Chapter 9 Population Growth

Martens

Population Growth

• Given suitable conditions, aquatic terrestrial populations have a great capacity for growth

• Planktonic populations of diatoms increase each spring, zooplankton increase due to extra food

Geometric & Exponential Population Growth

• Presence of abundant resources (Geometric and exponential rates)

• Population growing as its maximum rate grows slowly at first

• Cannot continue indefinetly

Geometric Growth

• When generations do not overlap, growth can be modeled geometrically

• Nt = N0 A^t

• Nt = number of individuals at time t

• N0 = initial number of individuals

• A = geometric rate of increase (average number of offspring left by an individual during one time interval)

• t = number of time intervals or generations

Example :

N0 is 996 individuals

A = 2.4177

If t = 3 N3 = 996 × 2.4177³ = 14,076

Exponential Growth

• Continuous population growth in an unlimited environment can be modeled exponentially

• Populations with overlapping generations

• As pop. size (N) increases, the rate of population increase gets larger

• Nt = N0 e^rt

• Nt = number of individuals at time t

• N0 = base of natural logs

• r = per capita rate of increase

• t = number of time intervals

• NOT NEEDED TO DO IN TEST

Exponential Growth in Nature

• Assumption of constant rate of per capita increase may seem unrealistic

• Exponential growth for only short periods of time, if abudant resources are present

• Growth begins at low densities in favorable conditions

• Exponential growth may be important during:

Establishment in new environments

Temporary favorable conditions

Recovery from exploitation

Exponential Growth (Scots pine)

• Population grew exponentially for nearly 500 years

• Pollen accumulation rate in lake sediments can be used as an index of population size

North American Whooping Cranes

• Whooping cranes were reduced to 22 individuals in 1940 due to hunting and habitat destruction

• Population grew exponentially to 220 individuals by 2005

• Exponentially grew from 22 to 220 due to the legislation placed

Slowing of Exponential Growth

• Eurasian collared doves expanded into western Europe in the 20th century

• Population grew exponentially for a decade or more

• Rate of population growth behan to slow, suggests the pop. was approaching environmental limits

Environmental limitation is incorporated into the model of logistic pop growth