Spreading waves of invasive species

Ramanantoanina, Andriamihaja (2014-03)

Thesis (PhD)--Stellenbosch University, 2014.

Thesis

ENGLISH ABSTRACT: Invasive species are well known to harm economy as well as ecological assets and impair ecosystems functioning around the world. Timely control and management of new incursions of invasive species necessitate predictive tools that can anticipate areas that are susceptible to the invasion as well as the rate of the species spread. Early models predicted that a single species invading a homogeneous landscape advances its range at a constant rate which is determined by the population's growth and dispersal rate. Although this result has been successfully used in numerous cases, it leaves unanswered di erent patterns of range expansion that have been observed in nature. The purpose of this thesis was to model and investigate di erent factors that can in uence the spread of a species, with an emphasis on the rate of spread. First, we investigated the in uence of an initial population with mixed dispersal abilities. In a rst case, we assumed that all individuals have the same dispersal ability with the exception of few individuals which are signi cantly better dispersers. In a second case, we assumed that the dispersal abilities in the initial population are log-normally distributed. A system of integrodi erence equations was used to model the spatiotemporal dynamics of the population. We found that the dispersal abilities were spatially sorted. The instantaneous rate of spread was found to be fully determined by the growth and dispersal abilities of the population at the advancing edge of the invasion. The results therefore suggest that data collected from the core of the invasion may underestimate the spread of the population. Finally, our results suggest that the three patterns of range expansions presented by Shigesada and Kawasaki in 1997 can be alternatively explained by the mixture of individuals with di erent dispersal abilities in the initial population. Second, we studied the in uence of environmental heterogeneity on the spread of a population using integrodi erence model in which growth and dispersal parameters are functions of habitat quality. Two environmental structures were considered. The rst structure consists of a fragmented environment in which the habitat quality is given by step functions. This environment was used to investigate the in uence of landscape fragmentation on the rate of spread. In the second environment structure, the habitat quality varies sinusoidally in space. This case was used to examine the in uence of the amplitude of environmental variations. Lower and upper bounds of the asymptotic rate of spread was derived and veri ed using numerical simulations. In the case of fragmented environment, we further investigated the proportion of favourable habitat that is optimal for the spread of the population. The results suggest that the presence of unfavourable habitats can act to accelerate the spread of a population. Finally, an increase in the variability of the growth or dispersal processes can accelerate or decelerate the spread of a population depended on whether growth and dispersal parameters oscillate in or out of phase. Lastly, we investigated how two density-dependent dispersal behaviours, namely prey evasion (PE) and predator pursuit (PP), shape the dynamics of a predatorprey system. PE portrays the tendency of prey avoiding predators by dispersing into adjacent patches with fewer predators, while PP describes the tendency of predators to pursue the prey by moving into patches with more prey. We used a spatially explicit metapopulation model to capture the dynamics of the species. Local populations were modelled based on the Beddington predation model, and di erent locations were linked by dispersal which incorporate PE and PP. Exhaustive numerical simulations were used to investigate the e ects of PE and PP on the spatial synchrony, the persistence of metapopulation as well as the rate of spread. Results show that both PE and PP can alter spatial synchrony although PP has a weaker desynchronising e ect than PE. The predator-prey system without PE and PP expanded in circular waves. The e ect of PE can push prey to distribute in a circular ring front, whereas the e ect of PP can change the circular waves to anisotropic expansions. The e ects of PE and PP further enhanced the population size, broke down spatial synchrony and promoted the persistence of populations. Finally, weak PE and PP can accelerate the spread of prey while strong and disproportionate intensities slow down the range expansion.

AFRIKAANSE OPSOMMING: Indringerspesies is alom bekend om beide ekonomiese en ekologiese sisteme te benadeel en die funksionering van ekosisteme regoor die wêreld negatief te beïnvloed. Gepaste monitering en bestuur van nuwe aanvalle van indringerspesies vereis gereedskap wat kan voorspel watter areas is vatbaar vir indringers sowel as die tempo van die verspreiding van spesies. Vroeë modelle het voorspel dat 'n enkele spesie wat 'n homogeniese landskap binne treë versprei teen 'n konstante tempo wat bepaal word deur die spesie bevolking se groeikoers en verspreidings tempo. Alhoewel hierdie resultaat suksesvol gebruik was in menigte gevalle, laat dit verskillende patrone van reeks uitbreiding wat waargeneem word in die natuur steeds onbeantwoord. Die doel van hierdie tesis was om die verskillende faktore wat die verspreiding van 'n spesie beïnvloed te modelleer en te ondersoek, met die klem op die tempo van verspreiding. Eerstens, het ons die invloed van 'n oorspronklike bevolking met gemengde verspreidings vermoëns ondersoek. In 'n eerste geval, het ons aanvaar dat alle individue dieselfde verspreidings vermoëns besit met die uitsondering van enkele individue wat aansienlik beter versprei. In 'n tweede geval, het ons aanvaar dat die verspreidings vermoëns in die aanvanklike bevolking log-normaal versprei. 'n Stelsel van integro-verskil vergelykings was gebruik om die tydruimtelike dinamika van die bevolking te modelleer. Ons het gevind dat die verspreiding vermoëns ruimtelik gesorteer was. Die oombliklike tempo van verspreiding was gevind om ten volle bepaal te word deur die groei en verspreiding vermoëns van die bevolking op die bevorderings rand van die inval. Die resultate dui dus daarop dat data wat versamel is vanuit die kern van die inval kan die verspreiding van die bevolking onderskat. Ten slotte, ons resultate dui daarop dat die drie patrone van reeks uitbreidings aangebied deur Shigesada en Kawasaki in 1997 kan alternatiewelik verduidelik word deur die mengsel van individue met verskillende verspreiding vermoëns in die oorspronklike bevolking. Tweedens, het ons die invloed van heterogeniteit van die omgewing op die verspreiding van 'n bevolking bestudeer deur 'n integro-verskil model te gebruik waarin groei en verspreiding veranderlikes funksies is van habitat kwaliteit. Twee omgewings strukture was oorweeg. Die eerste struktuur het bestaan uit 'n gefragmenteerde omgewing waar die habitat kwaliteit deurgegee word as trap funksies. Hierdie omgewing was gebruik om die invloed van die landskap versnippering op die tempo van verspreiding te ondersoek. In die tweede struktuur omgewing, het die habitat kwaliteit sinusoïdaal gewissel in die ruimte. Hierdie saak was gebruik om die invloed van die amplitude van die omgewing variasies te ondersoek. Onderste en boonste grense van die asimptotiese tempo van verspreiding was afgelei en geveri eer deur gebruik te maak van numeriese simulasies. In die geval van 'n gefragmenteerde omgewing, het ons verdere ondersoek ingestel oor die verhouding van gunstigde habitat wat optimaal is vir die verspreiding van die bevolking. Die resultate dui daarop dat die teenwoordigheid van ongunstige habitatte kan optree om die verspreiding van 'n bevolking te versnel. Ten slotte, 'n toename in die wisselvalligheid van die groei of verspreiding prosesse kan die verspreiding van 'n bevolking versnel of vertraag afhangende of die groei en verspreiding parameters ossilleer binne of buite fase. Laastens, het ons ondersoek hoe twee digtheids-afhanklike verspreidings gedrag, naamlik prooi ontduiking (PE) en roofdier strewe (PP), die dinamika van 'n roofdier -prooi stelsel vorm. PE beeld die neiging van die prooi om die roofdiere te vermy deur te versprei na aangrensende gebiede met minder roofdiere, terwyl PP beskryf die neiging van roofdiere om prooi na te streef deur te beweeg na gebiede met meer prooi. Ons het 'n ruimtelik eksplisiete meta populasie model gebruik om die dinamika van die spesies vas te vang. Plaaslike bevolkings was gemodelleer deur middel van die Beddington roofdiere model, en verskillende plekke was verbind deur verspreiding wat beide PE en PP inkorporeer. Vele numeriese simulasies was gebruik om die gevolge van PE en PP op die ruimtelike sinkronie, die voortbestaan van die meta populasie sowel as die tempo van verspreiding te ondersoek. Resultate toon dat beide PE en PP die ruimtelike sinkronie kan verander hoewel PP het 'n swakker desinkronie e ek as PE. Die roofdier -prooi stelsel sonder PE en PP het uitgebrei in sirkelvormige golwe. Die e ek van PE kan prooi forseer om te versprei in 'n ring, waar die e ek van PP die sirkelvormige golwe kan verander na anisotrope uitbreidings. Die gevolge van die PE en PP verder versterk die grootte van die bevolking, breek die ruimtelike sinkronie en bevorder die voortbestaan van bevolkings. Ten slotte, swak PE en PP kan die verspreiding van die prooi versnel, terwyl sterk en oneweredige sterkte vertraag die uitbreidings reeks.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/86761
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