Math. Model. Nat. Phenom.
Volume 8, Number 6, 2013Ecology
|Page(s)||80 - 95|
|Published online||28 November 2013|
Spatial Demogenetic Model for Studying Phenomena Observed upon Introduction of the Ragweed Leaf Beetle in the South of Russia
1 Institute of Arid Zones, Southern
Scientific Centre of the Russian Academy of Sciences Chekhov street,
2 Zoological Institute of the Russian Academy of Sciences University Quay, 1, 199034 Saint Petersburg, Russia
3 Vorovich Research Institute of Mechanics and Applied Mathematics, Southern Federal University Stachki street, 200/1, 344090 Rostov-on-Don, Russia
Corresponding author. E-mail: email@example.com
The introduction of the ragweed leaf beetle in the South of Russia in 1978–1989 was accompanied by a number of spectacular phenomena that determined the general success of the ragweed control and further dispersal and acclimatization of the beetles: (i) formation of solitary population waves (SPW), characterized by an extremely high density of the phytophage population at the narrow band of the front of a moving wave defoliating nearly all ragweed plants, and (ii) rapid, within 5-6 generations, development of flight in the leaf beetle species that in its homeland lost the ability to fly. We present here a demogenetic model capable of reproducing both these phenomena, assuming that the flight ability of a phytophage population is governed by a single diallelic locus with flight and flightless alleles that determine three genotypes of the ragweed leaf beetle. Simulation results agree well with the practical recommendation of retaining a high density of common ragweed in the release area in order to provide the necessary conditions for the initial increase of the leaf beetle population and the formation of the wave. The model confirms the earlier hypothesis that the SPW is the key factor that determines efficiency of weed biocontrol program. We demonstrate also that the formation of the wave has crucially accelerated the development of the beetles’ ability to fly.
Mathematics Subject Classification: 92B05 / 92D25 / 92D50 / 92D40
Key words: spatio-temporal dynamics / trophic system / Allee effect / taxis–diffusion–reaction / trophotaxis / demogenetic Kostitzin model / gene surfing / biological control / weed control / Ambrosia artemisiifolia L. / Zygogramma suturalis F.
© EDP Sciences, 2013
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