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We will be playing around with this a fair bit today to try and reinforce the basic concepts:

A reminder of the terms:

• H = prey density
• P = predator density
• r = exponential growth rate
• a = predation rate (how many prey are eaten)
• b = conversion efficiency (some product of birthrate and the predation rate; prey consumption efficiency needed to give birth to a new predator)( note that in the derivation done in class I effectively used b=ap )
• m = mortality rate (per capita or expressed as a percentage; this is basically a negative exponential growth rate)

Driving equations in this form then become:

Prey Growth:

dH/dt = rH - aPH

(second term acts to slow growth rate so the effective growth rate is r-aP)

Predator Growth:

dP/dt = bPH - mP

(first term serves to effectively slow the mortality rate so the effective growth rate is bH-m)

There is no growth of prey at the point where r =aP

There is no growth of predators at the point where m = bH

Your goal is to eventually manipulate the r,a,b and m parameters so that you end up with plots that look like this:

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When you have a successful model, Publish it via this worksheet.

Week 5