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A Mathematical Model for Biocontrol of the Invasive Weed Fallopia japonica
Stephen A Gourley1, Jing Li2, Xingfu Zou3
1Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK. s.gourley@surrey.ac.uk.
Bulletin of Mathematical Biology
|August 6, 2016
Summary
Mathematical modeling shows that biocontrol of invasive Japanese knotweed (Fallopia japonica) using the psyllid Aphalara itadori is effective only if the insect digests plant biomass rapidly. Otherwise, knotweed growth remains unbounded.
Area of Science:
- Ecology
- Mathematical Biology
- Invasive Species Management
Background:
- Fallopia japonica (Japanese knotweed) is a highly invasive weed causing ecological and economic damage.
- Aphalara itadori, a Japanese sap-sucking psyllid, is a natural enemy with a specific diet on F. japonica, making it a candidate for biocontrol.
Purpose of the Study:
- To develop and analyze a mathematical model for biocontrol of F. japonica using A. itadori.
- To investigate the conditions under which A. itadori can effectively control F. japonica populations.
Main Methods:
- A stage-structured mathematical model was formulated, considering stem and rhizome biomass for F. japonica and larval and adult stages for A. itadori.
- Model dynamics were analyzed based on the parameter 'h', representing insect digestion time of plant biomass.
- Equilibrium analysis was performed to determine population stability and growth dynamics.
Main Results:
- Model dynamics are critically dependent on the insect's biomass handling time (h).
- If 'h' is too large, uncontrolled growth of both plant and insect populations occurs.
- A sufficiently small 'h' leads to a potentially stable, positive equilibrium, indicating successful biocontrol.
Conclusions:
- Effective long-term biocontrol of F. japonica with A. itadori requires rapid consumption and digestion of plant biomass by the insect.
- If digestion is slow, A. itadori can only decelerate knotweed growth, not achieve complete control.
