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

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.

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.

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

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

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!

Control of Feral Cats

• Culling & trapping are expensive

• Time-consuming• Labor intensive• Controversial• Disease

NYTimes

www.wildliferesearchmanagement.com.au

Diseases• Feline Immunodeficiency Virus

=FIV

• Feline Leukemia Virus=FeLV

www.morgansplace.com

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

• 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

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

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?

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

• 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

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?

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

Describing Rates Mathematically

• Seem complicated

• Can be analyzed numerically and graphically

• Easier to align with biological factors

1

dBrB

dtdB B

rBdt K

Exponential Growth Model

0rtN N e

dNrN

dt

Graph of Total Population Equation of Total Population

Equation of Population Change

Logistic Growth Model

0

1 1

1

rt

KN

Ke

N

dN NrN

dt K

Graph of Total PopulationEquation of Total Population

Equation of Population Change

Cat-Bird Dynamics

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

Predator-Prey with Logistic Growth

/1

1

B

CCr

dt

dC

CK

BBr

dt

dB

C

BBirds

Cats

Try an Example

/1

1

B

CCr

dt

dC

CK

BBr

dt

dB

C

B

Starting Values

Graph of (Cat, Bird) Trajectory

Cats

Birds

What happens if a cat disease is introduced to the

system?

??/

1

1

B

CCr

dt

dC

CK

BBr

dt

dB

C

BBirds

Cats

The S-I-R Disease Equations

dtdR

dtdI

dtdS

/

/

/ Describes how the number of susceptible, infected, and recovered individuals changes with time

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

Differential equations for FeLV

To the Computer Lab!

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.

Wrapping it up• Yahoo article and worksheet

www.flickr.com/photos/bostich/3048320868/