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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!