#### Transcript POPULATION GROWTH

```POPULATION
GROWTH
What is a population?
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A group of organism of the same species
living in the same habitat
at the same time
where they can freely interbreed
How can populations change?
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Natality
Mortality
Immigration
Emigration
Natality
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Increases population size
Each species will have its own maximum birth
rate
Maximum birth rates are seen when conditions
are ideal
This can lead to exponential growth
Mortality
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Mortality reduces population growth
It operates more when conditions are not ideal
infectious disease
Immigration
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It increase population growth
It operates when populations are not completely
isolated
Emigration
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It decrease population growth
It operates when populations are not completely
isolated
Interactions
Population growth =
(Natality + Immigration) - (Mortality + Emigration)
Population growth
K
3
2
Numbers
1
Time
Phases of population growth
Phase 1: Log or exponential phase
 Unlimited population growth
 The intrinsic rate of increase (r)
 Abundant food, no disease, no predators etc
Phase 2: Decline or transitional phase
 Limiting factors slowing population growth
Phase 3
Plateau or stationary phase
 No growth
 The limiting factors balance the population’s
capacity to increase
 The population reaches the Carrying Capacity
(K) of the environment
 Added limiting factors will lower K
 Removing a limiting factor will raise K
Factors affecting the carrying
capacity
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Food supply
Infectious disease/parasites
Competition
Predation
Nesting sites
dN
dt
Modelling population growth, the
maths
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Population growth follows the numbers of individuals in a
population through time.
The models try to trace what will happen little by little as time
passes by
A small change in time is given by ∆t
This is usually reduced to dt
Time may be measured in regular units such as years or even
days or it may be measured in units such as generations
A small change in numbers is given by ∆N
This is usually reduced to dN
A change in numbers as time passes by is given by: dN/dt
Exponential growth
Numbers
Time
Exponential growth
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The J-shaped curve
This is an example of positive feedback
1 pair of elephants could produce 19 million
elephants in 700 years
Modelling the curve
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dN/dt= rN
r is the intrinsic rate of increase
Example if a population increases by 4% per year
dN/dt= 0.04N
Real examples of exponential
growth
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Pest species show exponential growth
humans provide them with a perfect environment
Alien species
When a new species is introduced accidentally or
deliberately into a new environment
It has no natural predators or diseases to keep it
under control
European starling (Sturnus vulgaris)
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Between 1890 and 1891, 160 of
these birds were released in Central
Park New York.
California.
An estimate population of between
140 and 200 million starlings now
exist in North America
One of the commonest species of
bird on Earth
Image Credit: http://www.columbia.edu/
European starling (Sturnus vulgaris)
Current distribution
CJKrebs (1978) Ecology
decemlineata)
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A potato pest from North America
decemlineata)
Begon, Townsend & Harper (1990) Ecology
r-strategists boom and bust!
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Maximum reproductive potential when the
opportunity arrives
Periodic population explosions
Pests and pathogens (disease causing organisms)
are often r-species
The Carrying Capacity
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Darwin observed that a population never
continues to grow exponentially for ever
There is a resistance from the environment
The food supply nesting sites decrease
Competition increases
Predators and pathogens increase
This resistance results from negative feedback
K
Numbers
Time
The Carrying Capacity
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This too can be modelled
It needs a component in it that will slow down the
population growth as it reaches a certain point, the
carrying capacity of the environment (K)
The equation is called the logistic equation
dN/dt = rN[(K-N)/N]
When N<K then dN/dt will be positive
the population will increase in size
When N=K then dN/dt will be zero
the population growth will stop
Should N>K then dN/dt will become negative
the population will decrease
K-strategists long term investment
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These species are good competitors
They are adapted to environments where all the
niches are filled
They have long life spans
Lower reproductive rates but …
High degree of parental care thus …
Low infant mortality
K-strategist flowering plants produce fewer seeds
with a large amount of food reserve
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