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Chapter 52 Population Ecology

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Page 1: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Chapter 52Chapter 52

Population Ecology

Page 2: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Earth’s Fluctuating Populations

• To understand human population growth

– we must consider the general principles of population ecology

• Population ecology is the study of populations in relation to environment

– including environmental influences on population density and distribution, age structure, and variations in population size

Page 3: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Concept 52.1: Dynamic biological processes influence population density, dispersion, and demography

• A population

– is a group of individuals of a single species living in the same general area

Page 4: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

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

Page 5: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Density: A Dynamic Perspective

• Determining the density of natural populations

– is possible, but difficult to accomplish

• In most cases

– it is impractical or impossible to count all individuals in a population

Page 6: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Density is the result of a dynamic interplay

– between processes that add individuals to a population and those that remove individuals from it

Figure 52.2

Births and immigration add individuals to a population.

Births Immigration

PopuIationsize

Emigration

Deaths

Deaths and emigration remove individuals from a population.

Page 7: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Patterns of Dispersion

• Environmental and social factors

– influence the spacing of individuals in a population

Page 8: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• A clumped dispersion

– is one in which individuals aggregate in patches

– may be influenced by resource availability and behaviour

Figure 52.3a

(a) Clumped. For many animals, such as these wolves, living in groups increases the effectiveness of hunting, spreads the work of protecting and caring for young, and helps exclude other individuals from their territory.

Page 9: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• A uniform dispersion

– is one in which individuals are evenly distributed

– may be influenced by social interactions such as territoriality

Figure 52.3b

(b) Uniform. Birds nesting on small islands, such as these king penguins on South Georgia Island in the South Atlantic Ocean, often exhibit uniform spacing, maintained by aggressive interactions between neighbors.

Page 10: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• A random dispersion

– is one in which the position of each individual is independent of other individuals

Figure 52.3c

(c) Random. Dandelions grow from windblown seeds that land at random and later germinate.

Page 11: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Demography

• Demography is the study of the vital statistics of a population

– and how they change over time

• Death rates and birth rates

– are of particular interest to demographers

Page 12: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Life Tables

• A life table

– is an age-specific summary of the survival pattern of a population

– is best constructed by following the fate of a cohort

Page 13: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

The life table of Belding’s ground squirrels

Table 52.1

Page 14: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Survivorship Curves

• A survivorship curve

– is a graphic way of representing the data in a life table

Figure 52.4

1000

100

10

1

Num

ber

of s

urvi

vors

(lo

g sc

ale)

0 2 4 6 8 10

Age (years)

Males

Females

Page 15: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Survivorship curves can be classified into three general types

– Type I, Type II, and Type III

Figure 52.5

I

II

III

50 10001

10

100

1,000

Percentage of maximum life span

Num

ber

of s

urvi

vors

(lo

g sc

ale)

Page 16: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Reproductive Rates

• A reproductive table, or fertility schedule

– is an age-specific summary of the reproductive rates in a population

Page 17: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

A reproductive table

Table 52.2

Page 18: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Concept 52.2: Life history traits are products of natural selection

• Life history traits are evolutionary outcomes

– reflected in the development, physiology, and behaviour of an organism

Page 19: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Species that exhibit semelparity, or “big-bang” reproduction

– reproduce a single time and die

Figure 52.6

Life History Diversity

Page 20: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Species that exhibit iteroparity, or repeated reproduction

– produce offspring repeatedly over time

Page 21: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Some plants produce a large number of small seeds

– ensuring that at least some of them will grow and eventually reproduce

Figure 52.8a

(a) Most weedy plants, such as this dandelion, grow quickly and produce a large number of seeds, ensuring that at least somewill grow into plants and eventually produce seeds themselves.

Page 22: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Other types of plants produce a moderate number of large seeds

– that provide a large store of energy that will help seedlings become established

Figure 52.8b

(b) Some plants, such as this coconut palm, produce a moderate number of very large seeds. The large endosperm provides nutrients for the embryo, an adaptation that helps ensure the success of a relatively large fraction of offspring.

Page 23: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

“Trade-offs” and Life Histories

• Organisms have finite resources

Figure 52.7

Researchers in the Netherlands studied the effects of parental caregiving in European kestrels over 5 years. The researchers transferred chicks among nests to produce reduced broods (three or four chicks), normal broods (five or six), and enlarged broods (seven or eight). They then measured the percentage of male and female parent birds that survived the following winter. (Both males and females provide care for chicks.)

EXPERIMENT

The lower survival rates of kestrels with larger broods indicate that caring for more offspring negatively affects survival of the parents.

CONCLUSION

100

80

60

40

20

0Reduced

brood sizeNormal brood

sizeEnlarged

brood size

Par

ents

sur

vivi

ng th

e fo

llow

ing

win

ter

(%)

MaleFemale

– which may lead to trade-offs between survival and reproduction

• Parental care of smaller broods

– may also facilitate survival of offspring

RESULTS

Page 24: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Concept 52.3: The exponential model describes population growth in an idealized, unlimited environment

• It is useful to study population growth in an idealized situation

– in order to understand the capacity of species for increase and the conditions that may facilitate this type of growth

Page 25: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Per Capita Rate of Increase

• If immigration and emigration are ignored

– a population’s growth rate (per capita increase) equals birth rate minus death rate

ΔNΔt

= B - D

B = bN

D = mN

ΔNΔt = bN - mN

r = b - mr = per capita rate of increase

Page 26: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Zero population growth

– occurs when the birth rate equals the death rate (r = 0)

• The population growth equation can be expressed as

dNdt rN

Page 27: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Exponential Growth

• 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

Page 28: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• The equation of exponential population growth is

dN

dt rmaxN

Page 29: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Exponential population growth

– results in a J-shaped curve

Figure 52.9

0 5 10 150

500

1,000

1,500

2,000

Number of generations

Pop

ulat

ion

size

(N

)

dNdt

1.0N

dNdt

0.5N

Page 30: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• The J-shaped curve of exponential growth

– is characteristic of some populations that are rebounding

Figure 52.10

1900 1920 1940 1960 1980

Year

0

2,000

4,000

6,000

8,000

Ele

phan

t pop

ulat

ion

Page 31: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Concept 52.4: The logistic growth model includes the concept of carrying capacity

• Exponential growth

– cannot be sustained for long in any population

• A more realistic population model

– limits growth by incorporating carrying capacity

Page 32: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

The Logistic Growth Model

• Carrying capacity (K)

– is the maximum population size the environment can support

• In the logistic population growth model

– the per capita rate of increase declines as carrying capacity is reached

Page 33: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• We construct the logistic model by starting with the exponential model

– and adding an expression that reduces the per capita rate of increase as N increases

Figure 52.11

Maximum

Positive

Negative

0N K

Population size (N)

Per

cap

ita r

ate

of in

cre

ase

(r)

Page 34: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• The logistic growth equation

– includes K, the carrying capacity

dNdt

(K N)Krmax N

Page 35: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Table 52.3

A hypothetical example of logistic growth

Page 36: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• The logistic model of population growth

– produces a sigmoid (S-shaped) curve

Figure 52.12

dNdt

1.0N Exponential growth

Logistic growth

dNdt

1.0N1,500 N

1,500

K 1,500

0 5 10 150

500

1,000

1,500

2,000

Number of generations

Pop

ulat

ion

size

(N

)

Page 37: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Figure 52.13a

800

600

400

200

0

Time (days)0 5 10 15

(a) A Paramecium population in the lab. The growth of Paramecium aurelia in small cultures (black dots) closely approximates logistic growth (red curve) if the experimenter maintains a constant environment.

1,000

Nu

mb

er

of

Pa

ram

eci

um

/ml

The Logistic Model and Real Populations• The growth of laboratory populations of paramecia

– fits an S-shaped curve

Page 38: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Some populations overshoot K

– before settling down to a relatively stable density

Figure 52.13b

180

150

0

120

90

60

30

Time (days)

0 16014012080 100604020

Nu

mb

er

of

Da

ph

nia

/50

m

l

(b) A Daphnia population in the lab. The growth of a population of Daphnia in a small laboratory culture (black dots) does not correspond well to the logistic model (red curve). This population overshoots the carrying capacity of its artificial environment and then settles down to an approximately stable population size.

Page 39: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Some populations

– fluctuate greatly around K

Figure 52.13c

0

80

60

40

20

1975 1980 1985 1990 1995 2000

Time (years)

Nu

mb

er

of

fem

ale

s

(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.

Page 40: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

The Logistic Model and Life Histories

• Life history traits favoured 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

Page 41: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Concept 52.5: Populations are regulated by a complex interaction of biotic and abiotic influences

• There are two general questions we can ask

– about regulation of population growth

• What environmental factors stop a population from growing?

• Why do some populations show radical fluctuations in size over time, while others remain stable?

Page 42: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Population Change and Population Density• 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

Page 43: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Determining equilibrium for population density

Figure 52.14a–c

Density-dependent birth rate

Density-dependent death rate

Equilibrium density

Density-dependent birth rate Density-

independent death rate

Equilibrium density

Density-independent birth rate

Density-dependent death rate

Equilibrium density

Population density Population density Population density

Birt

h or

dea

th r

ate

per

capi

ta

(a) Both birth rate and death rate change with population density.

(b) Birth rate changes with populationdensity while death rate is constant.

(c) Death rate changes with populationdensity while birth rate is constant.

Page 44: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Density-Dependent Population Regulation• Density-dependent birth and death rates

– are an example of negative feedback that regulates population growth

– are affected by many different mechanisms

Page 45: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Competition for Resources

• In crowded populations, increasing population density

– intensifies intraspecific competition for resources

Figure 52.15a,b

100 100

100

0

1,000

10,000

Ave

rag

e n

um

be

r o

f se

ed

s p

er

rep

rod

uci

ng

ind

ivid

ua

l (lo

g s

cale

)

Ave

rag

e c

lutc

h s

ize

Seeds planted per m2 Density of females

0 7010 20 30 40 50 60 802.8

3.0

3.2

3.4

3.6

3.8

4.0

(a) Plantain. The number of seeds produced by plantain (Plantago major) decreases as density increases.

(b) Song sparrow. Clutch size in the song sparrow on Mandarte Island, British Columbia, decreases as density increases and food is in short supply.

Page 46: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Territoriality

• In many vertebrates and some invertebrates

– territoriality may limit density

• Cheetahs are highly territorial

– using chemical communication to warn other cheetahs of their boundaries

Figure 52.16

Page 47: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Oceanic birds

– exhibit territoriality in nesting behaviour

Figure 52.17

Page 48: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Health

• Population density

– can influence the health and survival of organisms

• In dense populations

– pathogens can spread more rapidly

Page 49: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Predation

• As a prey population builds up

– predators may feed preferentially on that species

Page 50: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Toxic Wastes

• The accumulation of toxic wastes

– can contribute to density-dependent regulation of population size

Page 51: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Intrinsic Factors

• For some populations

– intrinsic (physiological) factors appear to regulate population size

Page 52: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Population Dynamics

• The study of population dynamics

– focuses on the complex interactions between biotic and abiotic factors that cause variation in population size

Page 53: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Stability and Fluctuation• Long-term population studies

– have challenged the hypothesis that populations of large mammals are relatively stable over time

Figure 52.18

The pattern of population dynamics observedin this isolated population indicates that various biotic and abiotic factors can result in dramatic fluctuations over time in a moose population.

Researchers regularly surveyed the population of moose on Isle Royale, Michigan, from 1960 to 2003. During that time, the lake never froze over, and so the moose population was isolated from the effects of immigration and emigration.

FIELD STUDY

Over 43 years, this population experiencedtwo significant increases and collapses, as well as several less severe fluctuations in size.

RESULTS

CONCLUSION

1960 1970 1980 1990 2000Year

Moo

se p

opul

atio

n si

ze

0

500

1,000

1,500

2,000

2,500

Steady decline probably caused largely by wolf predation

Dramatic collapse caused by severe winter weather and food shortage, leading to starvation of more than 75% of the population

Page 54: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Extreme fluctuations in population size

– are typically more common in invertebrates than in large mammals

Figure 52.19

1950 1960 1970 1980Year

1990

10,000

100,000

730,000

Com

mer

cial

cat

ch (

kg)

of

mal

e cr

abs

(log

sca

le)

Page 55: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Metapopulations and Immigration

• Metapopulations

– are groups of populations linked by immigration and emigration

Page 56: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• High levels of immigration combined with higher survival

– can result in greater stability in populations

Figure 52.20

Mandarte island

Small islands

Nu

mb

er

of

bre

ed

ing

fe

ma

les

1988 1989 1990 1991Year

0

10

20

30

40

50

60

Page 57: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Population Cycles

• Many populations

– undergo regular boom-and-bust cycles

Figure 52.21 Year1850 1875 1900 1925

0

40

80

120

160

0

3

6

9

Lynx

pop

ulat

ion

siz

e (t

hous

and

s)

Har

e po

pula

tion

size

(t

hous

and

s)

Lynx

Snowshoe hare

Page 58: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Concept 52.6: Human population growth has slowed after centuries of exponential increase

• No population can grow indefinitely

– and humans are no exception

Page 59: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

The Global Human Population

• The human population

– increased relatively slowly until about 1650 and then began to grow exponentially

Figure 52.22

8000 B.C.

4000 B.C.

3000 B.C.

2000 B.C.

1000 B.C.

1000 A.D.

0

The Plague Hum

an

pop

ulat

ion

(bill

ions

)

2000 A.D.

0

1

2

3

4

5

6

Page 60: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Though the global population is still growing

– the rate of growth began to slow approximately 40 years ago

Figure 52.231950 1975 2000 2025 2050

Year

2003

Per

cent

incr

ease

2.2

2

1.6

1.4

1.2

1

0.8

0.6

0.4

0.2

0

1.8

Page 61: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Regional Patterns of Population Change• To maintain population stability

– a regional human population can exist in one of two configurations

• Zero population growth = High birth rates – High death rates

• Zero population growth = Low birth rates – Low death rates

Page 62: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• The demographic transition

– is the move from the first toward the second state

Figure 52.24

50

40

20

0

30

10

1750 1800 1850 1900 1950 2000 2050

Birth rateDeath rate

Birth rateDeath rate

Year

Sweden Mexico

Birt

h or

dea

th r

ate

per

1,00

0 pe

ople

Page 63: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• The demographic transition

– is associated with various factors in developed and developing countries

Page 64: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Age Structure

• One important demographic factor in present and future growth trends

– is a country’s age structure, the relative number of individuals at each age

Page 65: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Age structure

– is commonly represented in pyramids

Figure 52.25

Rapid growth Afghanistan

Slow growth United States

Decrease Italy

Male Female Male Female Male FemaleAge Age

8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8 8 6 4 2 0 2 4 6 8Percent of population Percent of population Percent of population

80–8485

75–7970–7465–6960–6455–5950–5445–4940–4435–3930–34

20–2425–29

10–145–90–4

15–19

80–8485

75–7970–7465–6960–6455–5950–5445–4940–4435–3930–34

20–2425–29

10–145–90–4

15–19

Page 66: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Age structure diagrams

– can predict a population’s growth trends

– can illuminate social conditions and help us plan for the future

Page 67: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Infant Mortality and Life Expectancy

• Infant mortality and life expectancy at birth

– vary widely among developed and developing countries but do not capture the wide range of the human condition

Figure 52.26

Developed countries

Developing countries

Developed countries

Developing countries

Infa

nt

mo

rta

lity

(de

ath

s p

er

1,0

00

birt

hs)

Life

exp

ect

an

cy (

yea

rs)

60

50

40

30

20

10

0

80

60

40

20

0

Page 68: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Global Carrying Capacity

• Just how many humans can the biosphere support?

Page 69: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

Ecological Footprint

• The ecological footprint concept

– summarizes the aggregate land and water area needed to sustain the people of a nation

– is one measure of how close we are to the carrying capacity of Earth

Page 70: Chapter 52 Population Ecology. Earth’s Fluctuating Populations To understand human population growth – we must consider the general principles of population

• Ecological footprints for 13 countries

– show that the countries vary greatly in their footprint size and their available ecological capacity

Figure 52.27

16

14

12

10

8

6

4

2

00 2 4 6 8 10 12 14 16

New Zealand

AustraliaCanada

Sweden

WorldChina

India

Available ecological capacity (ha per person)

SpainUK

Japan

GermanyNetherlands

Norway

USA

Eco

log

ica

l foo

tprin

t (h

a pe

r pe

rson

)