1. 1 Chapter 11 Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

2. 2 Chapter 10 (Part 1)

3. 3 Why must species very high reproductive rates have a Type III survivorship curve ? If these species didn’t have a Type III survivor-ship curve the Earth would be covered with their bodies. Why must species low reproductive rates have a Type I survivorship curve ? If these species didn’t have a Type I survivor- ship curve they would be extinct.

4. 4 What is the expected relationship b/t reproductive rate and patterns of survival ? The greater the number offspring produced, the less energy / care the parent can invest in each offspring, the lower the survivorship of juveniles.

5. 5Age dxdxdxdx nxnxnxnx LxLxLxLx mxmxmxmx Lx mxLx mxLx mxLx mx X L x m x 01806601.000000 12404800.72710.7270.727 21202400.36420.7281.456 3601200.18220.3641.092 460600.091000 Total660 R 0 = R 0 =1.8193.275

6. 6 Generation Time ( T ) T = Sum (X L x m x ) / R 0 T = 3.275 / 1.819 T = 1.80 Per Capita Rate of Increase ( r ) r = Ln (R 0 ) / T r = Ln (1.819) / 1.80 r = 0.332

7. 7Age nxnxnxnx LxLxLxLx mxmxmxmx Lx mxLx mxLx mxLx mx X L x m x 06601.0000 14800.7272 22400.3642 31200.1821 4600.0910 Total R0 = R0 = R0 = R0 =

8. 8Age nxnxnxnx LxLxLxLx mxmxmxmx Lx mxLx mxLx mxLx mx 06601.000000 14800.72721.4541.454 22400.36420.7281.456 31200.18210.1820.546 4600.091000 Total R0 = R0 = R0 = R0 =2.3643.456

9. 9 Generation Time ( T ) T = Sum (X L x m x ) / R 0 T = 3.456 / 2.364 T = 1.46 Per Capita Rate of Increase ( r ) r = Ln (R 0 ) / T r = Ln (2.364) / 1.46 r = 0.589

10. 10 Effect of shifting reproduction to younger age classes? Increased R 0 1.819 vs. 2.364 (30% increase) Decreased T1.800 vs. 1.46 (19% decrease) Increased r0.332 vs. 0.589 (77% increase) Should natural selection favor early reproduction ? If r = “fitness”, this analysis suggests YES.

11. 11 Any disadvantages to earlier reproduction? Smaller mothers produce fewer, smaller, and(or) less vigorous young. Smaller mothers at a disadvantage in competition for resources, less able to provide for young. Survivorship of small mothers and young lower.

12. 12  Effect of increased prey density (food) on life history traits of predator? Lx:Lx: mx:mx: R0:R0:  T:  r: Increase ( ↑ vigor, better defenses) Increase ( ↑ eggs, ↓ abortion) Increase (given L x and m x increase) Decrease (rapid growth accelerates maturation) Increase ( given ↓T & ↑R 0 )

13. 13Age dxdxdxdx nxnxnxnx LxLxLxLx mxmxmxmx Lx mxLx mxLx mxLx mx X L x m x 08008501.000000 125500.05920011.811.8 215250.0292507.2514.5 35100.0123003.610.8 4550.0063502.18.4 Total850 R0 =R0 =R0 =R0 =24.7545.5

14. 14 Generation Time ( T ) T = Sum (X L x m x ) / R 0 T = 45.5 / 24.75 T = 1.84 Per Capita Rate of Increase ( r ) r = Ln (24.75) / 1.85 r = 1.74

15. 15 Type of Survivorship Curve ? Type III Most individuals die at a very young age. Those that get past juvenile period have lower mortality rate. Type of Life History Pattern ? r−selected: Life table indicates short life span, low juvenile survivorship, and high birth rates.

16. 16Age nxnxnxnx LxLxLxLx mxmxmxmx Lx mxLx mxLx mxLx mx X L x m x 08501.000000 18000.941000 27500.882000 37000.82410.8242.47 46500.76532.2959.18 56000.70632.11810.59 65000.58831.76410.58 72000.23530.7054.94 8500.05930.1771.42 R 0 = 7.8839.17

17. 17 Generation Time ( T ) T = Sum (X L x m x ) / R 0 T = 39.17 / 7.88 T = 4.97 Per Capita Rate of Increase ( r ) r = Ln (7.88) / 4.97 r = 0.415

18. 18 Type of Survivorship Curve ? Type I Most individuals survive juvenile age. Most mortality is in oldest age classes. Type of Life History Pattern ? K−selected: Life table indicates longer life span, high juvenile survivorship, and low birth rates.

19. 19  Geometric Growth  Exponential Growth  Logistic Population Growth  Limits to Population Growth  Density Dependent  Density Independent

20. 20  When generations do not overlap, growth can be modeled geometrically. N t = N o λ t  N t = Number of individuals at time t.  N o = Initial number of individuals.  λ = Geometric rate of increase.  t = Number of time intervals or generations.

21. 21 Molles: Ecology 2 nd Ed.  Currently 100 individuals  Population rate, = 2 N t = N o t  After 5 years, pop has 3200 100 x 2 5

22. 22  Continuous population growth in an unlimited environment can be modeled exponentially. dN / dt = r max N  Appropriate for populations with overlapping generations.  As population size (N) increases, rate of population increase (dN/dt) gets larger.

23. 23  For an exponentially growing population, size at any time can be calculated as: N t = N o er max t  N t = Number individuals at time t.  N 0 = Initial number of individuals.  e = Base of natural logarithms.  r max = Per capita rate of increase.  t = Number of time intervals.

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25. 25  As resources are depleted, population growth rate slows and eventually stops: logistic population growth.  Sigmoid (S-shaped) population growth curve.  Carrying capacity (K) is the number of individuals of a population the environment can support.  Finite amount of resources can only support a finite number of individuals.

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28. 28 dN/dt = r max N(1-N/K)  r max = Maximum per capita rate of increase under ideal conditions.  When N nears K, the right side of the equation nears zero.  As population size increases, logistic growth rate becomes a small fraction of growth rate.  Highest when N=K/2.  N/K = Environmental resistance.

29. 29  Environment limits population growth by altering birth and death rates.  Density-dependent factors  Disease, Resource competition  Density-independent factors  Natural disasters, Weather

30. 30 Molles: Ecology 2 nd Ed.  Boag and Grant - Geospiza fortis was numerically dominant finch (1,200)  After drought of 1977, pop. fell to (180)  Food plants failed to produce seed crop.  1983 - 10x normal rainfall caused population to grow (1,100) due to abundance of seeds and caterpillars.

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32. 32  Grant and Grant documented several ways finches utilized cacti:  Open flower buds in dry season to eat pollen  Consume nectar and pollen from mature flowers  Eat seed coating (aril)  Eat seeds  Eat insects from rotting cactus pads

33. 33  Finches tend to destroy stigmas, thus flowers cannot be fertilized.  Wet season activity may reduce seeds available to finches during the dry season.  Opuntia helleri main source for cactus finches.  Negatively impacted by El Nino (1983).  Stigma snapping delayed recovery.  Interplay of biotic and abiotic factors.

34. 34 Molles: Ecology 2 nd Ed. Fig 11.20

35. 35 Molles: Ecology 2 nd Ed.  On average, small organisms have higher rates of per capita increase and more variable populations than large organisms Fig 11.21

36. 36 Molles: Ecology 2 nd Ed.  Populations of marine pelagic tunicate ( Thalia democratica ) grow at exponential rates in response to phytoplankton plumes  Filter feeders

37. 37 Molles: Ecology 2 nd Ed.  Algae bloom in spring off Australian coast  Numerical response can increase pop. size dramatically due to extremely high reproductive rates Figure 11.22

38. 38 Molles: Ecology 2 nd Ed.  Pacific Gray Whale ( Eschrichtius robustus ) divided into Western and Eastern Pacific subpopulations Summer here Winter here

39. 39 Molles: Ecology 2 nd Ed.  Examined whales killed by whalers  Estimated avg. annual mortality rate of 0.089 and calculated annual birth rate of 0.13  r = 0.13 - 0.089 = 0.041  Gray Whale pop. growing at 4.1% per yr

40. 40 Molles: Ecology 2 nd Ed.  Reilly et.al. used annual migration counts from 1967- 1980 to obtain growth rate  Thus from 1967-1980, pattern of growth in California Gray Whale pop fit exponential model: N t = N o e 0.025t Figure 11.22

41. 41 Molles: Ecology 2 nd Ed.  What type of growth curve? Figure 11.27

42. 42 Molles: Ecology 2 nd Ed. Are we at carrying capacity?  Will resources become limited for humans? Figure 11.27

43. 43 Molles: Ecology 2 nd Ed. Distribution of the Human Population

44. 44 Molles: Ecology 2 nd Ed. Variation in Human Population Density

45. 45 Molles: Ecology 2 nd Ed. Age Distributions for Human Populations: Predictors of Future Population Growth Population Size Will be Stable Population Size Will Decline Population Size Will Increase Rapidly Age Class % of Population

46. 46 Molles: Ecology 2 nd Ed. Historical and Projected Human Populations Figure 11.26

47. 47 Molles: Ecology 2 nd Ed. Can the current growth rate of the global human population be sustained ? If not, what will slow or reverse human population growth ? What Will the Future Bring ?

48. 48 Molles: Ecology 2 nd Ed.  Trend of decreasing per capita availability of farmland and freshwater.  Trend of decreasing total crop land, range land, and forest  13 of 15 major marine fisheries are in a state of near or total collapse.  Humans already consume 40% of global primary productivity.

49. 49 Molles: Ecology 2 nd Ed.  Death Rate Solution: Decrease Lx  Malnutrition  Disease  Warfare  Pollution  Chemical  Radiation  Birth Rate Solution: Decrease m x  Increase age of first reproduction (T)  Education/employment for girls/women  Decrease R 0  Universal availability of contraceptives  Decrease infant mortality  Increase standard of living

50. 50 Molles: Ecology 2 nd Ed.  Green Revolution (Part 2) ???  Renewable and clean energy sources (solar, wind, hydro)  Medical research to combat new and resistant diseases  Warp Drive ???

51. 51 Molles: Ecology 2 nd Ed. Or maybe we should be doing something NOW ?

52. 52 Molles: Ecology 2 nd Ed.  With abundant resources, pop’s can grow at geometric or exponential rates  As resources depleted, pop growth rate slows, eventually stops: logistic population growth  Environment limits population growth by changing birth and death rates  On avg., small organisms have higher (r) and more variable pops. – while large organisms have lower (r) and less variable pops

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