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ZOOLOGY Principles of Ecology

Population Growth Part 1

Paper : 12 Principles of Ecology

Module : 09 (a) Population Growth Part 1

Development Team

Paper Coordinator: Prof. D.K. Singh

Department of Zoology, University of Delhi

Principal Investigator: Prof. Neeta Sehgal


Content Writer: Dr. Laxmi Narula

SGTB Khalsa College, University of Delhi

Content Reviewer: Prof. K.S. Rao Department of Botany, University of Delhi

Co-Principal Investigator: Prof. D.K. Singh


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Description of Module

Subject Name ZOOLOGY

Paper Name Principles of Ecology: Zool 012

Module Name/Title Population Growth

Module ID M9 a; Population Growth Part 1

Keywords

Exponential and Geometric population growth, net reproductive rate,

Biotic potential, semelparous and iteroparous reproductive strategies,

„r‟ and K selected species

Contents

1. Learning Outcomes

2. Introduction

3. Exponential Population Growth

3.1. Semelparous and Iteroparous Reproductive Strategies

3.2. Exponential Growth in Semelparous Species

3.3 Examples of exponential growth

4. „r‟ and „k‟ reproductive strategies in Populations

5. Summary

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1. Learning Outcomes

After studying this module, you shall be able to know about

• Need for population growth

• Patterns of population growth

• Factors that determine exponential and sigmoid type of population growth.

• Semelparous and iteroparous population reproductive strategies

• Exponential Reproduction in semelparous Species

2. Introduction

To grow with time is an inherent property of all forms of life. Study of population growth is at the

core of applied ecology. It informs about the abundance or rarity of population with time, which in

turn determines the structure of community in an ecosystem. Depending on the size of organisms and

their reproductive potentials a population may grow in size from every minute, hour, days (bacteria

and viruses and protozoans), months or seasons (insects, fish and birds) or once in several years

(elephants and flowering plants like bamboo). Bamboo lives for 100 to 120 years before the produce

seeds and die.

Figure 1: Reproductive potential of organisms

Source: Author and ILLL in house

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The maximum reproductive potential under unlimited environmental resources/ conditions is known

as biotic potential (Chapman1928). Maximum reproductive rate denoted as rmax is observed only

under unlimited environmental conditions to which there is always an environmental resistance. An

unlimited growth of a population as calculated from its reproductive potential/ biotic potential is never

observed in nature. For example the slowest breeding animal like elephant, a single pair would have

over 19 million decedents alive after 750 years. A single pair of house flies with life span of 14 to 30

days, each female can lay 9000 eggs in its life span in batches of 500. Thus in seven generations a

single pair would produce six trillion houseflies per year. A single oyster can produce 55 to 114

million eggs. In nature no population reproduces as per its biotic potential as since all the resources

are not unlimited. As is clear from the above example if given an opportunity with the biotic potential

the whole land will be occupied only by a few species and the biodiversity will be lost. It can easily be

visualized from the following example of paramecium population colonized from a single cell within

six days.

Figure 2(a): Population growth of paramecium from a single cell in six days


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Figure 2(b): Human population growth

(Source: Author and ILLL in house)

Populations have a characteristic pattern of increase known as the growth forms. Two basic patterns

are described on the basis of the shape of the growth curve namely

„J’ shaped or exponential growth form

„S‟ or sigmoid shaped or logistic growth form

These two forms can be combined or modified or both in various ways depending on the

characteristics of a population and environmental conditions

Following are the two growth forms of the populations:

1. Exponential growth

2. Logistic growth

3. Exponential Population Growth

Exponential growth of a population was noted for the first time by Thomas Robert Malthus (1766-

1834) an economist. In 1798, he published his essay on “Principles of population” in which he

proposed that the populations tend to increase faster than the means of their subsistence. He

proposed that the populations increase in geometrical (2, 4, 8, 16, and so on) whereas, their food

increases arithmetical (2, 4, 6, 8, and so on) progression. Using an exponential form of population

growth, two fruit flies could produce enough offspring to fill the space between the Earth and the

Sun in only one year, if all of the offspring survived. Exponential growth is one of two growth rates

ecologists recognize in nature, but there are many other factors that keep the world from becoming

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overrun with any one population; may it be fruit flies or other organisms that show exponential

growth.

Figure 3: Malthusian growth

Source: http://montessorimuddle.org/wp-content/uploads/2011/06/malthus-base.png CC

3.1. Semelparous and Iteroparous Reproductive Strategies

The reproductive strategy of an organism can either be Semelparous or Iteroparous.

Semelparous: A Semelparous species reproduces only once before it dies. A delay in the breeding

season may exert a regulative effect on their population growth. If the adults breeding in one season

rarely or never survive to breed in the next has an important effect on their dynamics. In discrete

breeding species the population may breed only once at a specific time of the year.

The word semelparity comes from the Latin word semel ' once or single time' and word pario' to

beget' and was coined by evolutionary biologist Lamont Cole. As the single reproductive event of

semelparous organisms is usually large as well as fatal, it is considered by some as "big bang"

reproduction. Pacific salmon (Oncorhynchus spp.) is a classic example of a semelparous organism

which lives for many years in the ocean before swimming to the freshwater stream of its birth,

spawning, and dying. Other semelparous animals include some species of butterflies, cicadas, and

mayflies, many arachnids, and some molluscs such as some species of squid and octopus. In plant

kingdom an annual is a plant that completes its life cycle in a single season, and is usually

semelparous.

http://montessorimuddle.org/wp-content/uploads/2011/06/malthus-base.png

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Figure 4a: Pacific salmon is an example of a semelparous organism

Source: http://en.wikipedia.org/wiki/Semelparity_and_iteroparity#mediaviewer/

File: Oncorhynchus_nerka_2.jpg CC

Iteroparous can reproduce more than once in its lifetime. The term iteroparity comes from the Latin

itero, to repeat, and pario, to beget. Thus, there is two or more overlapping generation of organisms

living at any one time. In other words one generation of young individuals coexist with one older

generation in reproductively active state.

Human is example of an iteroparous organism as humans are biologically capable of having offspring

many times over the course of their lives. Iteroparous vertebrates include most fishes and reptiles, all

birds and all mammals. Among invertebrates, most mollusca and many insects (for example,

mosquitoes and cockroaches) are iteroparous. Most perennial plants are iteroparous.

Figure 4b: The pig is an example of an iteroparous organism

Source: http://en.wikipedia.org/wiki/Semelparity_and_iteroparity#mediaviewer/

File:Sow_with_piglet.jpgCC

http://en.wikipedia.org/wiki/Semelparity_and_iteroparity#mediaviewer/File:Oncorhynchus_nerka_2.jpg

http://en.wikipedia.org/wiki/Semelparity_and_iteroparity#mediaviewer/File:Oncorhynchus_nerka_2.jpg

http://en.wikipedia.org/wiki/Semelparity_and_iteroparity#mediaviewer/File:Sow_with_piglet.jpg

http://en.wikipedia.org/wiki/Semelparity_and_iteroparity#mediaviewer/File:Sow_with_piglet.jpg

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3.2 Exponential Population Growth in Semelparous Species

In Semelparous life history, birth rate and the density of the organisms plays an important role in

determining the growth pattern.

a) Multiplication rate remains constant („Ro‟ Net reproductive rate or birth rate remains constant)

b) Multiplication rate depends on population size (density Dependent)

A. Multiplication Rate remains Constant: Consider a species with a single annual breeding season

and a life span of one year. Let each female produce Ro female offspring on the average, that survive

to breed the following year, then population numbers N in generations t = 0, 1, 2, ... is equal to:

Nt+1 = RoNt.

Nt: Population size of females at age time t.

Nt+1: Population size at the time t+1

Ro: Net reproductive rate is the number of female offspring produced per female per generation

When t is large then this equation can be approximated by an exponential function

Table 1: Population growth of a hypothetical population with constant multiplication rate

Generation, t Population size, Nt= No x R Nt

0 10 10

1 1.5 x10=15 15

2 1.5 x15 22.5

3 1.5 x 22.5 33.75

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Figure 5: Hypothetical exponential population growth


A change in the Ro results in a change in the shape of the growth curve as it is clear from the fig 6. An

increase in the net reproductive rate increases the population more rapidly.

Figure 6: Examples of geometric population growth with discrete generations. Starting population is 10

and Ro 1.05, 1.10, 1.15 and 1.20. As the value of Ro increases the population size increases more rapidly

(Change in the slope of the curve) Source: Author and ILLL in house (Kreb)

B. Multiplication rate depends on population size (density): Populations normally do not grow with a

constant multiplication rate, if we look at the trajectory (Turn over) of a species population through

time, a variety of dynamics is observed in populations such as small fluctuations, chaotic fluctuations

or cyclical oscillations.

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The multiplication rate changes with the change in the population density. At high density birth rate

decreases or death rate increases due to several factors such as epidemics, predation or shortage of

resources. At low densities birth rate increases and death rate decreases due to less parasitic and

predatory attacks and sufficient of resource availability resulting in fluctuations, oscillations or

decline of the population.

This can be simply expressed in mathematical model showing a linear relationship between

Population density (N) on X -axis and net reproductive rate (R0) on Y- axis.

Figure 7: Net reproductive rate as a linear function of population density in this hypothetical data equilibrium

density is 100 Source: Author and ILLL in house

The point where line crosses Ro= 1 is a point of equilibrium in the population density. At this point,

birth rate equals the death rate.

How to measure population density from this curve?

It is measured in terms of deviation from the equilibrium point by the following formula:

z = N - N eq

Where

z= is the deviation from the equilibrium density

N= Observed population density

Neq= Equilibrium population size when R0 is= 1

R0= 1.0-B (N- Neq) (This shows Equation of a straight line)

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= 1 - Bz

(-) B = slope of the line

z = the deviation from the equilibrium density. (N- Neq)

R0 = is the net reproductive rate.

In the above figure, the slope of the line that is B is= 0.02 and Neq is = 100

Therefore, N (t+1) = R0Nt

= (1.0 - Bzt)Nt

The properties of this equation depend on equilibrium density and the slope of the line.

3.3 Examples of exponential growth

If B= 0.11; Neq=100; N0= 10

Nt +1= R0Nt and R0= (1- Bz)

Where z= (N - Neq)

N1 = [(1- 0.011 (10 -100)] x 10 (For N1 starting population is 10)

= [1.99] x10= 19.9

N2 = [1 - 0.011(19.9-100)] x 10

= [1.881] x 19.9= 37.4

Similarly N3= 63.1

N4= 88.7

N5 =99.7

Thus the population converges towards 100 Neq

If „L‟ denotes the value of BNeq is the populations will behave differently with the change in the value of B.

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Figure 8 (a): Convergent oscillations are seen if L is between 1 and 2


Figure 8 (b): Indefinite stable oscillations result if L is between 2 to 2.57


Figure 8 (c): When the value of L approaches more than 2.57 populations fluctuate in a chaotic manner

Source: Author and ILLL in house (krebs)

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It can be concluded that

a. An equilibrium state is observed if L is between 0 to1

b. Convergent oscillations are seen if L is between 1 and 2 (Fig 8a)

c. Indefinite stable oscillations result if L is between 2 to 2.57 (Fig 8b)

d. When the value of L approaches more than 2.57 populations fluctuate in a chaotic manner (Figure 8c)

4. „r‟ and „k‟ reproductive strategies in Population

„K‟ selected populations live under more predictable environment, they are subjected to density

related mortality, spend less energy on reproduction, favours efficient use of environment. Population

growth is sigmoid shaped based on Verhulst Pearl logistic equation

In „r‟ selected populations live under more harsh conditions and show exponential population growth.

After attaining their maximum size may show a decline or complete population crash because the

resources are completely exhausted.

Table 6: Differences between “r” and “K” selection species

Parameters “r” selection “K” selection

Climate conditions Variable and unpredictable; uncertain Fairly constant and predictable.

Mortality reasons Often Catastrophic More Directed

Survivorship curves Mostly Type III Usually Types I and II

Population size

1. Variable in Time,

2. Non-equilibrium well below carrying capacity of

environment;

3. Unsaturated communities or portions thereof

ecologic vacuums;

4. Fast recolonization

1. Fairly Constant in Time

2. Equilibrium, at or near carrying

capacity saturated communities

3. No recolonization

Intra- and Inter-

specific competition Variable, often negligent (lax) Usually intense (keen )

Selection favours

1. Rapid Development

2. High r max

3. Early reproduction

4. Small body size

5. Single reproduction (semelparous)

1. Slower Development

2. Greater competitive ability

3. Delayed reproduction

4. Larger body size

5. Repeated reproduction (Iteoparous)

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6. Many small offspring 6. Fewer larger progeny

Length of life Short, usually less than a year Longer, usually more than a year

Stage in succession Early Late, climax

5. Summary

To grow and sustain themselves in an ecosystem is an inherent property all populations.

The population growth is a result of addition of new individuals through natality and by

immigrations and their decline is by mortality and emigration.

The difference between these two parameters (natality and mortality) is given as instantaneous rate

(„r‟) of population increase.

Malthus proposed that the populations increase in geometrical (2, 4, 8, 16, and so on) whereas, their

food increases arithmetical (2, 4, 6, 8, and so on) progression

When the environmental conditions are unlimiting the populations expand geometrically or

exponentially. It is observed in small populations entering into a new vacant habitat.

Exponential growth also known as Malthusian growth is characterized by constant birth and death

rate (intrinsic rate of increase) and a stable age distribution maintained indefinitely.

A species is considered semelparous when it reproduces only a single time before it dies

Populations with Semelparous life history can have:

Constant multiplication rate or

Multiplication rate depends on population size (density Dependent )

Net reproductive rate as a linear function of population density At equilibrium density Nq , dN / dt

is 0 and R ( net reproductive rate) is 1

Iteroparous species can reproduce more than once in its lifetime. Thus there are two or more

overlapping generation of organisms living at any one time

In „r‟ selected populations that show exponential population growth after attaining their maximum

size may show a decline or complete population crash because the resources are completely

exhausted.

„L‟ is multiple of equilibrium density and slope of the curve. The value of „L‟ determines the

behavior of the population whether it converges towards equilibrium or show oscillations or

fluctuations.

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„r‟ selected species are mostly Semelparous populations, show exponential growth , most of them

have small life span(except some plants and fish), have high turnover rate and produce large number

of eggs/ young ones.

„K‟ selected species are mostly iteroparous and can have exponential or sigmoid growth pattern.

They have a long life span and produce less number of progeny.

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