Ecology Population - Population Ecology Population...

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Unformatted text preview: Population Ecology Population Population: A group of sympatric interbreeding individuals of the same kind. interbreeding Properties: 1. Survivorship 2. Fertility 3. Growth rate Population Ecology Population 4. Age distribution 5. Age specific life expectancies Age 6. 6. Immigration Rate/Emigration Rate Population Ecology: First Principle Population General Laws or Principles 1. Populations tend to grow exponentially “A population will grow (or decline) population exponentially as long as the environment experienced by all individuals in a population remains constant.” (Turchin 2001) 2001) Population Ecology Population This assumes, however, that the growth This parameter is not equal to zero. Populations with negative growth will Populations decline exponentially just as populations decline with positive growth will increase exponentially. exponentially. E xponential Growth 6000 P opula tion S iz e , N 5000 4000 3000 2000 1000 0 0 5 10 15 Generations or Time Units 20 25 Population Ecology: First Principle Population If we take the natural log of population size, If N, however, we can make the growth curve linear. Natural Log of a Population with Overlapping Generations 9.0 8.0 Slope = r N a tura l Log of N 7.0 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0 5 10 15 Generations or Time Units 20 25 Population Ecology Population Another important concept is the difference Another between a deterministic model of population deterministic growth and a stochastic model. stochastic Population Ecology Population In deterministic models conditions are In deterministic specified leading to an exact outcome based on the parameters assigned. on Population Ecology Population In stochastic models population parameters In stochastic vary according to some kind of a frequency distribution. This distribution has a “central tendency” (a mean), but also has a range of variability around the mean. variability Vortex will give you deterministic output, but Vortex will also do stochastic simulations. will 7000 Deterministic growth using arithmetic mean (1.05) Stochastic growth with low variance (0.02) Stochastic growth with high variance (0.08) "Most Likely" stochastic growth uising the geometric mean (1.04) 6000 5000 4000 3000 2000 1000 0 0 10 20 30 40 50 Time 60 70 80 90 100 Population Ecology: Second Principle Population 2. Principle of Self-limitation Population growth cannot go on forever; Population there is an upper bound beyond which the population cannot increase. population The usual model, the logistic model, is The flawed but is sufficient for our purposes. flawed Population Ecology Population In this model a formal limit, known as the carrying In capacity, K, is added to the exponential growth equation. equation. Beverton Holt Model 1000 Population Size, N 750 500 250 Deterministic Growth Stochastic Growth 0 0 20 40 60 80 Time Units or Generations 100 Population Ecology: Third Principle Population 3. Consumer-resource interactions tend to Consumer-resource produce oscillations. produce In fact, something as simple as a time lag In between the population and its interaction with the carrying capacity can produce these oscillations. oscillations. Tau = 3 r = 0.5 1400 1200 Population Siz e 1000 800 600 400 200 0 0 20 40 60 Time 80 100 120 Population Ecology Population Three kinds of populations 1. Populations with discrete generations. No Populations overlap between adults and offspring. overlap Examples: periodical cicadas, annual plants This is called discrete population growth. This discrete Population Ecology Population 2. Populations having continuous growth and Populations overlapping generations with no age distribution effects. distribution Examples: Paramecium, some rodent Examples: Paramecium some populations. populations. This is called continuous population growth. This continuous Population Ecology: Populations with age classes age 3. Populations with distinct age classes that have Populations growth which is affected by distribution of individuals among age classes. individuals Examples: Most bird and mammal populations. N.B. If population has a stable age distribution, we N.B. can use the model on the previous slide. can Deterministic Models for Density Independent Growth Independent Discrete versus Continuous Growth Difference equations used for discrete growth. Differential equations used for continuous Differential growth. growth. Basic Parameters Basic 1. Nt = Population size at time, t 2. b = per capita birth rate d = per capita death rate per 3. I = immigration rate 3. E = emigration rate emigration Deterministic Models and Density Independent Growth Independent Simple Difference Equation: Nt+1 = Nt(b-d) + (I-E) Deterministic Models and Density Independent Growth Independent We usually ignore I and E and collapse (b - d) We to a single growth parameter called R or λ. Where R = a growth parameter per generation Where growth and λ = a growth parameter per unit time period (usually called the finite rate of increase). increase). Deterministic Models and Density Independent Growth Independent This allows us to write: Nt+1= NtR or Nt+1= Ntλ Generalizing: Generalizing: Nt = N0Rt or or Nt = N0λt Continuous Growth Models Continuous We use a differential equation: dN/dt = rN Where r = the intrinsic rate of increase and Where the r=b–d Solved form: Nt = N0 ert Where e = the base of natural logs Discrete versus Continuous Growth Discrete Growth is positive if R > 1 of if r > 0. Growth positive No growth if R = 1 or r = 0. Declining population if R < 1 or r < 0. Discrete versus Continuous Growth Discrete If we graph lnNt versus time, growth becomes If linear with: linear slope = lnR in discrete growth, or the slope = r in continuous growth. or slope D iscrete or "Geometric" Growth 1200 1000 P opula tion S iz e , N 800 600 400 200 0 0 5 10 15 Generations or Time Units 20 25 Natural Log of a Population with Discrete Generations Slope = lnR 8.0 7.0 Natural Log of N 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0 5 10 15 Generations or Time Units 20 25 E xponential Growth 6000 5000 P opula tion S iz e , N 4000 3000 2000 1000 0 0 5 10 15 Generations or Time Units 20 25 Natural Log of a Population with Overlapping Generations 9.0 8.0 Slope = r 7.0 N a tura l Log of N 6.0 5.0 4.0 3.0 2.0 1.0 0.0 0 5 10 15 Generations or Time Units 20 25 Human Population Growth since 1650 Human 7.00 Number in billions 6.00 5.00 4.00 3.00 2.00 1.00 0.00 1650 1700 1750 1800 1850 Year Figure 1.6a. Human population growth since 1650 1900 1950 2000 Figure 6. Natural Log of Human Population Growth Since 1650 The 2006 human population data from the population reference bureau. reference Region Population in Millions Birth rate per thousand Death rate per thousand r ( per individual) Doubling time (years) Percent under 15 years World 6555 21 9 0.012 58 29 Africa 924 38 15 0.023 30 42 North America1 332 14 8 0.006 116 20 Latin America2 586 21 6 0.015 46 30 Asia 3968 20 7 0.012 58 29 Europe 732 10 12 ‑0.001 NA 16 Oceania3 34 17 7 0.010 69 25 The 2007 human population data from the population reference bureau. reference Region Population in Millions Birth rate per thousand Death rate per thousand r ( per individual) Doubling time (years) Percent under 15 years World 6625 21 9 0.012 58 28 Africa 944 38 14 0.024 29 41 North America1 335 14 8 0.006 116 20 Latin America2 569 21 6 0.015 46 30 Asia 4010 4010 19 7 0.012 58 28 Europe 733 10 11 ‑0.001 NA 16 Oceania3 35 18 7 0.010 69 25 The 2008 human population data from the population reference bureau. reference Region Population in Millions Birth rate per thousand Death rate per thousand r ( per individual) Doubling time (years) Percent under 15 years World 6.705 21 8 0.012 58 28 Africa 967 37 14 0.024 29 41 North America1 338 14 8 0.006 116 20 Latin America2 577 21 6 0.015 46 30 Asia 4052 4052 19 7 0.012 58 27 Europe 736 11 11 0 NA 16 Oceania3 35 18 7 0.011 63 25 The 2009 human population data from the population reference bureau. reference Region Population in Millions Birth rate per thousand Death rate per thousand r ( per individual) Doubling time (years) Percent under 15 years World 6810 20 7 0.012 58 27 Africa 999 36 12 0.024 29 40 North America1 341 14 8 0.006 116 20 Latin America2 580 20 6 0.014 50 30 Asia 4117 4117 19 7 0.012 58 27 Europe 738 11 11 0 NA 15 Oceania3 36 18 7 0.011 63 24 The 2010 human population data from the population reference bureau. reference Region Population in Millions Birth rate per thousand Death rate per thousand r ( per individual) Doubling time (years) Percent under 15 years World 6892 20 8 0.012 57.75 27 Africa 1030 37 13 0.024 28.88 41 North America1 344 13 8 0.006 115.5 20 Latin America2 585 19 6 0.013 53.3 29 Asia 4157 4157 19 7 0.012 58 26 Europe 739 11 11 0 NA 16 Oceania3 37 18 7 0.011 63 24 World human demographic trends since 1981. All data from the population reference bureau. the Year World Population Birth Rate Death Rate r Estimate (Billions) Per Thousand Per Thousand Projected Growth in Numbers Actual Average Growth Per Year During Per Individual Per Year (Millions) Specified Time Period (Millions 1981 4.492 28 11 0.017 77 1985 4.845 27 11 0.016 78.1 1981-85: 88.3 1987 5.026 28 10 0.018 91.3 1985-87: 90.5 1989 5.234 28 10 0.018 95.1 1987-89: 104.0 1991 5.384 27 9 0.018 97.8 1989-91: 75.0 1995 5.702 24 9 0.015 86.2 1991-95: 79.5 2000 6.067 22 9 0.014 85.5 ‘95-2000: 73.0 2003 6.314 22 9 0.013 82.6 2000-03: 2006 6.555 21 9 0.012 2006-07: 70.0 2007 6.625 21 9 0.012 2007-08: 80.0 2008 6.705 21 8 0.012 80.9 2008-2009: 105.0 2009 6.810 20 8 0.012 67.4 2009-2010: 82.0 2010 6.892 20 8 0.012 69.7 82.3 Human demographic trends in North America since 1981. since Year Population Estimate (Billions) Birth Rate Per Thousand Death Rate Per Thousand R Per Individual Projected Growth In Numbers Per Year (Millions) 1981 0.25 16 9 0.007 1.76 1985 0.26 15 8 0.007 1.83 1987 0.27 15 9 0.006 1.62 1989 0.27 16 9 0.007 1.9 1991 0.28 16 9 0.007 1.97 1995 0.29 15 9 0.006 1.75 2000 0.31 14 8 0.006 1.86 2003 0.323 14 8 0.005 1.62 2006 0.332 14 8 0.006 2.00 2008 0.338 14 8 0.006 2.03 2009 0.341 14 8 0.006 3.00 2010 0.344 13 8 0.006 3.00 Human demographic trends in Asia since 1981. Human Year Population Estimate (Billions) Birth Rate Per Thousand Death Rate Per Thousand R Per Individual Projected Growth In Numbers Per Year (Millions) 1981 2.61 29 11 0.018 47.4 1985 2.83 28 10 0.018 51.4 1987 2.93 28 10 0.018 53.2 1989 3.06 28 9 0.019 58.7 1991 3.16 27 9 0.018 57.4 1995 3.38 24 8 0.016 54.5 2000 3.68 22 8 0.014 51.9 2003 3.83 20 7 0.013 50.1 2006 3.97 20 7 0.012 47.9 2008 4.05 19 7 0.012 48.9 2009 4.12 19 7 0.012 70.0 2010 4.16 19 7 0.012 40.0 Human demographic trends in Africa since 1981. 1981. Year Population Estimate (Billions) Birth Rate Per Thousand Death Rate Per Thousand r Per Individual Growth In Numbers Per Year (Millions) 1981 0.49 46 17 0.029 14.4 1982 0.50 46 17 0.029 14.7 1985 0.55 45 16 0.029 16.2 1987 0.60 44 16 0.028 17 1989 0.65 45 15 0.030 19.8 1991 0.68 44 14 0.030 20.7 1992 0.69 43 14 0.029 20.3 1995 0.72 41 13 0.028 20.4 1996 0.73 41 13 0.028 20.7 1998 0.76 40 15 0.025 19.2 2000 0.80 38 14 0.024 19.4 2001 0.81 38 14 0.024 19.7 2003 0.86 38 14 0.024 20.9 2005 0.91 38 15 0.023 21.2 2006 0.92 38 14 0.024 22.3 2008 0.967 37 14 0.024 23.5 2009 0.999 36 12 0.024 32.0 2010 1.030 37 13 0.024 31.0 Population Growth in Africa and Asia Africa’s peak r was in 1989-91, but its Africa’s absolute population growth has started increasing again since 1998. Absolute growth about 32 million per year. about Note that Asia (40 million) and Africa (31 Note million) accounted for almost 86.6% of world population growth in 2010 (82 million). The remainder of the world added 11 million people. people. Top Ten Countries by Population Size in 2007 in Country Population Birth Rate per thousand (in Millions) Death Rate per Intrinsic rate of increase Projected Growth per year thousand (b-d)/1000 Projected Doubling Time (years) (millions) 1. China 1318 12 7 0.005 6.61 138.6 2. India 1132 24 8 0.016 18.26 43.3 3. US 302 14 8 0.006 1.82 115.5 4. Indonesia 232 21 7 0.014 3.27 49.5 5. Brazil 189 21 6 0.014 2.67 49.5 6. Pakistan 169 31 8 0.023 3.93 30.1 7. Bangladesh 149 27 8 0.019 2.76 36.5 9. Russia 142 10 15 -0.005 -0.71 -138.6* 8. Nigeria 144 43 18 0.025 3.65 27.7 10. Japan 128 9 9 0.000 0.00 NA Total 3905 World 6625 Percent 58.9 46.09 21 9 0.012 79.98 58.9 57.75 Top Ten Countries by Population Size in 2008 in Country Population Birth Rate per thousand Intrinsic rate of increase thousand (in Millions) Death Rate per Projected Growth per year (b-d)/1000 Projected Doubling Time (years) (millions) 1. China 1,324.7 12 7 0.005 6.64 138.6 2. India 1,149.3 24 8 0.016 18.5 43.3 3. US 304.5 14 8 0.006 1.78 115.5 4. Indonesia 239.9 21 6 0.015 3.63 46.2 5. Brazil 195.1 20 6 0.013 2.55 53.5 6. Pakistan 172.8 31 9 0.022 3.84 31.5 7. Nigeria 148.1 43 18 0.025 3.75 27.7 8. Bangladesh 147.3 24 7 0.017 2.53 40.8 9. Russia 141.9 12 15 -0.003 -0.43 -231.0 10. Japan 127.7 9 9 0 0 NA Total 3951.3 World 6705 Percent 58.9 42.76 22 8 0.012 80.0 53.5 57.75 Top Ten Countries by Population Size in 2009 in Country Population Birth Rate per thousand Intrinsic rate of increase thousand (in Millions) Death Rate per Projected Growth per year (b-d)/1000 Projected Doubling Time (years) (millions) 1. China 1,331 12 7 0.005 6.67 138.6 2. India 1,171 25 8 0.017 20.1 40.8 3. US 307 14 8 0.006 1.85 115.5 4. Indonesia 243 21 6 0.015 3.67 46.2 5. Brazil 191.5 17 6 0.010 1.92 69.3 6. Pakistan 181 30 7 0.023 4.21 30.1 7. Bangladesh 162 23 7 0.016 2.61 43.3 8. Nigeria 153 41 15 0.026 4.03 26.5 9. Russia 142 12 15 -0.003 -0.43 -231.0 10. Japan 128 9 9 0 0 NA Total 4009 World 6810 Percent 58.9 42.76 20 8 0.012 82.2 52.0 57.75 Top Ten Countries by Population Size in 2010 in Country Population Birth Rate per thousand Intrinsic rate of increase thousand (in Millions) Death Rate per Projected Growth per year (b-d)/1000 Projected Doubling Time (years) (millions) 1. China 1,338 12 7 0.005 6.71 138.6 2. India 1,189 23 7 0.015 17.97 46.2 310 14 8 0.006 1.86 115.5 235.5 20 6 0.014 3.31 49.5 5. Brazil 193 17 6 0.010 1.94 69.3 6. Pakistan 185 30 7 0.023 4.30 30.1 7. Bangladesh 164 22 7 0.015 2.48 46.2 8. Nigeria 158 42 17 0.024 3.58 28.9 9. Russia 142 12 14 -0.002 -0.28 -346.60 10. Japan 127 9 9 0 0 NA 3. US 4. Indonesia Total 4041 World 6810 Percent 58.6 42.76 20 8 0.012 82.0 51.1 57.75 Top Eleven Countries by Growth Rates (more than 3% per year) than Country Population In Millions Birth Rate per thousand Death Rate per Thousand Intrinsic rate of increase (b – d)/1000 Projected Growth per year (Millions) Projected Doubling Time Time in Years 1. Mayotte 0.2 39 3 0.036 0.007 19.3 2. Palestine 4.2 37 4 0.033 0.141 21.0 3. Mali 12.7 48 15 0.033 0.427 21.0 4. Malawi 13.6 48 16 0.032 0.442 21.7 5. Yemen 22.2 41 19 0.032 0.722 21.7 6. Timor-Leste 1.1 42 11 0.032 0.037 21.7 7. Niger 14.7 46 15 0.031 0.463 22.4 8. Uganda 29.2 48 16 0.031 0.919 22.4 9. Liberia 3.9 50 18 0.031 0.123 22.4 10. Guinea-Bissau 1.7 50 19 0.031 0.054 22.4 10. Congo, Dem. R. 66.5 44 13 0.031 2.094 22.4 Highest Fertility Worldwide Highest Country Lifetime Lifetime Births per woman woman Country Lifetime Lifetime Births per woman woman Niger 7.4 Zambia 6.2 GuineaBissau 7.1 Angola 6.6 Malawi Chad 6.3 6.3 Burkina Faso 6.0 6.0 Somalia 6.7 Mali 6.0 Uganda 6.7 Dem. Rep. of Dem. Congo Congo 6.5 Lowest Fertility Worldwide Lowest Country Italy Lifetime Births Lifetime per woman per Country Lifetime Births per Lifetime woman woman 1.4 1.2 San Marino Slovakia 1.2 1.2 Germany Ukraine 1.3 1.3 Portugal Denmark 1.3 1.4 Hungary Moldova 1.3 1.3 Romania South Korea 1.3 1.3 Austria Poland 1.4 1.3 Japan Taiwan 1.3 1.1 Latvia 1.4 BosniaHerzegovina Sample Problems 1. You survey an annual insect and find 5000 You females per acre. One year later you census the population and find 6000 females per acre. What is the net replacement rate, R, for this population? for Sample Problems Sample 2. What size will the population be 3 years from What the original census if the population continues to grow at the same rate? 5 years later? ten years later? In what year would the population reach 100,000? the Sample Problems Use equation: Nt = NoRt a) R = 6000/5000 = 1.20 Sample Problems b) After 3 years the population will be: After N3 = N0R3 = (5000)(1.2)3 = 8640 c) After 5 years: After N5 = (5000)(1.2)5 = 12442 (5000)(1.2) d) After ten years: After 10 N10 = (5000)(1.2)10 = 30958 30958 Sample Problems e) To solve for the last part we write the equation: 100,000 = (5000)(1.2)t Simplifying, we write: Simplifying, 100,000/5000 = 1.2t or 20 = 1.2t 100,000/5000 Taking logs, we have: Taking ln20 = (ln1.2)*t or 2.996 = (0.182)*t ln20 t = 16.4 years Since the population reproduces only once a year Since the answer must be rounded up to: the 17 years Sample Problems The birth rate for Latin America in 1978 was The 33 per thousand, while the death rate was ten per thousand. What was the intrinsic rate of increase, assuming a stable age distribution? Sample Problems Use the equations: r=b–d Nt = N0ert a) Given r = b-d, Given we have r = 33/1000-10/1000 = 0.023 0.023 Sample Problems If the population size was 344 million, what If was the projected population in 1982? was From 1978 to 1982 is four years. From b) Therefore: b) N4 = N0(e0.023*4) = 344 million*(e0.092) = (344 million)*(1.096) = 377.15 million 377.15 Sample Problems Between 1982 and 1990 the population Between increased from 377 million to 415 million, what was the r during that time? Given this r value, what is the doubling time? What is λ? value, Sample Problems c) From 1982 to 1990 is 8 years. Therefore: 415 million = 377 million(e8r) Simplifying: 415/377 = 1.10 = e8r Taking natural logs: ln 1.10 = 8r or 0.096/8 = or r = 0.012 0.012 Sample Problems d) Doubling time Doubling 0.693/r = 0.693/0.012 = 57.7 years 57.7 e) λ = er = e0.012 = 1.012 1.012 Got it?? ...
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This note was uploaded on 01/23/2012 for the course BIOL/EVPP 307 taught by Professor Crerar during the Summer '11 term at George Mason.

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