section iii population ecology
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Section III Population Ecology
鄭先祐生態主張者 Ayo
Japalura@hotmail.com
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 3
Chap. 6 Population Growth1. Tabulating changes in population age structure
through time– Time-specific life tables
– Age-specific life tables
2. Fecundity schedules and female fecundity, and estimating future population growth
3. Population growth models– Deterministic models
– Geometric models
– Logistic models
– Stochastic models
Road Map
2003 chap.6 Population Growth生態學 4
6.1 Life tables• The construction of life tables is termed demograph
y.
– 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 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 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 = Lx
• ex = Tx / nx
2003 chap.6 Population Growth生態學 8
2003 chap.6 Population Growth生態學 9
0
0.5
1
1.5
2
2.5
3
3.5
Age (years)
n
(log
sca
le)
x1
0
1 142 3 4 5 6 7 8 9 10 11 12 13
Fig. 6.2 Time-specific survivorship curve
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 12
2003 chap.6 Population Growth生態學 13
0
0.5
1
1.5
2
2.5
3
3.5
n (l
og s
cale
) x
Age (years)
1 2 763 4 5
Fig. 6.3 Age-specific survivorship curve for the American robin.
2003 chap.6 Population Growth生態學 14
Fig. 6.5 Hypothetical comparison of cohort survivorship of humans born in 1930.
Comparison in the accuracy of life tables
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 16
Type I
Type II
Type III
Many mammals
Many birds,small mammals,lizards, turtles
Many invertebrates
Age
Num
ber
of
surv
ivors
(n )
(log s
cale
) x
1000
100
10
1
0.1
Fig. 6.4
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 18
2003 chap.6 Population Growth生態學 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 = lx mx
• Ro = 1; population is stationary
• Ro > 1; population is increasing
• Ro < 1; population is decreasing
• Table 6.3
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 21
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 24
100
200
300
400
500Pop
ula
tion in
siz
e (
N)
0
Generations30
R =1.20 0
R =1.15 0
R =1.10 0
R =1.05 0
10 20
N +1 = R N t 0 t
Fig. 6.7
R 值愈大,族群的成長愈快
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 26
1910 1920 1930 1940 1950
Num
ber
of
rein
deer
2000
1500
1000
500
0
YearFig. 6.8 a
2003 chap.6 Population Growth生態學 27Fig6.8b和c
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 30
1830
1930
1960
1975
1987
1998
2009
2020
2033
20462100
0
1
2
3
4
5
6
7
8
9
10
11
13
12
14
Bill
ions
of
people
2-5 millionYears ago
7,000BC
6,000BC
5,000BC
4,000BC
3,000BC
2,000BC
1,000BC
1AD
1,000AD
2,000AD
3,000AD
Year
4,000AD
Fig. 6.9 The world population explosion.
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 32
2003 chap.6 Population Growth生態學 33
•Fertility rates • Theoretic replacement rate: 2.0– but Actual replacement rate: 2.1
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 35
0
1
2
3
4
5
20 40 60 80 100
r = 0.02
r =0.01
r = 0(equilibrium)
Time (t)
In (
N)
Fig. 6.10
•The starting population is N=10
–r is analogous to Ro
» In a stable population» r = (ln Ro) / Tc
• Tc generation time
2003 chap.6 Population Growth生態學 36
族群加倍的時間
• 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
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 38
Pop
ula
tion s
ize
K
Time
Logistic “S” shaped curve
Geometric “J” shaped curve
2003 chap.6 Population Growth生態學 39
Logistic growth assumptions
1. Relation between density and rate of increase is linear
2. Effect of density on rate of increase is instantaneous
3. Environment (and thus K) is constant
4. All individuals reproduce equally
5. No immigration and emigration
2003 chap.6 Population Growth生態學 40
Logistic growth assumptions
• Testing assumptions – Early laboratory cultures Pearl 1927
• Figure 6.12
– Complex studies and temporal effects• Figure 6.13
2003 chap.6 Population Growth生態學 41
150
300
450
600
750A
mount
of
yeast
K = 665
0 2 4 6 8 10 12 14 16 18 20
Time (hrs)Fig. 6.12 yeast
2003 chap.6 Population Growth生態學 42
200
400
600
800Time
N
Num
ber
per
12
gra
ms
of
wheat
Logistic curve predicted by theory
Time (weeks)
50 100 180
Callandra oryzaeRhizopertha dominica
Fig. 6.13 grain beetles
2003 chap.6 Population Growth生態學 43
Difficulty in meeting assumptions in nature
1. Each individual added to the population probably does not cause an incremental decrease to r
2. Time lags, especially with species with complex life cycles
3. K may vary seasonally and/or with climate
4. Often a few individuals command many matings
5. Few barriers to prevent dispersal
2003 chap.6 Population Growth生態學 44
Effect of time lags– Robert May (1976)
– Incorporated time lags into logistic equation
– dN / dt = rN[1-(Nt- /K)]
• dN / dt = Rate of population change
• r = per capita rate of population growth
• N = population size
• K = carrying capacity.
• Nt-= 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 -
• Nt-= population size in the past
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 46
Effect of response time• Ratio of time lag () to response time (1/r) or r
controls population growth (Figure 6.14)– r 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 chap.6 Population Growth生態學 47
K
Time (t)
Smooth response
K
Time (t)
Num
ber
of
indiv
iduals
(N
)
K
Time (t)
Damped oscillations
period
am
plit
ude
Stable limit cycle
r small (<0.368)
r medium (>0.368,<1.57)
r large (>1.75)
Num
ber
of
indiv
iduals
(N
)N
um
ber
of
indiv
iduals
(N
)
Fig. 6.14
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 49
N
N
N
t
t
t
r small (2.000–2.499)
r medium (2.499–2.570)
r large (>2.570)
Fig. 6.15
2003 chap.6 Population Growth生態學 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 chap.6 Population Growth生態學 51
0
0.10
0.20
0.30
Pro
port
ion o
f obse
rvati
ons
6 8 10 12 14
Population size
Fig. 6.16 stochastic frequency distribution
2003 chap.6 Population Growth生態學 52
Pop
ula
tion d
ensi
ty
Time
Extinction
Possible stochastic
path
Fig. 6.17
2003 chap.6 Population Growth生態學 53
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
2003 chap.6 Population Growth生態學 54
Applied Ecology
Human 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%
2003 chap.6 Population Growth生態學 55
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
2003 chap.6 Population Growth生態學 56
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
2003 chap.6 Population Growth生態學 57
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
2003 chap.6 Population Growth生態學 58
問題與討論!
Japalura@hotmail.com
Ayo 台南站: http://mail.nutn.edu.tw/~hycheng/
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