title: Effects of time delay and space on herbivore dynamics: linking inducible defenses of plants to herbivore outbreak.
abstract: Empirical results indicate that inducible defenses of plants have effects on herbivore populations. However, little is known about how inducible defenses of plants have influences on herbivore outbreak when space effect is considered. To reveal the relationship between inducible defenses and herbivore outbreak, we present a mathematical model to describe the interaction of them. It was found that time delay plays dual effects in the persistence of herbivore populations: (i) large value of time delay may be associated with small density of herbivore populations, and thus causes the populations to run a higher risk of extinction; (ii) moderate value of time delay is beneficial for maintaining herbivore density in a determined range which may promote the persistence of herbivore populations. Additionally, we revealed that interaction of time delay and space promotes the growth of average density of herbivore populations during their outbreak period which implied that time delay may drive the resilience of herbivore populations. Our findings highlight the close relationship between inducible defenses of plants and herbivore outbreak.
authors.affiliation: Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, P.R. China.|School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China.
authors.forename: Gui-Quan
authors.initials: GQ
authors.lastname: Sun
authors.affiliation: Department of Children's Medical Laboratory Diagnosis Center, Qilu Children's Hospital of Shandong University, Jinan 250022, P.R. China.
authors.forename: Su-Lan
authors.initials: SL
authors.lastname: Wang
authors.affiliation: Department of Children's Medical Laboratory Diagnosis Center, Qilu Children's Hospital of Shandong University, Jinan 250022, P.R. China.
authors.forename: Qian
authors.initials: Q
authors.lastname: Ren
authors.affiliation: Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, P.R. China.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Jin
authors.affiliation: College of Physics Science and Technology, Yangzhou University, Yangzhou, Jiangsu Province, 225002, P.R. China.
authors.forename: Yong-Ping
authors.initials: YP
authors.lastname: Wu
mesh_terms: D000465:Algorithms; D000818:Animals; D017753:Ecosystem; D020387:Food Chain; D060434:Herbivory; D008962:Models, Theoretical; D010944:Plants