Project Status Report: Ecology and Environment Project · Project Status Report: Ecology and...

94
Project Status Report: Ecology and Environment Project Holling, C.S., Bell, D.E., Clark, W.C., Dantzig, G.B., Fiering, M.B., Jones, D.D., Rashid, Z., Velimirovic, H., Walters, C.J. and Winkler, C. IIASA Collaborative Paper June 1974

Transcript of Project Status Report: Ecology and Environment Project · Project Status Report: Ecology and...

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Project Status Report: Ecology and Environment Project

Holling, C.S., Bell, D.E., Clark, W.C., Dantzig, G.B., Fiering, M.B., Jones, D.D., Rashid, Z., Velimirovic, H., Walters, C.J. and Winkler, C.

IIASA Collaborative PaperJune 1974

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Holling, C.S., Bell, D.E., Clark, W.C., Dantzig, G.B., Fiering, M.B., Jones, D.D., Rashid, Z., Velimirovic, H., Walters,

C.J. and Winkler, C. (1974) Project Status Report: Ecology and Environment Project. IIASA Collaborative Paper.

IIASA, Laxenburg, Austria, CP-74-006 Copyright © June 1974 by the author(s). http://pure.iiasa.ac.at/171/ All

rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom

use is granted without fee provided that copies are not made or distributed for profit or commercial advantage.

All copies must bear this notice and the full citation on the first page. For other purposes, to republish, to post on

servers or to redistribute to lists, permission must be sought by contacting [email protected]

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SR-74-2-EC

PROJECT STATUS REPORT:

ECOLOGY AND ENVIRONMENT PROJECT

June 21, 1974

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STATUS REPORT FOR ECOLOGY & ENVIRONMENT PROJECT

We presenthere the extendedoutline and copies of the

illustrations used in the StatusReport of the IIASA

Ecology and Environment Project, presentedat Schloss

Laxenburg on 21 June 1974.

Section 1., "General Review", is covered in the outline.

Section 2., "A Case Study of EcosystemManagement", is

the subject of a major monographnow in preparation.

Section 3., on SelectedConceptualDevelopments,is in

part documentedin IIASA ResearchReports RR-73-3 and

RR-74-3.

C.S. Holling - Project Leader

D.E. Bell

W.C. Clark

G.B. Oantzig

M.B. Fiering

D.O. Jones

Z. Rashid

H. Velimirovic

C.J. Walters

C. Winkler

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NOTES FOR

IIASA STATUS REPORT

ECOLOGY AND ENVIRONMENT PROJECT

Presented21 June 1974

1. General Review of Ecology/EnvironmentProject

1.1 Background

1.2 Strategy

1.3 Tactics

1.4 Tasks Chosen in the First Year

2. A Case Study of EcosystemManagement

2.1 The Budworm Problem, the Setting, the Goal

2.2 Bounding the Problem

2.3 Budworm EcosystemModel

2.3.1 Stochasticmodel of the weather

2.4 Model Analysis

2.4.1 The site model

2.4.2 Statesof the system

2.4.3 Validation of multi-site model

2.5 Policy Analysis

2.5.1 Introduction

2.5.2 Indicators

2.5.3 Preferences

2.5.4 Budworm-forest optimization model

2.5.5 Compressedpolicy analysis

2.5.6 Generatingpolicy alternatives

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IIASA STATUS REPORT

Ecology/EnvironmentProject

21 June 1974

EXTENDED OUTLINE

1. GENERAL REVIEW

1.1 BACKGROUND

- The alternateapproachesto innovation at IIASA:- global problems -- e.g., energy, food,population,resourcesand their interaction; global climatic change;Law of the Sea,

or

universal problems -- e.g., new universal conceptsandmethods for regional problems occurring in all countries.

- we have chosen to focus on the latter regional problems.

- Rationale: The past managementof ecological systems(e.g., agricultural, forest, fish, water) has been asuccessfulapplication of the trial-and-errorapproachof dealing with ignorance -- interventionsare incre-mental and if problems arise, then a revised incrementalaction can be made.- The result has been phenomenalincreasesin productionof food and fibre.- But now incrementalacts produce more extensiveandintensive consequences(witness the unexpectedresultsof some insecticidepest control experience; the scaleof unexpectedconsequencesof some large hydroelectricdevelopments;the possible scale of some man-inducedclimatic shifts)- And other consequencesare emerging from accumulationof past incrementaldecisions (witness resistancetoinsecticide; sudden pollution "episodes,"emergenceof"new" pest species)

- Presentremedial responsesto these "emergencies"are as ad hoc as their original cause (witness restrictionson DDT use)

- Conclusion: Trial-and-error seems to be an increasinglydangerousstrategy for deallng wlth the unknown. we needa new strategy for dealing with ignorance.

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1.2 STRATEGY

Goal: To develop, test, and transfer the interrelatedconceptsand techniquesneeded for a new scienceof ecosystemmanagement/engineering.

Aims:1. Conceptual:

to representand categorizethe resilience andstability behavior of ecological systems(how do such systemsabsorb the "unexpected"?What structuresresult in highly resilientsystems, i.e., ones capableof absorbing largeshocks?)

2. Methodological:

to link and apply the existing set of systemsanalytic techniques (modelling, mathematicalanalysis, policy analysis, decision theory)

to develop and apply new techniquesto copewith the unknown (qualitative modelling andanalysis, resilience indicators, generationof strategicalternates(from fail-safe tosafe-failure))

to develop communication ヲ ッ イ セ 。 エ ウ that can linkthe analyst, decision-maker,and constituents.

1.3 TACTICS

The above goals and aims are the long term necessitiesifIIASA is to make a significant and lasting contribution.But there are short term needs -- immediate problems,immediate demands.

Hence, a tactic is needed

- to assureshort term results within the frameworkof the long term objective,

- to maintain realism re sourcesof data, validation,testing and policy relevance,

- to maintain an applied and not abstractfocus,

- to assuregenerality and transferability of resultsof short term applied subprojects.

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Figure 1: Matrix Organizationof Ecology and EnvironmentProject,

showing the interrelationshipbetween appliedproblems and the fundamentalconceptualandmethodologicalareas.

Conceptual MethodologicalAreas

AppliedBehavior of

Areas ecol. systems Indicators Standards Methodology

SingleSpeciesManage- iment

Eco-systemHanage-ment

IEn-viron-mentalManage-ment

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The solution is a matrix ッ イ ァ 。 ョ ゥ コ 。 エ セ ッ ョ (Figure 1) whichrelates applied problems with fundamental issues,so that each applied problem Cdn contribute to thefundamental issuesand still provide a specific casestudy of linking ecology/economics,modelling, policyanalysis, and decision theory.

- セ。」ィ case study must have the following ingredients:

(1) A regional problem of:

single speciesmanagement:pest, disease,fisc, wildlifeecosystemmanagement:multiple land and resourceuse in a

region (hydroelectric, fisheries,hunting, mining, forestry,tourism)

environmentalmanagement:industrial pollution

(2) Good data -- both extensive and intensive

(3) Universal, Le., sharedby a numb·'!: of nations

(4) Client(s) with managementexperienceand interest

(5) Intersectsthe interestsof at least one other IIASAproiect.

1.4 TASKS CHOSEN IN THE FIRST YEAR

(the ones starredare selectedfor detailed discussionin our status report)

FUNDAMENTAL

(1) Resilience and Stability Behavior of ResourceSystems

*-- theore .cal analysesof multi-equilibria・ セ ッ ャ ッ ァ セ 」 。 ャ models,

retrospectivestudies demonstratingresponsetostressof ecological, anthropological,andresourcesystems,

measuresof resilience (ecological "Reynolds"numbers)

a framework for generatingresilience indicators.

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(2)* Environmental Standardsand Management forResilient Systems

APPLICATION

(1) Modelling and Simulation for EnvironmentalImpact Assessment(with SCOPE, UNEP)

(2) Developmentand Use of Ecological Modules forResourceDevelopmentSimulation ("A ModuleLibrary" )

CASE STUDIES

(1)* Regional EcosystemManagement: A Case Study ofForest and Pest Mangement (with CanadaDepartmentof the Environment)

(2) Regional EcosystemAnalysis and Policy Options:A Case Study of Human Impact on High Mountain Areas(with MAB)

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2. A CASE STUDY OF ECOSYSTEM MANAGEMENT

2.1 THE BUOWORM PROBLEM, THE SETTING, THE GOAL

Universality

- the budworm-pestcomplex is a classic exampleof pest managementwithin an ecosystem,whetherthe pest is one of agricultural or forest crops

- budworm speciespresentsignificant economicproblems throughout the whole of the north-easternpart of North America (Fig. 2), thePacific region, the U.S.S.R., forested regionsof Europe (e.g. Poland) and Japan

Data:

a group of 25 entomologists,foresters, economistshave been eXhaustively studying this problem inCanada for the past 30 years - the first sig-nificant example of interdisciplinary researchin ecology

the best of sampling proceduresand statisticalanalysis; detailed understandingof many causativelinks

extensiveand intensive validation data: a14,310 sq. mile area (approximately the size ofthe Republic of Moldavia (USSR) or of theNether1ands)wasdivided into 265 sUbregionseach of 54 sq. miles; key variables (pestdensities, forest condition, harvestingandspraying activity) were measuredin each sub-region, every year for the past 30 years.

Clients and Collaborators:

Scientific: CanadaDept. of the Environmentresearchteam; Institute of ResourceEco1ogy,Universityof British Columbiamodelling team.

Managementand Policy: CanadaDept. of the En-vironment Policy Branch; Provinceof New Brunswick, Forest Industry.

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Figure 2: Map of EasternNorth Americashowing the area of spruce bud\'/orrn infestationssince 1909.

ATLANTIC

OCEAN

I-..lI

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Interest for Other IIASA Projects

Methodology - provides a test bed for

a) developing optimization techniquesformore complex systems

b) interfacing utility theory with a complexsimulation model

c) developing compressedpolicy analytictechniquesfor more complex systems.

Conclusion: An admirable case study for demonstratingthe way to combIne the best of ecology/economics,modelling, poltcy analysis and decision theory.

2.2. BOUNDING THE PROBLEM

- It is essentialto bound the problem in space,time and key speciesand still retain the keypropertiesof behavior and the key needs formanagement.

Time:

The pattern in time has been traced back to1770 - typical pattern in Fig. 3

Le.

- 34-72 years periodicity of outbreaks- betweenoutbreaksthe pest is extremely

rare

- outbreakdensities increaseby 2-3 ordersof magnitude

- outbreakslast 6-17 years.

Bounding time:

We need a (1) time horizon which can contain twooutbreaks,i.e. 150-200 years

(2) time resolution of one yearwith seasonalevents represented.

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The Pattern in Time

w 300セa::« 250-l

2: 200n:::o3= 150o::::>l1l 100LLoa:: 50wenセ 0z

34- 72 YEAR S 7-16YEARS

Pigure 3: Representativehistorical pattern of sprucebudworm outbreak. There have been four majoroutbreakssince 1770.

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Space:

- As in many pest species, the budwormdispersesover long distances:amodal distanceof 50 miles from onesite;

- therefore, it is essentialto have aminimum area at least twice that radius,i.e., 14,000 - 15,000 sq. miles;

- the area chosen is therefore a14,310 sq. mile area which containsmost of the CanadianProvince of NewBrunswick (Fig. 4).

Spatial Resolution:

Behavior of the system is highlyheterogeneousin space and in time(Fig. 5). Therefore, spatial dis-aggregationis essential.

All elementsof the systemare similarlyheterogeneous:

distribution of primary hostspecies; 「 。 ャ ウ 。 セ fir (Fig. 6),

- distribution of harvestingactivitiesis heterogeneous(Fig. 7),

- distribution of recreationalpotentialis heterogeneous(Fig. 8).

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Figure 4: Study area within the ProvAnce of New Brunswick usedin the current study. The hatchedarea includes theprimary forested regions of New Brunswick.

N

i

I • • I I ! I : I l-----lo 10 Zll 30 40 se foO 70 80 .0 I

SCALE IN MILES

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FIGURE Sa: THIS FIGURE SHOWS ATYPICAL OUTBREAK IN A SEQUENCE OF COMPUTER-DRAWN MAPS OF BUDWORM DENSITY AS GENERATED WITH THE SIMULA-TION MODEL.EACH SQUARE REPRESENTS ONE OF lHE 265 SITESTHE VERTI-CAL DIMENSION IS THE LOGARITHM OF BUDWORM EGG DENSITY FOR THATSIMULATED YEAR.IN THIS SEQUENCE NO SPRAYING OCCURS BUT LOGGINGFOLLOWS THE HISTORICAL PATTERN NOTE THE GROWTH. SPREAD.AND COLLAPSE DURING THE SIX YEARS SHOWN.

YEAR 2 4 6 8

I

セn

. . . . I

. セ|G

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FIGURE 5 b; FIGURES 5b AND 5c SHOW A LONGER SIMULATION SEQUENCE.THE OUTBREAK IN THE FIRST DECADE IS THE SAME AS THATOF FIGURE 5a.A SECOND OUTBREAK BEGINS IN THE FOURTHDECADE AND FOLLOWS A SIMILAR PATIERN.

NO SPRAYING

YEAR

YEAR

1

11

3

13

5

15

7

17

9

19

Iセ

WI

?<...-

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NO SPRAYING

FIGURE 5c

YEAR

YEAR

YEAR

40

45

50

41

46

51

42

47

52

43

48

53

44

49

54

I

+'I

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01

02-03

104

セ U06

l-07

08

09

10

11

12

I 13

セ T: QセI,-i 16

17!--I 18

19

20

21

22

23

24セ

i 25r---: 26

セ Wi 28L _

!"igure 6 ;

PROPORTION FIR

• >.65

•.56-.65

li!::iii!;:;!il::!i!:1 46- . 55

D .35-.45

D <.35

セ 。 ー of study area showing the initial 9roportion ofland in fir, the host tree speciesof the 「 オ 、 カ ャ ッ イ セ N

This complex spatial mosaic strongly influences thesystem dynamics.

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Figure 7: The logging intensity is also spatially hetero-geneous. This map shows the mileage from eachsite to the nearest?rocessingmill.

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

••o§o

DISTANCE

0-20 MILES

21-40 MILES

41- 60 MILES

61 -80 MILES

81 -100 MILES

>100 MILES,ORUNHARVESTABLE

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:i?ure 8: This map shows the spatial distrlbution of thepresent recreationpotential for each site. Currenlpreferencesstrano]" favor the areas セ ゥ エ ィ coastal orlake recreationopportunities.

PRESENT POTENTI

iセiitMtMiャャャゥャャ0203040506070809101112131415

I I 01I

I

k,セ: 02l-i 03

1-04

セZ07

I 08

r09I--I 10セI 11r-i 12r-セ Sセ Ti 15ヲMセI 16

lI'18

19

20

21

22

23

24

セ [28

•IID

HIGH

MODERATELY HIG

MODERATELY LO

VERY LOW

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These heterogeneitieshave emerged from thedynamic historic interplay between the forest andthe budworm as a consequenceof the dispersalpowersof the pest. The 50 mile modal probability ofdispersalsuggestsa minimum resolution of about1/5 - 1/10 that distance.

Rence the area is divided into 265 6x9 mile areas.(Fig. 9)

Species

An ecosystemof this extent has hundredsofthousandsof species.The understandingof the dynamics isso detailed, however, that the essentialbehaviorcan be capturedby the interrelation between 5 setsof species,each of which representthe key species(roles) that determine the major dynamics of theforest ecosystemand its resulting diversity, speciesmixture and structure.

The principal tree speciesare birch, spruceand balsam (Fig. 10);

in the absenceof budworm and its 。 ウ ウ ッ 」 ゥ 。 セ ・ 、

natural enemiesbalsam outcompetesspruce andbirch and so would tend to result in a mono-culture of low spatial diversity;

budworm shifts that competitive edge sincebalsam is most susceptible,spruce less soand birch not at all. Thus there is a dynamicrhythm with balsamhaving the advantagebetweenoutbreaksand spruce and birch during outbreaks- this producesa diverse speciesmix and greatspatial and temporal variability;

betweenoutbreaksthe budworm is rare but notextinct - its numbers are controlled by naturalenemies (insectivorousbirds, parasites) - butthe key characteristic of this control is thatthere is an upper thresholdof budworm ntmiliers,which, if exceeded,allows the budworm to "escape",i.e. there is a distinct but limited stabilityregion at low budworm densities;

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Figure 9:

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This figure shows the numbering and indexing systemfor the 265 subregions,or "sites," in the studyarea.

01

02

03

04

05

06

07

08

09

10

11

12-13

14

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2526

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+

r---} 2 3 4 5 6

7 8 9 10 11 12 13 14 15 I 1617 18 19 20 21 22 23 24 25 2f>

27 28 29 10 31 32 33 34 35 36

37 38 39 40 41 42 43 44 45 46

47 48 49 50 .51 52 53 54 55 56

57 58 59 60 61 62 63 64 65 66

67 68 69 70 71 72 73 74 75 76

77 78. 79 80 81 82 83 84 85 86

87 88 89 90 91 92 93 94 95 96

97 , 98 99 100 i 101 102 103 104 105 106

107 108 109 110 ' 111 112 113 114 115 116

117 118 119 120 121 122 123 1124 125 126

127 128 129 130 13i 132 133 1134 135 136

137 138 139 140 141 142 143 144 145 146

147 . 1481149 150 151 152 153 154 155 156

157 158 159 160 161 162 163 164 165 166

167 168 169 170 171 172 173 174 175 176

177 178 179 180 181 182 183 184 185 186

187 188 189 190 191 192 193 194 195 196

197 198 199 200 201 202 203 204 205 206

207 208 209 210 211 212 213 214 215 216

217 218 219 220 221 2Z2 223 224 225 226,

227 228 229 230 231 232 233 234 235 236

237 238 239 '240 241 242 243 244 245

246 247 248 249 250 251 252 253

254 255 256 257 25B 259 260

261 262 263 264 265

-i2 'セ

セセ_セB

9

10

11

12

13

If..

1516

17

18

Gセ2Qj

[セ22

23

24

25 I26

27

28

29

G H J K L M N 0 P Q R 1ST u

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Figure 10: The key roles or variables and their interrelations in the naturalecosystem. The principal tree species (birch, spruce and balsam fir)have a dynamic interaction of their own. This interaction is altered<bythe presenceof budworm which consumessome spruce but primarily balsam.The budworm is in turn affected by a complex of natural enemiesand therandom effects of weather.

81 RCH

SPRUCE

セセ

BALSAM

DWORM1I" ·NA TURA L

WEATHER

ENEMIES IIVoI

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- in a deterministicworld, the budworm wouldnever escape. But there is a stochasticdriving variable, weather, which can flipthe budworm out of this stability region.

Outbreakscannot occur unless the forest haspartially recoveredfrom the previous out-break (enough food, therefore). When thathappens, the budworrn then remains in controlby natural enemiesuntil the weather shiftsto years with warm dry summers. In thoseconditions, the larvae develop so rapidlythey reduce the period of vulnerability topredation and can achieve densitiesabovethe escapethreshold.

At that point, an outbreak is inevitableirrespectiveof weather.

Conclusion:

1. Time horizon 150 - 200 years

2. Time resolution 1 year with seasonalcausation

3. Spatial area 14,000+ sq. miles

4. Spatial resolution 265 5x9 mile subregions

5. Key variables to capture the behavior: ideally

three tree species,budworm, natural enemies,

and weather.

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How many state variables emerge from this boundingof the problem?

IDEAL NUMBER OF STATE VARIABLES

In one subregion 1

Birch 1

Spruce by age 30

Balsam by age 70

Budworm 1

Natural enemies 1

Weather 1)) retains memory

Tree stress 1)

Foliage new 1

Foliage old 1

Number of statevariablesper subregion 107

Total number of state variablesin all 265 subregions 107 x 265 28,355

Therefore, even this drastic simplificationgeneratesan impossible number of statevariables -- further simplification is necessary.

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SIMPLIFIED NUMBER OF STATE VARIABLES

THE GOAL: A Well TestedModel of the System for Tes-ting of Behavior and of Policy Alternates

(a} Full Simulation Model

Subregion

Balsam 25

Budworm 1

Weather 1

Foliage New 1

Foliage Old 1

29

Full Region

7,685

The test of the statevariables representedimplicitly rather than explicitly.

(b} Simplified Simulation Model

Subregion

Balsam 2

Budworm 1

Weather 1

Stress 1

5

Full Region

1,325

- Any further simplification destroys thebehavior in space and time, and eliminatesmanagementoptions.

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Conclusion:

(1) Spatial heterogeneityproducesthis

curse of dimensionality.

(2) Spatial heterogeneityis an essential

property here and in all ecological systems

managementproblems.

(3) Therefore, this representsa major

methodological issue.

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2.3 BUDWORM ECOSYSTEM MODEL

An early, first-cut simulation model of the spruce budwormjbalsam fir ecosystemdemonstratedthe feasibility of modelling thatsystemwith a high degree of realism (Stander, 1973). However,before that model could be used for seriousmanagementplanning,some major revisions and refinementswere required. Manyimportant featureswere only implicit in the first version andhad to become explicit before the model could be a proper vehiclefor policy analysis. In early 1973, the first iteration of amore precise and explicit model was designed (Jones, 1974).This document served as the basis for a workshop sponsoredbyEnvironmentCanadaheld in Fredericton,New Brunswick, inMay 1974. The refined model of that workshop became the basisfor the IIASA budworm project and is describedbriefly in thissection. Full documentationand detailed analysesof the bud-worm model will be preparedfor publication in a subsequentIIASA researchreport.

The general features of the natural budwormjforest system havebeen describedin previous sections. The model used here onlyincorporatesthe two major species-- spruce budworm and balsamfir. The normal life history events occurring in New Brunswickare illustrated in Figure 11. This figure shows the approximatetime for various life stagesthroughout the year. In reality,of course, there is some variation in the dates for each eventas well as some overlap between the various events among thetree and budworm populations. In the model, we take the sequenceof events to be that as shown in Figure 11. The budwormgenerationtime is one year, making that a convenient iterationtime for the model.

The basic structureof the model is ゥ セ ャ オ ウ エ イ 。 エ ・ 、 in Figure 12.For each of the 265 sites there is a budworm survival modeland a forest responsemodel which run in parallel. Thesemodels compute for each site the various effects of the bud-worm upon the forest and the forest upon the budworm. Thesecomputationsare repeatedfor all sites. Once each iteration,dispersaloccurs betweenall sites and the model advancesonetime step. The various possiblepolicies are arbitrarilydesignatedas budworm control policy or forest managementpolicy. These are distinguishedas to where the policy leversare attachedin the model algorithms.

The fine structure of the budworm and forest models isillustrated in Figure 13. The yearly sequenceof computationfor the forest is shown as the inner cycle and that for thebudworm as the outer cycle. The format of Figure 13 is meantto illustrate the continuity of the process. There is no oneunique starting point in this system, but for purposesof modelconstruction, and comparisonwith field data, the simulation

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model starts its yearly iteration in the fall, i.e., with theinitial egg density for each site. The computationalse-quence is basedon the conceptof survivals. The functionswhich relate the survival from one stage to another appearin the small circles of the budworm cycle. Weather, of course,affects all stagesof the budworm and many aspectsof forestgrowth. However, it has been determinedby field experimentthat 86% of the variance in the total generationsurvival canbe explained by the variation in large larval survival (SL).It is at this stage that weather has its most pronouncedeffect.Milder climate affects survival by shortening the developmenttime and thus reducing parasiteand predator attack. Warm-dry weather at this time of year promotes survival whilecool-damp weather retards it. It is at this point that weather,and thereby stochasticvariation, enters the model.

The propensity to dispersefrom one site to another increaseswhen conditions on the native site deteriorate. Additionally,successfulegg laying in a new home site dependsupon thelocal conditions there. The budworm can dispersefor longdistances; some reports indicate over 100 miles. Theprobability function used in this model has a maximum distanceof 75 miles and an averagedistanceof approximately 50 miles.

There is a separatebut equivalent forest responsemodel foreach of the 265 sites. On each site the proportion of landin fir is fixed. Trees on each site are subdivided into 25different age classesand a simple bookkeepingaLgorithmmaintains an updated inventory of the amount in each class.Mortality to balsam fir is consideredto be both "natural"and budworm induced. An empirical relationship is used totranslatethe amount of accumulatedstressfrom previous de-foliation to actual tree mortality. This is an age specificresponse. Forest acreageupon which the balsam fir have dledreverts back to the first age class.

Let us now refer again to Figure 13 and review the major budworm-fir interactions. At (a) we have the effect of branch surfacearea and foliage quantity upon the survival of small larvae.At (b) the large larvae remove foliage. The amount availableaffects the large larval survival and subsequentadultfecundity. At (c) the amount of forest available and thelevel of defoliation affect adult egg laying success.

The policy models are flexible, limited only by the imaginationof the model user. The essentialpolicy attachmentpoints canbe manipulated in any way desired. For instance, the policycan change the survival of the budworm at any stage to depictsuch things as spraying, introduction of parasitesand mani-pulation of the micro-climate. The age structure of theforest can be changedto depict logging or burning. The amount

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of forest cover on any site can be changedby clearing orcultivation of alternatespecies. The density of foliage ina stand could be reduced by thinning. Traditionally, thepolicies used in New Brunswick have been spraying and logging.Some spraying has been tried on adults but most has beendirected against large larvae. Spraying is employed at alevel to kill between 80 and 90% of the large larvae. Buteven at this high mortality level, they can still eat a con-siderableamount of foliage. Logging and other silva culturetactics have been used, but the reality of the situation isthat the logging capacity is too small to affect much of theprovince in any year.

Policies which are not in the traditional repertoire can, ofcourse, be included in the simulation model. All that we re-quire is some knowledge or estimation of the relationshipbetween the action proposedand its subsequenteffect on theelementsof the simulation model.

References

Jones, D.O., 1974. "Biology of the Budworm Model". IIASARM-74-3, IIASA,Laxenburg, Austria

Stander, J.M., 1973. "A Simulation Model of the SpruceBudworm and the Forest in New Brunswick". MS,Inst. Res. Ecol., University of British Columbia.

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15 August

1 September

1 May

1 June

15 July

25 July

1 August

- 28 -

CALENDAR OF EVENTS

Eggs hatch into instar I

First dispersal

Overwintering hibernaculaformed

Emergenceas instar II

Seconddispersal

Trees begin developmentof spring

foliage and flowers

Transformationto instar III

Developmentto instars IV

V

VI

Destructivedefoliation

Pupation

Adult moth emergence

Mating

Dispersal

Egg laying complete

Figure 11: Sequenceof life history events for the sprucebudworm and balsam fir forest in New Brunswick.

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BUDWORM BUDWORM FOREST FORESTCONTROL SURVIVAL RESPONSE MANAGEMENTPOLICY MODE L MODEL POLl CY

tor each tor eachsite site

DIS PER SAL

BETWEENSITE S

Figure 12: The basic model structure for the budworm/forestsimulation model. Budworm survival, forest responseand control policies are independentfor each of the265 sites. Once each year dispersaloccurs betweenthe sites and then the processis repeatedfor the nextsimulatedyear.

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Figure 13:

THE BUDWORM- FOREST CYCLE. The outer ringdepicts the budworm survival model. Each small circle representsasurvival function relating one stage to the next. A stochasticweather parameterenters through large larval survival, SL. The innerring depicts the forest growth and responsemodel. Aging and mortalityto trees as well as growth and defoliation of needlesoccur in thismodel. At (a), (b) and (c) are points of important model linkages(see text). Attachment points for control and managementpoliciesare not shown.

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2.3.1

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Stochasticmodel of the weather

1. Need for a Model of the Weather

a) temporal persistencetriggers outbreaks

b) degreeof spatial homogeneitydeterminesnature ofspreadand dispersal

c) clarify whether long runs are due to persistenceorto the fact that marginal probability of some weathersis high

d) if significant persistencecan be shown, what is thelength of the memory

e) use of 3 classesof weather

f) initial results using 100-year ウ ・ ア オ ・ ョ 」 セ

2. Various Models Used in the Study

a) trinomial distribution - independenttrials - use inprogramming solution

b) Markov matrix for stand model - modal and averagevalues versus end-to-end

c) synthesisusing raw data - lags, offsets in spaceand time, log transform - 1000 year production at9 sites.

3. Tests on the Data

a) turning point

b) runs

c) lag-l and lag-2 matrices.

4. Generationof Synthetic Sequences

a) basis for the technique in principal components

b) results of correlation analysis, showing positiveeffects within groups (heat and precipitation) andnegativeeffects across them

c) comparisonwith moments calculatedfrom 33-yearhistorical records is quite satisfactory

d) use of averagetrace seems justified.

KEY POINTS

The few simulation runs which have already been made,including those made with incorrect models of weather,

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show the important influence of weather patternsonsystem response. It therefore follows that a thoroughstudy of temporal and spatial characteristicsis warrantedif our long simulation runs are to generatevalid sta-tistical measuresof performance. The records availablein New Brunswick are not long enough to reach definiteconclusionsabout thesepatterns,but strongly suggest(negative) correlation structureswhich imply fluctuatingtime seriesand a consequentoutbreak frequency.

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Pigure 14:

-33-

Records from these nine weather gauge stationswereused to investigatethe statisticalpatternsofweather.

N

1

o 10 20 30 40 50 60 70 80 90 100

SCALE IN MILES

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2.4 MODEL ANALYSIS

2.4.1 The site model

Before an attempt was made to look at the entireregional simulation model, it was worthwhile to examine thebehavior of the budworm model for d single site. Additionally,the severaldifficulties with the IIASA computationalfacilities preventedthe ヲ セ ャ ャ simulation model's implemen-tation during the course of this project. Thus, the 。 カ 。 セ ャ 。 「 ャ ・

capacity limited us to the single site model. From the manypossible examples and scenarios,two are chosen for illustration.

The first simulates the behavior of a single site with noimmigration. That is, it is as if the site were an ゥ ウ ャ 。 セ 、

surroundedby an area with no potential hosts. The initialconditions assumedwere a mature forest with an average treeage of 50 years. A one hundred year synthetic weather trace\,as applied; no external policies were used. Becausethereare 28 statevariables included in the forest and budworm,it is impossible to depict accurately the state space forthis system. Instead, we resort to a pseudo-statevariablethe amount of foliage per acre. This variable ・ ク セ ゥ 「 ゥ エ ウ someof the propertieswe would セ ゥ ォ ・ in a true state variable.Figure 15 shows the time history of egg density plottedlogarithmically against ヲ o セ ャ 。 ァ ・ per acre. The initial con-dition is marked with the X. Note the two large swings witha maximum change in budworm of 5 orders of rnaqnltJde. Figure 16shows a time plot of the number of eggs (drlthmetic scale)and the amount of ヲ ッ ャ セ 。 ァ ・ per tree. As it happens in thisparticular simulation run, in year 71 the budworm level reachedsuch a high point that all the available foliage was removedand all the adults emigrated from the site, leaving none forthe following year.

As the budworm has not gone extinct in New Brunswick, thisexample shows the important effect of dispersal in the spatialmosaic of the problem. As is, this model servesas an セ ョ 、 ゥ ᆳ

cation of the initial outbreak on a single site before dis-persal becomesa dominant feature. Figure 17 is a phaseplot with the same initial conditions as the above example.But this time we allow ,11 the emigrating budworm to re-enterthe plot as if we had a large uniform forest. Additionally,we have placed a lower limit on the budworm population. Thislimit of 10-5 budworm per acre is equivalent to 1 budworm in500 sq. km. Note that the swings in this phase plot are muchwider and that the average length of time between outbreaksbecomes longer. Figure 18 shows the time plot for the variablesof the first example.

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Analysis of a single site model indicates that for mostpurposesthe model can be collapsed into 4 primary dimensions.First ゥ セ the level of budworm; this can be taken at any stage,but the most convenienthas turned out to be エ セ ・ density oflarge larvae. The secondprimary dimension is the total amountof new foliage (i.e., green needles) which appearsin thespring. The third dimension is the surface area of branchesper acre of forest; this effectively collapsesthe tree agestructure into a single quantity. Finally, the fourth primarydimension is the weather. The weather is taken to be one ofthree categoriesra'her than a continuousvariable. The useof these primary dimensionsmakes it possible to developウ ・ カ ・ イ セ セ qualitative measuresof system behavior. These areオ セ ウ 」 オ ウ ウ ・ 、 in subsequentsections.

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-36-

K M M M セ M M M M K M M K M M M M ヲ M M K M M K M M M M M ヲ M M M K M M M K M M M M M K o....:i

z0

セa::c:> 0-セ (V)

I

Z

0Z

x .-J

l.1J W0 0z a

0セN l.1J

a::u lLJ«....... r-l.1J -c:> (/')«-I0 セl.L a:::

0 aセ 3:

0:::>CD

N

bセ

";'"0セ

ooセ

Noセ

(")

oセ

+-_...--+ -+--_-+-__--+--+------'-_--4--+-...--+0(")0'0セ

-.toセ

AllS N30 993 セ h Z エ o m ッ ョ X

Figure 15

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2.0

I NO IN-MIGRATION I

1.5

セ 1.0

0.5 L N セ .../ II.I.···

FT I 3 8:'''''''''' \

: セ. .. .

.....

: .• ••• '0 •••••••••••

NE 11000

Iw-.JI

0.0 , I' I I r==" , I .- " I I I

o 20 40 60TIME ( YEARS)

BUDWORM SITE MODEL

80 100

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104\ I I I -+- ,'- I

Iwex>I

4.03.0

FULL IN-MIGRATION WITHLOWER LIMIT TO EGG DENSITY

1.0 2.0FOLIAGE / ACRE INDE X

BUDWORM SITE MODEL

103

10-3 II I IO0

I--L--I I I { Ii ,

> 102

t--cJ)

ZUJ 10

セ0

<!><!>UJ 0

0::03: 10-'0::::>m

10-2

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2.0

15

I FULL IN- MIGRAT 10 N WITHL_LOWER LIMIT TO EGG DENSITY

セ 10

FT / 3.8:.0' " . .... : . I

w\L>I

0.5

.... NE/1000..

1008020 40 60TIME (YEARS)

BUDWORM SITE MODEL

0.0' "i I , Ie", I I'" , Io

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2.4.2

-40-

Stalesof the system

The managementquestionsare ・ ウ ウ ・ ョ エ ャ 。 ャ セ ケ qualitative;the behavior of the system is essentiallydescribedby shifts betweenqualitative states.

Hence a major compressioncan be made by redefiningthe system into a small number of qualitativelydistinct states,each of which has a specificecological meaning and a specific set of appropriatemanagementactions.

The key criterion: the system is dominatedbythresholdswhich define distinct stability regionsbehavior betweenthresholdsis qualitatively thesame.

Examples:

Recruitment curves for budworm (i.e., populationchangebetween t + t+l vs. density), Figure 19.

Thus the three weather types can produce a numberof different thresholdswhich separateregions ofincreasingpopulation from those of decreasingpopulation.

The same phenomenonoccurs with follage, Figure 20.This simply illustrates thresholdsin one dimension.There are, in reality, four essentialdimensions:foliage, surface area covered by susceptibletrees,budworm, and weather -- and other thresholdsappearin these dimensions.

The result of carving up this four-dimensionalspaceis a potential 25 distinct statesdefined by allpossible combinationsof increaseand decreaseforfoliage, surfacearea, and budworm at each of thethree weather types. Figure 21.

But we may compress further since the dynamics ofthe system cluster these 25 statesinto distinctand unique groupings and each of these groupingsimplies specific levels of impact and specificintensitiesand kinds of managementactions. Fig.22.

Figure 16 provides an illustrative example of anapplication of these conditions in defining thestatesat one particular surface area.

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Conclusion:

The gualitative behavior of the system can be

representedby eight distinct stages. This, then,

makes it possible:

(1) to succinctly representthe dynamics as

transition and residenceprobabilities

among the states;

(2) to provide an environment for compressed

policy analysis outside the simulation

model and interacting with the model only

as a check. (See section 2.5.5)

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FLgure 19a: necruitment 」 オ イ カ セ for egg density in oneyear 。 ァ 。 ゥ セ ウ エ egg density in the previousyear セ ッ イ エ N セ G イ ・ B L ··/eatl'er classes.

oolO

oo-.j'

wwOCIr-

OC0LL セ

W> (f)0::: LJ..J:::::> CLU >-1-- rZW 0:::2: wr-- I:::> I-0:: «U WUJ 3:0::

2:0::03:0:::>CO

00lO

ooNセ

0 z\ 0

0

\\ ......

00

Wex:>L

0 セ

0 «lO

>-セ

If)

Z0 W0 0-.j'

L0:::0

0 :;0セ N 0

::>CD

0

0 0 0 0 0 0 0 00 0 0 0 0 0 0セ N 0 ex:> lO -.j' N

(l+lN) ,l+L S セ 11 1"V Al1SN30 セ c Z ャ o m o ョ X

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-43- 00\I')

Fig1U'!f ±lb: Ratio of larval density in one year to thatin the previous year for various levels ofbranch surface area. (Also 1tc, 19d)

"-e{

UJa::

0.c 0セ

If) UJU

=> «0 セ

U-a::- ::J :::>

0::: セ(f)

<{ X a x> e:! UJ «

セ Nセ

II « 0 2a:: -J V') 0

0 W < ("')

(,9 :2: « >-u.. e:! a:: If) t-o-l Z U1

0::: 0 1\ 1\ 20 LL If) wI- If) Cl

U<{ If)u..

<{ 00

I- l1J N

Z a::l1J <{セ

I-l1J-

=> U 0

0.:: 0<{ 0U u.. (,9

0l1J 0.:: II 0

0.:: 0:: 0 セ

=> W セ

If) I 1\

::E l-e:!a:: W セ

0 セ ci

セII

(f)

0=>m 0

0 8 8 00 0<D -.i N ci

( IN/l+lN) c ゥ P Q j G エ セ IN3WllnCiJ3Ci WCiOMOnS

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BUDWORM RECRUITMENT FACTOR FOR VARIOUSSURFACE AREAS (S)

WEATHER = OK FOLlAGE= MAXIMUM

.....z...........

+.....z-0::0I--

"'lセ

...- セ

"lセ I--1"\• Z0- W

"" セ0

I---::J0::UW0::

セ0::0セ0::JCO

300

2.00

1.00

-_.--._._._._ .._.__.. _._.-_.

5= 02

$,= NO'RMALIZED SURFACE

AREA =( SA I SAMAX )

I......I

0.00 , I I : I I I I I I I

o 50 100 150

INITIAL BUDWORM DENSITY (Nt)

200 250

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BUDWORM RECRUITMENT FACTOR FOR VARIOUSSURFACE AREAS (S )

S =NORMALIZED SURFACE A RE A == ( SA I SAMAX )

,....,1.50.....

z.......

.....+-z

a::oI-

セ 1.00Ii.

I-ZWセI-

::Ja::uwa:: 0.50

セa::oセo::::>al

WEATHER = POOR FOLIAGE= MAXIMUM

Iセ

VII

250200150100500.00 I I I I I. I I I I I I

oINITIAL b u d w o r セ ⦅ d e n s i t y (N. )

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-46-

Figure 20: The recruitment factor for foliage forvarious levels of budworm expressed astheir defoliation rate D.

ooIf')

V> 0

:::> 0-.i

0-0:::<{>0::

0 L0 cr

0 0LL セ q -0 t- M l-

V> :::J u LI-0:: W lD W

LL0 I- 0 LL

Z wI- « wC) 0:: 1fJ セ

« w w «U <t'1lLL z <t --lLL ww 00 cr crcr:::J <tu 1..L

I- 1fJ W 00

Z I- 0

« N --l

W W If') «w ....セ -I cr 11 l-t-

:>

I- 0 W t- Z

- -'....JI.L OJ

:::> «lLJ

(J) t-

o:: cr cr0

w 0U > LwlLJ cr

00:: 0

w ....セ

Wt-

セW :>-' t-III« In ....J

<tcr t--I w cr

> 00 w

cr セ

LL cr 00c::i

0 0 0 0If') 0 If') 0

0 ci

( L+lL:l/ '1.::1) セoャj|Q]Q ャnSセQiョセISセ 39\1110=1

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POTENTIAL STATES OF THE BUDWORM SYSTEM

Foliage Surfacearea Larvae Weather

1 + 12 + 23 + 34 + 15 + 26 + 37 18 29 3

10 + + 111 + + 212 + + 313 + 114 + 215 + 316 + + + 117 + + + 218 + + + 319 + 120 + 221 + 322 + + + 123 + + + 224 + + + 325 ? ? ? ?

F < 0.90 + .0074 * L

Figure 21: The potential 25 distinct statesdefined byall possiblecombinationsof increaseanddecreasefor foliage, surfacearea, and bud-worm at each of the three weather types.State 25 representsirreversible tree mortality.

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QUALITATIVE STATES OF THE SYSTEM

Conditions

No. Super state Foliage Surface Larvaearea

Sl Endemic +,0 +,0 -,0 if o.k. or poorweather

+ if good weather

S2 Threat +,0 +,0 -,0 if poor weather+ if o.k. or good

weather

S3 Outbreak 1 +,0 +,n + all weather

II

S4 Outbreak 2 - +,0 +,- or 0iI S5 Outbreak 3 - - +,- or 0,,

S6 Postoutbreak1 +,0 - -,0 if poor or o.k.weather

+ if good weather

S7 Postoutbreak2 +,0 +,0 -,0 all weather

S8 Irreversible Foliage < Irreversible mortalltytree mortality threshold

+ Increase

Decrease

o No change

Figure 22: The 25 statescluster into 8 distinct and uniquegroupings. Each of these groupings implies specificlevels of impact and specific intensitiesand kindsof managementactions.

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FIGURE 23: AN ILLUSTRATIVE EXAMPLE OF THE CONDITIONS THAT DEFINE THE 8QUALITATIVE STATES FOR ONE PARTICULAR SURFACE AREA AND WEATHER.

3.8 -.--- ., A:IIlJ f'"N:J 1'TCtO.J 1<C1 7""""LJ 74:l'f4if I I I 1 I I I i I I I Iii I i I I ... - Iii II i

I

'""'"I

BUDWORM ISOCLINE (POOR WEATH )

FOLIAGE ISOCLINE

BRANCH AND TREE MORTALITYTHRESHOLDS

SURFACE AREA = 0.6

S N P セ ...

3.5

1.0

0.5

t= 2.0LL

UJC)<{セ 1.5oLL

2.5

I

50 100LARVAL DENSITY (N)-

200 300 400 5

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2.4.3

-50-

Validation of multi-site model

Validation data available

egg densities, foliage condition, spraying, andharvestingacts in each of 265 regions for eachof 30 years.

validation is necessaryof the pattern in spaceand time, and of the numerical ranges

NOT site and year specific numerical agreement

- Thus choice of statistics:

egg densities, tree hazard3 moments and why.

Difficulties in Validation

- dispersalthe major unknowntesting alternatehypotheses

- size of model

needs for timing

- limitations of computer -- PDP o.k. when linkedwith big machine.

Preliminary Example of PatternPredictedand Relation toReal World. (Figures 24, 25.)

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HISTORICAL DATA

Egden Hazard

MU SO MU SO SKEW KURT

1945 0.300 0.000

1946 2.550 0.000

1947 15.000 0.000

1948 75.000 0.000

1949 150.000 0.000 1.792 2.706 9.705 10.705

1950 499.385 400.413 2.766 4.625 5.058 6.111

1951 1270.816 955.167 3.955 5.576 1.935 3.027

1952 1062.825 948.155 4.181 5.603 1. 296 2.417

1953 572.811 522.321 2.796 4.542 2.689 4.160

1954 462.911 310.688 7.770 5.790 0.028 1.540

1955 564.549 420.328 6.487 5.100 0.013 1. 527

1956 579.530 1052.807 8.309 6.054 0.096 1.276

1957 144.767 187.055 8.694 4.449 0.033 2.088

1958 41.906 69.856 2.509 4.056 0.805 2.765

1959 168.964 168.704 2.151 3.608 2.666 4.185

1960 218.543 221.842 3.577 4.375 2.027 3.652

1961 137.283 136.193 3.562 3.821 0.788 1.994

1962 142.343 243.681 3.351 4.278 0.860 2.402

1963 320.461 1474.181 2.762 4.040 1.411 2.757

1964 180.500 203.408 2.321 3.252 2.528 3.863

1965 219.729 272.177 3.887 4.249 0.723 1.938

1966 156.441 145.215 3.672 4.062 0.512 1.659

1967 171.774 134.370 2.223 3.434 2.043 3.416

1968 362.551 361.551 2.811 3.998 1.876 3.226

1969 645.495 493.483 6.845 4.840 0.043 1.477

1970 809.866 576.693 5.574 4.037 0.189 2.073

1971 709.960 454.841 7.947 4.445 0.143 2.031

1972 317.036 232.043 9.528 3.919 0.750 3.398

1973 716.558 458.090 8.951 3.683 0.000 2.048

Figure 24: Historical trend of statisticalmeasuresforegg density and hazard for the study area.

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FIGURE 25a:COMPUTER SIMULATION MAPS OF BUDWORM EGG DENSITYFOR THREE SCENARIOS. (1) NO SPRAYING ;(2) SPRAYINGAT INTENSITY 2; (3) SPRAYING AT INTENSITY 6.

YEAR 1 3 5 7 9

NOSPRAY

SPRAY

= 2

SPRAY= 6

I

U'lIV

I

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a>,....

"-,....

..0L!)

NI!),....

('t),....

,....,....

0:: >- >-« « «wO::C\I 0::<0>- tl.1I tl.1Ien en

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2.5 POLICY ANALYSIS

2.5.1 Introduction

(A) The oroblem: How do we use our understanding

of the ecosystemto evaluateand improve our managementof the

resource?

- the validated model as a source ofpotential standing of budworm-forestecosystembehaviors and its responseto managementoptions;

- the techniquesof systemsanalysis asways of manipulatingmodel options torealize that potential;

- the goal of policy analysis describedhere as the reconciliation of manage-ment feasibility (defined by the model)and social desirability of managedsystem behavior.

(B) The nature of policy analysis

- the point to be made here is that policyquestionsare design questions;

- a managementpolicy is a set of ruleswhich specifies the conditions underwhich various managementoptions willbe applied to the ecosystem;

- those rules thus determine the system'sbehavior in the same way as, say,feeding responsecurves of budworm larvae;

- by designingour managementrulesappropriately,we may influence the waythe managedsystem functions; i.e., wedesign its behavior;

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- this "appropriate" design of managementrules to achieve some desiredpatternof system behavior can only result froman analysis of our ecosystemmodel;policy is consequenceof, not a conditionto, that analysis.

(C) The processof policy design

the design of managementpolicy is seenas a process in which we seek to in-fluence the managedsystem behavior,bringing what is technically feasibleinto line with what is socially desirable;

- there are clearly many issuesat stakehere: a rigorous exploration of possiblemanagementalternatives; an estimation oftheir effects on the system behavior; thewhole intractableproblem of definingsocial goalsandpreferences;

- no single approachcan bring about aparticularly satisfactoryreconciliationof these contrastingdimensionsof thepolicy design problem, and it is onlythrough the judicious combination of avariety of techniquesand methodologiesthat we have been able to make incrementalprogress;

- the presentationswhich follow will dealwith a number of thesemethods in somedetail:

(1) Indicators -- ways of speakingabout and quantifyingsystemsbehavior (responseto policy) in a mannerwhich is meaningful to us, which relatesas directlyas possible to the implicit and explicit criteria weuse in our judgmentsof "social desirability."

(2) Preferences-- given that we can satisfactorilydescribesystemsbehavior with our indicators, itremains to develop techniqueswhich allow us toconsistently"rank" alternativebehaviors on asocial desirability scale.

(3) Optimization -- application of various mathematicalprogramming techniquesunder the assumptionthat youcan specify goals and wish to explore managementoptions which will realize the goals.

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(4) Simulation and CPA -- sort of the converseofoptimization in which you take certain managementpolicies as given and seek to trace their implica-tions for system behaviors.

(5) Generationof policies -- where to combine all ofthe above in various combinationsto yield a smallnumber of qualitatively different managementpoliciesfor considerationof the policy maker and societyin general.

(D) Other miscellaneousworries

- Recall that at the beginning of thissection we defined our overall concern asone of investigating セ ッ キ the detailedtechnical information and understandingconcernedin our model of the budwormsystem could be used to evaluateand im-prove our managementpolicies.

- In the sectionswhich follow, we treat theideal case in which the model is assumedto cover the entire field of relevancetothe managerandpolicy maker, and thepolicy maker is assumedto have an"appropriate" degreeof faith in the model.

- We note, however, without further commentfor the present, two areas in which theseassumptionsmay commonly and significantlybe violated:

(1) Credibility -- no matter how "valid" it may be, themodel -- and technical information in generalwill not be used in the managementand policy makingcontext unless it is credible to its intended user.Keeping information credible as it is processedthrough simulations, dynamic proqrams, and dimension-reducing transforms is an often セ ュ ー ッ ウ ウ ゥ 「 ャ ・ and alwaysdifficult task.

(2) Completeness-- no model is complete, as everyonehasremarked often enough. A problem hardly anyone hasdealt with is how this incompleteness can be explicitlytaken into account in the formulation of managementー ッ ャ ゥ セ ケ N Our indicator work touches briefly here, aswe try to provide easy points of contact between theuser'smental models of a wide range of concernsandour explicit model of one particular C8ncern. Theissue of "too much" specification, as raised byLindblom and his followers, remains untouched.

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(E) Summary

Policy analysis is the processof designingrules for the application of managementoptions. It combines a variety of method-ologies and techniquesto organize technicallyfeasible managementoptions in a way whichinduces the managedsystem to behave in adesiredmanner. As policies must be imple-mented within a broader institutional context,questionsof credibility and inclusivenessarecentral to any policy analysis effort.

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2.5.2

Goal:

Indicators

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(1) to develop a graded series of information displaysfrom very general and comprehensibleto verydetailed and diagnostic so that the decision makercan choose the appropriate level

(2) to design a specific set for one "decision maker"as an example.

Tactical, Primary Indicators

(1) Economic:

Profit of loggingCost of spraying

(2) Resource:

Potential merchantablewoodProportion harvested

(3) Recreational,Wildlife

Detectablebudworm damageTree mortalityObserved logging effectsRecreational/wildlifediversity

(4) Social

Unemployment (forest industry)

StrategicIndicators

(1) Known relationshipswith known form

EcosystemState Indicators

residenceprobabilities r) in 8 states- spatial variation of Pr- temporal variation of Pro

(2) Known relationshipswith unknown form

Persistenceof Forest SpeciesMix

- surrogate= life span of fir

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Micro Diversity

- surrogate= age diversity of fir

Macro Diversity

- surrogate= ecological patch size

Insecticide "side-effects"

- surrogates averagedosageper sprayedplotareal extent of sprayingduration of spraying

(3) Unknown relations, impacts, objectives

The effort to prepare the above list makes brutally clearhow much knowledge is missing from the available data and themodel. There will always be relationshipsleft out whoseexistencewe know but whose form we do not. There will, aswell, be missing relationshipswhose existencewe do not evensuspect. And what is true of these relationshipsis equallytrue of the overall objectives of the development. The societalobjectiveswhich seem soclearat the moment can dramaticallyshift, leaving society with a policy and a systemwhich cannotitself shift to meet these new needs. The growing demand forenvironmental impact assessmentproceduresis one clearsymptom of such a shift of objectives. An assessmentbasedsolely on the presumptionof sufficient knowledge can thereforelead to approval of a plan that could not be adaptedto absorbthe unexpected.

Few systems-- ecological, economic, and social -- are in astateof delicatebalance, poised precariously in some optimumstate. The ones that are do not last, for all systemsexperiencetraumas and shocks over their period of existence. The onesthat survive have explicitly been those that have been able toabsorb these changes. They have, therefore, an internal re-silience. Resilience, in this sense,determineshow mucharbitrary disturbance,both of rate and of intensity, a systemcan absorb before it suddenly shifts into a fundamentallydifferent behavior. A review of resilience and stability canbe found in Holling, 1973.

In addition to the traditional indicators, it would thereforebe useful to have a categorywhich gave some senseof theresilienceof a plan -- of its capacity itself to absorb theunexpected. The key requirementof these resilience indicatorsis that they measurethe degree to which alternateoptions areforeclosed.

But how can these indicators be developed? There are threemutually exclusive classesof resilience indicators:

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(a) Resilience in environmentalcapital

At any point in time, there exists a reservecapitalof resourcesthat are drawn upon for any policy. This reservecapital has a certain existing quantity and quality. Therefore,those indicators which measurethe amount and kind of resourcesused should also be given a resiliencedimension, so that theremaining environmentalcapital can be measured. It is thisremaining capital inventory that buffers the developmentincase of the appearanceof unexpectedand unhappy consequences.Modified developmentsor new developmentsof the future drawfrom this reserve. Example: a recreationalland developmentwill produce certain effects which can be evaluatedby tra-ditional recreationalsocial indicators. But the land usedis drawn from a reserveof a certain size and with certainintrinsic qualitites for absorbingrecreation. These quantitiesand qualities of the remaining reserveshould be measuredbyadding a resiliencedimension to existing recreationalindicators.

(b) Resiliencewith respectto systemsboundaries

Social-ecologicalsystemsare dynamic systems inwhich the structureand functional interrelationsthemselvesestablishintrinsic boundariesor thresholdsof stability.Phosphatesadded to an aquatic ecosystemare incorporatedintoexisting biogeochemicalcycles. But there is a limit to theamount that can be added without destroying the integrity of thecycle. Therefore, a measureof an indicator that expressedthe absoluteamount of phosphateadded should be matchedwithone that expressedthe total amount in relation to the systemboundary for phosphate. In some cases, the model itself canbe used to identify some of these thresholds. In other cases,with less knowledge, the boundary would be expressedas a guessa standardor threshold similar to public health standards.Again, the task will be first to identify those social, physical,and ecological variableswhich are statevariables for thesystem,and second, to add a resiliencedimension which measuresthe amount in relation to the system boundary or standard.

(c) Resilienceof benefits

Major emphasisis now placed on indicators whichexplicitly measurethe net economic and social benefits of adevelopment. But there is a resilience counterpartto theseas well. If the developmentplan or policies fail unexpectedly,or if social objectives shift to require their removal, therewill be a cost attachedto this failure. A model provides an

, explicit way to measurecost of failure. After a simulationhas run long enough with a specific policy to generatea con-sistentbehavior of the indicators, sensitiveelementsof thatpolicy can be arbitrarily removed, and the same cost and bene-fit indicators can reflect the consequencesof this policy

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failure. Example: regional insect pest control projects canhave a number of forms. One might be intensive and extensiveinsecticide spraying. Another might mix cultural practiceswith limited and controlled application of insecticideatcritical times or in critical places. Both policies, duringtheir implementation,might achieve similar benefits, butsudden removal of insecticide could occur as result of risingcosts or government regulation. In the first policy, suchremoval could produce intensive outbreakscovering largeareas,with disastrouseffects on benefits. In the secondpolicy, the loss of benefits could be minor. The impact ofpolicy failure can thereforebe expressedby this loss ofbenefits. These indicators measurenot the relative fail-safefeatures of different plans, but the degree of safe-failureof those plans.

Resilience Indicators:

(1) EnvironmentalCapital

unutilized resourceunutilized recreationalareas

(2) UnexpectedStates

distanceto irretrievable tree deathdistanceto budworm extinction

(3) Cost of Failure

cost of selective removal of spraying actscost of removal of harvestingacts.

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2.5.3 Preferences

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1. What do we want out of the forest?

There are two aims of a decision analysis -- the secondis the more formal aim, the first the more realistic.

(a) to help the decision maker understandhisown preferences,perhapsclearing upinconsistenciesand misconceptions;

(b) to define a criterion by which forestpolicies may be evaluated.

What are the factors which affect preferences?(Fig. 26)

It has become clear that the aim is to maintain a highlevel of income from the logging industry whilst at thesame time keeping the employment level high and pre-serving (or improving) the recreationalvalue of theforest.

Hence the value of the forest may be determinedfromthe history

t=O,1 , 2 , 3 , 4 ,•..

profit in year t

level of unemployment in year t

recreationalvalue of forest in year t.

2. How does the theory work in practice?

It is not appropriateto discuss the theoreticalpossibilities here. The following relatesbrieflywhat happened,and predicts what will happen as thework proceeds.

The decision maker first evaluateda recreationalindex.(Figs. 27,28)

It was establishedthat preferencesfor the recreationaspectswere independentof the profit and unemploymentlevels. ({Rt}and ({p t }, {Uti) are mutually utility

independent . )

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Thus one subproblemis to find a utility function for thetime series

The factors involved here are the mean level, maximumlevel, minimum level, variance, variability, and so on.It seems to be difficult to evaluatea time serieswhere interdependencyis very strong, particularlywhen the idea of time preference (discounting) isintroduced. A guess is that the utility functionwill be something such as

tL a u (Rt Rt - l )t

for some simpler function u.

Similarly for the profit and unemployment.

3. Where did the simulation model come in?

It is possible to establishtrade-offs between P, U, Rjust by inventing figures out of one's head. However,it is of the utmost importance to keep the decisionmaker's feet firmly on the ground. He must be ableto see how his decisionsaffect the real world (thesimulation model) .

For example, it can be easy to discard or overemphasizethe recreationalaspects,or to forget that a decisionwhich leads to lossesand unemploymentnow in favor ofhigh gains later will be hard to implement.

By getting results from the model, it may be possible tosee that simplifying assumptionsare in order (unemploy-ment is always zero in any sensiblepolicy for example),and to check the accuracyof the utility function forvalues that it will meet most often.

The drawback of a simulation model is that it can makethe decision analysisharder. With a lack of informationconcerninghow histories develop, it is much easier forthe decision maker to make simplifying assumptions.

Increasedaccuracyshould not be a drawback, but it isin terms of finding an optimal policy.

The more complex the objective function, the more difficultwill be the optimization.

There is a procedural trade-off between accuracy in theobjective and the optimization.

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4. Conclusions

A decision analysis can be performedwith the modest aimof merely clarifying the decision maker's attitude towardsthe subject matter,andfor a complex problem a real worldmodel is essentialfor testing a decision maker'sformal preferencesagainst his intuitive feeling.

If the aim of the decision analysis is to find an optimalpolicy by an optimization procedure, it may be thatoversophisticationleads to an intractableproblem.Approximation has to come in somewhere.

An analysis of such a problem should include a sensitivityanalysis of the optimal policy to the objective function.(It may be that any policy keeping a good profit over50 years ensuresfull employment and suitable recreation.)

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FIGURE 26

MANAGEMENT

SIMULATIONMODEL

OPTIMIZATION

FORESTCONDITION

ECONOMICS EMPLOYMENT SOCIAL

PROFIT

PREFERE1'CES1-------------'

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DEFOLIATION

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FIGURE 27

LOGGINGPROPORTIONOLD TREES DIVERSITY

DAMAGE STAND COMPOSITION

ACCESSIBILITYRECREATIONALPOTENTIAL

RECREATIONALVALUE

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DEFOLIATION

I GOOD

o

LOGGING

GOODI Io 7

15

-67-

FIGU RE 28

MEDIUM

MEDIUMI

35

45

BAD

BAD

100

100

GOOD MEDIUM BAD

GOOD

MEDIUM

BAD

GOOD MEDIUM BAD

MEDIUM MEDIUM BAD

BAD BAD BAD

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2.5.4 Budworm-forestoptimization model

1. The Problem

The simulation model describedearlier in this reportrepresentsthe behavior of the budworm-forestsystem on anygiven site and in any given year through a relatively smallnumber of variables and nonlinear relations. The statevariables are the forest compositionvariables, the eggdensity, and an index comprising the effects of budwormattacks on the forest in the past. Complicationsarisemainly due to the dispersionof adult budworm moths,which by laying eggs on sites different from those oftheir origin provide the only link betweendifferent sites.If it were not for this, each site would be independentof the others and could- be optimized independently.

Let N be the number of sites under consideration(N = 265)and N: the number of time periods オ セ 、 ・ イ considerati8n(around 100). When consideringthe whole area andincluding contaminationsdue to dispersalof adult bud-worm moths, the total number of variables and relationsis N x N x (number of variables (and relations) per siteand timesperiod) and the problem becomesuntractableforgeneralnonlinear programmingmethods. Also a morespecializeddynamic programming approachgets into troubledue to the large number of statevariables (N x (mll--nber ofstatevariables in one site). s

tt

2. Simplifying Assumptions

If we representthe relations of a model by a box, theinformation neededas arrows pointing into the box, andthe information calculatedby the model as outgoingarrows, we can representthe processon any given site

- and time period t by

where superscriptt refers to the time period and

t t t tX = (Xl I X 2' ••• , セ ) is thetvectorof forest composition,

i.e. Xi area covered by trees of agei in tIme period t. N number oftree age classesin forest

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It index condensingpast budworm attack history

Et egg density (egg/acre)

wt weather type

t t t t tP (Pl, P2' ... , PN) logging vector, i.e. Pi acres of age

group i trees logged in period t

spraying policy on larvae

spraying policy on adults

eggs laid on other sites by moths originatingfrom the site

eggs laid by moths from other sites who dispersedinto site under consideration.

With this notation we can then representthe processinthe whole area by the information flow diagram in Figure29,where the subscriptsrefer to エ セ ・ site. In Figure29 only2 sites are shown explicitly. All the others interact throughthe dispersionmodel (OM) and are taken collectively intoaccount by the arrows E from other sites, and EIN to othersites. 0

Observe from Figure29 that if on any given site, say site j,we have a good ・ ウ エ ゥ ュ 。 セ ・ of ErN. for all t we can solve sitej independentlyand forget ] about the interactions.

On the heuristics that an optimal policy would keep thebudworm under control in the whole area, and hence theproportion of adults dispersedwould be relatively small andwould not vary wildly from one site to another,it isreasonableto expect that

Et

- EiNiI

°i

is small with respect to Ef and that the error introducedbyassuming

is negligible.

a ウ ウ セ ー エ ゥ ッ ョ 1: For an optimal policy Et

i 1, ... ,265andt=1,... ,Nt

• °i

tEIN for alli

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It is important to point out that the validity of thisassumptioncan be checked a posteriori by testing theoptimal policies obtained from the site optimization onthe simulation model.

The site model has a dynamic structureand could be solved byapplying a dynamic ー イ ッ ァ イ セ ョ ュ ゥ ョ ァ technique. There areN + 1 statevariables, where N is the number of age classesin the forest (Et , It and N-l of the componentsofXt = (Xi, X5"'" セ I L since one of them is dependentonthe others セ ィ イ ッ オ ァ ィ

Nt

i=lx セセ

constant forest area. To successfully

apply the dynamic programming technique it is important tohave a small number of statevariables, say no more than6 or 8. This requires a high degreeof aggregationin theforest model which necessarilydistorts somewhat theeconomics. Instead an alternativeapproachcan be pursuedwhich does not require aggregatingthe forest age classesand which allows the computationalrequirementsto be re-duced considerably. The details of this approachwill becontainedin the final report and in the presentstatusreport only the simplifying assumptionsmade will bestated:

Assumption 2: The value of the forest is the sum of thevalue of its trees, i.e.

V(X t , Et , It) =NE

i=lX t. (t tp. E, I )セ セ

where V(X t , Et , It) ゥ s エ エ ィ ・ エ カ 。 ャ セ ・ of the forest when itsstate is defined by (X , E , I ) and

t tPiCE , I )

Assumption 3:

value of an acrr of i year old trees whenegg density = E and foliage index = It.

ap. (E,I)セ

dE

ap. (E,I)セ

aI

< 0

<

i.e. the value of a tree is highest in the absenceof anybudworm effect and diminishes as the index on past history

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increasesor the egg density increases(becauseof po-tential damage in the future).

As was mentioned, the problem solution simplifies con-siderably when making these last two assumptions. Thissimplified method was programmedand run using data providedby the CanadianForest Service as to spraying costs andbenefits from the lumber industry.

3. Results

The results of the computer runs can be convenientlypresentedin form of policy tables, as in Figures30 and 31.There is one policy table for each age group and it tellswhat the optimal policy is on an area covered by trees ofage i, as a function of the values of the index I(F in Figures30 and 3]) and the egg density (E in Figures

30 Ind 31). Thus for an area coveredwith 51 ケ ・ セ イ old trees(see Figure 30), according to the values for f セ and ED ittells us to a) None, i.e. do nothing this year, b)Log orc) Spray. In this last case the computer also specifies thedosageand whether larvae or adults should be sprayed.

Such tables were generatedfor different assumptionsasto the selling price of one cubic unit (cunit)-of lumberand for differentvalues for the discount rate.

It turns out from the optimization that there is an optimalcutting age for undamagedtreesand that it is optimalto always log all trees this age and older, no matter whatthe contaminationeffect is or has been. This optimalcutting age is given in Figure 32as a function of the valueof a cubic unit of wood and in Figure 33 as a function ofthe interest rate.

Preliminary runs done in Vancouver using the above policiesin the simulation program seem to justify the simplifyingassumptionsmade and give a considerableimprovementovermanagementpolicies currently in use, as can be seen inFigure 34 which gives the fraction of bad recreationalsitesas a function of time for both policies over the nexthundred years as predictedby the simulation model (adefinition of bad recreationalsites is presentedinSection 2.5.3).

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I-..JIVI

pt+' st .., st .. ,I t· A-I I I I'I I ;! i I

st stIi A-I' I I

I It

pt st stj ii A,

, J

ptI

クセMLIlr- 1 •

eセM 1 !III:

pt"2 St..2 St-t2

_ x.t-:) ( ( X'-,

セMMャエKA L ---..'I.t"2, . ') ,

t + 1 ftGtセ t + So. 1--.1 i "';:t"2

MMM||eセMG [ZGZ|GBMMBGセGROエZWGo! / U: • \OIN;

t t t t t,---l tセ r: EIN _ E4 , ⦅セ ⦅セ __セ A ⦅ セ l セ

FRO "'1 7'M TO OTHER FROM' D!,., TO OTHER fOROM I cTNセセZN j"l0 U1HERCTH::R SiTES OTHER SI1ES Oll-iER L_ SiTES

SilES \ sm:s \ SiTES / \\ / \

, / \t t t+1 \ t .. , t"2 \ t"2lEE I セ \ - / - \-セ M Q '/ OJ \ :Nj _t I i:.D; \t:.H'; j "t+1 i ='0: t:.INj. t .. 2

セj Nセ \ Xj I l \ 1\] M M セ M j [ jr.t-1 \ 、セ '\. '-t+l \- I-. t " 2セ⦅セ ., II> I 'l • i> .I

E t- 1 t セ '"".t I t+ 1 セ b. ,=.t.. ; t.+ t. I. &o=t+:<:J r:.; I . セjG t 1:,.·lIT · --'1-I-r,-4

-+ j M M M M イ ョ セ ·,.'pt·1,..t+, d'" セ エ K R ウ エ K R 」 Z [ エ B R

. ..J. .,J 1-. _, _J I j A j J 'j Aj

Nセ \セ

!..lJl-

V>

----TIME PERIOD t TIME PERIOD t .. , TIME PERIOD t .. 2

FIGURE 29

Information flow diagram for budworm model

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FI GURE 30

PQLlCY TABLES FQR REPRESENTATIVE AGES

(PRICE = 55 $/cunit ; p =.05 )

AGE 113.8 ......-------....,

tNONE

AGE 413.8 NLNNMMMMMMMカNLNNLNNLNLセ

iNONE

8 19Eo - 8

0+-------1o IgEo -

0+-------4o

IgEo - 8

NONEt

AGE 513.8 ....------.,.,"l""'::""'llI'n

IgEe - 8

NONE

0+-------1o

t

AGE 213.8 M イ M M M M M M M M B N L N N N L N N L セ

AGE 31 AGE 61

19Ee ----+ 8

NONE

0+-------1o

t3.8 .,...-----".,...,..,.....

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FIGURE 31

o +- M M Q N T Z セ

o IgED - 8o+---------1

o Ig ED - 8

POLICY TABLES FOR AGES 42 - 47( PRICE = 55 $ J c un it ; 1=.05 l

AGE 42 AGE 453.8 3.8

t iFr NONE Fr NONE

AGE 433.8 -r-----..,.,....,....-:l"T"""I

tNONE

o +--------io IgED - 8

3.8

i

AGE 46

NONE

IgED - 8

AGE 443.8 MイMMMMMNNLNLNNNLNNNNNセ

iNONE

o+---------1o IgED _ 8

AGE 473.8 N N N N N N N M M M M M M イ セ .......

iNONE

oNー」AcZャcャゥャZZゥNNゥNセセセ

o IgE D _ a

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FIGURE 32: OPTIMAL CUTTING AGE VS SELLING PRICE

- I(.f) DISCOUNT FACTOR:: 5 %

a: 70<!W>--wl!)

<! 60 セ セI

-.><J1

l!)I

Zt-t-:::JU

-J 50<!セ-t-a...0

40 45 50

SELLING

55 60

1?RICE ( S/cunit )

65

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70l/)

a::«w>-

W<9 60«<9zI--I--:::>u 50..J«セ

I--0..o

FIGURE 33 :OPTIMAL CUTTING AGE VS. DISCOUNT FACTOR

SELLING PRICE =55. $ /cuntt

-...I

'"I

D 2 3. 456

DISCOUNT

7 8

FAC TOR

9 10

( DJo )

11 12 13

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I-.J-.JI

セ セ

- ....rL........-r"'\ ...rl.l.J セ セ

..r-t セ--0--0--0セセ -0-

X--X--X USING CURRENT POLICY

0--0---0 USING POLICY FROM OPTIMIZATION PROGRAM

.....

u.. 0.4ozor-セ 0.2a::LL

Vl<UJa::< 0.6

r

1.0I. 1".-,-------------1t

'\ I \ x..... ,..x_...., X I \ / .....x__ ><! ク⦅セ

0.8 , , セ '\ / x- -x- -I \ LLセ⦅Mク, x--x-, , ,

, \ I

I " II \ 4" 'x セ ,I' ,x, ' /, xI x--x:,

Iセク

.o<CD

10090807060..40 50YEAR

3020100.0 I I I , I I I 1 I , I I I I I I I I I I I

o

FIGURE 34:FRACTION OF "BAD" AREAS VS. YEAR OF SIMULATION

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2.5.5 Compressedpolicy analysis

1. Justification

(al The Winkler-Dantzig procedure,which emphasizesdynamic programming, was necessitatedbecauseof the non-linearity of the biological system. Each forest sub-regionis characterizedby a manageablenumber of state variables,but if the forest is disaggregatedinto even a few sub-regions,the total number of system variables is enormous. Linearprogramming cannot be used, so we compromiseby running anaggregatedmodel. This gives a global optimum in a mathe-matical sense,but this optimum is highly local in a spatialsense.

(bl One procedure is to impose this global policyon the simulation program and then systematicallyto monitorthe outputs and to make appropriateadjustments. But eventhis is very time-consuming-- a 200-year simulation runrequires nine hours on the PDP 11/45. So we seek comple-mentary descriptionsof the forest ecosystemwhichaccommodateinteractive algorithms for policy generationandtesting.

2. Simple approaches

(al Regressionanalysis - estimate larvaldensity by the first order autoregressivefunction

a i + b.Lt .1 ,1

with values Lt taken from a 30,OOO-yearrun of the stand model.

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Consider linkages to representthe epidemiology

Calculation of quasi-steadystatevalues.These are used to re-calculatetransfer and

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Migration No Migration

i ni a. b. Pi a. b. Pi1 1 1 1

1 7510 -1.85 .111 .240 -5.43 .191 .429 linear

2 14807 -3.41 .224 .232 -11.6 .414 .435 linear

3 7682 -4.70 .377 .252 -14.9 .576 .409 linear

The use of bivariate linear regressionfunctions obviouslyshould not be promoted, although estimatorsof higher degreemight be more appropriate. A few trial fits show that quad-ratic functions are not significantly better.

(b) Autocorrelationanalysis

Migration and No Migration peak near 50, buttheir characteristicssupport different underlying processes.The correlogramis shown as Figure 35.

(c) Single stand Markov analysis

As a prelude to more relevant forms of policyanalysis, note that policy is specifiedby a rule to performone or more acts when a particular system state is attained.This gives a new Markov matrix for each policy, and a newcost. Benefits may be estimatedas functions of (i) meantransition times betweenpairs of states,and (ii) mean de-tention times in states. These may be summed and discounted,then shown as net of cost (or however). This gives a preliminaryformalism for ranking policies. Autocorrelationverifiesapplicability of single lags. Figures 36, 37, and 38 show thestatisticsof the consolidationof all systemconditions into8 states,and the Markov transitionsbetween them.

3. Spatial disaggregation

(a)of the system.

(b)(c)

detention time.(d) Advantageswith regard to policy.(e) Computationalexperience.(f) Figure 39 shows the notation used in the

policy analysis.

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0.4

0.3

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FIGURE 35

セ0.2

ex:セN= 8000 1\

t-Z 1\

I \W 1 \u I \u. Iu. I MIGRATION_____.: \w0 IU I I \

0.1 I I \z I I0 I I

セ I ,...J \ 1w I ,ex: I Iex: I0 Iu I ,f2 I

\ I::> I<{ , ,

0.00 , 10 20 30 ItO' 47 50 \ 60,

lagセI ,

- .02 \\

I \.... ....._____________..... _...,.- - ..............1 ....,--.,..-.04

-.06 CORRELOGRAM - LARVAL DENSITY

-.08 ( ANNUAL VALUES)

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Figure 36

1 2 3 4 5 6 7 8

1 927 673 9 5 Endemic

2 108 6257 646 50 2 Threat

3 20 9971 599 35 Outbreak 1

4 4 7 167 198 19 445 Outbreak 2

5 3 270 148 84 Outbreak 3

6 28 7 733 642 Post-outbreak

7 544 98 19 3767 Post-outbreak

81529 2984 Destruction

TRANSITION FREQUENCIES, 30,000 years, MIGRATION

1 2 3 4 5 6 7 8

1 1272 719 4 11

2 ill 10886 418 1267 109

3 41 5920 377 5

4 16 392 1 1142 1034 13 212

5 33 272 161 842 6

6 315 425 5 686 315

7 269 56 13 1535

8 218 907

TRANSITION FREQUENCIES, 30,000 years, NO MIGRATION

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Figure 37

1 2 3 4 5 6 7 8

1 .574 .417 .006 .003

2 .015 .886 .091 .007

3 .002 .938 .056 .003

4 .005 .008 .199 .236 .023 .5305 .006 .535 .293 .166

6 .020 .005 .520 .455

7 .123 .022 .004 .851

8 .151 .849

S.S. .054 .235 .354 .028 .017 .047 .148 .117

TRANSITION AND STEADY STATE PROBABILITIES

MIGRATION

1 2 3 4 5 6 7 8

1 .634 .358 .002 .005

2 .009 .851 .033 .099 .009

3 .006 .933 .059 .001

4 .006 .140 .406 .368 .005 .075

5 .025 .207 .123 .641 .005

6 .180 .243 .003 .393 .180

7 .139 .030 .007 .824

8 .194 .806

S.S. .067 .426 .211 .094 .044 .058 .062 .038

TRANSITION AND STEADY STATE PROBABILITIES

NO MIGRATION

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Figure 38

1 2 3 4 5 6 7 8 Resid.

1 19 3 15 31 119 37 40 43 2.42 42 4 13 29 117 35 38 41 8.93 39 34 3 36 94 9 12 13 6.44 22 16 28 42 61 5 9 34 1.35 18 30 36 94 9 12 13 13 2.26 20 16 28 42 61 5 9 34 2.17 15 11 23 38 126 21 4 50 6.78 13 10 22 36 124 43 7 49 6.6

MEAN FIRST PASSAGE (yrs)

MIGRATION

3 4 5 6 7 8 Resid.

1 15 3 53 15 24 26 86 132 2.72 38 2 50 12 21 24 84 129 6.7

3 46 21 5 17 27 29 89 133 5.2

4 30 6 56 11 11 13 73 117 1.7

5 26 5 55 17 23 8 69 133 1.1

6 21 5 55 17 26 17 61 134 1.7

7 13 8 58 19 29 31 16 136 5.8

8 26 10 60 22 31 5 66 27 5.2

MEAN FIRST PASSAGE (yrs)

NO MIGRATION

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FIGURE 39

A

c

SPATIAL DISAGGREGATION

B

D

Ir

A . WAFFLE OF3 ..

z·· LINKAGESB IJ 2

C (STATE 1)0-

D -l--

A B C D

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4. Policy manipulation

(a) Based on treating so as to move residenceprobabilities toward a given target vector.

(b) Pose as a 0,1 problem, where the decision isto apply act Ai in regions characterizedby Si' or not.

(c) Assumptionsof ergodicity and additivity aretenable; subsequentwork must prove this.

(d) Developmentof Aijk array, and 0,1 approxima-tion -- the influence coefficients across all states. Thedefinition of time and transientprobability levels isdifficult.

(e) Weighted objective function and costfunction (Figure 40).

(f) Random sampling, systematicsweeteningandmathematicalprogramming as tools for locating the optimalsolution; deficienciesof the procedures.

(g) Computationalexperience.

Key Points

Becauseof the high dimensionality of the full system, it isprudent to seek compressionsof system descriptionand per-formance which retain the richnessand variety necessarytodiscriminate among policies and which are sufficientlydescriptive to reflect and convey ecological values, whilebeing appropriatefor simple searchprocedures. Elementarytheory of Markov matrices provides the basis for economicvaluation; this is elaboratedby linkages which model spatialdisaggregation. A linear model of system responseis developedto identify near-optimalpolicies under a quadraticobjective.

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Figure 40

Initial residenceprobabilities:

Final residenceprobabilities:

Desired residenceprobabilities:

Initial deviations: セ N]

Final deviations: セ セ]

Budgetaryconstraint:

Weighting factors:

c*

w.]

H' k セ。ッ ok セッNj] i l] l]

this defines セ ォ

subject to:

-1 < aijk < 1

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2.5.6 Generatingpolicy alternatives

(A) Overview

- Under CPA, we discussedthe general approachofpolicy analysis through incremental improvementson exogenouslydeterminedpolicies.

- At the presentstage of our researchwe havegenerateda set of 6 extreme managementpolicies for imple-mentation on the full simulation model. The long term behaviorof the forest system under each of thesepolicies is monitoredand evaluated,using the indicators, preferenceanalysis, andstatistical indices discussedearlier. Desirableaspectsofeach policy are isolated and used as the basis for furtherpolicy design improvement.

- We have no policy evaluation results to demonstrateat ー イ ・ ウ ・ ョ セ simply becausethe ecosystemsimulation model pluspolicy rules form a packagewhich exceedsthe memory capacityof IIASA's PDP system. What we can do, however, is brieflyoutline the program we intend to implement on our own facilitiesin Vancouver.

(B) The first generationpolicy alternatives

(1) No management;

(2) Unconstrainedstand optlmization;

(3) Constrainedstand optimization, where themaximum processingcapacity of the existinglogging industry is set externally on (2);

(4) Recreationmaximization, acting as anadditional constrainton (3) above;

(5) Budworm minimization, replacing the sprayingpolicy of (3) above;

(6) Variability transformation,operatedindependentlyof (2) above; this will rely heavily uponapproachesdiscussedunder CPA.

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(C) The secondgenerationpolicy alternatives

- This is where we will begin to modify and integratethe six extreme policies discussedabove. It is pointless tospeculateat any length about anticipatedresults, but oneexample may provide some flavor of the direction the work willtake.

- Preliminary analysis suggeststhat once policy(6) has transformedthe forest system from high temporal-lowspatial variability to low temporal-highspatial variability,the latter statewill be イ ・ ャ セ エ ゥ カ ・ ャ ケ persistent. That is, weexpect it to drift only slowly back into a time-variant systemand believe this trend will be easily reversiblewith minorpolicy interventions. The systemwill thus be transformedfrom its present,delicately poised state -- artificiallymaintainedat high spraying cost and in constantrisk ofmassive outbreak -- into an almost self-sustainingsystem inwhich the inevitable local outbreaksfail to propagate,andthus constitutean acceptableaspectof system behavior. Oncemore, insteadof massive investmentsin a fail-safe system,we will have designedone which is safe for failure.

- If these hopes for the developmentof variabilitytransforming policies turn out to be Justified, then the nextstage of policy design will begin to test the economic and re-creationalpolicy packagesdescribedearlier on the transformedsystem. It is not unreasonableto suspectthat the almost self-sustainingnature of the transformedsystemwill allow us topursue such "social benefit" policies most of the time, revertingto variability-orientedpolicies only as circumstancesdemandthat the systembe nudged back towards its desired long termstate.

- Now, this sounds suspiciouslylike a case ofhaving your cake and eating it too, but optimism isn't quiteheresy even in ecology, and we find it a pleasantway to enda story.