Resting Stages and the Population Dynamics of Harmful Algae in ...

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4.2 Chemostat CultureThe chemostat model represents a somewhat novel approach for analysis ofalgal species with transitions to resting stages. From the mathematical modelwe deduced thatMB∗NB∗ = 1 δ D + γ δ .Thus our model suggests that if the transition rates are constant, then they canbe calculated by knowing the steady state population values and the dilutionrate.References[1] Clodong, S. and Blasius, B., 2004.Chaos in a periodically forced chemostatwith algal mortality. Proceedings of the Royal Society of London B 271,1617-1624.[2] Green, J. C., Hibberd, D. J. and Pienaar, R. N., 1982. The taxonomyof Prymnesium (Prymnesiophyceae) including a description of a new cosmopolitanspecies, P. patellifera sp. nov., and further observations on P.parvum (N. Carter). British Phycological Journal 17:4, 363-382.[3] Grover, J.P., Crane, K.W., Baker, J.W., Brooks, B. W., and Roelke, D.L., 2011. Spatial variation of harmful algae and their toxins in flowingwaterhabitats: a theoretical exploration. Journal of Plankton Research,33, 211-227.[4] Jordan, R.W. and Chamberlain, A.H.L., 1997. Biodiversity among haptophytealgae. Biodiversity and Conservation 6:1, 131-152.[5] Southard, G.M., Fries, L.T. and Barkoh, A., 2010. Prymnesium parvum:the Texas experience. Journal of American Water Resources Association46:1, 14-23.[6] Larsen, A., and S. Bryant. 1998. Growth rate and toxicity of Prymnesiumparvum and Prymnesium patelliferum (Haptophyta) in response to changesin salinity, light and temperature. Sarsia 83: 409-418.[7] Roelke, D. L., R. M. Errera, R. Kiesling, B. W. Brooks, J. P. Grover, L.Schwierzke, F. Urena-Boeck, J. Baker, and J. L. Pinckney. 2007. Effectsof nutrient enrichment on Prymnesium parvum population dynamics andtoxicity: Results from field experiments, Lake Possum Kingdom, USA.Aquatic Microbial Ecology 46: 125-140.[8] Igarashi, T., Satake, M., Yasumoto, T., 1999.Structural and partial stereochemicalassignmentsfromprymnesin-1andprymnesin-2:potenthemolyticand ichthyotoxic glycosides isolated from the red tide alga Prymnesiumparvum. Journal of the American Chemical Society 121, 8499-8511.13
[9] Brooks, B.W., James, S.V., Valenti, T.W., Urena-Boeck, F., Serrano, C.,Schwierzke, L., Mydlarz, L.D., Grover, J.P., Roelke, D.L., 2010. Comparativetoxicity of Prymnesium parvum in inland waters. Journal of the AmericanWater Resources Association 46, 45-62.[10] Tillmann, U., 2003. Kill and eat your predator: a winning strategy of theplanktonic flagellate Prymnesium parvum. Aquatic Microbial Ecology 32,73-84.14
Page 1 and 2: Resting Stages and the PopulationDy
Page 3 and 4: (Baker et al., 2007). It was discov
Page 5 and 6: and therefore it is the summation o
Page 7 and 8: dMdt= µ maxRMK +R−DM −δM +γN
Page 9 and 10: The second condition for Case 1 is
Page 11 and 12: So if we are in Case 1 of feasibili
Page 13: 10.90.8Case 2 of Chemostatmotil cel

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