Lecture 6 Population

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Sivaselvi K

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Position In SyllabusGlobal Environmental Crisis, Biogeochemical Cycles, Climate

Change, Ozone Hole, Overpopulation, Energy Crisis, Water CrisisPeriodical 1

Ecology, Biodiversity Loss, Deforestation and Land Degradation, Food Crisis, Pollution (Water, Air, Land, Thermal, Noise), Sewage

Domestic and Industrial and Effluent treatmentPeriodical 2

Solid waste (municipal, medical, e-waste, nuclear), Environmental Management, Conventions, Regulations and Impact Assessment,

Sustainable Development.Final Exam

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Outline

• Introduction• Population Facts• Population Growth• Population Forecasting• Population Pyramids• Effect of Population on

Environment

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Introduction

• A population is all the organisms that both belong to the same species & live in the same geographical area

• Demography is a social science which entails the statistical study of human populations

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Population Facts• Annual growth:

– Peak 87 mi/yr in 1987– 75 mi/yr in 2002 – 77 mi/yr in 2007

• High growth in the Middle East, South Asia, Southeast Asia, Latin America& Sub-Saharan Africa

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Current Level of Overpopulation• To avert disaster, population must be reduced:

– US by at least one-third, – World: by two-thirds

• The Planet-documentary: We already consume five times more than that the planet can supply

• In 2006, WWF's "Living Planet" report: Current world population living with European luxury would need 3 Earths

Sources: http://en.wikipedia.org/wiki/Overpopulation#Effects_of_overpopulation. David Pimentel, Cornell University, and Mario Giampietro.

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Population Explosion

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World Population 20-21st Centuries

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Population Growth Distribution

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Definitions• Birth Rate: # of live births per 1000 pop: in

a given year• Growth Rate: % of persons naturally

added/subtracted from a population in a yr (not migration)

• Doubling Time: Yrs. for population to double at current growth rate

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Why is growth high in underdeveloped countries?

• Low women literacy• Less knowledge, availability & social acceptance

of family planning• Children looked upon as more hands to work & a

pension plan (instead of an additional expense & impediment to womens’ careers in urban areas)

• Child marriage• High mortality rate prompts high birth rates• Stable families based on traditional values for

more children. Increased instability in urban areas due to divorce and separation limits the number of children

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Causes of Sudden Increase in Population in 18th Century

• Reduced mortality rates due to:– Better nutrition– Improved medicine– Improved sanitation– Improved living standards

• Birth rates are also falling but more slowly• Developing world has a lot of young

population in the reproductive age group

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Population forecasting

• Arithmetic increase method• Geometric Increase Method• Incremental Increase method• Logistic Curve Method

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Arithmetic Increase Method• Assume, population increases linearly:

dP/dt = kPn = P0 + nxˉ

Pn = Population after n years/periodsP0 = Starting populationn = # of years or periodsxˉ = average of population increase

= [(P1-P0) + (P2-P1) +…]/n

* A period may be a decade, or century for instance

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Geometric Increase Method• Percentage of Population increase is

constantPn = P0 (1+ r/100)n

Pn = Population after n years/periodsP0 = Starting populationn = # of years or periodsr = % growth rate

• r1 = 100(P1-P0)/P0; r2 = 100(P2-P3)/P2, …• r = (r1*r2*r3*…rn)1/n

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Incremental Increase Method

Pn = P0 + nxˉ + n(n+1)/2 yˉ

Pn = Population after n years/periodsP0 = Starting populationn = # of years or periodsxˉ = average of population increase

= [(P2-P1) + (P3-P2) +…]/(n)yˉ = Average of incremental increase

= {[(P2-P1) - (P1-P0)] + [(P3-P2) - (P2-P1)]… }/(n-1)

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Verhulst’s Logistic Curve Method

y’ = (ay) – (by2 ) or dN/dt = rN (1-N/k)

• y = N = population; y’ = dN/dt• a = r rate of growth• b = r/k• k = carrying capacity: Maximum population

that can be supported by the environment…achieved at t = ∞

Exponentional Term: causes steep increase

Breaking/ Limiting Term: Causes leveling off.

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Logistic Sigmoidal Curve

Years (t)

Popu

latio

n (N

)

Carrying Capacity (k)

Death Phase

t*

k/2

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FormulaeN = ert k /(c1 + ert)

– c1 = e rt*– t* = time taken for reaching half the carrying

capacity…N = k/2.

N = k/[1+ e–r(t-t*)]t = t* - (1/r) ln[(k/N) -1]t* = (1/r) {ln[(k/N0) – 1]}

r = r0/(1-N0/k)

– r0 = growth rate at start– N0 = Starting population

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Population Pyramids

Age-Sex Pyramid or Age Structure Diagram

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Expanding—Youth Bulge

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Stationary—slight bulge & slimming

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Contracting—after massive bulge

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Effects of Population on Environment

• Tremendous strain on the environment• Intensifying factor for all environmental

problems• Inertial factor for all remedies• Deplete all natural resources

– Non-renewable resources depleted rapidly– Renewable resources depleted beyond

replenishment capacity• Risks catastrophic collapse

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Socioeconomic Effects of Overpopulation• Famine, Starvation, Malnutrition• Poverty, low standards of living• Low life expectancy• Exploitation, degradation of moral and

ethical standards• Increased crime• Epidemics• Conflict and war

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Problem

Yr Population

1930 25000

1940 28000

1950 34000

1960 42000

1970 47000

From the given data, forecast the population in 2000.

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Preliminary Calculations

Yr Population

Increase/ decade % increase Incremental Increase

1930 25000 28000-25000 =3000

100* (3000/25000) = 12

6000-3000 =3000

1940 28000 34000-28000 =6000

100* (6000/28000) = 21.4

8000-6000 =2000

1950 34000 42000-34000 =8000

100* (8000/34000) = 23.5

5000-8000 =-3000

1960 42000 47000-42000 =5000

100* (5000/42000) = 11.9

1970 47000

First make the calculations in the 3 unshaded columns

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Intermediate ResultsUse a decade as the time period. n = 4...(1930 to 1970)• Average Increase/decade (x—):

x— = [(P1-P0) + (P2-P1) +…]/n= (3000+6000+8000+5000)/4 = 5500

• Growth rate (r):r = (r1*r2*r3*…rn)1/n = (12*21.4*23.5*11.9)1/4 = 16.37%Note it’s the nth root of the product of the individual percentages.

• Avg. of Incremental Increase (y—):y— = (3000+2000-3000)/3 = 667

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Forecasting from 1970-2000Always forecast populations from the last given data.

So, forecast from 1970 onwards. Never forecast from 1930. Thus, n = 3…………….(1970 to 2000)

Arithmetic Method: Pn = P0 + nxˉ; P2000 = 47000 + 3*5500 = 63500

Geometric: Pn = P0 (1+ r/100)n; ;

P2000 = 47000 (1+ 16.37/100)3 = 74066

Incremental Method: Pn = P0 + nxˉ + yˉ *n(n+1)/2; ; P2000 = 47000 + 667*3*5500 + 3(3+1)/2 = 67502

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Problem: Logistic Growth Population stabilizes at 15 billion. In 1986,

population was 5 billion; Growth rate was 1.7%. When would N be 7.5 billion and 14 billion respectively?

• k = 15 billion = carrying capacity = max .population that can be supported

• N0 = 5 billion• r0 = 1.7% = 1.7/100 = 0.017• t* = ?• When N = 14 billion, t = ?

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Problem contd…

r = r0/(1-N0/k)= (1.7/100)/(1-5/15) = 0.0255….as a fraction; not a percentage

t* = (1/r) {ln[(k/N0) – 1]}= (1/0.0255) {ln[(15/5) – 1]}= 27.18 = 28 yrs

t = t* - (1/r) ln[(k/N) -1]= 28- (1/0.0255) ln[(15/14) – 1]= 130 yrs

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Thank You