Laura Outline

MATH 260

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

Harmless?

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

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)

…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

Look at Individual Population Model

• Put single species model (LAURA)

Calculate carrying capacity for each species

• Relate indiviual data and the logistic equation, growth rate

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

Data (multiple slides)

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

Two Species Model

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

•

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

Solutions (general to logistic eq’n)

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

Two-species interaction data

• Reproduction rate • New carrying capacities • Competition coefficients!