EXPLORATIONS OF ASPECTS OF MIXOTROPHY USING MATHEMATICAL MODELS by KENNETH W. CRANE Presented to the Faculty of the Graduate School of The University of Texas at Arlington in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT ARLINGTON August 2010 Copyright © by Kenneth W. Crane 2010 All rights reserved ACKNOWLEDGEMENTS This work could not have been completed without the financial support of the Biology Department and the University in the form of teaching assistantships and fellowships. I especially want to thank the Graduate School for providing the Graduate Dean’s Dissertation Fellowship that made the completion of this dissertation possible. My supervising professor, James P. Grover, made the completion of this work possible with advice on academics, research topics and methodologies, writing, and the funding of a research assistantship. I would also like to thank the other members of my committee, Thomas Chrzanowski, Laura Gough, Hristo Kojuharov, and Laura Mydalrz, for their time and advice. Finally, the financial and moral support of my family was essential to the completion of this challenge. July 8, 2010 iii ABSTRACT EXPLORATIONS OF ASPECTS OF MIXOTROPHY USING MATHEMATICAL MODELS Kenneth W. Crane, Ph.D. The University of Texas at Arlington, 2010 Supervising Professor: James P. Grover This work examined three theoretical aspects of mixotrophy, the simultaneous use of phototrophic and heterotrophic nutritional modes, and one practical application. The first study addressed the coexistence of microorganisms pursuing diverse nutritional strategies. It was found that in the range of model environments explored that all four types of organisms were predicted to persist for certain parameter combinations. The most successful mixotrophs were predicted to be primarily autotrophic, supplementing photosynthesis with bacterivory. The second study extended the first one by focusing on the effects of environmental parameters governing resource supplies and the responses of populations and ecosystem properties in relation to relative supplies of light and phosphorus. The model generally predicts that mixotrophs are abundant under wide ranges of resource supplies and leave a signature on the properties of aquatic ecosystems, such as phosphorus recycling. The third study further extends the model by incorporating seasonal variations in physiology. The densities of organisms and their growth limitations in response to this seasonal forcing were analyzed, along with the ecosystem iv properties of phosphorus flux and the C:P ratios of the organisms. The predictions of this seasonal model suggest that mixotrophs change the growth limitations of other organisms, and increase the recycled P flux in the microbial food web. The final study examined the consequences of adding mixotrophy to a model for Prymnesium parvum, a harmful algal species that forms blooms in Texas in the winter. This modified model was unable to account for the winter increase in the P. parvum population in Texas. Overall, this work gives insights into the role of mixotrophy in aquatic microbial communities. v TABLE OF CONTENTS ACKNOWLEDGEMENTS ................................................................................................................ iii ABSTRACT ...................................................................................................................................... iv LIST OF FIGURES .......................................................................................................................... ix LIST OF TABLES .......................................................................................................................... xiii Chapter Page 1. INTRODUCTION ............................................................................................................ 1 2. COEXISTENCE OF MIXOTROPHS, AUTOTROPHS, AND HETEROTROPHS IN PLANKTONIC MICROBIAL COMMUNITIES .............................................................................................................. 7 2.1 Introduction ...................................................................................................... 7 2.2 Model Formulation ......................................................................................... 10 2.2.1 Algae ............................................................................................. 10 2.2.2 Zooflagellates ................................................................................ 14 2.2.3 Mixotrophs ..................................................................................... 15 2.2.4 Bacteria ......................................................................................... 17 2.2.5 Environment .................................................................................. 18 2.3 Parameter Values .......................................................................................... 19 2.3.1 Algae ............................................................................................. 19 2.3.2 Zooflagellates ................................................................................ 19 2.3.3 Mixotrophs ..................................................................................... 20 2.3.4 Bacteria ......................................................................................... 20 2.4 Numerical Simulations ................................................................................... 20 2.5 Results ........................................................................................................... 22 2.6 Discussion ..................................................................................................... 25 vi 3. STEADY STATE ANALYSIS OF ENVIRONMENTAL PARAMETERS AND IMPLICATIONS FOR ECOSYSTEM PROPERTIES IN A MODEL INCLUDING MIXOTROPHY .......................................... 33 3.1 Introduction .................................................................................................... 33 3.2 Model Description .......................................................................................... 34 3.3 Numerical Calculations .................................................................................. 39 3.4 Results ........................................................................................................... 41 3.4.1 Population Persistence and Dynamics .......................................... 41 3.4.1.1 Phosphorus Supply (Pin) ................................................ 41 3.4.1.2 Mixing Depth ................................................................. 44 3.4.1.3 Surface Irradiance (Iin) ................................................... 47 3.4.1.4 Organic C supply (Cin) and turbidity (kbg) ...................... 49 3.4.2 Ecosystem Properties ................................................................... 52 3.4.2.1 Phosphorus Supply (Pin) ................................................ 52 3.4.2.2 Mixing Depth ................................................................. 54 3.4.2.3 Surface Irradiance (Iin) ................................................... 54 3.4.2.4 Organic Carbon Supply (Cin) and turbidity (kbg)............. 57 3.5 Discussion ..................................................................................................... 57 4. SEASONAL VARIATION OF COMMUNITY COMPOSITION AND ECOSYSTEM PROPERTIES .............................................................................. 63 4.1 Introduction .................................................................................................... 63 4.2 Model Formulation ......................................................................................... 65 4.3 Numerical Solutions ....................................................................................... 67 4.4 Results ........................................................................................................... 67 4.4.1 Temporal dynamics ............................................................................... 67 4.4.1.1 Algae .............................................................................................. 69 4.4.1.2 Bacteria .......................................................................................... 69 4.4.1.3 Zooflagellates and Bacteria ........................................................... 69 4.4.1.4 Mixotrophs ..................................................................................... 72 vii 4.4.1.5 Mixotrophs and Bacteria ................................................................ 72 4.4.1.6 Algae, Bacteria, and Zooflagellates ............................................... 75 4.4.1.7 Algae, Mixotrophs, and Bacteria .................................................... 75 4.4.2 Comparisons of winter and summer ...................................................... 81 4.4.2.1 Population Densities for BAZ ......................................................... 81 4.4.2.2 Population Densities for BAM ........................................................ 83 4.4.2.3 Recycled P flux .............................................................................. 85 4.4.2.4 Seston C:P ratios ........................................................................... 85 4.5 Discussion ..................................................................................................... 85 5. A MODEL FOR P. PARVUM WITH MIXOTROPHY .................................................... 91 5.1 Introduction