L e c ture 2 L e c ture 2 Population E Population E c ology - - PDF document

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L e c ture 2 L e c ture 2 Population E Population E c ology c ology Po pula tio n Gro wth, Po pula tio n Gro wth, Co mpe titio n a nd Pre da tio n Co mpe titio n a nd Pre da tio n BF BF L L F F Bio lo g y Co nc e pts Bio lo g y

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SLIDE 1

1

L e c ture 2 L e c ture 2

Population E c ology

Po pula tio n Gro wth, Co mpe titio n a nd Pre da tio n

Population E c ology

Po pula tio n Gro wth, Co mpe titio n a nd Pre da tio n

BF L F Bio lo g y Co nc e pts BF L F Bio lo g y Co nc e pts

  • Po pula tio n g ro wth
  • I

ntra spe c fic Co mpe titio n (I nte rspe c fic )

  • Pre da tio n (Pa ra sitism/ Virule nc e )
  • Be ha vio r
  • E

vo lutio n?

  • Po pula tio n g ro wth
  • I

ntra spe c fic Co mpe titio n (I nte rspe c fic )

  • Pre da tio n (Pa ra sitism/ Virule nc e )
  • Be ha vio r
  • E

vo lutio n?

slide-2
SLIDE 2

2

T he T ra g e dy o f the Co mmo ns T he T ra g e dy o f the Co mmo ns

  • Ope n pa sture c a n suppo rt 10 c a ttle
  • Curre ntly g ra ze d b y 10 he rdsme n

e a c h with o ne

  • Ope n pa sture c a n suppo rt 10 c a ttle
  • Curre ntly g ra ze d b y 10 he rdsme n

e a c h with o ne

  • One o f the he rdsme n a dds
  • ne mo re if he c a n ma ke a

pro fit.

  • Adding o ne mo re a nima l =

le ss fo o d fo r e a c h a nima l, b ut sinc e he o nly ha s o nly 1/ 10 o f the he rd, he ha s to pa y o nly 1/ 10 o f the c o st.

  • One o f the he rdsme n a dds
  • ne mo re if he c a n ma ke a

pro fit.

  • Adding o ne mo re a nima l =

le ss fo o d fo r e a c h a nima l, b ut sinc e he o nly ha s o nly 1/ 10 o f the he rd, he ha s to pa y o nly 1/ 10 o f the c o st.

T he T ra g e dy o f the Co mmo ns T he T ra g e dy o f the Co mmo ns

  • Shrinking pro fit ma rg ins ⇒

e ithe r g o o ut o f b usine ss o r a lso a dd mo re a nima ls.

  • Mutua l e xplo ita tio n

c o ntinue s until o ve rg ra zing a nd e ro sio n de stro y the pa sture syste m, a nd a ll the he rdsme n a re drive n o ut o f b usine ss…

  • Ha rdin 1968
  • Shrinking pro fit ma rg ins ⇒

e ithe r g o o ut o f b usine ss o r a lso a dd mo re a nima ls.

  • Mutua l e xplo ita tio n

c o ntinue s until o ve rg ra zing a nd e ro sio n de stro y the pa sture syste m, a nd a ll the he rdsme n a re drive n o ut o f b usine ss…

  • Ha rdin 1968
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SLIDE 3

3

  • St. Ma tthe w I

sla nd Co lla pse

  • St. Ma tthe w I

sla nd Co lla pse

  • Sma ll numb e r o f

re inde e r c o lo nize d the isla nd

  • I

nc re a se ra pidly

  • Use up a ll o f the

re so urc e s

  • Po pula tio n

c o lla pse s

  • Sma ll numb e r o f

re inde e r c o lo nize d the isla nd

  • I

nc re a se ra pidly

  • Use up a ll o f the

re so urc e s

  • Po pula tio n

c o lla pse s

Po pula tio n Gro wth Po pula tio n Gro wth

  • E

xpo ne ntia l Gro wth

  • E

xpo ne ntia l Gro wth

Population Size Population Size Time Time

Nt = N0ert N Nt

t = N

= N0

0e

ert

rt

dN/dt = rN dN/dt = rN dN/dt = rN

Nt = popln @ time t r = growth rate N Nt

t =

= popln popln @ time t @ time t r = growth rate r = growth rate

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SLIDE 4

4

Po pula tio n Gro wth Po pula tio n Gro wth

  • E

xpo ne ntia l Gro wth

  • E

xpo ne ntia l Gro wth

Population Size Population Size Time Time dN/dt = rN dN/dt = rN dN/dt = rN high r high r moderate r moderate r low r low r

Po pula tio n Gro wth Po pula tio n Gro wth

  • E

xpo ne ntia l Gro wth

– Disc re te T ime Nt+1 = Nt * R

  • R = a ve ra g e re pro duc tio n
  • E

xpo ne ntia l Gro wth

– Disc re te T ime Nt+1 = Nt * R

  • R = a ve ra g e re pro duc tio n
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SLIDE 5

5

Po pula tio n Gro wth Po pula tio n Gro wth

  • L
  • g istic Gro wth (Ma lthus)
  • I

ntra spe c ific c o mpe titio n

  • L
  • g istic Gro wth (Ma lthus)
  • I

ntra spe c ific c o mpe titio n

Population Size Population Size Time Time

dN/dt = rN(1- N/K) dN/dt = rN(1- N/K)

Carrying Capacity of Environment (K) Carrying Capacity of Environment (K)

Period of Exponential Growth Period of Exponential Growth

Nt = N0K N0 + (K−N0)e−r0t

Population Density (N) Population Density (N)

Density-dependent death rate - d Density-dependent death rate - d Density-independent birth rate - b Density-independent birth rate - b Equilibrium Density Equilibrium Density 1 dN N dt 1 dN N dt

Population Density (N) Population Density (N)

Density-independent death rate Density-independent death rate Density-dependent birth rate Density-dependent birth rate 1 dN N dt 1 dN N dt

Population Density (N) Population Density (N)

Density-dependent death rate Density-dependent death rate Density-dependent birth rate Density-dependent birth rate

Density-Dependant Factors Regulate Population Size Density-Dependant Factors Regulate Population Size

1 dN N dt 1 dN N dt

r = b-d

as N r stabilizing

r = b-d

as N r stabilizing

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SLIDE 6

6

Po pula tio n Gro wth Po pula tio n Gro wth

  • L
  • g istic Gro wth

– Disc re te T ime Nt+1 = Nt (1+r(1-Nt/ K ))

  • R = a ve ra g e re pro duc tio n
  • K

= c a rrying c a pa c ity

  • L
  • g istic Gro wth

– Disc re te T ime Nt+1 = Nt (1+r(1-Nt/ K ))

  • R = a ve ra g e re pro duc tio n
  • K

= c a rrying c a pa c ity

Whic h g ra ph o f po pula tio n g ro wth c o uld not b e g e ne ra te d b y this e q ua tio n? Nt+1 = Nt (1+r(1-Nt/ K )) Whic h g ra ph o f po pula tio n g ro wth c o uld not b e g e ne ra te d b y this e q ua tio n? Nt+1 = Nt (1+r(1-Nt/ K ))

  • A
  • B
  • A
  • B
  • C
  • D
  • C
  • D
  • E
  • T

he y c o uld all b e g e ne ra te d

  • F
  • None c o uld b e g e ne ra te d
  • E
  • T

he y c o uld all b e g e ne ra te d

  • F
  • None c o uld b e g e ne ra te d
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SLIDE 7

7

Po pula tio n Gro wth Po pula tio n Gro wth

  • L
  • g istic Gro wth

– Disc re te T ime Nt+1 = Nt (1+r(1-Nt/ K ))

  • L

imit Cyc le s

  • Cha o s
  • L
  • g istic Gro wth

– Disc re te T ime Nt+1 = Nt (1+r(1-Nt/ K ))

  • L

imit Cyc le s

  • Cha o s

Re a l Po pula tio n Gro wth Re a l Po pula tio n Gro wth

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SLIDE 8

8

  • Huma n

po pula tio n g ro wth

  • Huma n

po pula tio n g ro wth

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SLIDE 9

9

Human Population Age Distribution More Developed Countries Human Population Age Distribution More Developed Countries

Age Interval Age Interval

Number of people (Millions) Number of people (Millions) Females Females Males Males

80 - 90 70 - 80 60 - 70 50 - 60 40 - 50 30 - 40 20 - 30 10 - 20 0 -10 80 - 90 70 - 80 60 - 70 50 - 60 40 - 50 30 - 40 20 - 30 10 - 20 0 -10

Long periods of no net growth lead to even distribution Long periods of no net growth lead to even distribution Po pula tio n Summa ry fo r the US Po pula tio n Summa ry fo r the US 2000 2025 2050

http://blue.census.gov/

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SLIDE 10

10

Population Age Distribution Less Developed Countries Population Age Distribution Less Developed Countries

Age Age

300 300 300 300 Number of people (Millions) Number of people (Millions) Females Females Males Males

Po pula tio n Summa ry fo r Ug a nda Po pula tio n Summa ry fo r Ug a nda 2000 2025 2050 http://blue.census.gov/ Very high reproductive rate

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SLIDE 11

11

Human Population Growth Human Population Growth

Year Year Population (Billions) Population (Billions)

1 1 2 2 3 3 4 4 5 5 6 6 Agriculture & domestification of animals Agriculture & domestification of animals 4 million 4 million 7 million 7 million Hunter Gatherers Hunter Gatherers

Adapted from: Cohen, “How Many People Can the Earth Support” Adapted from: Cohen, “How Many People Can the Earth Support”

10,000 BC 10,000 BC 8,000 BC 8,000 BC 2,000 AD 2,000 AD 4,000 BC 4,000 BC Bubonic Plague Bubonic Plague Industrial Revolution Industrial Revolution (1400) (1400) (1800) (1800) Modern Medicine (reduced mortality) Modern Medicine (reduced mortality) (1900) (1900) Fossil Fuel Fossil Fuel 6,289,870,258* (4/30/2003)

http://www.census.gov/main/www/popclock.html http://www.census.gov/main/www/popclock.html

6,363,174,549 (4/28/2004) 6,432,150,287 (4/22/05)

Now projected to reach 9 Billion and level off

6 Billion (1999) 6 Billion (1999)

http://www.census.gov/ipc/prod/wp02/wp02-1.pdf

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SLIDE 12

12

Demographic Transition Demographic Transition

Stage 1 High birth rate High, but fluctuating death rate Stage 1 High birth rate High, but fluctuating death rate Stage 2 Declining death rates Continuing high birth rates Stage 2 Declining death rates Continuing high birth rates Stage 3 Declining birth and death rates Stage 3 Declining birth and death rates Stage 4 Low death rate Low, but fluctuating birth rate Stage 4 Low death rate Low, but fluctuating birth rate

Wha t do yo u think is the huma n c a rrying c a pa c ity o f e a rth? Wha t do yo u think is the huma n c a rrying c a pa c ity o f e a rth?

  • A - 6 b illio n
  • B - 9 b illio n
  • C - 12 b illio n
  • D - 15 b illio n
  • A - 6 b illio n
  • B - 9 b illio n
  • C - 12 b illio n
  • D - 15 b illio n
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SLIDE 13

13

Huma n Po pula tio n Gro wth a nd Bio dive rsity Huma n Po pula tio n Gro wth a nd Bio dive rsity

  • Huma n I

nflue nc e s o n Bio dive rsity

– Immigr

ation into ne w pla c e s

– Destr

uc tion o f ha b ita t a nd spe c ie s

– F

r agme ntation o f ha b ita t

– Intr

  • duc tion o f no n-na tive spe c ie s

– Compe tition with a g ric ulture

  • Huma n I

nflue nc e s o n Bio dive rsity

– Immigr

ation into ne w pla c e s

– Destr

uc tion o f ha b ita t a nd spe c ie s

– F

r agme ntation o f ha b ita t

– Intr

  • duc tion o f no n-na tive spe c ie s

– Compe tition with a g ric ulture

T he F unda me nta l E c o lo g ic a l Nic he : “ An n-dime nsio na l hype r-vo lume e ve ry po int o n whic h a spe c ie s

c a n survive a nd re pro duc e inde finite ly in the a b se nc e o f o the r spe c ie s” (Hutc hinso n)

T he F unda me nta l E c o lo g ic a l Nic he : “ An n-dime nsio na l hype r-vo lume e ve ry po int o n whic h a spe c ie s

c a n survive a nd re pro duc e inde finite ly in the a b se nc e o f o the r spe c ie s” (Hutc hinso n)

Food size Food size temperature temperature h u m i d i t y h u m i d i t y

slide-14
SLIDE 14

14

I nte rspe c ific Co mpe titio n I nte rspe c ific Co mpe titio n

Food size Food size temperature temperature h u m i d i t y h u m i d i t y

niche overlap leads to competition

T he Re a lize d E c o lo g ic a l Nic he :

the nic he a c tua lly o c c upie d in the pre se nc e o f o the r spe c ie s

T he Re a lize d E c o lo g ic a l Nic he :

the nic he a c tua lly o c c upie d in the pre se nc e o f o the r spe c ie s

Food size Food size temperature temperature h u m i d i t y h u m i d i t y

slide-15
SLIDE 15

15

One species eats seeds of one size range Number consumed Number consumed Seed size (one niche dimension)

Partial niche overlap can lead to Niche Partitioning and Competitive Coexistence

Species 1 Species 2 Number consumed Number consumed Seed size

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SLIDE 16

16

Complete niche overlap Species 1: Strong competitor Species 1: Strong competitor Species 2: Weak competitor, driven to extinction Species 2: Weak competitor, driven to extinction Number consumed Seed size

Strong niche overlap can lead to Competitive Exclusion

Observed Distributions: Is this due to competition? Or differential tolerance of desiccation? Do an Experiment! Chthamalus in upper intertidal zone Chthamalus in upper intertidal zone Mean tidal level Mean tidal level Balanus in lower intertidal zone Balanus in lower intertidal zone

slide-17
SLIDE 17

17

Spring high tide Spring high tide Neap high tide Neap high tide Mean tidal level Mean tidal level Neap low tide Neap low tide Could not become adults due to competition Could not become adults due to competition Larval Settlement Zone Larval Settlement Zone Adult Distribution Adult Distribution Realized Niche Realized Niche Barnacles subject to desiccation Barnacles subject to desiccation Spring low tide Spring low tide Larval Settlement Zone Larval Settlement Zone Adult Distribution Adult Distribution

Distribution of Two Barnacle Species – Balanus and Chthamalus Distribution of Two Barnacle Species – Balanus and Chthamalus

Balanus Balanus Chthamalus Chthamalus

Fundamental Niche Fundamental Niche

L

  • tka -Vo lte rra

I nte rspe c ific Co mpe titio n L

  • tka -Vo lte rra

I nte rspe c ific Co mpe titio n

  • dN1/ dt = r

1*N1 ((K 1 – N1 – (a *N2))/ K 1)

  • dN2/ dt = r

2*N2 (K 2 – N2 - (b *N1))/ K 2)

– T wo lo g istic g ro wth mo de ls – T wo spe c ie s N1 a nd N2 – a : impa c t o f spe c ie s 2 o n spe c ie s 1 – b : impa c t o f spe c ie s 1 o n spe c ie s 2

  • dN1/ dt = r

1*N1 ((K 1 – N1 – (a *N2))/ K 1)

  • dN2/ dt = r

2*N2 (K 2 – N2 - (b *N1))/ K 2)

– T wo lo g istic g ro wth mo de ls – T wo spe c ie s N1 a nd N2 – a : impa c t o f spe c ie s 2 o n spe c ie s 1 – b : impa c t o f spe c ie s 1 o n spe c ie s 2

slide-18
SLIDE 18

18

L

  • tka -Vo lte rra Co mpe titio n

L

  • tka -Vo lte rra Co mpe titio n

Pre da tio n Pre da tio n

  • Ha re a nd L

ynx Cyc le s

  • T

ra pping da ta de sc rib e d b y e q ua tio ns b y L

  • tka (1925) a nd Vo lte rra (1926)
  • Ha re a nd L

ynx Cyc le s

  • T

ra pping da ta de sc rib e d b y e q ua tio ns b y L

  • tka (1925) a nd Vo lte rra (1926)
slide-19
SLIDE 19

19

What drives the oscillation? What drives the oscillation?

Snowshoe Hare and Lynx Population Population Cycles Snowshoe Hare and Lynx Population Population Cycles

1840 1840 1930 1930 11 years 11 years 1870 1870 1900 1900

Number of Pelts (thousands) Number of Pelts (thousands) 150 150 50 50 100 100 Hudson Bay Company Trapping Records (1840 –1940) Hudson Bay Company Trapping Records (1840 –1940)

Hare Hare Lynx Lynx

Pre da tio n Pre da tio n L

  • tka -Vo lte rra

Pre da to r-Pre y E q ua tio ns L

  • tka -Vo lte rra

Pre da to r-Pre y E q ua tio ns

  • dx/ dt

= Ax - Bxy

  • dy/ dt

=

  • Cy + Dxy

– x : numb e r o f pre y – y : numb e r o f pre da to rs – xy : e nc o unte r ra te o f pre da to r a nd pre y – A : g ro wth ra te o f pre y – B : e ffic ie nc y o f pre da to r – C : de nsity de pe nde nt de a th o f pre da to rs – D : c o nve rsio n o f pre y to pre da to r

  • dx/ dt

= Ax - Bxy

  • dy/ dt

=

  • Cy + Dxy

– x : numb e r o f pre y – y : numb e r o f pre da to rs – xy : e nc o unte r ra te o f pre da to r a nd pre y – A : g ro wth ra te o f pre y – B : e ffic ie nc y o f pre da to r – C : de nsity de pe nde nt de a th o f pre da to rs – D : c o nve rsio n o f pre y to pre da to r

slide-20
SLIDE 20

20

L

  • tka -Vo lte rra Osc illa tio ns

L

  • tka -Vo lte rra Osc illa tio ns
  • Pe rio dic Cyc ling
  • Pre y L

e a ds Pre da to r

  • Pe rio dic Cyc ling
  • Pre y L

e a ds Pre da to r

Pre da to r-Pre y Mo de ls Pre da to r-Pre y Mo de ls

  • Ag e nt-b a se d Pre da to r-Pre y

– Gra ss

  • Spre a ds o ut fro m o the r g ra ss

– Ra b b its

  • Wa lk a ro und ra ndo mly a nd use e ne rg y
  • I

f the y la nd o n g ra ss the y e a t it

  • I

f the y e a t e no ug h the y re pro duc e

  • I

f the y run o ut o f e ne rg y the y die

  • Ag e nt-b a se d Pre da to r-Pre y

– Gra ss

  • Spre a ds o ut fro m o the r g ra ss

– Ra b b its

  • Wa lk a ro und ra ndo mly a nd use e ne rg y
  • I

f the y la nd o n g ra ss the y e a t it

  • I

f the y e a t e no ug h the y re pro duc e

  • I

f the y run o ut o f e ne rg y the y die

slide-21
SLIDE 21

21

Pre da to r-Pre y Mo de ls Pre da to r-Pre y Mo de ls E vo lutio n a nd Se le c tio n E vo lutio n a nd Se le c tio n

  • I

n the a b se nc e o f se le c tio n if we sta rt with 16 diffe re nt c o lo rs o f ra b b its (in the pre vio us mo de l), ho w ma ny o f tho se c o lo rs will pe rsist in the lo ng run?

– A - 16 – B - 10-15 – C - 8-10 – D - 1-2

  • I

n the a b se nc e o f se le c tio n if we sta rt with 16 diffe re nt c o lo rs o f ra b b its (in the pre vio us mo de l), ho w ma ny o f tho se c o lo rs will pe rsist in the lo ng run?

– A - 16 – B - 10-15 – C - 8-10 – D - 1-2

slide-22
SLIDE 22

22

Ra b b its a nd Gra ss with Co lo r Ra b b its a nd Gra ss with Co lo r

  • E

vo lutio n?

  • Se le c tio n?
  • E

vo lutio n?

  • Se le c tio n?

Wha t is ha ppe ning ? Wha t is ha ppe ning ?

  • E

vo lutio n?

  • Se le c tio n?
  • E

vo lutio n?

  • Se le c tio n?
slide-23
SLIDE 23

23

E vo lutio n E vo lutio n

  • De sc e nt with mo dific a tio n
  • Cha ng e in g e ne fre q ue nc y in a

population o ve r time

– Muta tio n – Mig ra tio n – Se le c tio n – Ge ne tic Drift

  • De sc e nt with mo dific a tio n
  • Cha ng e in g e ne fre q ue nc y in a

population o ve r time

– Muta tio n – Mig ra tio n – Se le c tio n – Ge ne tic Drift – Ge ne tic Drift – Ge ne tic Drift