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Title: Understanding Population Trends

Introduction

A population is all the organisms that both belong to the same species and live in the

same geographical area. The area that is used to define the population is such

that inter-breeding is possible between any pair within the area and more probable than

cross-breeding with individuals from other areas. Normally breeding is substantially

more common within the area than across the border.

Population growth is the change in population size (N) over time, and this is determined

by births, deaths, immigration and emigration, Population growth can be modelled by a

geometric curve (that is, a non-linear curve). This will be either an S-shaped (sigmoidal)

curve or an exponential curve. If the population size doubles between each time interval

then this form of geometric growth is called exponential growth. Studies of both short-

lived and long-lived organisms have indicated that population growth, and therefore the

form and shape of population growth curves, is ultimately controlled by three factors:

1. the initial population size (N0)

2. a population growth factor (R) which measures the rate at which a population

would grow if it had unlimited resources

3. the carrying capacity (K), which is determined by environmental factors.

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TASK 1: Population of Rhinoceros

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Time interval

(t) =

Rhinoceros Population A Rhinoceros Population B

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generation

Pop size (N) Growth factor

(R)

Pop size (N) Growth factor

(R)

0 N0 = 30 N0 = 20

1 58 1.9 39 2.0

2 123 2.1 82 2.1

3 236 1.9 161 2.0

4 484 2.1 318 2.0

5 955 2.0 643 2.0

Geometric

mean

=2.0 =2.0

Table 1: Population growth oh rhinoceros

Question:

1. What type of population growth does Rhinoceros have, and why are the final

population sizes different?

The population growth of rhinoceros is exponential. In the final population sizes

different maybe because of rhinos are so isolated that they may rarely or never

meet to breed. So, the differences quite big.

2. What type of growth do each of the rhinoceros populations show:

exponential or sigmoidal ?

The growth type of the rhinoceros populations show is exponential curve.

3. Check the three factors that influence population growth. Why is there a

difference in population size between these two populations at time interval

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5? Is it due to differences in initial population size, the growth factor, or the

environment?

there are three factors that influence population growth which are the initial

population size, the growth factor, and carrying capacity which influenced by the

environment.

According to the table 1 we noted that the growth factor for both Rhinoceros

populations are quite balance and they even have the same geometric mean that

is 2 and so it would not affect the population growth. Beside that, both of the

Rhinoceros populations are living in the same area and so the environment factor

should be the same and this also would not give much influenced to their growth.

Therefore, we can say the differences in population size between the two

Rhinoceros populations at time interval 5 are due to the first factors, its initial

population. Population A has more population size than population B and so at

time interval 5, Population A also has more population size than population B

where the geometric mean for both populations are constant.

TASK 2: Population of Koala

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Time interval

(t) =

Koala Population A Koala Population B

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generation

Pop size (N) Growth factor

(R)

Pop size (N) Growth factor

(R)

0 N0 = 20 N0 = 20

1 36 1.8 31 1.6

2 63 1.8 47 1.5

3 118 1.9 66 1.4

4 212 1.8 103 1.6

5 375 1.8 150 1.5

Geometric

mean

=1.8 =1.5

Table 2: Population growth of Koala

Question :

1. What type of population growth does the Koala have, and why are the final

population sizes different?

The population growth of koala is exponential. The final population sizes different

maybe because of the of food supply problem. It is because they eat only

Eucalyptus leaves (also known as gum leaves). So when the leaves decrease or

humans clearing of the eucalypt forests there is no food supply and koala not

have their food anymore.

2. What type of growth do each of the koala populations show: exponential or

sigmoidal?

The growth type of the koala populations’ show is exponential.

3. For the two koala populations, why is there a difference in population size

at time interval 5? Is it due to differences in initial population size, the

growth factor, or the environment?

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From the table 2 the initial population size for both Koala Population A and B are

the same which is 20, so it is not the main factor which will affect the population

growth in future. The environment factor also should be the same and this also

would not give much influenced to their population growth.

Therefore, we can say the differences in population size between the two Koala

populations at time interval 5 are due to the second factors, the growth factor.

Population A has higher growth factor than Population B where the geometric

means of them are 1.8 and 1.5 respectively. Hence Population A has higher

population growth

4. In Table 2, if the data for koala population A were for the same, but under

plentiful rainfall conditions, and the data for koala population B were for

drought conditions, why might the populations show a change in the

growth factor (R) ? Remember that the growth factor R = Births – Deaths.

The populations show a change in the growth factor because of changes in the

balance of the ecosystem can lead to dieback. A decline in koala populations has

also been observed in times of drought. The death rate for koala population B is

more higher because the starvation. They don’t have enough basic need or

source in drought condition. While the population A the birth rate is higher

because they have enough sources and have a good condition to stay alive.

TASK 3: Population of Zebra

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Time interval

(t) =

generation

Zebra Population A Zebra Population B

Pop size (N) Growth factor

(R)

Pop size (N) Growth factor

(R)

0 N0 = 20 N0 = 20

1 80 4.0 50 2.5

2 230 2.9 100 2.0

3 400 1.7 220 2.2

4 500 1.3 360 1.6

5 550 1.1 460 1.3

6 580 1.1 520 1.1

7 590 1.0 550 1.1

8 595 1.0 570 1.1

9 600 1.0 580 1.0

10 600 1.0 600 1.0

Geometric

mean

=1.4 =1.4

Table 3: Population growth of zebra

Question:

1. What type of population growth does Zebra have, and how does carrying

capacity affect the final population size?

The population growth of zebra is sigmoidal. The final population size is same.

2. What type of growth does each of the populations show: exponential or

sigmoidal?

The growth type of the zebra populations show is sigmodial.

3. Which population, A or B, has the highest growth factor?

Both populations have the same growth factor.

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4. Is the growth factor (R) constant? Describe any changes that occur in R.

No, the growth factor is not constant there has some changes. For the first until

fifth time interval the growth factor is increase and for six into 10 time interval the

growth factor is decrease and the value is constant.

5. What is the carrying capacity (K or the asymptote of the curve) for each

population?

The carrying capacity for zebra A is when the population size is 600 which is at

the ninth generation. While for the for zebra B the population size not reach the

carrying capacity at the ninth generation.

TASK 4: Population of Zebra

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Time interval

(t) =

generation

Population A Population B

Pop size (N) Growth factor

(R)

Pop size (N) Growth factor

(R)

0 N0 = 20 N0 = 20

1 90 4.5 50 2.5

2 220 2.4 120 2.4

3 340 1.5 210 1.8

4 410 1.2 260 1.2

5 440 1.1 260 1.0

6 450 1.0 230 0.9

7 450 1.0 200 0.9

8 440 1.0 170 0.9

9 460 1.0 150 0.9

10 450 1.0 150 1.0

Geometric

mean

=1.4 =1.2

Table 4: Population growth of zebra

Question:

1. What type of growth do each of the Zebra populations show: exponential or

sigmoidal?

The growth type of the Zebra populations show is sigmodial.

2. Which population, A or B, has the highest growth factor?

Population A, has the highest growth factor.

3. Is the growth factor (R) constant ? Describe any changes that occur in R.

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The growth factor (R) for population A and B are not constant. The changes of R

is decrease from first generation to last generation for population A while the

growth factor for population B also decrease from first generation to ninth

generation but increase when reach at last generation.

4. Has the carrying capacity (K or the asymptote of the curve) for population

A changed? If so, in what way?

No.

5. Both zebra populations had the same initial population size. Why has one

population out-competed the other? Check the three factors that control

population growth.

There are three factors that control population growth which are initial population

size, growth factor and environment. Initial population not influence or control

population growth because it has same initial population size.

The growth factor is the factor influence and control population growth of zebra

because maybe the birth rate of the population B is low than population A while

for the death rate for population B is higher than population A.

The environment factor is the factor influence and control population growth

because Zebra's are prey to lions and spotted hyenas. Zebra is threatened by

hunting and by habitat change from ranching and other kinds of farming. Zebra

is threatened by local livestock that compete with it for water and food. Maybe

the resistance of zebra B is more lower. So in the competition they are less resist

with environment and it is now so small that environmental hazards, such as

drought, can easily affect the species.

6. If the data in Table 3 are for the two populations living separately, and in

Table 4 for the same populations living together, what has been the effect

of competition on R for both zebra populations?

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The effect of competition on R for zebra population in Table 3 is same because

the growth factor for both population zebra in Table 3 is 1.4 while the effect of

competition on R for zebra population in Table 4 is different because the growth

factor for both population A and B is 1.4 and 1.2.

Discussion

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1. What is the difference between exponential and logistic (sigmoidal)

growth?

Exponential growth (including exponential decay) occurs when the growth rate of

a mathematical function is proportional to the function's current value. In the case

of a discrete domain of definition with equal intervals it is also called geometric

growth or geometric decay (the function values form a geometric progression).

With exponential growth of a positive value its rate of increase steadily increases,

or in the case of exponential decay, its rate of decrease steadily decreases.

Exponential growth model is one that exists when the rate of growth is

proportional to the existing amount. For this, a population needs ideal conditions:

bacteria in a patria dish, radioactive decay or compound interest in a saving

amount.

The logistics is a different kind of behavior which is more realistic to population

not in ideal conditions: the rate of growth is proportional to the amount but there

is also a damping factor due to competition and limited resources. This model

works that at first the rate of growth getting faster then it slows down since there

are too many individual competing on limited space. When this population

reaches its equilibrium state, the rate of growth is zero and if there will be no

interactions; the size of the population will stay constant.

2. How do populations gain and lose individuals?

If the birth rate and the immigration rate high, it will increases the population of

individuals while if the death rate and emigration rate increases, it will decreases

the population of individuals.

3. What are the characteristics of a population which has a high intrinsic rate

of increase?

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When there are unlimited physical environment factors, the decreasing of prey

population and the population is out-competed in competition for resource, the

population growth will increase. The Law of the Minimum states that population

growth is limited by any resource like food, shelter, water supply, space

availability, and (for plants) soil and light in the shortest supply. Population

growth decreases when the population is eliminated by other population when

competition for physical environment factor occurred. Besides that, the

increasing of prey population may decrease the population growth.

The population that have high intrinsic rate of increase for sure can breed easily

and can adapt well in a habitat. Besides that , when its breed the number of the

young or the birth rate must be higher so that the death rate will not influence or

affect the population size even the rate of death is high. Another characteristic is

the antibody of the species is tough so they will not easily get sick . If a species

do not have tougher antibody, it will easily get sick and will die.

Births equal to deaths, a stable population size usually means that the rate of

death of its members is equal to the rate of birth. For example, organisms with a

tendency to produce large numbers of offspring also have a tendency to lose an

equally large number of offspring whereas those which produce few offspring

likely engage in a reproductive strategy which results in a much higher likelihood

of survival for any given offspring.

4. What are the environmental factors which act to (1) increase population

growth and (2) decrease population growth?

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The environmental factor which acts to decrease population growth is habitat

destruction. Destruction of habitats leads directly to a reduction in the number of

individuals present in a given population.

Destruction of habitat also leads to high probability of extinction. Following

habitat destruction, resulting populations are left in small, isolated fragments. The

probability of extinction among these isolated populations is high due to their

inherently small size. The likelihood of repopulation from other fragments may be

reduced due to the habitat isolation, a second consequence of habitat

destruction. Habitat destruction also has a tendency to affect other, especially

downstream ecosystems. Excessive erosion from clear cut forests clogs the

steams in which salmon hatch and develop thus helping decimate salmon

populations. Habitat destruction tends to turn mature ecosystems into disturbed

ecosystems. Since some organisms are well adapted to growth in disturbed

ecosystems. Habitat destruction also tends to favour the growth of some

organisms while disfavouring the growth of many others (particularly, K

strategists).

Some environmental factors affecting population growth include, bacteria and

disease for example West Nile, natural disasters fort example Tsunamis and

unbalanced Predator Prey relationship For Ex. A Decline in the population foxes

will cause in increase in the hair population

5. What happens if the population size exceeds the carrying capacity?

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Natural Selection will take it course meaning some will die. If the population size

exceeds the carrying capacity the birth rate will drops then the death rate will

increases, then the population returns to the normal carrying capacity. The

process will be repeated continuously. If the population size increase more than

the carrying capacity, the graph will decrease means that the population size

decrease again since the habitat cannot supply enough basic needs source.

6. Why is a random change in K from year to year a problem for management

of commercially exploited wild populations?

If the random change in K from year to year it will influence the population of wild

populations. For instance, if carrying capacity fish is low so the population growth

of the fish will low or decrease. So the income for fisherman will decrease

because the size population growth of fish is small. While if the carrying capacity

fish high so the population growth of the fish high or increases. So the income for

fisherman will increases because the size population growth of fish wide.

7. What will you do if there is a good season and deer populations for the

next season are predicted to overshoot carrying by 20 %?

Actually, we should control the deer harvesting activity. When we control this

activity, the population growth of dear will increases and the growth of deer will

achieve the carrying capacity level.

Conclusion

The shape of population growth curves, is ultimately controlled by three factors:

the initial population size (N0)

a population growth factor (R) which measures the rate at which a population

would grow if it had unlimited resources

the carrying capacity (K), which is determined by environmental factors.

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REFERENCES

https://www.savethekoala.com/koalasendangered.html

http://www.greatlakes.local-e.nsw.gov.au/environment/9815/9817.html

http://cheddarbay.com/0000koala/koala.html

http://www.wwf.org.my/about_wwf/what_we_do/species_main/rhino/index.cfm

http://www.africaguide.com/wildlife/zebra.htm

http://en.wikipedia.org/wiki/Plains_Zebra

http://www.awf.org/content/wildlife/detail/zebra

http://www.encyclopedia.com/doc/1O8-Sshapedgrowthcurve.html

http://wiki.answers.com/Q/List_4_contributing_factors_that_affect_population