1. ECOLOGY MATH

2. 1)Population density = # of members/unit of area

3. ECOLOGY MATH 2) Growth rate (per capita) = change in number of members/time r = N/ t ( N = births –deaths)

4. FYI Per capita = per person

5. ECOLOGY MATH 3) ZPG = Zero Population Growth birth rate = death rate r = 0

6. ECOLOGY MATH 4) Change in population at any one instant N/ t = rN Ex 1. A population of 500 experiences 55 births and 5 deaths during a one year period. What was the reproductive rate during this year?

7. ECOLOGY MATH Ex. 1 A population of 500 experiences 55 births and 5 deaths during a one year period. What was the reproductive rate during this year? Ans. N/ t =rN 50/1 = r(500) =.1 or 10%

8. ECOLOGY MATH 5) Intrinsic Rate of Increase (r max ) -Fastest rate of growth possible -Pop. Reproducing w/out limits -Resources abundant dN/dt= r max N

9. ECOLOGY MATH dN/dt= r max N Ex. 2 A population of bacteria with a rmax=.7 per day has a current population of 15,000 cells. How many bacteria will exist in 15 days if resources remain readily available?

10. ECOLOGY MATH dN/dt= r max N dN/15 =.7(15,000) N = 157,500 cells

11. ECOLOGY MATH 6)Logistical growth model - availability of resources limits growth - carry capacity (K) – max # of individuals of a pop. Supported dN/dt = r max N (K-N/K)

12. ECOLOGY MATH Logistical growth model dN/dt = r max N (K-N/K) Note: As N = K then r = zero Ex 3. K is estimated at 500, the population size is currently 400 and r is.01. What is the growth rate?

13. ECOLOGY MATH Logistical growth model dN/dt = r max N (K-N/K dN/dt = (.01)(400)(100/500) dN/dt =.8 What does this actually mean?.8 births per year

14. ECOLOGY MATH Logistical growth model dN/dt = r max N (K-N/K dN/dt = (.01)(400)(100/500) dN/dt =.8 What does this actually mean?.8 births per year

15. This applies to… Age structures K – resources available The trophic level that provides the resources Primary productivity impacts pop. growth for all levels above Cause and effect for food chains/webs