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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 Selflimitation 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. Consumerresource interactions tend to
Consumerresource 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(bd) + (IE) 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 198185: 88.3 1987 5.026 28 10 0.018 91.3 198587: 90.5 1989 5.234 28 10 0.018 95.1 198789: 104.0 1991 5.384 27 9 0.018 97.8 198991: 75.0 1995 5.702 24 9 0.015 86.2 199195: 79.5 2000 6.067 22 9 0.014 85.5 ‘952000: 73.0 2003 6.314 22 9 0.013 82.6 200003: 2006 6.555 21 9 0.012 200607: 70.0 2007 6.625 21 9 0.012 200708: 80.0 2008 6.705 21 8 0.012 80.9 20082009: 105.0 2009 6.810 20 8 0.012 67.4 20092010: 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 198991, 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 (bd)/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 (bd)/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 (bd)/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 (bd)/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. TimorLeste 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. GuineaBissau 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 = bd,
Given we have r = 33/100010/1000 = 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.
 Summer '11
 Crerar

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