Download Populations Models

POPULATION
GROWTH
What is a population?




A group of organism of the same species
living in the same habitat
at the same time
where they can freely interbreed
© 2010 Paul Billiet ODWS
How can populations change?




Natality
Mortality
Immigration
Emigration
© 2010 Paul Billiet ODWS
Natality




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
© 2010 Paul Billiet ODWS
Mortality



Mortality reduces population growth
It operates more when conditions are not ideal
Overcrowding leading to competition, spread of
infectious disease
© 2010 Paul Billiet ODWS
Immigration


It increase population growth
It operates when populations are not completely
isolated
© 2010 Paul Billiet ODWS
Emigration


It decrease population growth
It operates when populations are not completely
isolated
© 2010 Paul Billiet ODWS
Interactions
Population growth =
(Natality + Immigration) - (Mortality + Emigration)
© 2010 Paul Billiet ODWS
Population growth
K
3
2
Numbers
1
© 2010 Paul Billiet ODWS
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
© 2010 Paul Billiet ODWS
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
© 2010 Paul Billiet ODWS
Factors affecting the carrying
capacity





Food supply
Infectious disease/parasites
Competition
Predation
Nesting sites
© 2010 Paul Billiet ODWS
dN
dt
Modelling population growth, the
maths





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
© 2010 Paul Billiet ODWS
Exponential growth
Numbers
Time
© 2010 Paul Billiet ODWS
Exponential growth



The J-shaped curve
This is an example of positive feedback
1 pair of elephants could produce 19 million
elephants in 700 years
© 2010 Paul Billiet ODWS
Modelling the curve




dN/dt= rN
r is the intrinsic rate of increase
Example if a population increases by 4% per year
dN/dt= 0.04N
© 2010 Paul Billiet ODWS
Real examples of exponential
growth


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
© 2010 Paul Billiet ODWS
© 2010 Paul Billiet ODWS
European starling (Sturnus vulgaris)




Between 1890 and 1891, 160 of
these birds were released in Central
Park New York.
By 1942 they had spread as far as
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
© 2010 Paul Billiet ODWS
Image Credit: http://www.columbia.edu/
European starling (Sturnus vulgaris)
Current distribution
CJKrebs (1978) Ecology
The Colorado Beetle (Leptinotarsa
decemlineata)


A potato pest from North America
It spread quickly through Europe
© 2010 Paul Billiet ODWS
© P Billiet
The Colorado Beetle (Leptinotarsa
decemlineata)
Begon, Townsend & Harper (1990) Ecology
r-strategists boom and bust!



Maximum reproductive potential when the
opportunity arrives
Periodic population explosions
Pests and pathogens (disease causing organisms)
are often r-species
© 2010 Paul Billiet ODWS
The Carrying Capacity






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
© 2010 Paul Billiet ODWS
K
Numbers
© 2010 Paul Billiet ODWS
Time
The Carrying Capacity







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
© 2010 Paul Billiet ODWS
K-strategists long term investment







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
© 2010 Paul Billiet ODWS