The development of a spatio-temporal model for water hyacinth, Eichhornia crassipes (Martius) Solms-Laubach (Pontederiaceae), biological control strategies

Van Schalkwyk, Helene (2016-12)

Thesis (MCom)--Stellenbosch University, 2016.

Thesis

ENGLISH SUMMARY : The sustainable and cost-effective management of the notorious water hyacinth weed remains a challenge in South Africa. In this study, a reaction-diffusion model, consisting of a system of delayed partial differential equations, is developed to mathematically describe the population growth and dispersal of water hyacinth and the interacting populations of the various life stages of the Neochetina eichhorniae weevil as a biological control agent (BCA) in a temporally variable and spatially heterogeneous environment, subject to homogeneous Neumann boundary conditions on a bounded two-dimensional spatial domain. The primary objectives are to establish a spatio-temporal model which may be used to investigate the efficiency of different biological control release strategies, providing guidance towards the optimal magnitude, frequency, timing and distribution of BCA releases, and to evaluate the cost-effectiveness of local mass rearing programmes in biological control. Although previous studies have started to examine the influence of temperature on the population dynamics of the two species and the control of the weed under constant conditions, the model developed in this study is the first to evaluate the effect of introducing spatial dynamics. In addition, for the first time in research of water hyacinth management, different BCA release strategies are compared by means of mathematical modelling to provide practical recommendations for efficient and cost-effective biological control of water hyacinth in South Africa without having to conduct formal field experiments. Numerical solutions emphasize the benefit of frequent releases of Neichhorniae compared to a once-off release in the long term, as well as the advantage of more distributed releases along the edges of an infested water body. Furthermore, releases commencing in summer appear to be significantly more efficient and cost-effective than releases commencing in winter. The model is applied to a real-world release site in order to illustrate how the model may be utilized to provide guidance towards suitable BCA release strategies, which may minimize costs while maximizing the benefit for a specific site.

AFRIKAANSE OPSOMMING : Die volhoubare en koste-effektiewe bestuur van die berugte waterhiasint onkruid bly ’n uitdaging in Suid-Afrika. In hierdie studie word ’n reaksie-diffusiemodel, wat bestaan uit ’n stelsel van vertraagde parsi¨ele differensiaalvergelykings, ontwikkel om die bevolkingsaanwas en verspreiding van die waterhiasint en die interaktiewe bevolkings van die verskillende lewenstadiums van die Neochetina eichhorniae-kewer as ’n biologiese beheeragent in ’n dinamiese en ruimtelik- heterogene omgewing wiskundig te beskryf, onderhewig aan homogene Neumann-randwaardes op ’n begrensde, tweedimensionele ruimtelike gebied. Die primere doelstellings is om ’n model tot stand te bring wat gebruik kan word om die doeltreffendheid van verskillende biologiese beheervrylatingstrategiee te ondersoek, om leiding te verskaf met betrekking tot die optimale omvang, frekwensie, tydsberekening en verspreiding van beheeragentvrylatings, en om die koste- effektiwiteit van plaaslike massakweekprogramme in biologiese beheer te evalueer. Alhoewel vorige studies begin het om die invloed van temperatuur op die bevolkingsdinamika van die twee spesies en die beheer van die onkruid onder konstante toestande te ondersoek, is die model wat in hierdie studie ontwikkel is die eerste om die effek van die bekendstelling van ruimte- like dinamika te evalueer. Bykomend, vir die eerste keer in navorsing van waterhiasintbestuur, is verskillende biologiese beheeragentvrylatingstrategiee met mekaar vergelyk met behulp van wiskundige modellering om praktiese aanbevelings vir doeltreffende en koste-effektiewe biologiese beheer van waterhiasint in Suid-Afrika te voorsien sonder om formele veldeksperimente uit te voer. Numeriese oplossings beklemtoon die voordeel van gereelde vrylatings van N. eichhorniae in vergelyking met ’n eenmalige vrylating in die langtermyn, asook die voordeel van meer verspreide vrylatings langs die kante van ’n besmette waterliggaam. Verder vertoon vrylatings wat in die somer begin om aansienlik meer doeltreffend en koste-effektief te wees as vrylatings wat in die winter begin. Die model word toegepas op ’n werklike vrylatingsgebied om te illustreer hoe die model gebruik kan word om leiding te verskaf met betrekking tot geskikte biologiese beheeragentvrylatingstrategiee, wat kostes mag minimeer terwyl die voordeel gemaksimeer word vir ’n spesifieke scenario.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/100191
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