Chapter 53
Population Ecology
Overview: Counting Sheep
• A small population of Soay sheep were
introduced to Hirta Island in 1932
• They provide an ideal opportunity to study
changes in population size on an isolated
island with abundant food and no predators
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Lectures by Chris Romero, updated by Erin Barley with contributions from Joan Sharp
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Figure 53.1 What causes a sheep population to
fluctuate in size?
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Concept 53.1: Dynamic biological processes
influence population density, dispersion, and
demographics
• A population is a group of individuals of a
single species living in the same general area
• Population ecology is the study of populations
in relation to environment, including
environmental influences on density and
distribution, age structure, and population size
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Density and Dispersion
Density and Dispersion
• Density is the number of individuals per unit
area or volume
• Dispersion is the pattern of spacing among
individuals within the boundaries of the
population
– Density is the result of an interplay between
processes that add individuals to a population
and those that remove individuals
– Immigration is the influx of new individuals
from other areas
– Emigration is the movement of individuals out
of a population
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– Clumped: individuals aggregate in patches
– Uniform: individuals are evenly distributed
(territoriality)
– Random: position of each individual is
independent of other individuals
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Figure 52.3 Patterns of dispersion within a
population’s geographic range
Density: A Dynamic Perspective
• In most cases, it is impractical or impossible to
count all individuals in a population
• Sampling techniques can be used to estimate
densities and total population sizes
(a) Clumped.
(b) Uniform.
• Population size can be estimated by either
extrapolation from small samples, an index of
population size, or the mark-recapture method
(c) Random.
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Figure 53.2 Determining population size using the
mark-recapture method
APPLICATION
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Figure 53.3 Population dynamics
Births
Births and immigration
add individuals to
a population.
Immigration
Deaths
Deaths and emigration
remove individuals
from a population.
Emigration
Hector’s dolphins
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Demographics
Life Tables
• Demography is the study of the vital statistics
of a population and how they change over time
• A life table is an age-specific summary of the
survival pattern of a population
– Death rates and birth rates are of particular
interest to demographers
– It is best made by following the fate of a cohort,
a group of individuals of the same age
– The life table of Belding’s ground squirrels
reveals many things about this population
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Table 53-1
Survivorship Curves
• A survivorship curve is a graphic way of
representing the data in a life table
– The survivorship curve for Belding’s ground
squirrels shows a relatively constant death rate
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Survivorship Curves
Number of survivors (log scale)
Figure 53.5 Survivorship curves for male and
female Belding’s ground squirrels
• Survivorship curves can be classified into three
general types:
1,000
– Type I: low death rates during early and middle
life, then an increase among older age groups.
(Humans, large mammals)
100
– Type II: the death rate is constant over the
organism’s life span. (Squirrels)
Females
10
Males
1
0
2
8
4
6
Age (years)
10
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Figure 53.6 Idealized survivorship curves: Types I,
II, and III
Number of survivors (log scale)
– Type III: high death rates for the young, then a
slower death rate for survivors. (Fish, clams,
insects)
Concept 53.2: Life history traits are “products of
natural selection”
• An organism’s life history comprises the traits
that affect its schedule of reproduction and
survival:
1,000
I
– The age at which reproduction begins
100
II
– How often the organism reproduces
– How many offspring are produced during each
reproductive cycle
10
III
1
0
50
Percentage of maximum life span
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100
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Life History Diversity
• Life histories are very diverse, two contrasting
types:
1. Species that exhibit semelparity, or big-bang
reproduction, reproduce once and die
Concept 53.3: The exponential model describes
population growth in an idealized, unlimited
environment
• Exponential population growth model
– It is useful to study population growth in an
idealized situation
• Examples: salmon, agave plant
– Idealized situations help us understand the
capacity of species to increase and the
conditions that may facilitate this growth
2. Species that exhibit iteroparity, or repeated
reproduction, produce offspring repeatedly
• Highly variable or unpredictable environments
likely favor big-bang reproduction, while
dependable environments may favor repeated
reproduction
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Per Capita Rate of Increase
Per Capita Growth Rate
• Population growth rate = Per capita rate of
increase
•
– If immigration and emigration are ignored, a
population’s growth rate equals birth rate minus
death rate during a time interval
– N = population size
r=b–d
N
For a population sample size of 1000 (N =
1000) there were 60 births and 10 deaths
over a one year period. What is the growth
rate?
A. .5 per individual per year
B. .05 per individual per year
C. .005 per individual per year
60-10/1000 = .05
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Population Growth Rate
• Per capita birth and death rates
– The average # of birth (b) or deaths (m for
mortality) per individual per unit time
– If there are 34 births per year in a population of
1000,
• b = 0.034
– If the death rate in a population is 16 deaths per
year,
• m= 0.016
– Zero population growth occurs when the birth
rate equals the death rate
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• Most ecologists use differential calculus to
express population growth as growth rate at a
particular instant in time:
– per capita birth rate - per capita death rate =
rN: per capita rate of change in a population
size
ΔN =
Δt rN
where N = population size, t = time, and r = per capita
rate of increase = birth – death
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• Exponential population growth is population
increase under idealized conditions
– Under these conditions, the rate of reproduction
is at its maximum, called the intrinsic rate of
increase
– Equation of exponential population growth:
dN =
dt rmaxN
Figure 53.10 Exponential Population Growth
• Exponential population growth results in a Jshaped curve
2,000
Population size (N)
Exponential Growth
dN 1.0N
dt =
1,500
dN
0.5N
dt =
1,000
500
0
0
Exponential Population Growth Model
• Populations with a high rN (per capita rate of
increase) will have a steeper J-shaped curve than
ones with a lower value
• The J-shaped curve of exponential growth
characterizes some rebounding populations
Concept 53.4: The logistic model describes how a
population grows more slowly as it nears its
carrying capacity (K)
• The logistical growth model
– Exponential growth cannot be sustained for long
in any population
– A more realistic population model limits growth
by incorporating carrying capacity
– Carrying capacity (K) is the maximum
population size the environment can support
• Influenced by many factors such as: available
water and food, predators, soil nutrients, suitable
nesting sites
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Figure 53.11 Exponential growth in the African
elephant population of Kruger National Park
8,000
6,000
4,000
2,000
0
1900
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5
10
Number of generations
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Elephant population
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1920
1940
Year
1960
1980
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The Logistic Growth Model
• In the logistic population growth model, the
per capita rate of increase declines as carrying
capacity is reached
– We construct the logistic model by starting with the
exponential model and adding an expression that
reduces per capita rate of increase as N approaches
K
(K − N)
dN
=
dt rmax N K
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Population growth predicted by the logistic model
• The growth of laboratory populations of
paramecia fits an S-shaped curve if the
experimenter maintains a constant environment.
Exponential
growth
dN 1.0N
=
2,000
Number of Paramecium/mL
Population size (N)
• The logistic model of population growth
produces a sigmoid (S-shaped) curve
dt
1,500
K = 1,500
Logistic growth
1,000
dN 1.0N
=
dt
1,500 – N
1,500
500
0
0
5
10
Number of generations
The Logistic Model and Real Populations
15
1,000
800
600
400
200
0
0
5
10
Time (days)
15
A Paramecium population in the lab
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The Logistic Model and Real Populations
• Some populations overshoot K before settling
down to a relatively stable density
• Some populations fluctuate greatly and make it
difficult to define K
Number of Daphnia/50 mL
The Logistic Model and Real Populations
– Some populations have regular cycles of boom
and bust
180
150
– Some populations show an Allee effect, in which
individuals have a more difficult time surviving
or reproducing if the population size is too small
120
90
60
– The logistic model fits few real populations but
is useful for estimating possible growth
30
0
0
20
40
60
80 100 120 140 160
Time (days)
(b) A Daphnia population in the lab
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The Logistic Model and Real Populations
• Many populations undergo regular boom-andbust cycles
80
60
40
20
1975
1980
1985
1990
1995
2000
Time (years)
(c) A song sparrow population in its natural habitat. The
population of female song sparrows nesting on Mandarte Island,
British Columbia, is periodically reduced by severe winter
weather, and population growth is not well described by the
logistic model.
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160
Lynx
9
80
6
40
3
0
1850
Figure 52.21
Snowshoe hare
120
Lynx population size
(thousands)
0
Hare population size
(thousands)
Number of females
• Some populations
fluctuate greatly
around K: not
well described by
the logistical
model
The Logistic Model and Real Populations
0
1875
1900
Year
1925
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Figure 53.14 White rhinoceros mother and calf
The Logistic Model and Life Histories
• Life history traits favored by natural selection
may vary with population density and
environmental conditions
– K-selection, or density-dependent selection,
selects for life history traits that are sensitive to
population density
– r-selection, or density-independent selection,
selects for life history traits that maximize
reproduction
– The concepts of K-selection and r-selection are
somewhat controversial and have been criticized by
ecologists as oversimplifications
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Concept 53.5: Many factors that regulate
population growth are density dependent
Population Change and Population Density
• There are two general questions about regulation
of population growth:
– What environmental factors stop a population
from growing indefinitely?
• In density-independent populations, birth rate
and death rate do not change with population
density
• In density-dependent populations, birth rates
fall and death rates rise with population density
– Why do some populations show radical
fluctuations in size over time, while others
remain stable?
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Fig. 53-15
Birth or death rate
per capita
Density-dependent
birth rate
Equilibrium
density
Equilibrium
density
Population density
(a) Both birth rate and death rate vary.
Birth or death rate
per capita
Densityindependent
death rate
Densitydependent
death rate
Densityindependent
birth rate
Density-Dependent Population Regulation
Density-dependent
birth rate
Density-dependent
death rate
Equilibrium
density
Population density
(b) Birth rate varies; death rate is constant.
• Density-dependent birth and death rates are an
example of negative feedback that regulates
population growth
– They are affected by many factors, such as
competition for resources, territoriality, disease,
predation, accumulation of toxic wastes, and
intrinsic factors
– Example: Cheetahs are highly territorial, using
chemical communication to warn other cheetahs
of their boundaries
Population density
(c) Death rate varies; birth rate is constant.
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Gannets defend their territory by pecking others
Population Dynamics
• The study of population dynamics focuses on
the complex interactions between biotic and
abiotic factors that cause variation in population
size
– Long-term population studies have challenged
the hypothesis that populations of large
mammals are relatively stable over time
– Weather can affect population size over time
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Concept 53.6: The human population is no longer
growing exponentially but is still increasing rapidly
Immigration, Emigration, and Metapopulations
• Metapopulations are groups of populations
linked by immigration and emigration
• Human population growth
– No population can grow indefinitely, and
humans are no exception
– High levels of immigration combined with
higher survival can result in greater stability in
populations
Aland
˚ Islands
EUROPE
5 km
Occupied patch
Unoccupied patch
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Human Population Growth Rate
• The human population increased relatively
slowly until about 1650 and then began to grow
exponentially
• Though the global population is still growing, the
rate of growth began to slow during the 1960s
6
5
4
3
2
The Plague
8000
B.C.E.
4000 3000
2000 1000
B.C.E. B.C.E. B.C.E. B.C.E.
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0
1000
C.E.
1
2000
C.E.
0
2.2
Annual percent increase
7
Human population (billions)
The Global Human Population
2.0
1.8
1.6
1.4
2005
1.2
Projected
data
1.0
0.8
0.6
0.4
0.2
0
1950
1975
2000
Year
2025
2050
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• To maintain population stability, a regional
human population can exist in one of two
configurations:
– Zero population growth =
High birth rate – High death rate
– Zero population growth =
Low birth rate – Low death rate
• The demographic transition is the move from
the first state toward the second state
Figure 53.24 Demographic transition in Sweden
and Mexico, 1750–2025 (data as of 2005)
Birth or death rate per 1,000 people
Regional Patterns of Population Change
50
40
30
20
10
Sweden
Birth rate
Death rate
0
1750
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1800
Mexico
Birth rate
Death rate
1850
1900
Year
1950
2000
2050
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Age Structure
• The demographic transition is associated with an
increase in the quality of health care and
improved access to education, especially for
women
• Most of the current global population growth is
concentrated in developing countries
• One important demographic factor in present
and future growth trends is a country’s age
structure
– Age structure is the relative number of
individuals at each age
– Commonly represented in pyramids
– Male/female represented by color
– Percent of population at each age is represented
by a horizontal bar. Young at bottom, elderly at
top.
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Figure 53.25 Age-structure pyramids for the human
population of three countries (data as of 2005)
Rapid growth
Afghanistan
Male
10 8
Female
6 4 2 0 2 4 6
Percent of population
Slow growth
United States
Age
85+
80–84
75–79
70–74
65–69
60–64
55–59
50–54
45–49
40–44
35–39
30–34
25–29
20–24
15–19
10–14
5–9
0–4
8 10
8
Male
Female
6 4 2 0 2 4 6
Percent of population
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No growth
Italy
Age
85+
80–84
75–79
70–74
65–69
60–64
55–59
50–54
45–49
40–44
35–39
30–34
25–29
20–24
15–19
10–14
5–9
0–4
8
8
Male
Female
Infant Mortality and Life Expectancy
• Infant mortality and life expectancy at birth vary
greatly among developed and developing
countries but do not capture the wide range of
the human condition
6 4 2 0 2 4 6 8
Percent of population
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50
Life expectancy (years)
Infant mortality (deaths per 1,000 births)
60
40
30
20
80
Estimates of Global Carrying Capacity
60
• The carrying capacity of Earth for humans is
uncertain
• The average estimate is 10–15 billion
40
20
10
0
0
Indus- Less industrialized
trialized
countries countries
Indus- Less industrialized
trialized
countries countries
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Limits on Human Population Size
• The ecological footprint concept summarizes
the aggregate land and water area needed to
sustain the people of a nation
Figure 53.27 The amount of photosynthetic
products that humans use around the world
– It is one measure of how close we are to the
carrying capacity of Earth
– Countries vary greatly in footprint size and
available ecological capacity
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• A population of 500 experiences 55 births
and 5 deaths during a one year period. What
is the reproductive (growth) rate for the
population during the one-year period?
A. .01/ year
Log (g carbon/year)
13.4
9.8
5.8
Not analyzed
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• For a population sample size of 1000 (N =
1000) there were 60 births and 10 deaths
over a one year period. If the population
maintains the current growth pattern, a plot
of its growth would resemble
B. .05/year
A. exponential growth
C. .1/year
B. K-selected growth
D. 50/year
C. ZPG (zero population growth)
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You should now be able to:
1. Define and distinguish between the following
sets of terms: density and dispersion; clumped
dispersion, uniform dispersion, and random
dispersion; life table and reproductive table;
Type I, Type II, and Type III survivorship
curves; semelparity and iteroparity; r-selected
populations and K-selected populations
2. Explain how ecologists may estimate the
density of a species
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3. Explain how limited resources and trade-offs
may affect life histories
4. Compare the exponential and logistic models of
population growth
5. Explain how density-dependent and densityindependent factors may affect population
growth
6. Explain how biotic and abiotic factors may
work together to control a population’s growth
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