breeding pond dispersal of interacting california red-legged frogs

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  • BREEDING POND DISPERSAL OF INTERACTING CALIFORNIA RED-LEGGED

    FROGS (RANA DRAYTONII) AND AMERICAN BULLFROGS (LITHOBATES

    CATESBEIANUS) OF CALIFORNIA: A MATHEMATICAL MODEL WITH

    MANAGEMENT STRATEGIES

    HUMBOLDT STATE UNIVERSITY

    By

    Iris Acacia Gray

    A Thesis

    Presented to

    The Faculty of Humboldt State University

    In Partial Fulfillment

    Of the Requirements for the Degree

    Master of Science

    In Environmental Systems: Mathematical Modeling

    December, 2009

  • BREEDING POND DISPERSAL OF INTERACTING CALIFORNIA RED-LEGGED

    FROGS (RANA DRAYTONII) AND AMERICAN BULLFROGS (LITHOBATES

    CATESBEIANUS) OF CALIFORNIA: A MATHEMATICAL MODEL WITH

    MANAGEMENT STRATEGIES

    HUMBOLDT STATE UNIVERSITY

    By

    Iris Acacia Gray

    Approved by the Masters Thesis Committee:

    Dr. Borbala Mazzag, Major Professor Date

    Dr. Christopher Dugaw, Committee Member Date

    Dr. Sharyn Marks, Committee Member Date

    Dr. Christopher Dugaw, Graduate Coordinator Date

    Jena Burgess, Vice Provost Date

    Research, Graduate Studies & International Programs

  • ABSTRACT

    BREEDING POND DISPERSAL OF INTERACTING CALIFORNIA RED-LEGGED

    FROGS (RANA DRAYTONII) AND AMERICAN BULLFROGS (LITHOBATES

    CATESBEIANUS) OF CALIFORNIA: A MATHEMATICAL MODEL WITH

    MANAGEMENT STRATEGIES

    Iris Acacia Gray

    The invasion of American Bullfrogs (Lithobates catesbeianus) in the western United

    States has had a direct negative effect on the persistence of many native fauna. Native ranid

    frogs, in particular, face threats to their populations due to the competition and predation

    imposed by this behaviorally similar invader. The California Red-legged Frog (Rana dray-

    tonii) has been listed as a threatened species since 1996 due in part to the introduction

    of American Bullfrogs. A stage-based modeling effort has been developed for interact-

    ing American Bullfrogs and California Red-legged Frogs within a single pond (Doubledee

    et al., 2003). We modified and expanded this model to encompass several ponds by imple-

    menting juvenile dispersal between them. Movement rules were created using assumptions

    based in part on dispersal data collected for a California Red-legged Frog population within

    eight specific ponds in the Marin County area. They incorporate the probability of the ju-

    venile population being able to disperse a given distance and the probability of choosing

    to move to a specific pond when several possibilities are present. We performed param-

    eter studies for three unknown parameters: predation of tadpole and juvenile California

    Red-legged Frogs by adult American Bullfrogs and predation/competition of overwintered

    Bullfrog tadpoles on/with California Red-legged Frog eggs. This study provides combi-

    nations of these rates which facilitate coexistence between these species over a specified

    duration within the study ponds. Given a specific duration of coexistence (60 years) we

    iii

  • explored the effect of bullfrog tadpole, metamorph, and juvenile/adult focused eradication

    efforts as management strategies. The optimal rates of eradication associated with each

    of these tactics benefiting California Red-legged Frog persistence were established. We

    determined that seasonal ponds need not be managed, as they act as a refuge to the Cal-

    ifornia Red-legged frog, and thus aid in its long term survival. We found that removing

    at least 75% of the American Bullfrog tadpole population every year or draining ponds

    (100% Bullfrog tadpole eradication) at least every two years are sufficient strategies for

    managing all permanent ponds to achieve population levels exhibited by seasonal ponds.

    However, our model showed that without management permanent ponds connected (within

    a predetermined dispersal range) to seasonal ponds were able to harbor some population of

    California Red-legged frog beyond our assumed value of 60 years. Furthermore, we outline

    the areas in which further research could be implemented to enhance our model.

    Key words: California Red-legged Frog, American Bullfrog, stage-based model, dis-

    persal, coexistence, management.

    iv

  • ACKNOWLEDGMENTS

    First and foremost, I would like to thank the members of my thesis committee. Dr.

    Bori Mazzag, Dr. Chris Dugaw, and Dr. Sharyn Marks were invaluable fixtures within this

    project. Special thanks to Dr. Sharyn Marks for sharing her knowledge of amphibians and

    for her careful and thorough edits. Through the few meetings we had discussing the biology

    and ecology of these frogs, she enabled me to gain an understanding of their world I per-

    haps could not have gathered on my own. Special thanks to Dr. Chris Dugaw for requiring

    me to learn the computer programming language LATEX. This skill will aid me in achieving

    my research goals for the rest of my life, throughout which Ill always be thankful to him.

    He was also quite helpful in removing barriers in understanding some the more sophisti-

    cated mathematical and statistical elements involved in completing this project. Among my

    committee members, I am most thankful to the Chair of my committee: Dr. Bori Mazzag.

    Special thanks goes out to her for her editing, her help in the projects basic design devel-

    opment and understanding of the mathematics involved, and her outstanding knowledge of

    the programming language Matlab throughout the entire course of this project. Further-

    more, Bori was much more to me than just an advisor, she also occasionally played the role

    of counselor. When personal problems plagued me, she was always there to listen, offer

    advice, kleenex, and big warm hug. For all that shes done for me, I fear Ill never be able

    to thank her properly.

    The experiences Ive shared with my colleagues over the years spent working on my

    Masters Degree and this project are immeasurably precious to me. I would like to espe-

    cially thank Emily Hobelmann, Ben Holt, Chris Panza, Liz Arnold, Nicole Batenhorst, The

    The Kyaw, Daniele Rosa, Holly Perryman, Michelle Moreno, Kyle Falbo, Michael Om-

    stead, and Rick Warnock in this respect. Theyve laughed with me, theyve struggled with

    v

  • me, and most importantly theyve done mathematics with me. Because of this, these people

    will always be in my heart.

    There were several professors which gave me support and guidance beyond the scope

    of their post. I would like to thank Dr. Sharon Brown, Professor Tim Lauck, Dr. Steve

    McKelvey, Professor Steve Wright, and Dr. Charles Biles. These individuals would always

    give me opportunities to talk about my project and provided help whenever possible.

    When I started getting serious about the topic of my thesis project, Dr. Sharyn Marks

    suggested I join the HSU club Herpetology Group. I am so thankful to Sharyn for this

    suggestion and to the individuals involved for providing me with so much help in under-

    standing the biology, behavior, and ecology involved with these particular species. I would

    like to thank Dr. Hartwell Welsh, Jamie Bettaso, Dr. W. Bryan Jennings, Oliver Miano,

    Ryan Bourque, Justin Garwood, Karen Pope, Jada Howarth, Mike Best, Elijah Best, Shan-

    non Chapin, Luke Groff, Mike van Hattem, Cheryl Bondi, and Jen Brown.

    I would also like to thank my awesome family for their unwavering interest and support

    of my academic pursuits. My mom Janice Gray, my dad Paul Gray, my sisters Jennifer Mar-

    tinez and Erica Avila, my brother-in-laws Anthony Martinez and Jered Avila, my nephew

    Jacob, and my niece Allorah have been so incredibly understanding of my absence during

    this long processes. Thanks also goes out to my good friends back home Erica, CJ, and

    now little Charlotte Lassen for their encouragement and support.

    For employing me over the entire course of my Masters work, I would like to thank Joe

    Doherty, current owner, and Fukiko Marshall, previous owner of Tomo Japanese Restaurant

    Inc. Joe has been such an fantastic boss and friend. He even let me leave Tomo for an entire

    semester in order to focus more on my thesis. My coworkers at this establishment are not

    merely coworkers to me, they are my Tomo family. I would like to thank in particular

    Ellie Woods, Rachel Baker de Kater, Samuel Man Sam Hamilton, Jeremiah Hammond,

    vi

  • Nathan Rushton, Ryan Roberts, Vaden Hoffman, Aislinn Anderson, Bryce Peebles, and

    Rex Garland for allowing me to yammer on and on about my thesis topic while we worked

    together.

    Against his wishes, I would like to give individual thanks to Oliver Miano. Long before

    I formulated the topic of this thesis project, Oliver was the first person to inform me of the

    bullfrog problem. He had just acquired a male albino bullfrog. We were admiring it in the

    backyard of our house on Zelia Court as he told me of how the introduction of bullfrogs

    have become a problem on the West Coast of the U.S. through competition with and pre-

    dation of native frogs. Little did I realize that years later I would have the opportunity to

    model this very problem and achieve a Masters degree in the process. I have learned so

    much from Oliver about herpetology and so many other topics. I am incredibly lucky to

    have, and very thankful for, his presence in my life. I therefore dedicate this body of work

    to him.

    vii

  • TABLE OF CONTENTS

    ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .