POPULATION DYNAMICS- EQUATIONS TO
THINK ABOUT
Population Density
Pop Density = Number of Individuals
Area
Calculate the density of 56 cheetahs living in a 250
km2 area.
Estimating Population Size
Mark and Recapture Method
M(marked) = m(recaptured – marked)
N (pop. Size) n (total recaptured)
10 harp seals are tagged. The following year 25 are
caught and 3 are tagged. What would be the
estimated population?
POPULATION GROWTH CALCULATIONS
Pop Change = (B + I ) – (D+E) X 100%
N(initial pop. Size)
Calculate the population change of 10,000 penguins
if there are 4500 births, 2000 deaths and 300
immigrants.
Calculate the growth rate if a population of giraffes
increases from 1560 individuals to 1780 individuals in the
following season.
N(t) = N(0)λt
Assuming a constant growth rate how big would
this population be in 4 years from time 0.
INSTANTANEOUS GROWTH
dN
 rN
dt
Calculate the instantaneous population growth rate
of a dish of bacteria if the population is 1000 cells
and r = 0.035 per hours.
Note: r can be converted to lambda in the following
manner  er which translates into lambda
Doubling Time
td = 0.69
r
How long would it take the population of bacteria
(above) to double in size? How long would it take to
reach a population of 8000 cells?
How long would the population take to get 20,000
cells?
GROWTH RATES WITH CARRYING CAPACITY
dN
 N
 rN 1  
dt
 K
If rmax is 0.3, calculate the growth in population of
moose if there are 2000 individuals and the carrying
capacity of the environment is 3000. What if there were
4000 individuals and the carrying capacity was the same?
Homework Questions
1. Calculate the area occupied by a population of 2300 lions if the density is 1200 km 2.
2. A research group captures 50 grey wolves and tags them. A year later they capture 40
grey wolves, of which 7 are tagged. What is the estimated population of wolves?
3. An island population of 267 iguanas has 120 births, 35 deaths and 40 have been washed
away in a storm to a neighbouring island. If the growth rate was +40% how many arrived
to the island?
4. If the growth rate is 1.15, and the current population of raccoons is 1789, what would
have been the population last year?
5. A population of moose has a growth rate of 1.03. If the initial population is 1000, what
would be the population in 10 years (assume constant rate).
6. The growth rate of a particular fly is 0.55 per week. If there is an initial population of 34
individuals, how many would there be the next week and in two weeks?
7. How long would it take the population in #6 above to double in time? How long would it
take to reach 2176 individuals? How long would it take to reach 20,000 individuals?
8. Calculate the increase in a population of white-tailed deer if r = 0.2 and the carrying
capacity of the environment is 10,000, when the population is 3000 individuals, 10,000
individuals and 12,000 individuals?