1. Changes in Population Sizes
SBI4U
Miss Richardson

2. Measuring Population Change
Populations can be open (have migration) or closed (have no migration, ie: island)
Populations are affected by births, deaths, immigration and emigration
Change =  [(births + immigration)] – (death + emigration)]    x 100% per capita                           Initial population size (n)

3. Population Growth Models
Population growth depends on the interaction between the population and the environment.
There are three common models:
Geometric Growth
Exponential Growth
Logistic Growth

4. Geometric Growth, λ
The population grows at a fixed rate over a fixed time interval
Expressed as a decimal or percent
Seen in individuals who reproduce at fixed time intervals
N(t) = N(0) λt
λ = N(t+1)/N(t)

5. Example
Deer exhibit geometric growth.  With an initial population of 1000 deer there are 250 births, 100 deaths in a year. 
Calculate the geometric growth rate
The population in 3 years
The population in 10 years

6. Example

7. Exponential Growth
Describes a population growing continuously at a constant rate
The rate constant for exponential growth is r and r = birth rates (b) – death rates (d) The instantaneous growth rate is derived through calculus and represented by this equation.
dN/dt = rN0
The doubling time of this type of growth can be approximated by this simplified formula
td = 0.69            r

8. Example
Bacteria exhibit exponential growth with sufficient food and space. If you start with 100 bacteria and they have an exponential growth rate of 0.4 per hour,
calculate the instantaneous rate
the doubling time
how many bacteria will there be in 3 doubling times?

9. Example

10. Logistic Growth
This type of growth describes a population growing continuously at a constant rate but is limited by the carrying capacity of the environment, K. The instantaneous growth is represented by this equation.
r = the intrinsic growth rate N = population at a given time K is the carrying capacity of the environment

11. Example Population of Moose r (K-N)/K Growth Rate dN/dt 10 0.4
990/1000
3.96 20
980/1000
7.84
100
900/1000 36

12. r-strategists
Species that live close to their biotic potential (r) are referred to as r-strategists
These individuals:
Have short life span
Become sexually mature at young age
Produce large broods of offspring
Provide little/no parental care

13. K-strategists Species that live close to their carrying capacity (K)
These individuals:
Have long life spans
Become sexually mature later in life
Produce few offspring per reproductive cycle
Provide a high level of parental care