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Effects of time delay and space on herbivore dynamics: linking inducible defenses of plants to herbivore outbreak.

Sun GQ, Wang SL, Ren Q, Jin Z, Wu YP - Sci Rep (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: 1] Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, P.R. China [2] School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China.

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.

No MeSH data available.


Time series of herbivore populations with (L is the space length). (A) Stable solutions with τ = 3.2 < τc; (B) Periodic solutions with τ = 4.8 > τc.
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f3: Time series of herbivore populations with (L is the space length). (A) Stable solutions with τ = 3.2 < τc; (B) Periodic solutions with τ = 4.8 > τc.

Mentions: In order to better show the outbreak of herbivore populations, time series are shown in Fig. 3. In Fig. 3(A), herbivore populations exhibit a oscillation behavior with decreased amplitude and converge to a constant state with τ < τc. This figure suggests that periodic outbreak of herbivore will not appear with τ < τc. However, when τ > τc, herbivore populations will outbreak with fixed period and amplitude as evolution time is long enough showed in Fig. 3(B).


Effects of time delay and space on herbivore dynamics: linking inducible defenses of plants to herbivore outbreak.

Sun GQ, Wang SL, Ren Q, Jin Z, Wu YP - Sci Rep (2015)

Time series of herbivore populations with (L is the space length). (A) Stable solutions with τ = 3.2 < τc; (B) Periodic solutions with τ = 4.8 > τc.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4471659&req=5

f3: Time series of herbivore populations with (L is the space length). (A) Stable solutions with τ = 3.2 < τc; (B) Periodic solutions with τ = 4.8 > τc.
Mentions: In order to better show the outbreak of herbivore populations, time series are shown in Fig. 3. In Fig. 3(A), herbivore populations exhibit a oscillation behavior with decreased amplitude and converge to a constant state with τ < τc. This figure suggests that periodic outbreak of herbivore will not appear with τ < τc. However, when τ > τc, herbivore populations will outbreak with fixed period and amplitude as evolution time is long enough showed in Fig. 3(B).

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: 1] Complex Systems Research Center, Shanxi University, Taiyuan, Shanxi 030006, P.R. China [2] School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China.

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.

No MeSH data available.