Download - Feral Cats & Bird Extinctions on Islands
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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 TimesSeptember 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 SummerallNational 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-FrançaisCapital 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 cancerAmerican 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
Populations1. 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 estimatesChanges 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
1
dB rBdtdB BrBdt K
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Exponential Growth Model
0rtN N e
dN rNdt
Graph of Total Population Equation of Total Population
Equation of Population Change
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Logistic Growth Model
0
1 1
1
rt
KNK eN
dN NrNdt K
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
/1
1
BCCr
dtdC
CKBBr
dtdB
C
BBirds
Cats
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Try an Example
/1
1
BCCr
dtdC
CKBBr
dtdB
C
B
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?
??/
1
1
BCCr
dtdC
CKBBr
dtdB
C
BBirds
Cats
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The S-I-R Disease Equations
dtdRdtdIdtdS
/// Describes how the number of
susceptible, infected, and recovered individuals changes with time
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The State Diagram for FeLVA modified S-I-R model
• X+Y+Z = total population
SusceptibleX
Death
1-Immune
Z
Develop Symptoms
Y
b
mm
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/