quantifies the time evolution of multiple follicles and their competitive interaction during one wave. Not discriminating between follicles, growth and decline are given by fixed rates. Competition is introduced via a growth-suppressing term, equally supported by all follicles. We prove that the number of dominant follicles is determined exclusively by the ratio of follicular growth and competition. This number turns out to be independent of the number of subordinate follicles. The asymptotic behavior of the corresponding dynamical system is investigated rigorously, where we demonstrate that the \(\omega \)-limit set only contains fixed points. When also including follicular decline, our ODEs perfectly resemble ultrasound data of bovine follicles. Implications for the involved but not explicitly modeled hormones are discussed.
KeywordsDifferential equation models Ovarian follicles Follicular maturation Follicular waves Cows Humans
Mathematics Subject Classification37C20 92B05 92B25
We would like to thank Dr. S. Butler for sending us the data that have been used by Cummins et al. (2012). AL, JP, and SR gratefully acknowledge funding by Federal Ministry of Education and Research (BMBF) e:Bio Project BovSys (FKZ031A311). Furthermore, we thank the anonymous reviewers for their useful comments, which truly helped improving our manuscript.
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