II. Population Growth

A. Exponential Growth Model, B. Logistic Growth Model

Exponential Growth Model

• Exponential population growth= population increase under idealized conditions 

• Rate of increase at maximum= r_max > 0 and is constant

The equation of exponential population growth is

• dN/ dt = r_maxN 

• When graphed produce J shaped exponential curve

Limits of Exponential Growth

• Why don't populations grow exponentially?

  • Cant continue exponentially because of  Environmental resistance -> limits set by environment

  • Run out of food resources, living space, and would build up toxic wastes 

Logistic Growth Model

Takes into account environmental resistance

Carrying capacity (K)

When graphs looks like s shaped curve (sigmoid) which flattens at K

Carrying capacity -> more realistic

First part of equation same as exponential then add K,

dN/ dt = rinst N ( (K-N)/ K)

(K-N)/ K, reflects decline in growth as pop reaches K

If N is not close to K -> (K-N)/K =1 -> high growth rate

If N close to K -> (K-N)/K approached 0 and low growth rate

When N-K -> (K-N)

Limitations to logistic model

• Curves in nature usually not perfectly logistic (more wobble at K)

  • Occurs because populations fluctuate around K 

  • environment changes 

  • K may change