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Feral Cats & Bird Extinctions on Islands Mathematical Biology Modeling Group School of Mathematical Sciences & School of Biological Sciences Serge Bloch, New York Times September 28, 2009 J. Fielder

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I am a poor mathematician…I remain mathematically semiliterate… ~ E. O. Wilson ~ Naturalist, 1994, page 122 M. Hayes Jennie Summerall National Portrait Gallery, Washington, D. C. Oil on canvas...I have succeeded to some extant in theoretical model building by collaborating with mathematical theoreticians…My role was to suggest problems to be addressed, to combine my intuition with theirs, and to lay out empirical evidence unknown to them. They were my intellectual prosthesis and I theirs.

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Key Goals of Today’s Lab Show how math can help explain ecological processes. Demonstrate how biologists and mathematicians can collaborate to address problems that neither group could address on their own.

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Overview of Today’s Lab Problem with feral cats on islands and a possible solution What role can math play? –A gentle intro to mathematical modeling in ecology and its use in evaluating management strategies ~ Take a break ~ Go to computer lab for a simulation of population dynamics on islands Wrap up

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The Problem with Feral Cats on Islands Kerguelen Islands (Chapuis 1995) –5 domestic founder cats –How many cats will there be in 25 years? –Before you answer, let’s take a closer look at the island… en.wikipedia.org glennmci.brinkster.net http://www.chthonic.f9.co.uk/b3ta/underage.jpg

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Port-aux-Français Capital settlement of Kerguelen Island, French Territory en.wikipedia.org/wiki/Port-aux-Français 60 winter inhabitants up to 120 summer inhabitants 5 founder cats?... 25 years later…30,000 cats Birds killed per year? > 3 million per year!

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Control of Feral Cats Culling & trapping are expensive Time-consuming Labor intensive Controversial Disease NYTimes www.wildliferesearchmanagement.com.au

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Diseases Feline Immunodeficiency Virus =FIV Feline Leukemia Virus =FeLV www.morgansplace.com

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Feline Leukemia Virus (FeLV) Retrovirus Found worldwide Spread by coming in contact with saliva, urine, feces, and nasal secretions American Association of Feline Practitioners and Cornell Feline Health Center, 2006

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Impossible to accurately predict the life expectancy of a cat with FeLV Signs of the disease Loss of appetite, weight loss Poor coat condition Enlarged lymph nodes, may lead to cancer Persistent diarrhea and fever Inflammation of the gums Seizures, behavior changes, and neurological disorders Primary stage Concentrated in bloodstream Some individuals become immune Secondary stage Later stage, infection in bone marrow and tissues Point of no return Leads to state of immune deficiency and cancer American Association of Feline Practitioners and Cornell Feline Health Center, 2006 FeLV Characteristics

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Questions What would you like to know before you introduce feline leukemia into the cat population on an island? http://www.petcareloop.com/images/twitter_question_mark.png?1255219975

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Some of Our Questions How deadly is the virus? How fast does it spread? Does introducing the disease actually do what you want it to do? How long will it take for the bird population to grow to recover?

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Modeling in Biology A tool for understanding –Population growth or decline –Ecological systems and process –What variables in a system are important –Transmission of disease –Migration of a population –Habitat utilization

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Lives in old-growth forests 1985-2003 19+ years of data 11,432 birds marked 32,054 capture events This is complex data! Cost > $30,000,000 Analyzed data using a collaborative workshop of biologists, statisticians, & mathematicians. Example: Modeling Northern Spotted Owl Population Data

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Types of Questions in Modeling Cat –Bird Populations 1.What information do we need to build a model? (what’s important? what’s not?) 2.What questions can the model answer? (what can the model predict?) 3.What questions can’t be answered by the model?

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Modeling Populations—2 Approaches Measuring Total population –Counts of animals, bacteria, trees, cells –Aided by sampling –Can be challenging/impossible to get accurate estimates Changes in population –Birth rates, death rates, infection rates, migration –Describe interaction between species

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Describing Rates Mathematically Seem complicated Can be analyzed numerically and graphically Easier to align with biological factors

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Exponential Growth Model Graph of Total PopulationEquation of Total Population Equation of Population Change

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Logistic Growth Model Graph of Total Population Equation of Total Population Equation of Population Change

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Cat-Bird Dynamics

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Tweety-Batman to the rescue! (along with differential equations)

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Predator-Prey with Logistic Growth Birds Cats

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Try an Example Starting Values

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Graph of (Cat, Bird) Trajectory Cats Birds

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What happens if a cat disease is introduced to the system? Birds Cats

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The S-I-R Disease Equations Describes how the number of susceptible, infected, and recovered individuals changes with time

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The State Diagram for FeLV A modified S-I-R model X+Y+Z = total population Susceptible X Death 1- Immune Z Develop Symptoms Y b m m Viremic (very brief) σ α b m

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Differential equations for FeLV

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To the Computer Lab!

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Conclusion What is modeling in biology, and how can it be used as a tool for understanding ecological systems? Biological influences on a system that go into building a model –birth rate, death rate, disease, im/em-igration, food supply, etc.

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Wrapping it up Yahoo article and worksheet www.flickr.com/photos/bostich/3048320868/

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