Theses and Dissertations at Montana State University (MSU)
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/733
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Item A biofilm model that avoids a tragedy of the commons(Montana State University - Bozeman, College of Letters & Science, 2021) Dayutis, Seth Aaron; Chairperson, Graduate Committee: Jack D. DockeryThe study of competition between multiple species is of great significance in biology. Competitive behavior is often observed to occur in biofilms and understanding cooperation between multiple species in a single biofilm is the center of much research. The species that grow in biofilms are frequently studied in chemostats, which have a rich history in mathematical modeling. In this thesis, a review of a mathematical chemostat model is presented in which a tragedy of the commons occurs. The chemostat model is then developed into a biofilm model to see if a tragedy occurs in a biofilm under similar conditions. The biofilm and chemostat model consist of two species, a cooperator and a cheater. The cooperator produces an enzyme that combines with a substrate to produce a nutrient. The nutrient is then consumed by the cooperator and cheater. The cooperator is at a disadvantage since it must allocate some of its nutrient uptake towards enzyme production. A one dimensional biofilm model is developed with reaction advection equations governing the behavior of the species and reaction-diffusion equations governing the behavior of the substrate, nutrient ,and enzyme. A set of numerical methods is then outlined on how to solve the system of equations. It is found that a tragedy of the commons is avoided in the biofilm and both species can persist when numerical simulations are run for a finite amount of time. It is then argued that the cooperative behavior exhibited by the two species is a stable equilibrium by approximating the steady state solutions. Further evidence is provided for the existence of a stable equilibrium by perturbing the system and finding that the perturbed system tends back to the equilibrium. Finally, the eigenvalues of the discretized linear system are computed and the results suggest that either the equilibrium is stable or moves away from the equilibrium slowly.Item Coexistence between a native (Valvata humeralis) and a non-native (Potamopyrgus antipodarum) gastropod in the Middle Snake River, Idaho : implications for invasive species impact(Montana State University - Bozeman, College of Letters & Science, 2012) Gates, Kiza Kristine; Chairperson, Graduate Committee: Billie L. Kerans; Billie. L. Kerans was a co-author of the article, 'Spatial, temporal, and diet partitioning combine with environmental stochasticity to enable coexistence between an invasive and a native gastropod' in the journal 'Biological invasions' which is contained within this thesis.; Billie. L. Kerans was a co-author of the article, 'Biotic interaction gradients between native and invasive species' in the journal 'Ecology' which is contained within this thesis.; Billie. L. Kerans was a co-author of the article, 'Competitive and facilitative mechanisms of a biotic interaction gradient' in the journal 'Oecologia' which is contained within this thesis.The dominant competitive abilities of many invasive species are frequently assumed to preclude biologically similar native species over time, but there has been little research exploring how interactions between invasive and native species may change with changes in biotic and abiotic conditions. Introduction of the invasive New Zealand mud snail Potamopyrgus antipodarum in the Snake River in the late 1980's raised many concerns for the native gastropods of this region; however, the native gastropod Valvata humeralis has maintained large populations and continued to coexist with P. antipodarum. I investigated the coexistence of P. antipodarum and V. humeralis in the Vista reach of the Middle Snake River. Diet, spatial, and temporal partitioning of V. humeralis were explored in populations that were invaded by P. antipodarum and uninvaded. A field growth experiment was used to measure the net intra- and interspecific effects of V. humeralis and P. antipodarum at varying densities and species proportions. Results of the field growth experiment were compared with field survey data. A laboratory growth experiment and a stoichiometric experiment were used to identify the interaction mechanisms between species. Valvata humeralis juveniles appeared to shift diet in the presence P. antipodarum. There was evidence of spatial partitioning from P. antipodarum by V. humeralis at the among population scale but not the within population or patch scales. The field growth experiment indicated that interspecific net effects of P. antipodarum on V. humeralis changed in direction with increasing P. antipodarum density. Field surveys showed a similar pattern. The laboratory growth experiment indicated that direct interference competition was the negative mechanism of the species interaction and confirmed field experimental results. Stoichiometric analyses suggested that P. antipodarum juveniles require more phosphorus than V. humeralis juveniles, but that stoichiometric facilitation was not likely an interaction mechanism. Facilitated growth of V. humeralis in the presence of P. antipodarum may have been caused by increased access to food and/or P. antipodarum digestive food conditioning. Results suggest that the impact of an invasive species on the native community may be a complex interplay between invader density, native species behavior, invader nutrient use, and environmental conditions.