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Page 1: Laura Outline

Laura Outline

MATH 260

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Biological Problem

• House-Wren and Bewick’s Wren competition relatively new (within the last 10 years) – Didn’t share territory until recently (SITE LAURA

PAPER)

• Wildlife ecologists want to understand competition coefficients regarding these two species

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Harmless?

http://www.paulnoll.com/Oregon/Birds/arrival-Wren-House.jpg

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Bewick’s Wren Nest

X

http://byteshuffler.com/rospo/blog/uploaded_images/NestEggs-729160.jpg (nest)

http://www.suttoncenter.org/images/House-Wren-Carroll.jpg (wren)

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…not if you’re a Bewick’s Wren

Egg Photo courtesy of The Nova Scotia Museum at http://museum.gov.ns.ca/mnh/nature/nsbirds/bns0276.htm

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Look at Individual Population Model

• Put single species model (LAURA)

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Calculate carrying capacity for each species

• Relate indiviual data and the logistic equation, growth rate

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US MAP with regions

• Trend lines for each species in large, separate regions

• Hope to see a straight line of each individual populations over time

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Data (multiple slides)

• Show population graphs of both birds’ population in all regions where they are no where near each other

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Two Species Model

• (Meghan) assumptions, what happened, equations, parameters, non-dimensionalization

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MODEL GOALEstimate competition Coefficients

α1 Competiton that pop.2 exerts on pop.1

α2 Competition of Pop 1 on pop.2

Fit coefficients using MATLAB

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Solutions (general to logistic eq’n)

• (Pete) Solutions to equations, linear stability• Behavior • Equilibrium

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Two-species interaction data

• Reproduction rate • New carrying capacities • Competition coefficients!


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