Average Mutual Information and fisheries impacts

Manuel Zetina Rejón

Simulation scenarios

0

0.5

1

1.5

2

2.5

0 5 10 15 20 25 30 35 40 45 50

Years of simulation

Rel

ativ

e fis

hing

eff

ort

• Campeche sound– Shrimp– Demersal– Pelagic– Beach seine– Octopus

• Terminos Lagoon– Finfish– Oyster– Blue crab

• All fisheries

Impact evaluation

Time

Rela

tive B

iom

ass

0

10%

-10%

Biomass

MC

TRResilience=

(R)

Persistence(P)

Recovery time(TR)

Magnitudeof change

(MC)

Disturbance

Δ F’s

Effects of fisheries

All

Shrimp

Demersal

Pelagic

Beach seine

OctopusFinfish

-10

-8

-6

-4

-2

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10Axis 1 (49 %)

Axi

s 2

(20

%)

Persistence

All

Shrimp

Demersal

Pelagic

Beach seine

Octopus

Finfish

-15

-10

-5

0

5

10

15

-15 -10 -5 0 5 10 15Axis 1 (72 %)

Axi

s 2

(9 %

)

Magnitude of Change

AllShrimp

Demersal

Pelagic

Beach seineOctopus

Finfish

-15

-10

-5

0

5

10

15

-15 -10 -5 0 5 10 15Axis 1 (70 %)

Axi

s 2

(10

%)

Recovery time

All

Shrimp

Demersal

PelagicBeach seine

Octopus

Finfish

-10

-8

-6

-4

-2

0

2

4

6

8

10

-10 -8 -6 -4 -2 0 2 4 6 8 10Axis 1 (57 %)

Axi

2 (

16 %

)

Resilience

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time

Rel

ativ

e B

iom

ass

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time

Rel

ativ

e B

iom

ass

Resilience indicator:Area of change (AC)

),()( tit MaxBBMax

),()( tit MinBBMin

dtBMinBMaxACfin

ini

t

t

tt )( )()(

0

0.2

0.4

0.6

0.8

1

1.2

1.4

Time

Rel

ativ

e B

iom

ass

Low Impacts = Low ACHigh Impacts = High AC

Area of Change

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2 6 10 14 18 22 26 30 34 38 42 46 50 2 6 10 14 18 22 26 30 34 38 42 46 50 2 6 10 14 18 22 26 30 34 38 42 46 50

Years of Simulation

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

ShrimpSC

Rel

ati

ve

Bio

mas

s

DemersalSC

PelagicSC

Beach seineSC

FinfishLT

OctopusSC

OysterLT

Blue crabLT

All

AC=102.8 AC=43.3 AC=201.3

AC=22.8 AC=37.0 AC=77.9

AC=0 AC=0 AC=258.4

All

Pelagic

Finfish

Shrimp

Demersal

Octopus

Beach seine

R 2 = 0.97

1

21

41

61

81

101

121

141

161

50 100 150 200 250 300

AC

MA

GN

ITU

DE

OF

CH

AN

GE

AllPelagic

Finfish

Shrimp

Demersal

Octopus

Beach seine

R2 = 0.96

1

6

11

16

21

26

31

36

RE

CO

VE

RY

TIM

E

Information Theory (Ulanowicz, 1986)

Average Mutual Information ( I ) measures the probability that a unit of energy flows to certain destination.

When uncertainty of the destination is high, I is bigger, quantifies degree of articulation in network/models.

Measure of organization, higher in mature and complex systems.

The I is higher while more complex trophic links.

I = Lower I = Higher

Hypothesis

When a fishery catch or remove biomass of group of species with simple trophic links, the impact of this fishery could be more severe, making ecosystem's stability and resilience vulnerable when high biomasses are extracted from the system

Average Mutual Information ( IF )

n

ii

t

iF I

C

CI

1

AC vs. IF

Oyster Blue crab Beach seine

Octopus Demersal

Shrimp Finfish

Pelagic

All

R2 = 0.6

-

0.5

1.0

1.5

2.0

2.5

3.0

- 1.0 2.0 3.0 4.0 5.0 6.0 7.0

I F

log

AC

Realistic Model

Simulation scenarios

(changes in fishingintensity)

Evaluationof Impacts

ModelValidation

Research strategy

0.20.40.60.81.01.21.41.6

Time seriesObserved data

0.5

1.0

1.5

2.0

2.5

3.0

1984 1988 1992 1996