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1011
PHLOX
POPULATION GROWTH RATE
dN = f (B, D, I, E) dt
POPULATION GROWTH TRENDS
Figs. 11.3, 11. 6 in Molles 2008
Geometric Growth Exponential Growth
I) STEADILY INCREASING POPULATIONS
1) Pulsed Reproduction2) Non-Overlapping Generations3) Geometric Rate of Increase (
1) Continuous Reproduction2) Overlapping Generations3) Per Capita Rate of Increase (r)
λ)
UNLIMITED POPULATION GROWTH A:(Geometric Growth)
Fig. 11.3 in Molles 2008
• Pulsed Reproduction
• Non-Overlapping Generations
UNLIMITED POPULATION GROWTH A:(Geometric Growth: Ratio of Successive Population Size)
Fig. 11.3 in Molles 2008
N7 =___N6
N8 =___
N7
Geometric Growth: Calculation of Geometric Rate of Increase (λ)
λ = Nt+1
______________
N t
Phlox drummondii
8
N0 = 996
N 1 = 2,408
λ =
Calculating Geometric Rate of Increase (λ)
Geometric Growth: Projecting Population Numbers
N0 = 996
Phlox drummondii
8 λ = 2.42
N2 =
N 1 = 2,408
N5 =
Problem A: The initial population of an annual plant is 500. If, after one round of seed production, the population increases to 1,200 plants, what is the value of λ?
Problem B. For the plant population described in Problem A, if the initial population is 500, how large will be population be after six consecutive rounds of seed production?
Problem C: For the plant population described above, if the initial population is 500 plants, after how many generations will the population double?
STEADILY INCREASING POPULATIONS (Geometric Growth: Rate of Population Growth)
Fig. 11.3 in Molles 2008
Nt = No λt
UNLIMITED POPULATION GROWTH B:(Exponential Growth)
Fig. 11.7 in Molles 2008
• Continuous Reproduction
• Overlapping Generations
dN
dT
dN___
dT=Rate
UNLIMITED POPULATION GROWTH BExponential Growth (Rate of Population Growth)
Fig. 11.6 in Molles 2006
EXPONENTIAL POPULATION GROWTH:Rate of Population Growth
dN___
dT
dN___
dT
dN___
dT
dN___
dT
N
Graph of dN/dT versus N (Exponential Growth)
1
0.5 rise
run
rise
rise
run
run
rmax =riserun
(= intrinsic rateof increase)
dN__dT
= rmax N
EXPONENTIAL POPULATION GROWTH:Rate of Population Growth
Intrinsic Rate of Increase
Population Size
Rate of Population Growth
rmax = b - d
Meaning of Intrinsic Rate of Increase (rmax)
rmax = individuals per individual per day
b = per capita birth rate (= births per individual per day)
d = per capita death rate (= deaths per individual per day)
= intrinsic rate of increase (r) during exponential growth
EXPONENTIAL POPULATION GROWTH:Predicting Population Size
dN__dT
= rmax N
Nt = No ermax t
(e = 2.718)
Problem D. Suppose that the Silver City population of Eurasian Collared Doves, with initial population of 22 birds, is increasing exponentially with rmax = .20 individuals per individual per year . How large will the population be after 10 years? After 100 years?
Problem E. How many years will it take the Eurasian Collared Dove population described above to reach 1000 birds?
LN(AB) = LN(A) + LN(B) LN(A/B) = LN(A) – LN(B)
LN(AB) = B LN(A) LN(e) = 1-----------------------------------------------------------------------------------------------------------
Problem F. “Doubling Time” is the time it takes an increasing population to double. What is the doubling time for the Eurasian Collared Dove population described above?
Problem E. Refer to the Eurasian Collared Dove population described earlier. How fast is the population increasing when the population is 100 birds? How fast is the population increasing once the population reaches 500 birds?
Problem F. How large is the Eurasian Collared Dove population when the rate of population change (dN/dt) is 5 birds per year? When the rate of population change (dN/dt) is 20 birds per year?
LOGISTIC GROWTH: Rate of Population Change
Fig. 11.11 in Molles 2006
N
T
Carrying Capacity (K):
Sigmoid Curve:
82
LOGISTIC GROWTH: Carrying Capacity
Figs. 11.11 in Molles 2006.
(Logistic Population Growth)
LOGISTIC GROWTH: Rate of Population Change
dN___
dT
dN___
dT
N
Graph of dN/dT versus N (Logistic Growth)
rise
run
rise
run
rise
run
rise
run
LOGISTIC GROWTH: Rate of Population Change
dN____
dT
r max N= ( )1 - N
K
“Brake” Term
LOGISTIC GROWTH: Predicting Population Size
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2 http://www.bigantlers.com/dall15c.jpg
3 http://www.oilcrash.com/images/d_price3.gif
4 http://www.akcenter.org/images/programs/oceans/beluga/ Raw-Count-Graph.gif
5 http://csiwhalesalive.org/csi04404b.jpg
6 http://www.behav.org/00gallery/ecol/carni_isle_royal_graph_1.gif
7 http://mall.ballparks.com/images/AV75.jpg
8 http://www.sbs.utexas.edu/bio406d/images/pics/plm/Phlox% 20drummondii%20flws4.jpg
9 http://www.photobirder.com/Bird_Photos/whooping_crane_2.jpg
10 http://www.learner.org/jnorth/images/graphics/c/crane_Sp04_020.jpg
11 http://www.em.ca/garden/phlox_drummondii1.JPG
12 http://newsimg.bbc.co.uk/media/images/42096000/jpg/_42096628_ crowd_416_ap.jpg