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. 16-7 in Ricklefs and Miller 2000 1

Population Size (N)

Fecundity

Density Dependent Factors: Factors Influenced by Population Density

Fig. 16-9 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. 16-15 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: Winter-Aug. 31

Rainfall: Sept. – Oct.

Effective Degree Days: Sept. – Oct.

Effective Degree Days: Winter-Aug. 31 (prev. year)

Predictions versus Observed

Fig. 9-12 in Cain et al. 2008

Andrewartha and Birth:DENSITY-INDEPENDENT FACTORS Regulate Populations

Fig. 16-7 in Ricklefs et al. 2000

ECOLOGISTS COUNTER:Thrip Populations ARE Controlled by

Density-Dependent Factors

The Debate Rages On ….

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2 http://www.unexco.com/conflour.jpg

3 http://www.caudata.org/daphnia/images/Daphnia_magna_large.jpg

5 http://www.ruhr-uni-bochum.de/boga/html/Conyza.canadensis.ja05.jpg

6 http://flogaus-faust2.de/photo/amarretr.jpg

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/wp-content/uploads/2007/11/dsc02948.JPG

12 http://www.explorewisconsin.com/CedarCreekWinery/cedarburg_winery2b.jpg

11 http://sylviabass.com/foodie/wp-content/uploads/2007/11/potato-rosemary-bread-rising.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/bio-sci/images/profiles/wheals2.gif