Look over these notes, but I’ll go trough this material on the overhead in class

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Look over these notes, but I’ll go trough this material on the overhead in class It explains the extra credit question on HW #2 (also see notes posted on HW back in Feb). The goal is to integrate INFORMATION with several prior concepts: - Calculating population growth rates

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Look over these notes, but I’ll go trough this material on the overhead in class

It explains the extra credit question on HW #2 (also see notes posted on HW back

in Feb).

The goal is to integrate INFORMATION with several prior concepts:

- Calculating population growth rates

- Species-Area relationships

- Species Niches

And to indicate how an Information-centered view of Ecology has numerous

relevancies for material we’ve discussed so far that has conceived free of information

Consider temporal variation in growth rates

Such as our rhino example in class

GOOD = 2.0

PGOOD = 0.5

For 1 population:

(2)0.5 × (0.1)0.5 = 0.447

For 2 populations:

Pop 1 Pop 2

Mean

Permutations

2

.1

1.05

1

1

2

Alternatives: 2 2

Alternatives: .1 .1

Alternatives: 2 .1

4

(2)? × (0.1)? × (1.05)? = ???

(2)0.25 × (0.1)0.25 × (1.05)0.5 =

For 3 populations:

Pop 1 Pop 2 Pop 3

Mean

Permutations (how to quickly find these)

2

1.367

0.733

0.1

1

3

3

1

Alternatives: 2 2 2

Alternatives: 2 2 .1

Alternatives: 2 .1 .1

Alternatives: .1 .1 .1

(2)1/8 × (1.367)3/8 × (0.733)3/8 × (0.1)1/8 = 0.818

Short-cut:

Binomial expansion and Pascal’s Triangle

(x+y)E

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

E =0

E=1

E=2

E=3

E=4

E=5

Pop 1 Pop 2 Pop 3

Mean

Permutations

2

1.367

0.733

0.1

1

3

3

1

Alternatives: 2 2 2

Alternatives: 2 2 .1

Alternatives: 2 .1 .1

Alternatives: .1 .1 .1

(2)1/8 × (1.367)3/8 × (0.733)3/8 × (0.1)1/8 = 0.818

Source

1.0

Sink

PMIN

# Populations (P)

# Populations

PMIN

AMIN

Area (A)

2 × 2 × 2 × 0.1 × 0.1 × 0.1 = ?

Growth rate?

2 × 0.1 × 2 × 0.1 × 2 × 0.1 = ?

What’s the difference between

the two scenarios?

QUESTIONS

Consider two 6-yr sequences:

Growth rate?

2 × 2 × 2 × 0.1 × 0.1 × 0.1 = ?

What’s the difference between

the two scenarios?

Can you extract information

About the future from either sequence?

Would it change your dispersal behavior?

2 × 0.1 × 2 × 0.1 × 2 × 0.1 = ?

A Worked Example (3 populations)

2 2 0.1 0.1 0.1

0.1 0.1 0.1 2 2

0.1 0.1 2 2 2 0.1

(2)5/6 × (0.1)1/6 = 1.10

0.918

(2)4/6 × (0.1)2/6 = 0.738

PMIN

# Populations

AMIN

Area

GEOM

• uniform dispersal
• but no spatial or temporal
• correlation

Information-free World

GEOM  ARITH - [2 – (n+1)cov]/(2n)

• Population growth rate
• increases with number
• of patches (n)

Information-free World

250

200

150

Mean persistence time

100

uniform dispersal, rho = 0

50

uniform dispersal, rho = 0.7

0

2

3

4

5

6

7

8

Number of patches

disperse

= 1-(probreproductive success)

Win-stay:lose-switch

A rule-of-thumb to bias settlement within

Productive habitats

site fidelity

= probreproductive success

2000

1500

1000

WSLS, rho = 0

500

WSLS, rho = 0.7

0

2

3

4

5

6

7

8

Number of patches

250

200

150

Mean persistence time

100

uniform dispersal, rho = 0

50

uniform dispersal, rho = 0.7

0

2

3

4

5

6

7

8

Number of patches

Conclusions

• dramatically alters their conclusions
• Temporal correlation (runs of good and bad years) can increase
• persistence because prior experience is informative
• It requires both temporal correlation AND the WSLS-rule
• to enhance population persistence – the appropriate behavior
• must be coupled with the appropriate environment
• Clear conservation message
• Organisms with information can survive in smaller areas (fewer patches)
• For given area/patches,  increases with information

Fundamental Niche

The Niche concept place in a Population Framework

R0 < 1.0

Realized Niche

R0 > 1.0

Factor Two

Factor One

Sunlight – resource (‘biotic’ factor)

Warm – abiotic factor

Photoperiod – INFORMATION

40% less photosynthesis

40% less gas exchange

Knock-out

Can’t determine photoperiod

Wild Type