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

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Mortality

Mortality reduces population growth It operates more when conditions are not ideal Overcrowding leading to competition, spread of

infectious disease

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Immigration

It increase population growth It operates when populations are not completely

isolated

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Emigration

It decrease population growth It operates when populations are not completely

isolated

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Interactions

Population growth = (Natality + Immigration) - (Mortality + Emigration)

© 2010 Paul Billiet ODWS

Population growth

K

Numbers

Time

1

23

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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

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Modelling population growth, the math 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

dtdN

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Exponential growth

Time

Numbers

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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 growthhumans provide them with a perfect environment

Alien speciesWhen 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

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

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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

Time

Numbers

© 2010 Paul Billiet ODWS

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

Patterns of Dispersion

Environmental and social factors Influence the spacing of individuals in a population

Patterns of Dispersion: Clumped

Clumped dispersion Individuals aggregate in patches Grouping may be result of the fact that multiple

individuals can cooperate effectively (e.g. wolf pack to attack prey or antelope to avoid predators) or because of resource dispersion (e.g. mushrooms clumped on a rotting log)

Patterns of Dispersion: Uniform

Uniform dispersion

Individuals are evenly distributed

Usually influenced by social interactions such as territoriality

Patterns of Dispersion: Random

Random dispersion: position of each individual is independent of other individuals (e.g. plants established by windblown seeds).

Uncommon pattern.