1. Population Growth (Ch. 11)

2. Population Growth 1) Geometric growth 2) Exponential growth 3) Logistic growth

3. Geometric Growth Growth modeled geometrically –Resources not limiting –Generations do not overlap Recall: 1) = N t+1 / N t 2) = R o

4. Geometric Growth Growth modeled geometrically –Resources not limiting –Generations do not overlap Equation: N t = N o t –N t = Number inds. @ time t –N o = Initial no. inds. – = Geometric rate of increase –t = Number time intervals

5. Geometric Growth Phlox (annual plant) Fig. 11.3

6. Exponential Growth Growth modeled exponentially –Resources not limiting –Generations overlap Recall: 1)Per Capita Rate of Increase (r) 2)r = (ln R o ) / T 3)r = b – d

7. Exponential Growth Equation: dN / dt = r max N dN / dt means “change in N per unit time” Recall r: per capita rate of increase (Ch. 10) r max : Special case of r (intrinsic rate of increase). b - d under optimum conditions –b = birth rate and d = death rate (rates per individual per unit time) As N increases, dN/dt gets larger.

8. Exponential Growth For exponential growth: N t = N 0 e r max t N t = No. inds. at time t. N 0 = Initial no. inds. e = Base natural logarithms r max = Intrinsic rate of increase t = Number time intervals Resources not limiting Geo: N t = N o t

9. Exponential Growth: Example Whooping crane

10. Exponential Growth: Example Hunting/habitat destruction Federally listed Endangered(1967). Down to 22!! Fig. 11.6

11. Exponential Growth: Example Raising birds: costumes avoid imprinting on humans

12. Exponential Growth: Example Teaching young birds to migrate (Wisconsin to Florida) 1996

13. Geometric or Exponential? GeometricExponential Generations N t = N 0 e r max t N t = N o t

14. Geometric or Exponential? GeometricExponential SeparateGenerationsOverlap λ = 1Population stabler = 0 λ > 1Population growingr > 0 λ < 1Population shrinkingr < 0 N t = N o t N t = N 0 e r max t

15. Logistic Population Growth Unlimited resources?? nothing lasts forever… As resources depleted: logistic population growth.

16. Logistic Population Growth As resources depleted, logistic population growth (generations overlap) –Sigmoid (S-shaped) curve. –Carrying capacity (K): number environment can support. Ex Fig. 11.8

17. Logistic Population Growth Yeast growth (limited alcohol) Max. 17% (34 proof) Fig. 11.9

18. Logistic Population Growth Equation: dN/dt = r max N (1-N/K) r max = Intrinsic rate of increase (ideal conditions) N = population size @ time t K = carrying capacity Or: dN/dt = r max N (K-N) K

19. How does this work? dN/dt = r max N (K-N) K N small: r max N (K-0) or ≈ r max N (1) K At small N, acts like exponential growth! N big: r max N (K-K) or ≈ r max N (0) K At larger N, growth slows: stops at K

20. Logistic Population Growth 1-N/K is “scaling factor” When N nears K, dN/dt nears zero. Fig. 11.13

21. Logistic Population Growth r: actual (realized) reproductive rate (b-d) Max. @ small N When N=K, r=0 So b=d and b-d=0 Above K? r negative dN/dt = r max N (1-N/K) Fig. 11.14

22. Concepts! Population growth (# added per unit time) highest when N=K/2 Maximum sustainable yield: largest sustainable harvest

23. Concepts! Environmental resistance –Density-dependent factors: depend on density (N/K) Disease, Resource competition –Density-independent factors: not related density Natural disasters (hurricane, fire, flood) dN/dt = r max N (1-N/K) N/K: reflects environmental resistance –Factors that limit population size

24. Organism Size and Population Density A search for patterns…… –Size vs. density (neg. correlation) –Generation time vs. size? Gen time Size

25. Generation time vs. size Positive correlation Log-log scale size vs. r max ? Size r max

26. r max vs. size Negative correlation Note log:log scale

27. Human Population How many? Where? Age distributions and growth potential How many?

28. Human Population How many? 7.09 billion (6/17/13) 7.02 billion (6/11/12) 6.925 billion (6/19/11) 6.448 billion (6/18/05) Check it out now at: http://www.census.gov/ipc/www/idb/worldpopinfo.php Where (continent)?

29. Human Population Where? Fig. 11.22 Fig. 11.23

30. Human Population Where?

31. Human Population Age distributions and growth potential, 2008 Fig. 11.24

32. Human Population “Population bomb”: potential of population to explode as people age 2000/2001-Present - New Silent Generation or Generation Z 1980-2000 - Millennials or Generation Y 1965-1979 - Generation X 1946-1964 - Baby Boom 1925-1945 – Silent Generation 1900-1924 – G.I. Generation

33. Human Population Human pop. curve: shape? What Earth’s K for humans?

34. Human Population Depends in part on lifestyle! –Ecological footprint: resource use –Biocapacity: resource supply –Deficit if use>supply: US largest deficit

35. Course sequence Natural history (Done!) Individuals (Done!) Populations (Done! Except Life Histories) Species interactions (You are here!) Communities/ecosystems Geographic/global ecology

36. 5 main types of interactions among species: Effect on Type of interaction species A species B Competition - - Predation + - Parasitism + - Commensalism + 0 Mutualism + +

37. Species Interactions: Competition (Ch. 13)

38. Competition (Ch. 13) Definition: –Individuals attempt to gain more resource in limiting supply –(-,-) interaction: both participants get less Intraspecific: Within species. Interspecific: Between species.

39. Competition Interference Competition: –Individuals interact with each other Resource (Exploitation) Competition: –Individuals interact with resource