Objective: SWBAT explain how competition for resources limits exponential growth and can be...
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Ch. 53 Exponential and Logistic Growth Objective: SWBAT explain how competition for resources limits exponential growth and can be described by the logistic growth model.
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Transcript of Objective: SWBAT explain how competition for resources limits exponential growth and can be...
Ch. 53 Exponential and Logistic
Growth
Objective:SWBAT explain how competition for
resources limits exponential growth and can be described by the logistic growth
model.
Unrealistic! Does not take into account
limiting factors (resources and competition). However, a good model for showing upper
limits of growth and conditions that would facilitate growth.
Exponential Growth
Exponential Growth Equation
Change inpopulation
sizeBirths
Immigrantsentering
populationDeaths
Emigrantsleaving
population
NB D
t
Per capita (individual)
B bND mN
NbN mN
t
Per capita growth rate
r b m
Nt
rN
dNdt
rmaxN
Under ideal conditions, growth rate is at its max
Exponential
growth results in a J curve.
Exponential Graph
Number of generations
Po
pu
lati
on
siz
e (N
)
0 5 10 15
2,000
1,500
1,000
500
dNdt
dNdt
= 1.0N
= 0.5N
Can occur when:
Populations move to a new area.
Rebounding after catastrophic event (Cambrian explosion)
Real Life Examples
Year
Ele
ph
ant
po
pu
lati
on
8,000
6,000
4,000
2,000
01900 1910 1920 1930 1940 1950 1960 1970
Takes into account limiting factors. More realistic. Population size increases until a carrying capacity
(K) is reached (then growth decreases as pop. size increases). point at which resources and population size are in
equilibrium. K can change over time (seasons, pred/prey
movements, catastrophes, etc.).
Logistic Growth
Logistic Growth Equation
dNdt
(K N)
Krmax N
Logistic growth
results in an S-shaped curve
Logistic Graph
Number of generations
Population growthbegins slowing here.
Exponentialgrowth
Logistic growth
Po
pu
lati
on
siz
e (N
)
0 5 1510
2,000
1,500
1,000
500
0
K = 1,500
dNdt
= 1.0N
dNdt
= 1.0N
1,500 – N1,500
( )
Real Life Examples
Time (days) Time (days)
(a) A Paramecium population in the lab
(b) A Daphnia population in the lab
Nu
mb
er o
f Paramecium
/mL
Nu
mb
er o
f Daphnia
/50
mL
1,000
800
600
400
200
00 5 10 2015 0 16040 60 80 100 120 140
180
150
120
90
60
30
0
Note overshoot
