catalytic network evolution model - reference material

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Chapter 4

Population Dynamics

4.1 The population dynamics equation


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Chapter 4. Population Dynamics

4.2 Attractors of the population dynamics equation


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4.2. Attractors of the population dynamics equation


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4.3 Attractor shape theorem

4.4 The attractor for a graph with no ACS

4.5 The dominant ACS of a graph


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4.6. Examples of the attractor for specific graphs

2

4

5

1

3

67

4.6 Examples of the attractor for specific graphs


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1 2 4

1 2 3

1

e)

g)

5

4 5

32 4

2 3a)

1

b)

1

2

3

1 2

d)1 2

c)

f)

3


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1

1

7 12

65432

8 9 10 11

e = ( 1 0 0 0 0 0 0 )

e = ( 0 0 0 0 0 0 1 )

e = ( 0 0 0 1 0 0 0 )

e = ( 0 0 0 0 0 0 0 0 0 0 1 1 ) / 2

e = ( 0 0 0 0 1 1 0 0 0 0 0 0 ) / 2

e = ( 1 1 0 0 0 0 0 0 0 0 0 0 ) / 2

1

1

2

3

2

3

2 4

3

b)

a)

6 75

T

T

T

T

T

T


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4.7 Timescale for reaching the attractor

4.8 Core and periphery of a graph


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4.9. Keystone nodes

=1.36 =1.001 1 1 =1.52

2

4

b)a)

1

5

4

3

2

1

3

5

1

2

3

4

5

1

2

3

5

4

d)c)

=1.191

4.9 Keystone nodes


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2

5

1

a) b)

3

2

5

4

1

4


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Chapter 5

Graph Dynamics

5.1 Graph dynamics rules


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Chapter 5. Graph Dynamics

New node

Selection

Population

Dynamics

Node with least Xi

Novelty

(step 3)

(step 2)

(step 1)


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5.2. Features of the graph dynamics

5.2 Features of the graph dynamics

5.2.1 Evolution in a prebiotic pool

5.2.2 Coupling of population and graph dynamics: two timescales

5.2.3 Absence of self-replicators


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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

20

40

60

80

100

120

140

160

180

200

n

numberoflinks

p=0.0025

p=0.005

p=0.001

no selection

5.2.4 Selection and novelty


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5.3. Implementation

5.3 Implementation

5.4 Results of graph evolution


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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

10

20

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80

90

100

110

n

s1

100 1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

20

40

60

80

100

120

140

160

n

s1

100 1

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

50

100

150

200

250

n

s1

100 1


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5.4. Results of graph evolution

0

10

20

30

40

50

60

0 2000 4000 6000 8000 10000

interdependency

n

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

x 104

0

10

20

30

40

50

60

70

80

90

100


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Chapter 6

Formation and Growth of

Autocatalytic Sets

6.1 The random phase


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6.1. The random phase

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

-1 0 1 2 3 4 5 6

P

(k)

in

k

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

-1 0 1 2 3 4 5 6

P

(k)

out

k


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Chapter 6. Formation and Growth of Autocatalytic Sets

1e-09

1e-08

1e-07

1e-06

1e-05

0.0001

0.001

0.01

0.1

1

0 2 4 6 8 10 12 14

D(d)

d

6.2 The growth phase


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6.2. The growth phase

6.2.1 Timescale for growth of the dominant ACS


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Chapter 6. Formation and Growth of Autocatalytic Sets

5

6

7

8

9

10

11

12

-11 -10 -9 -8 -7 -6 -5

ln(

g)

ln(p)

6.3 Fully autocatalytic graphs


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catalytic network evolution model - reference material

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