A Mathematical Model for Biocontrol of the Invasive Weed Fallopia japonica

We propose a mathematical model for biocontrol of the invasive weed Fallopia japonica using one of its co-evolved natural enemies, the Japanese sap-sucking psyllid Aphalara itadori. This insect sucks the sap from the stems of the plant thereby weakening it. Its diet is highly specific to F. japonica. We consider a single isolated knotweed stand, the plant’s size being described by time-dependent variables for total stem and rhizome biomass. It is the larvae of A. itadori that damage the plant most, so the insect population is described in terms of variables for the numbers of larvae and adults, using a stage-structured modelling approach. The dynamics of the model depends mainly on a parameter h, which measures how long it takes for an insect to handle (digest) one unit of F. japonica stem biomass. If h is too large, then the model does not have a positive equilibrium and the plant biomass and insect numbers both grow together without bound, though at a lower rate than if the insects were absent. If h is sufficiently small, then the model possesses a positive equilibrium which appears to be locally stable. The results based on our model imply that satisfactory long-term control of the knotweed F. japonica using the insect A. itadori is only possible if the insect is able to consume and digest knotweed biomass sufficiently quickly; if it cannot, then the insect can only slow down the growth which is still unbounded.

• Publication year

  2016

• Venue

  Bulletin of Mathematical Biology

• Publication date

  2016-08-01

• Fields of study

  Biology, Mathematics, Medicine, Environmental Science

• Identifiers
  DOI 10.1007/s11538-016-0195-8PMID 27491929PMCID 5039234
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

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