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Population Growth (Ch. 11)

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Population Growth (Ch. 11). Population Growth. 1) Geometric growth 2) Exponential growth 3) Logistic growth. Geometric Growth. Growth modeled geometrically Resources not limiting Generations do not overlap. Recall: 1)  = N t+1 / N t 2)  = R o. Geometric Growth.

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Population Growth (Ch. 11)

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  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)  = Nt+1 / Nt • 2) = Ro

  4. Geometric Growth • Growth modeled geometrically • Resources not limiting • Generations do not overlap • Equation: Nt = No t • Nt = Number inds. @ time t • No = 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: • Per Capita Rate of Increase (r) • r = (ln Ro) / T • r = b – d

  7. Exponential Growth • Equation: dN / dt = rmax N • dN / dt means “change in N per unit time” • Recall r: per capita rate of increase (Ch. 10) • rmax: 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. Geo: Nt = No t Exponential Growth • For exponential growth: Nt = N0 ermaxt • Nt = No. inds. at time t. • N0 = Initial no. inds. • e = Base natural logarithms • rmax = Intrinsic rate of increase • t = Number time intervals • Resources not limiting

  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? Nt = No t Nt = N0 ermaxt

  14. Geometric or Exponential? Nt = No t Nt = N0 ermaxt

  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. Fig. 11.8 Ex

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

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

  19. How does this work? • dN/dt = rmax N (K-N) K • N small: rmax N (K-0) or ≈ rmax N (1) K At small N, acts like exponential growth! • N big: rmax N (K-K) or ≈ rmax 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 dN/dt = rmaxN (1-N/K) • 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 Fig. 11.14

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

  23. Concepts! • N/K: reflects environmental resistance • Factors that limit population size 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 = rmaxN (1-N/K)

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

  25. Generation time vs. size • Positive correlation • Log-log scale rmax size vs. rmax? Size

  26. rmax 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. 11.23 Fig. 11.22

  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 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

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