Population Growth Models: Geometric and Exponential Growth Geometric Growth Exponential Growth.

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Transcript of Population Growth Models: Geometric and Exponential Growth Geometric Growth Exponential Growth.
Population Growth Models: Geometric and Exponential Growth
Geometric Growth Exponential Growth
Population Growth Models: Unrestrained Growth: How realistic?
Population Growth Models: Limits to Unrestrained Growth: Carrying Capacity (K)
Carrying Capacity: The Maximum Population Size of a Population that a Particular Ecosystem can Sustain
LOGISTIC GROWTH: Rate of Population Change
10
11
12
13
Saccharomyces cervisiae (Yeast)
Fig. 11.9 in Molles 2008
Logistic Population Growth: Yeast
K
Carrying Capacity (K): Maximum Population that a GivenPopulation can Support
Figs. 11.10, 11.11, 11.12, 11.26 in Molles 2008
Logistic Population Growth: Buffalo, Barnacles and Paramecia
Pattern of Human Population Growth?
Fig. 11.26 in Molles 2013
Previous 2000 yr Previous 40 yr
LOGISTIC GROWTH
K: Carrying Capacity
r realized: Realized Per Capita Rate of Increase
rmax: Intrinsic Rate of Increase: Maximum Possible Per Capita Rate of Increase
(= Sigmoidal Growth Curve)
Figs. 11.18 in Molles 2008
(Logistic Population Growth)
LOGISTIC GROWTH: Rate of Population Change
dN___
dt
dN___
dT
N
Rate of Population Change (Logistic Growth)(dN/dT versus N)
K
Rate of PopulationChange is Maximum
K2
NN
rrealized
Exponential Growth Logistic Growth
K
r max
r max
Per Capita Rate of Increase
rrealized
K
LOGISTIC GROWTH: Rate of Population Change
dN____
dt
r max N= ( )1  N
K
“Brake” Term on rmaxRate of Population
Growth (Exponential)
r realized rmax * (1  NK )
Realized Per Capita Rate of Increase
N r max r realized
=
(K = 100)
16
50
100
150
.02
.02
.02
.02
(1  NK )
_______________ ________
Problem A: Suppose a population of duckweed is growing logistically (r max = .08 duckweed/duckweed/day) in a styrofoam bowl with carrying capacity = 100 plants.
a)What is the rate of population change when N = 16?
b) What is the rate of population change when N = 50?
c) What is the rate of population change when N = 100?
d) What is the rate of population change when N = 150?
LOGISTIC GROWTH: Predicting Population Size
dN____
dT
r max N= ( )1  N
K
Problem B: Suppose sixteen duckweed (rmax = .08) are growing logistically in a styrofoam bowl with carrying capacity = 100 duckweed.
a) How big will the population be in ten days?
a) How big will the population by in one hundred days?
POPULATION REGULATION:Keeping Populations in Check
Density Independent Factors: Exert effects INDEPENDENT of Population Density
Density Dependent Factors: Factors Influenced by Population Density
Survivorship
vs.
Density Dependent Factors: Factors Influenced by Population Density
Fig. 9.14 in Cain et al. 2008
lx
Density Dependent Factors: Factors Influenced by Population Density
Survivorship
vs.
Fig. 9.14 in Cain et al. 2008
Density Dependent Factors: Factors Influenced by Population Density
Soybean (Glycine max)
lx
Fig. 167 in Ricklefs and Miller 2000 1
Population Size (N)
Fecundity
Density Dependent Factors: Factors Influenced by Population Density
Fig. 169 in Ricklefs and Miller 2000
Fecundity
Density Dependent Factors: Factors Influenced by Population Density
Fig. 9.13 in Cain et al. 2008
Density Independent and Density Dependent Factors(Summary)
Which has more impact on Population Regulation: Density Dependent or Density Independent Factors
Density Independent? Density Dependent?
DENSITY DEPENDENCE IS A MYTH!“The Distribution and Abundance of Animals”Andrewartha and Birch” (1954)
THRIPS
Population Fluctuation: Density Dependent or Density Independent Factors?
Fig. 1615 in Ricklefs and Miller 2000
Andrewartha and Birch: Thrip Density Predicted on Basis of CLIMATIC Variables
N = F (X1, X2, X3, X4)
Effective Degree Days: WinterAug. 31
Rainfall: Sept. – Oct.
Effective Degree Days: Sept. – Oct.
Effective Degree Days: WinterAug. 31 (prev. year)
Predictions versus Observed
Fig. 912 in Cain et al. 2008
Andrewartha and Birth:DENSITYINDEPENDENT FACTORS Regulate Populations
Fig. 167 in Ricklefs et al. 2000
ECOLOGISTS COUNTER:Thrip Populations ARE Controlled by
DensityDependent Factors
The Debate Rages On ….
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3 http://www.caudata.org/daphnia/images/Daphnia_magna_large.jpg
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4 http://www.coffeecreekwc.org/photos/birds/Song_Sparrow.jpg
7 http://www.ces.ncsu.edu/plymouth/graphics/ent/thriplarva1.jpg
8 http://www.ruf.rice.edu/~ecology/insects/ Thrip%20Phloeothripidae%20short%20wgs%20blk.jpg
9 http://hortipm.tamu.edu/pestprofiles/sucking/ghthrips/thripe.jpg
10 http://greenpreferred.com/wpcontent/uploads/2007/11/dsc02948.JPG
12 http://www.explorewisconsin.com/CedarCreekWinery/cedarburg_winery2b.jpg
11 http://sylviabass.com/foodie/wpcontent/uploads/2007/11/potatorosemarybreadrising.jpg
13 http://www.diwinetaste.com/html/dwt200701/images/SaccharomycesCerevisiae.jpg
14 http://student.biology.arizona.edu/honors99/group7/glycolysis.jpg
15 http://www.micro.siu.edu/micr201/images/Ethanol.gif
16 http://biology.kenyon.edu/courses/biol114/Chap08/longread_sequence.gif
17 http://www.bath.ac.uk/biosci/images/profiles/wheals2.gif