Complexity and stability of mutualistic local networks and meta-networks
| dc.contributor.advisor | Hui, Cang | en_ZA |
| dc.contributor.author | Nnakenyi, Chinenye Assumpta | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Computer Science. | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Computer Science. | en_ZA |
| dc.date.accessioned | 2021-01-13T10:26:28Z | |
| dc.date.accessioned | 2021-04-22T10:10:53Z | |
| dc.date.available | 2021-07-13T03:00:09Z | |
| dc.date.issued | 2021-03 | |
| dc.description | Thesis (PhD)--Stellenbosch University, 2021. | en_ZA |
| dc.description.abstract | ENGLISH ABSTRACT: Biotic interactions, either in local networks or in meta-networks, are ubiquitous in nature. Species interact with other species of different interaction strengths in the ecosystem. For example, mutualistic interactions, whereby species benefit from each other, have been found to play a significant role in the function and structure of ecological communities. Previous empirical and theoretical studies have shown the vital contribution of mutualistic interactions in maintaining diversity amidst perturbations from the environment. Such perturbations affect the species and their interactions, exerting pressure on the ecosystem. However, it is unclear how the strengths of species interactions affect species abundances in the communities, and understanding the mechanism behind the complexity and stability of mutualistic meta-networks and local networks remains a challenge to be addressed. In this thesis, using a random matrix approach, I found that the stability criteria of a block-structured network or matrix is obtained from max( r1; r2) m < 0, where m is derived from the expectation of the diagonal elements of the matrix, while r1 and r2 are derived from the off-diagonal elements of the matrix when the expectation of the off-diagonal elements is different from zero and equal to zero respectively. Also, using a Lotka-Volterra model of mixed interaction types in different proportions, that describes the dynamics of species abundances, I found that species abundances are determined more by the species’ sensitivities to the interaction pressures from their partners than by species’ impacts on their partners. Besides, the abundances of the rarest species was found to be a good indicator of the resilience of the communities. Even when modelling real mutualistic local networks using a modified Lotka-Volterra model that incorporates adaptive interaction switching (AIS) and environmental variables, I found that the AIS could destabilise the local networks. However, to explain the emergence of nestedness and modularity in those networks, I found AIS to be a key driving mechanism behind community nestedness, with the environmental variables playing a secondary role in explaining nestedness and modularity. Finally, using a competition-mutualism model of meta-networks, I showed the role of dispersal and the role of mutualism to the complexity and stability of the networks. I found that incorporating mutualism in the model of meta-networks is crucial to the functioning of the meta-networks, as mutualism increases the stability of the meta-networks, increases the total abundance of species, decreases unevenness in the species abundances, and increases nestedness more than in the model without mutualism. Also, I showed that dispersal is a strong stabilising factor for the meta-networks. Importantly, dispersal heterogeneity between local networks drives the changes in total abundance, unevenness, and compositional similarity of species in the meta-networks and the local networks, irrespective of the dispersal heterogeneity across species. That is dispersal heterogeneity between the local networks decreases total abundance, increases unevenness and decreases compositional similarity in the meta-networks and local networks. Knowledge about the dispersal rates between local networks and across species is crucial to understand the complexity and stability of the local and meta-networks. Hence, these findings have contributed to the stability and complexity of ecological networks, at both local and regional scales, which is relevant for the management and conservation of interaction networks with the objective of preserving the species functions and services in the ecosystem. | en_ZA |
| dc.description.abstract | AFRIKAANSE OPSOMMING: Biotiese interaksies, hetsy in plaaslike netwerke of in metanetwerke, is alomteenwoordig van aard. Spesies interakteer met ander spesies van verskillende interaksiesterkte in die ekosisteem. Daar is gevind dat onderlinge interaksies, waarby spesies by mekaar voordeel trek, byvoorbeeld ’n belangrike rol speel in die funksie en struktuur van ekologiese gemeenskappe. Vorige empiriese en teoretiese studies het die belangrike bydrae gelewer van mutualistiese interaksies om diversiteit te handhaaf te midde van versteurings uit die omgewing. Sulke versteurings beïnvloed die spesies en hul interaksies, wat druk op die ekosisteem uitoefen. Dit is egter onduidelik hoe die sterkte van spesie-interaksies spesie-oorvloed in die gemeenskappe beïnvloed, en die begrip van die meganisme agter die kompleksiteit en stabiliteit van mutualistiese metanetwerke en plaaslike netwerke is steeds ’n uitdaging om aan te spreek. In hierdie proefskrif, met behulp van ’n ewekansige matriks-benadering, het ek gevind dat die stabiliteitskriteria van ’n blokgestruktureerde netwerk of matriks verkry word vanaf max( r1; r2)m < 0, waar m afgelei word van die verwagting van die diagonale elemente van die matriks, terwyl r1 en r2 afgelei word van die af-diagonale elemente van die matriks, terwyl die verwagting van die af-diagonale elemente onderskeidelik van nul en gelyk aan nul verskil. Met behulp van ’n Lotka-Volterra-model van gemengde interaksietipes in verskillende verhoudings, wat die dinamika van spesie-oorvloed beskryf, het ek gevind dat spesie-oorvloed meer bepaal word deur die sensitiwiteit van die spesie vir die interaksiedruk van hul vennote as deur spesies se impak op hul vennote. Daar is ook gevind dat die oorvloed van die skaarsste spesies ’n goeie aanduiding is van die veerkragtigheid van die gemeenskappe. Selfs by die modellering van werklike onderlinge plaaslike netwerke met behulp van ’n aangepaste Lotka-Volterra-model wat aanpasbare interaksie-omskakeling (AIS) en omgewingsveranderlikes insluit, het ek gevind dat die AIS die plaaslike netwerke kan destabiliseer. Om die verskyning van geneste en modulariteit in daardie netwerke te verklaar, het ek egter gevind dat AIS ’n belangrike dryfveer is vir gemeenskapsneste, en dat die omgewingsveranderlikes ’n sekondêre rol speel in die verklaring van geneste en modulariteit. Ten slotte, met behulp van ’n kompetisie-mutualismemodel van metanetwerke, het ek die rol van verspreiding en die rol van mutualisme getoon vir die kompleksiteit en stabiliteit van die netwerke. Ek het gevind dat die integrering van mutualisme in die modelle van metanetwerk van kardinale belang is vir die funksionering van die metanetwerk, aangesien mutualisme die stabiliteit van die metanetwerke verhoog, die totale verskeidenheid spesies verhoog, ongelykhede in die spesie-oorvloed verminder, en die nes meer verhoog as in die modelle sonder wedersyds. Ek het ook getoon dat verspreiding ’n sterk stabiliserende faktor vir metawerke is. Wat belangrik is, is dat verspreidings heterogeniteit tussen plaaslike netwerke die veranderinge in totale oorvloed, ongelykheid en samestellingsgelykheid van spesies in die metanetwerke en plaaslike netwerke veroorsaak, ongeag die verspreiding van heterogeniteit tussen spesies. Dus, die verspredings heterogeniteit tussen die plaaslike netwerke verminder die totale oorvloed, verhoog ongelykhede en verminder die samestelling van die meta-netwerke en plaaslike netwerke. Kennis oor die verspreidingsnelheid tussen plaaslike netwerke en verskillende soorte is van kardinale belang om die kompleksiteit en stabiliteit van die plaaslike en metanetwerke te verstaan. Hierdie bevindings het dus bygedra tot die stabiliteit en ingewikkeldheid van ekologiese netwerke, op plaaslike en plaaslike skale, wat relevant is vir die bestuur en bewaring van interaksienetwerke met die doel om die spesiefunksies en dienste in die ekosisteem te bewaar. | af_ZA |
| dc.description.abstract | AFRIKAANSE OPSOMMING: Biotiese interaksies, hetsy in plaaslike netwerke of in metanetwerke, is alomteenwoordig van aard. Spesies interakteer met ander spesies van verskillende interaksiesterkte in die ekosisteem. Daar is gevind dat onderlinge interaksies, waarby spesies by mekaar voordeel trek, byvoorbeeld ’n belangrike rol speel in die funksie en struktuur van ekologiese gemeenskappe. Vorige empiriese en teoretiese studies het die belangrike bydrae gelewer van mutualistiese interaksies om diversiteit te handhaaf te midde van versteurings uit die omgewing. Sulke versteurings beïnvloed die spesies en hul interaksies, wat druk op die ekosisteem uitoefen. Dit is egter onduidelik hoe die sterkte van spesie-interaksies spesie-oorvloed in die gemeenskappe beïnvloed, en die begrip van die meganisme agter die kompleksiteit en stabiliteit van mutualistiese metanetwerke en plaaslike netwerke is steeds ’n uitdaging om aan te spreek. In hierdie proefskrif, met behulp van ’n ewekansige matriks-benadering, het ek gevind dat die stabiliteitskriteria van ’n blokgestruktureerde netwerk of matriks verkry word vanaf max( r1; r2)m < 0, waar m afgelei word van die verwagting van die diagonale elemente van die matriks, terwyl r1 en r2 afgelei word van die af-diagonale elemente van die matriks, terwyl die verwagting van die af-diagonale elemente onderskeidelik van nul en gelyk aan nul verskil. Met behulp van ’n Lotka-Volterra-model van gemengde interaksietipes in verskillende verhoudings, wat die dinamika van spesie-oorvloed beskryf, het ek gevind dat spesie-oorvloed meer bepaal word deur die sensitiwiteit van die spesie vir die interaksiedruk van hul vennote as deur spesies se impak op hul vennote. Daar is ook gevind dat die oorvloed van die skaarsste spesies ’n goeie aanduiding is van die veerkragtigheid van die gemeenskappe. Selfs by die modellering van werklike onderlinge plaaslike netwerke met behulp van ’n aangepaste Lotka-Volterra-model wat aanpasbare interaksie-omskakeling (AIS) en omgewingsveranderlikes insluit, het ek gevind dat die AIS die plaaslike netwerke kan destabiliseer. Om die verskyning van geneste en modulariteit in daardie netwerke te verklaar, het ek egter gevind dat AIS ’n belangrike dryfveer is vir gemeenskapsneste, en dat die omgewingsveranderlikes ’n sekondêre rol speel in die verklaring van geneste en modulariteit. Ten slotte, met behulp van ’n kompetisie-mutualismemodel van metanetwerke, het ek die rol van verspreiding en die rol van mutualisme getoon vir die kompleksiteit en stabiliteit van die netwerke. Ek het gevind dat die integrering van mutualisme in die modelle van metanetwerk van kardinale belang is vir die funksionering van die metanetwerk, aangesien mutualisme die stabiliteit van die metanetwerke verhoog, die totale verskeidenheid spesies verhoog, ongelykhede in die spesie-oorvloed verminder, en die nes meer verhoog as in die modelle sonder wedersyds. Ek het ook getoon dat verspreiding ’n sterk stabiliserende faktor vir metawerke is. Wat belangrik is, is dat verspreidings heterogeniteit tussen plaaslike netwerke die veranderinge in totale oorvloed, ongelykheid en samestellingsgelykheid van spesies in die metanetwerke en plaaslike netwerke veroorsaak, ongeag die verspreiding van heterogeniteit tussen spesies. Dus, die verspredings heterogeniteit tussen die plaaslike netwerke verminder die totale oorvloed, verhoog ongelykhede en verminder die samestelling van die meta-netwerke en plaaslike netwerke. Kennis oor die verspreidingsnelheid tussen plaaslike netwerke en verskillende soorte is van kardinale belang om die kompleksiteit en stabiliteit van die plaaslike en metanetwerke te verstaan. Hierdie bevindings het dus bygedra tot die stabiliteit en ingewikkeldheid van ekologiese netwerke, op plaaslike en plaaslike skale, wat relevant is vir die bestuur en bewaring van interaksienetwerke met die doel om die spesiefunksies en dienste in die ekosisteem te bewaar. | af_ZA |
| dc.description.abstract | ENGLISH ABSTRACT: Biotic interactions, either in local networks or in meta-networks, are ubiquitous in nature. Species interact with other species of different interaction strengths in the ecosystem. For example, mutualistic interactions, whereby species benefit from each other, have been found to play a significant role in the function and structure of ecological communities. Previous empirical and theoretical studies have shown the vital contribution of mutualistic interactions in maintaining diversity amidst perturbations from the environment. Such perturbations affect the species and their interactions, exerting pressure on the ecosystem. However, it is unclear how the strengths of species interactions affect species abundances in the communities, and understanding the mechanism behind the complexity and stability of mutualistic meta-networks and local networks remains a challenge to be addressed. In this thesis, using a random matrix approach, I found that the stability criteria of a block-structured network or matrix is obtained from max( r1; r2) m < 0, where m is derived from the expectation of the diagonal elements of the matrix, while r1 and r2 are derived from the off-diagonal elements of the matrix when the expectation of the off-diagonal elements is different from zero and equal to zero respectively. Also, using a Lotka-Volterra model of mixed interaction types in different proportions, that describes the dynamics of species abundances, I found that species abundances are determined more by the species’ sensitivities to the interaction pressures from their partners than by species’ impacts on their partners. Besides, the abundances of the rarest species was found to be a good indicator of the resilience of the communities. Even when modelling real mutualistic local networks using a modified Lotka-Volterra model that incorporates adaptive interaction switching (AIS) and environmental variables, I found that the AIS could destabilise the local networks. However, to explain the emergence of nestedness and modularity in those networks, I found AIS to be a key driving mechanism behind community nestedness, with the environmental variables playing a secondary role in explaining nestedness and modularity. Finally, using a competition-mutualism model of meta-networks, I showed the role of dispersal and the role of mutualism to the complexity and stability of the networks. I found that incorporating mutualism in the model of meta-networks is crucial to the functioning of the meta-networks, as mutualism increases the stability of the meta-networks, increases the total abundance of species, decreases unevenness in the species abundances, and increases nestedness more than in the model without mutualism. Also, I showed that dispersal is a strong stabilising factor for the meta-networks. Importantly, dispersal heterogeneity between local networks drives the changes in total abundance, unevenness, and compositional similarity of species in the meta-networks and the local networks, irrespective of the dispersal heterogeneity across species. That is dispersal heterogeneity between the local networks decreases total abundance, increases unevenness and decreases compositional similarity in the meta-networks and local networks. Knowledge about the dispersal rates between local networks and across species is crucial to understand the complexity and stability of the local and meta-networks. Hence, these findings have contributed to the stability and complexity of ecological networks, at both local and regional scales, which is relevant for the management and conservation of interaction networks with the objective of preserving the species functions and services in the ecosystem. | en_ZA |
| dc.description.version | Doctoral | en_ZA |
| dc.description.version | Doctoral | en_ZA |
| dc.embargo.terms | 2021-07-13 | |
| dc.format.extent | xviii, 235 pages : illustrations | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/10019.1/110247 | |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | en_ZA |
| dc.subject | Biotic communities -- Mathematical models | en_ZA |
| dc.subject | Mutualism (Biology) -- Mathematical models | en_ZA |
| dc.subject | Biodiversity | en_ZA |
| dc.subject | Ecological disturbances | en_ZA |
| dc.subject | Meta-network (Ecology) | en_ZA |
| dc.subject | Local network (Ecology) | en_ZA |
| dc.title | Complexity and stability of mutualistic local networks and meta-networks | en_ZA |
| dc.type | Thesis | en_ZA |