 Carrying
Capacity:
Maximum number of organisms that can be
sustained by available resources over a
given period of time
 Is
dynamic as environmental conditions are
always changing
 Fecundity:
The potential for a species to produce large
numbers of offspring in one lifetime.
 Birth
(natality), death (mortality),
immigration, emigration
 Population growth of any given
population is calculated mathematically
population change =
[(births +immigration) - (deaths + emigration)]
x 100
initial population size(n)
population change =
[(b + i) - (d + e)]
x 100
(n)



Open population – Population in which change
in number and density determined by births,
deaths, immigration, emigration
Closed population – Change in size determined
by natality and mortality alone
Biotic Potential –
Maximum reproductive rate (r) under ideal
conditions (intrinsic rate of natural increase) eg.
E. Coli...if doubled, unchecked for 24hrs they
would cover the earth 1m deep!!
Geometric growth () – pattern of population
growth where organisms reproduce at fixed
intervals at a constant rate.
 Eg. Animals with a specific breeding season.

 = N(t +1)
N (t)
 = fixed growth
N = Population in year (t + 1)
t = year

2000 seals give birth to 950 pups in May. During the next 12 months, 150
pups die. Assuming geometric growth, what will the harp seal population
be in two years? Eight years?
First Calculate Growth rate:
 N(0) = 2000
 N(1) = 2000 + 950 -150

= 2800
N(t + 1)
2800
=

= 1.4
N(t)
2000
After 2 years:
 N(t + 1) = N(t) 
N(2) = 2800 x 1.4
= 3920
OR
 N (2) = N (0)  2
= 3920
After 8 years:
N(8) = N(0)  8
= 2000 x (1.4)8
= 29520


A pattern of population growth where organisms reproduce
continuously at a constant rate
Ecologists are able to determine instantaneous growth
rate of the population expressed in terms of the intrinsic
(per capita) growth rate (r).
• difference between per capita birth rate, b, and per capita
death rates, d, where r = (b – d)
• population growth rate given by the expression...
dN
= rN
dt



dN/dt = instantaneous growth rate of population
r = growth rate per capita
N = population size
 For
populations growing exponentially,
the time needed for population to double
in size is a constant...
0.69
td =
r

A population of 2500 yeast cells in culture is growing
exponentially with an intrinsic growth rate r is 0.0575 per hour.
1. What is the initial instantaneous growth rate of the population?
Given: r = 0.0575, N = 2500
dN
= rN
dt
dN/dt = (0.0575)(2500)
= 144 per hour
2. What time will it take for the population to double in size?
td = 0.69
0.0575
= 12 hours
3. What will the size of the population be
after each of four doubling periods?
Doubling Times
Time in hours
Population size
0
0
2500
1
12
5000
2
24
10000
3
36
20000
4
48
40000
 Food, water, light, and
space within an
ecosystem are factors that limit population
growth as resources are consumed as the
population nears the ecosystem’s carrying
capacity
 The
growth rate drops below rmax in this
case
 Stable equilibrium (births=deaths) is often
reached
 Population number at carrying capacity is
represented by K.
 Logistic
growth is most common growth
pattern seen in nature as it represents the
effect of carrying capacity on the
population’s growth
 Logistic growth equation is as follows
K  N 
dN
 rmax N 

dt
K


dN
 population growth rate at a given time
dt
rmax  maximum intrinsic growth rate
N = population size at a given time
K = carrying capacity of the environment
A
population is growing continuously. The
carrying capacity of the environment is
1000 individuals and its r max (max
growth rate) is 0.50.
 Determine pop growth rates based on
pop sizes of 100 , 500, 900, 1000
K  N 
dN
 rmax N 

dt
 K 
r Max
Pop Size N
(K-N)
N
Pop Growth
Rate
0.50
100
900/1000
45
0.50
500
500/1000
125
0.50
900
100/1000
45
0.50
1000
0/1000
0
Question :
What is the relationship between population size and growth rate?
Answer:
When the pop is small the growth rate is slow. It increases as the pop
increases, then as it approaches carrying capacity, the growth rate
declines and eventually stops!!
 Lag
phase occurs when population is
small and increasing slowly
 Log phase occurs when population
undergoes rapid growth
 As available resources become limited,
population experiences environmental
resistance and stationary phase occurs
in which the population is at dynamic
equilibrium (b=d)
 Page
664 #1,
 Page 665 # 2 a & b
 Page 668 # 3-4,
 Page 669 # 2-3,
 Page 670 #4-7