Section III Population Ecology

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Section III Population Ecology

• ???
• ????? Ayo
• Japalura_at_hotmail.com

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Section Three Population Ecology

• Chap.6 Population growth (????)
• Chap.7 Physical environment (????)
• Chap.8 Competition and coexistence (?????)
• Chap.9 Mutualism (??)
• Chap.10 Predation (??)
• Chap.11 Herbivory (??)
• Chap.12 Parasitism (??)
• Chap.13 Evaluating the controls on population size

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Chap. 6 Population Growth
Road Map

• 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

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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)

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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)

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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 nx1
• lx proportion of organisms surviving to the
  beginning of age interval x ns / n0

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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 nx1) / 2
• Tx intermediate step in determining life
  expectancy SLx
• ex Tx / nx

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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
14
2
3
4
5
6
7
8
9
10
11
12
13
Age (years)
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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.

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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)

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3.5
3
2.5
2
n (log scale)
1.5
x
1
0.5
0
1
2
7
6
3
4
5
Age (years)
Fig. 6.3 Age-specific survivorship curve for the
American robin.
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Fig. 6.5 Hypothetical comparison of cohort
survivorship of humans born in 1930.
Comparison in the accuracy of life tables
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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

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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
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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

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Fecundity schedules

• Table components
• lx survivorship (number of females surviving in
  each age class
• mx age-specific fecundity
• Ro populations net reproductive rate Slx mx
• Ro 1 population is stationary
• Ro gt 1 population is increasing
• Ro lt 1 population is decreasing
• Table 6.3

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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

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6.3 Deterministic Models
Geometric Growth

• Predicting population growth (???????),????
• Ro
• Initial population size
• Population size at time t
• Population size of females at next generation
  Nt1 RoNt
• Ro net reproductive rate
• Nt population size of females at this generation

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Geometric Growth

• Dependency of Ro
• Ro lt 1 population becomes extinct
• Ro 1 population remains constant
• Population is at equilibrium
• No change in density
• Ro gt 1 population increases
• Even a fraction above one, population will
  increase rapidly
• Characteristic J shaped curve
• Geometric growth
• Figure 6.7

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R 1.20
0
500
R 1.15
0
R???,???????
400
300
Population in size (N)
N 1 R N
200
t 0 t
R 1.10
0
100
R 1.05
0
0
10
20
30
Fig. 6.7
Generations
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Geometric Growth

• Ro gt 1 population increases (cont.).
• Something (e.g., resources) will eventually limit
  growth
• Population crash
• Figure 6.8a
• Figure 6.8b
• Figure 6.8c

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2000
1500
Number of reindeer
1000
500
0
1910
1920
1930
1940
1950
Fig. 6.8 a
Year
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Fig6.8b?c
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Geometric GrowthHuman 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

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Geometric GrowthHuman 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)

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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.
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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

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• Fertility rates
• Theoretic replacement rate 2.0
• but Actual replacement rate 2.1

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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

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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 N10

0
20
60
80
100
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Fig. 6.10
Time (t)
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???????

• 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

• Nt N0ert
• Nt / N0 ert
• If Nt / N0 2, ert 2
• ln(2) rt
• 0.69315 rt
• t 0.69315 / r

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Logistic growth equations

• dN / dt rN(K-N)/K or
• dN / dt rN1-(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

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K
Geometric J shaped curve
Population size
Logistic S shaped curve
Time
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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

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Logistic growth assumptions

• Testing assumptions
• Early laboratory cultures Pearl 1927
• Figure 6.12
• Complex studies and temporal effects
• Figure 6.13

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750
K 665
600
450
Amount of yeast
300
150
0
2
4
6
8
10
12
14
16
18
20
Time (hrs)
Fig. 6.12 yeast
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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
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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

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Effect of time lags

• Robert May (1976)
• Incorporated time lags into logistic equation
• dN / dt rN1-(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

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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

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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 (lt0.368)
• Population increases smoothly to carrying
  capacity
• rt is large (gt1.57)
• Population enters into a stable oscillation
  called a limit cycle
• Rising and falling around K
• Never reaching equilibrium
• rt is intermediate (gt0.368 and lt1.57)
• Populations undergo oscillations that dampen
  with time until K is reached

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r small (lt0.368)
Smooth response
Number of individuals (N)
K
Time (t)
r t medium (gt0.368,lt1.57)
Damped oscillations
Number of individuals (N)
K
Time (t)
r t large (gt1.75)
Stable limit cycle
period
Number of individuals (N)
K
amplitude
Fig. 6.14
Time (t)
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Species with discrete generations

• Nt1 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

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r small (2.0002.499)
N
t
r medium (2.4992.570)
N
t
r large (gt2.570)
N
Fig. 6.15
t
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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)

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0.30
0.20
Proportion of observations
0.10
0
8
6
10
12
14
Population size
Fig. 6.16 stochastic frequency distribution
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Fig. 6.17
Population density
Possible stochastic path
Extinction
Time
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Stochastic Models

• Probability of extinction (d/b)N0
• The larger the initial population size
• The greater the value of b d
• The more resistant a population is to extinction
• Introduce biological variation into calculations
  of population growth
• More representative of nature
• More complicated mathematics

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Applied EcologyHuman Population growth and the
use of contraceptives

• 1992 Johns Hopkins study
• Developed countries
• 70 of couples use contraceptives
• Developing countries
• 45 of couples use contraceptives
• Africa, 14
• Asia, 50
• Latin America, 57

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Human Population growth

• China
• 1950s and 1960s
• Fertility was six children per woman
• 1970s
• Government planning and incentives to reduce
  population growth
• 1990
• 75 use birth control
• Fertility rate dropped to 2.2

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Human Population growth

• Other governments
• 1976, only 97 governments supported family
  planning
• 1988, 125 governments supported family planning
• As of 1989, in 31 countries, couples have no
  access to family planning
• Women
• Women in developing countries want fewer children
• In virtually every country outside of Saharan
  Africa, the desireds number of children is below
  3

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Low growth rates

• Countries concerned about low growth rates
• Some Western European countries and other
  developed countries
• Total fertility has dropped below the replacement
  level of 2.1
• Reduced populations concerns
• Affect political strength
• Economic structure

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• ?????!

Japalura_at_hotmail.com Ayo ???
http//mail.nutn.edu.tw/hycheng/