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Section III Population Ecology

Section III Population Ecology. 鄭先祐 生態主張者 Ayo Japalura@hotmail.com. Section Three Population Ecology. Chap.6 Population growth ( 族群成長 ) Chap.7 Physical environment ( 物理環境 ) Chap.8 Competition and coexistence ( 競爭與共存 ) Chap.9 Mutualism ( 共生 ) Chap.10 Predation ( 掠食 )

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Section III Population Ecology

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  1. Section III Population Ecology 鄭先祐 生態主張者 Ayo Japalura@hotmail.com

  2. Section Three Population Ecology • Chap.6 Population growth (族群成長) • Chap.7 Physical environment (物理環境) • Chap.8 Competition and coexistence (競爭與共存) • Chap.9 Mutualism (共生) • Chap.10 Predation (掠食) • Chap.11 Herbivory (素食) • Chap.12 Parasitism (寄生) • Chap.13 Evaluating the controls on population size 2003 生態學 chap.6 Population Growth

  3. Road Map Chap. 6 Population Growth • Tabulating changes in population age structure through time • Time-specific life tables • Age-specific life tables • Fecundity schedules and female fecundity, and estimating future population growth • Population growth models • Deterministic models • Geometric models • Logistic models • Stochastic models 2003 生態學 chap.6 Population Growth

  4. 6.1 Life tables • The construction of life tables is termed demography. • Construct life tables • Demonstrate the age structure of a population • Time-specific life table • Snapshot – age structure at a single point in time (time-specific life table) • Useful in examining long-lived animals • Ex. Dall Mountain Sheep (Figure 6.1 and Table 6.1) 2003 生態學 chap.6 Population Growth

  5. Time-specific life table • Snapshot – age structure at a single point in time (time-specific life table) • Useful in examining long-lived animals • Ex. Dall Mountain Sheep (Figure 6.1 and Table 6.1) 2003 生態學 chap.6 Population Growth

  6. Life Tables • Useful parameters in the life tables • x = age class or interval • nx = number of survivors at beginning of age interval x. • dx = number of organisms dying between age intervals = nx– nx+1 • lx = proportion of organisms surviving to the beginning of age interval x = ns / n0 2003 生態學 chap.6 Population Growth

  7. Life Tables • Useful parameters in the life tables • qx = rate of mortality between age intervals = dx / ns • ex = the mean expectation of life for organisms alive at the beginning of age x • Lx = average number alive during an age class = (nx+ nx+1) / 2 • Tx = intermediate step in determining life expectancy = SLx • ex = Tx / nx 2003 生態學 chap.6 Population Growth

  8. 2003 生態學 chap.6 Population Growth

  9. Fig. 6.2 Time-specific survivorship curve 3.5 3 2.5 2 n (log scale) 10 1.5 x 1 0.5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Age (years) 2003 生態學 chap.6 Population Growth

  10. Assumptions that limit the accuracy of time-specific life tables • Equal number of offspring are born each year • Favorable climate for breeding? • A need for an independent method for estimating birth rates of each age class • As a result, age-specific life tables are typically reported • Of 31 life tables examined, 26 were age specific and only 5 were time specific. 2003 生態學 chap.6 Population Growth

  11. Age-specific life tables • Needed for short-lived organisms • Time-specific life tables biased toward the stage common at the moment • Follows one cohort or generation • Population censuses must be frequent and conducted over a limited time • Ex. Table 6.2 and Figure 6.3 • Comparison in the accuracy of life tables (Figure 6.5) 2003 生態學 chap.6 Population Growth

  12. 2003 生態學 chap.6 Population Growth

  13. 3.5 3 2.5 2 n (log scale) 1.5 x 1 0.5 0 1 4 2 3 5 6 7 Age (years) Fig. 6.3 Age-specific survivorship curve for the American robin. 2003 生態學 chap.6 Population Growth

  14. Comparison in the accuracy of life tables Fig. 6.5 Hypothetical comparison of cohort survivorship of humans born in 1930. 2003 生態學 chap.6 Population Growth

  15. General types of survivorship curves (Figure 6.4) • Type I • Most individuals are lost when they are older • Vertebrates or organisms that exhibit parental care and protect their young • Small dip at young age due to predators • Type II • Almost linear rate of loss • Many birds and some invertebrates • Type III • Large fraction are lost in the juvenile stages • Invertebrates, many plants, and marine invertebrates that do not exhibit parental care • Large losses due to predators 2003 生態學 chap.6 Population Growth

  16. Type I 1000 Many birds, small mammals, lizards, turtles Many mammals 100 x Number of survivors (n ) (log scale) Type II 10 Many invertebrates 1 Type III 0.1 Fig. 6.4 Age 2003 生態學 chap.6 Population Growth

  17. 6.2 Reproductive rate • Fecundity • Age-specific birth rates • Number of female offspring produced by each breeding female • Fecundity schedules • Fecundity information in life table • Describe reproductive output and survivorship of breeding individuals. • Ex. Table 6.3 2003 生態學 chap.6 Population Growth

  18. 2003 生態學 chap.6 Population Growth

  19. Fecundity schedules • Table components • lx = survivorship (number of females surviving in each age class • mx = age-specific fecundity • Ro = population’s net reproductive rate = Slx mx • Ro = 1; population is stationary • Ro > 1; population is increasing • Ro < 1; population is decreasing • Table 6.3 2003 生態學 chap.6 Population Growth

  20. Fecundity schedules • Variation in formula for plants • Age-specific fecundity (mx ) is calculated differently • Fx = total number of seeds, or young deposited • nx = total number of reproducing individuals • mx = Fx / nx • Table 6.4 2003 生態學 chap.6 Population Growth

  21. 2003 生態學 chap.6 Population Growth

  22. 6.3 Deterministic Models: Geometric Growth • Predicting population growth (預測族群的成長)，需要知道： • Ro • Initial population size • Population size at time t • Population size of females at next generation = Nt+1= RoNt • Ro = net reproductive rate • Nt = population size of females at this generation 2003 生態學 chap.6 Population Growth

  23. Geometric Growth • Dependency of Ro • Ro < 1; population becomes extinct • Ro = 1; population remains constant • Population is at equilibrium • No change in density • Ro > 1; population increases • Even a fraction above one, population will increase rapidly • Characteristic “J ” shaped curve • Geometric growth • Figure 6.7 2003 生態學 chap.6 Population Growth

  24. R =1.20 0 500 R =1.15 0 R值愈大，族群的成長愈快 400 300 Population in size (N) N +1 = R N 200 t 0 t R =1.10 0 100 R =1.05 0 10 0 20 30 Fig. 6.7 Generations 2003 生態學 chap.6 Population Growth

  25. Geometric Growth • Ro > 1; population increases (cont.). • Something (e.g., resources) will eventually limit growth • Population crash • Figure 6.8a • Figure 6.8b • Figure 6.8c 2003 生態學 chap.6 Population Growth

  26. 2000 1500 Number of reindeer 1000 500 0 1910 1920 1930 1940 1950 Fig. 6.8 a Year 2003 生態學 chap.6 Population Growth

  27. Fig6.8b和c 2003 生態學 chap.6 Population Growth

  28. Geometric Growth：Human population growth • Prior to agriculture and domestication of animals (~10,000 B.C.) • Average annual rate of growth: ~0.0001% • After the establishment of agriculture • 300 million people by 1 A.D. • 800 million by 1750 • Average annual rate of growth: ~0.1% 2003 生態學 chap.6 Population Growth

  29. Geometric Growth：Human population growth • Period of rapid population growth • Began 1750 • From 1750 to 1900 • Average annual rate of growth: ~0.5% • From 1900 to 1950 • Average annual rate of growth: ~0.8% • From 1950 to 2000 • Average annual rate of growth: ~1.7% • Reasons for rapid growth • Advances in medicine • Advances in nutrition • Trends in growth (Figure 6.9) 2003 生態學 chap.6 Population Growth

  30. 14 Year 13 12 11 2100 2046 10 2033 9 2020 8 Billions of people 2009 7 1998 6 1987 5 1975 4 1960 3 1930 2 1830 1 0 2-5 million Years ago 7,000 BC 6,000 BC 5,000 BC 4,000 BC 3,000 BC 2,000 BC 1,000 BC 1 AD 1,000 AD 2,000 AD 3,000 AD 4,000 AD Fig. 6.9 The world population explosion. 2003 生態學 chap.6 Population Growth

  31. Human population statistics • Population is increasing at a rate of 3 people every second • Current population: over 6 billion • UN predicts population will stabilize at 11.5 billion by 2150 • Developed countries • Average annual rate of growth from 1960-1965: 1.19% • Average annual rate of growth from 1990-1995: 0.48% • Developing countries • Average annual rate of growth from 1960-1965: 2.35% • Average annual rate of growth from 1990-1995: 2.38% 2003 生態學 chap.6 Population Growth

  32. 2003 生態學 chap.6 Population Growth

  33. Fertility rates • Theoretic replacement rate: 2.0 • but Actual replacement rate: 2.1 2003 生態學 chap.6 Population Growth

  34. Overlapping generations • Many species in warm climates reproduce continually and generations overlap. • Rate of increase is described by a differential equation • dN / dt = rN = (b – d)N • N = population size • t = time • r = per capita rate of population growth • b = instantaneous birth rate • d = instantaneous death rate • dN = the rate of change in numbers • dN / dt = the rate of population increase 2003 生態學 chap.6 Population Growth

  35. 5 r = 0.02 4 r =0.01 3 In (N) r = 0 (equilibrium) 2 • r is analogous to Ro • In a stable population • r = (ln Ro) / Tc • Tc generation time 1 The starting population is N=10 0 20 60 80 100 40 Fig. 6.10 Time (t) 2003 生態學 chap.6 Population Growth

  36. Nt =N0ert Nt / N0 = ert If Nt / N0 = 2, ert = 2 ln(2) = rt 0.69315 = rt t = 0.69315 / r r = 0.01 t = 69.3 r = 0.02 t = 34.7 r = 0.03 t = 23.1 r = 0.04 t = 17.3 r = 0.05 t = 13.9 r = 0.06 t = 11.6 族群加倍的時間 2003 生態學 chap.6 Population Growth

  37. Logistic growth equations • dN / dt= rN[(K-N)/K]; or • dN / dt = =rN[1-(N/K)] • dN / dt = Rate of population change • r = per capita rate of population growth • N = population size • K = carrying capacity • S-Shaped Curve: Figure 6.11 2003 生態學 chap.6 Population Growth

  38. K Geometric “J” shaped curve Population size Logistic “S” shaped curve Time 2003 生態學 chap.6 Population Growth

  39. Logistic growth assumptions • Relation between density and rate of increase is linear • Effect of density on rate of increase is instantaneous • Environment (and thus K) is constant • All individuals reproduce equally • No immigration and emigration 2003 生態學 chap.6 Population Growth

  40. Logistic growth assumptions • Testing assumptions • Early laboratory cultures Pearl 1927 • Figure 6.12 • Complex studies and temporal effects • Figure 6.13 2003 生態學 chap.6 Population Growth

  41. 750 K = 665 600 450 Amount of yeast 300 150 18 0 2 4 6 8 10 12 14 16 20 Time (hrs) Fig. 6.12 yeast 2003 生態學 chap.6 Population Growth

  42. Logistic curve predicted by theory N Time 800 600 Rhizopertha dominica Number per 12 grams of wheat Callandra oryzae 400 200 50 180 100 Time (weeks) Fig. 6.13 grain beetles 2003 生態學 chap.6 Population Growth

  43. Difficulty in meeting assumptions in nature • Each individual added to the population probably does not cause an incremental decrease to r • Time lags, especially with species with complex life cycles • K may vary seasonally and/or with climate • Often a few individuals command many matings • Few barriers to prevent dispersal 2003 生態學 chap.6 Population Growth

  44. Effect of time lags • Robert May (1976) • Incorporated time lags into logistic equation • dN / dt = rN[1-(Nt-t /K)] • dN / dt = Rate of population change • r = per capita rate of population growth • N = population size • K = carrying capacity. • Nt-t= time lag between the change in population size and its effect on population growth, then the population growth at time t is controlled by its size at some time in the past, t - t • Nt-t= population size in the past 2003 生態學 chap.6 Population Growth

  45. Effect of time lags • Ex. r = 1.1, K = 1000 and N = 900 • No time lag, new population size • dN / dt = 1.1 x 900 (1 – 900/1000) = 99 • New population size = 900 + 99 = 999 • Still below K • With time lag, where a population is 900, although the effects of crowding are being felt as though the population was 800 • dN / dt = 1.1 x 900 (1 – 800/1000) = 198 • New population size = 900 + 198 = 1098 • Possible for a population to exceed K 2003 生態學 chap.6 Population Growth

  46. Effect of response time • Ratio of time lag (t) to response time (1/r) or rt controls population growth (Figure 6.14) • rt is small (<0.368) • Population increases smoothly to carrying capacity • rt is large (>1.57) • Population enters into a stable oscillation called a limit cycle • Rising and falling around K • Never reaching equilibrium • rt is intermediate (>0.368 and <1.57) • Populations undergo oscillations that dampen with time until K is reached 2003 生態學 chap.6 Population Growth

  47. r`small (<0.368) Smooth response Number of individuals (N) K Time (t) rtmedium (>0.368,<1.57) Damped oscillations Number of individuals (N) K Time (t) r t large (>1.75) Stable limit cycle period Number of individuals (N) K amplitude Fig. 6.14 Time (t) 2003 生態學 chap.6 Population Growth

  48. Species with discrete generations • Nt+1 = Nt + rNt [1 – (Nt / K)] • In discrete generations, the time lag is 1.0 • r is small (2.0) • Population generally reaches K smoothly • r is between 2.0 and 2.449 • Population enters a stable two-point limit cycle with sharp peaks and valleys • r is between 2.449 and 2.570 • More complex limit cycles • r is larger than 2.57 • Limit cycles breakdown • Population grows in a complex, non-repeating patterns, know as ‘chaos’ • Figure 6.15 2003 生態學 chap.6 Population Growth

  49. r small (2.000–2.499) N t r medium (2.499–2.570) N t r large (>2.570) N Fig. 6.15 t 2003 生態學 chap.6 Population Growth

  50. 6.4 Stochastic Models • Models are based on probability theory • Figure 6.16 • dN / dt = rN = (b – d) N • If b = 0.5, d = 0, and N0 = 10, • integral form of equation Nt = N0ert • So for the above example, Nt= 10 x 1.649 = 16.49 • Path of population growth (Figure 6.17) 2003 生態學 chap.6 Population Growth

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