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POPULATION GROWTH

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**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

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**How can populations change?**

Natality Mortality Immigration Emigration © 2010 Paul Billiet ODWS

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**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

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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 © 2010 Paul Billiet ODWS

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**Immigration It increase population growth**

It operates when populations are not completely isolated © 2010 Paul Billiet ODWS

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**Emigration It decrease population growth**

It operates when populations are not completely isolated © 2010 Paul Billiet ODWS

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**(Natality + Immigration) - (Mortality + Emigration)**

Interactions Population growth = (Natality + Immigration) - (Mortality + Emigration) © 2010 Paul Billiet ODWS

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Population growth Numbers Time K 3 2 1 © 2010 Paul Billiet ODWS

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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

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**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

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**Factors affecting the carrying capacity**

Food supply Infectious disease/parasites Competition Predation Nesting sites © 2010 Paul Billiet ODWS

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**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

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Exponential growth Numbers Time © 2010 Paul Billiet ODWS

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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

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**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

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**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

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© 2010 Paul Billiet ODWS

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**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 Image Credit: © 2010 Paul Billiet ODWS

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**European starling (Sturnus vulgaris)**

CJKrebs (1978) Ecology Current distribution

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**The Colorado Beetle (Leptinotarsa decemlineata)**

A potato pest from North America It spread quickly through Europe © P Billiet © 2010 Paul Billiet ODWS

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**The Colorado Beetle (Leptinotarsa decemlineata)**

Begon, Townsend & Harper (1990) Ecology

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**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

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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

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K Numbers Time © 2010 Paul Billiet ODWS

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**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

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**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

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