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2 nd Homework Assignment

2 nd Homework Assignment. Identify a small animal population (< 1,000) and learn a little about it. Full description on web page. Do not use African Wild Dogs! Basis for term paper project. Due: Monday, March 5 Note HW1 due March 1.

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2 nd Homework Assignment

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  1. 2nd Homework Assignment • Identify a small animal population (< 1,000) and learn a little about it. • Full description on web page. • Do not use African Wild Dogs! • Basis for term paper project. • Due: Monday, March 5 • Note HW1 due March 1

  2. M. Begon, J. L. Harper, C. R. Townsend, Ecology (Blackwell Science, Oxford, England, ed. 3rd, 1996).

  3. Status of Whooping Cranes? Crane count as of January 16, 2001: 177

  4. Traveling Car Analogy • Where’s the car? Where’s it going? • Current population size. • How fast is the car going? • Population growth rate. • How fast can the car go? • Carrying capacity.

  5. Population Growth • Nt+1 = Nt + B – D + I – E • Nt = population size at time “t” • B = total births • D = total deaths • I = total immigrants • E = total emigrants

  6. Discrete Population Growth Ignore immigration and emigration total births = births / individual (b) times total individuals (Nt) total deaths = . . . Divide both sides by Nt Define Lambda

  7. Continuous Population Growth Step 2 from discrete growth Subtract Nt from both sides Measure change in population density (dN) over a very small time interval (dt) Divide by N Define r

  8. Population Growth Essentials

  9. The Difference Between λ and r DISCRETE - λ CONTINUOUS - r 20 20 N 10 10 0 0 0 1 2 0 1 2 time

  10. Relationship Between λ and r *

  11. Exponential Population Growth Assuming constant r or λ r > 0, λ > 1 N r = 0, λ = 1 r < 0, λ < 1 Time / Generations

  12. Population Growth Transformed Because the formula is exponential, it is useful to express it logarithmically: ln(Nt) = ln(N0) + rt, I.e. y = b + mx r > 0, λ > 1 r = 0, λ = 1 ln(N) r < 0, λ < 1 Time / Generations

  13. Management Implications • Population increasing • r > 0, λ > 1 • Population stable • r = 0, λ = 1 • Population decreasing • r < 0, λ < 1

  14. Calculating Growth Rates • Question: • If there are 2 rabbits today, but 200 rabbits tomorrow, calculate r and lambda.

  15. Calculating Growth Rates • Question: • If there are 2 rabbits today, but 200 rabbits tomorrow, calculate r and lambda. • Answer: • lambda = 100 rabbits per rabbit per day. • r = ln(100) = 4.61 rabbits per rabbit per day.

  16. Reality? r = 0 Mean r = 0 N N Time (generations) Time (generations)

  17. Deterministic vs. Stochastic Factors Mean -1s.d. +1s.d. Frequency -2s.d. +2s.d. Growth Rate ~95%

  18. Whooping Cranes Mean r = 0.06 ±95% CI = 0.03 to 0.09 B. Dennis, P. L. Munholland, J. L. Scott, Ecological Monographs61, 115-143 (1991).

  19. 10 5000 50 1000 Deterministic vs. Stochastic Factors Long-term growth rate can be negative even with positive r where variation in growth rate is “high” mean r = 0.125, SD = 0.55 mean r = 0.125, SD = 0 Population Size Time Time

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