08 pop dynamics

What are the different ways populations grow? : 

What are the different ways populations grow? Exponential growth J shaped curve Logistic growth S shaped curve Carrying capacity

Slide 2: 

Exponential Growth “J” shaped curve increase in population size varies with number of individuals present number and amount added each generation increases by ever increasing amounts Natural populations only grow exponentially for short periods of time with abundant resources

Slide 3: 

Exponential Growth Examples Houseflies 1 fly to 5,598,720,000,000 flies (5.6 trillion) in just 1 year

Colonizing population of Scotch Pine : 

Colonizing population of Scotch Pine

Slide 5: 

Exponential Growth Equation Rate of population growth ~ change in number with change in time dN/dt = rN where: N = the population size t = time r = intrinsic rate of growth As population increases, the rate of population increase (dN/dt) also gets larger because r is multiplied by a larger and larger population size (N) So the rate of population growth accelerates

Slide 6: 

Using the equation: Solving the previous equation for N gives us: Nt = N0ert For a population with 2 individuals and per capita rate of increase of 1, what is population size after 32 years? N0 = 2 r = 1 t = 32 e = base of the natural log (ln) or 2.71828….. Nt = 2 x (2.718)32 = 1.6 x 1014 = 16 trillion!!

Slide 7: 

Exponential growth must slow down Collared dove expansion into western Europe begins by growing exponentially, but then slows down This slowing of growth is due to ….?

Slide 8: 

Logistic Growth “S” shaped curve exponential growth at beginning As resources are depleted, population growth rate slows and eventually stops levels off at carrying capacity Size is constant so births = deaths

Slide 9: 

Levels off due to low sugar and high alcohol

Slide 10: 

Levels off due to space limitations

Slide 11: 

Logistic Growth Model N is population size at some time t r is the intrinsic rate of increase under ideal conditions K is carrying capacity

Slide 12: 

Carrying Capacity (K) When N is small, what happens? N/K  0 ; dN/dt = rN As N approaches K, what happens? N/K  1 ; dN/dt  0 

Logistic harvesting model : 

Logistic harvesting model In logistic model, maximum growth occurs at K/2 Idea is to keep population at K/2