University of ScholarWorks at University of Montana

Graduate Student Theses, Dissertations, & Professional Papers Graduate School

1984

Predicting successional composition on a Pseudotsuga menziesii/ malvaceus habitat type in western Montana

Robert E. Keane The University of Montana

Follow this and additional works at: https://scholarworks.umt.edu/etd Let us know how access to this document benefits ou.y

Recommended Citation Keane, Robert E., "Predicting successional plant composition on a Pseudotsuga menziesii/ habitat type in western Montana" (1984). Graduate Student Theses, Dissertations, & Professional Papers. 7419. https://scholarworks.umt.edu/etd/7419

This Thesis is brought to you for free and open access by the Graduate School at ScholarWorks at University of Montana. It has been accepted for inclusion in Graduate Student Theses, Dissertations, & Professional Papers by an authorized administrator of ScholarWorks at University of Montana. For more information, please contact [email protected]. COPYRIGHT ACT OF 1976

Th is is an unpublished manuscript in v/h ich copyright sub ­ s is t s . Any further r e pr in tin g of its contents must be approved BY THE AUTHOR.

Ma n s f ie ld L ibrary Un iv e r s it y of Hontana Date : 1 ^ ô ____

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PREDICTING SUCCESSIONAL PLANT COMPOSITION

ON A PSEUDOTSUGA MENZIESII/PHYSOCARPUS MALVACEUS

HABITAT TYPE IN WESTERN MONTANA

By

Robert E. Keane I I

B.S., University of Maine, 1978

Presented in p artial fu lfillm e n t of the requirements for the degree of

Master of Science in Forestry

UNIVERSITY OF MONTANA

1984

Approved by:

.. Chairman, Board of Examiners

Dëan, Graduate Sch’

Date

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: EP38220

All rights reserved

INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted.

In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. UMT OwMTtatiorn PüWiahing

UMI EP38220 Published by ProQuest LLC (2013). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code

ProQuest

ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106 - 1346

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page i i

Keane I I , Robert E ., M.S., December 1984 Forestry

Predicting Successional Riant Composition on a Pseudotsuqa menziesii /Physocarpus malvaceus Habitat Type in Western Montana (96 pp.) ------

Director: Dr. Hans Zuuring 1

As resource management strategies intensify, forest land managers must be able to predict the probable response of forest vegetation to silvicultural treatments and wildfires so that management alternatives can be evaluated. A quantitative computer model of succession has been developed. This model predicts temporal changes in cover for major species in the Pseudotsuqa menziesii/ Physocarpus malvaceus habitat type. The model is based on a successional classification system which has recently been developed. In the model, species are established according to regenerative strategies and subsequent growth is modeled empirically via regression equations. Output is offered both in tabular and graphic form. Model validation yielded 63 and 85 percent accuracy in determining correct plant species cover. The computer program consisting of 21 subroutines was w ritten in FORTRAN 77 to facilitate the rapid execution of the succession model.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page i l i

Acknowledgements

My most sincere and heartfelt appreciation goes to all who helped

contribute to the completion of this study. Most Importantly, Or,

Steve Arno, Dr. Hans Zuuring, and Dennis Simmerman deserve thanks for

the priceless advice and help I received throughout the study, and to

Dr. Peter Stickney who provided invaluable insight into vegetational

processes and helped identify d iffic u lt . Thanks also go to Dr.

Jim Brown for the freedom to pursue my research goals; Or. Steve

Running for professional advice and constant lectures on modeling

morals; Dean Ben Stout for providing the subsistence during my first

graduate year; Dr. Jim Habeck fo r serving on my committee; and

members of the graduate room SC 460 whose encouragement was often needed

during late night sessions on the computer terminal. Lastly, I would

like to thank my wife Liz, for everything.

This project was funded by the USOA Forest Service under Cooperative

Agreement 22-C-3-INT-127.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page iv

TABLE OF CONTENTS

A b s tra c t...... Page i i

Acknowledgements ...... i i i

Table of C o n te n ts ...... iv

List of Tables...... vi

List of Illustrations...... vi

Chapter 1: Introduction ...... 1

Chapter 2: Literature Review ...... 3

Succession Theory ...... 3

Vegetation Ecology ...... 5

Chapter 3: Study Objectives ...... 11

Chapter 4: Methods ...... 12

Study A re a ...... 12

Study D esign ...... 14

Model Construction...... 17

Model Assumptions...... 27

Model V a lid a tio n ...... 28

Chapter 5: R e s u lts ...... 29

Model S tr u c tu r e ...... 29

Model Specifications ...... 37

Parameter Estimation ...... 37

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page v

TABLE OF CONTENTS (Con't)

Chapter 5: Results (con't)

Simulation R uns...... 38

Model V a lid a tio n ...... 38

Chapter 6; D is c u s s io n...... 41

Model S tr u c t u r e ...... 41

Parameter Estimation ...... 41

Validation and Refinement ...... 45

Chapter 7: Conclusions...... 47

Model Improvement ...... 47

Implications ...... 48

Literature Cited ...... 49

Appendices ...... 57

Appendix A ...... 58

Appendix 8 ...... 61

Appendix C ...... 65

Appendix D ...... 6 8

Appendix E ...... 74

Appendix F ...... 92

Appendix G ...... 94

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page vi

LIST OF TABLES

1. Modeling cover classes ...... Page 16

2. Treatment t y p e s ...... 16

3. Intensity types ...... 16

4. List of major s p e c ie s...... 18

5. Validation results by phase ...... 39

6. Validation results by pathway ...... 39

7. Validation results by treatment type ...... 39

LIST OF FIGURES

1. Map of study a r e a Page 13

2. Example ordination for dry phase ...... 20

3. Example ordination fo r moist phase ...... 21

4. Pathway diagram for dry p h a s e ...... 23

5. Pathway diagram fo r moist phase ...... 24

5. Species prio rity diagram ...... 26

7. Model flow chart ...... 30

8. Model pathway key fo r dry p h a s e ...... 33

9. Model pathway key fo r moist p h a s e ...... 34

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1

INTRODUCTION

The majority of the diverse serai communities present on western

Montana forest lands were created by timber harvesting practices and

w ild fire s . The vegetal composition of these conmunities influences

timber production, wildlife and livestock forage potential, recreation

opportunity, watershed characteristics, and reforestation problems. As

resource management strategies continue to intensify, land managers must

be able to predict the probable response of forest vegetation to

silvicultural treatments and wildfires so that various management

alternatives can be evaluated. The need to predict successional

compositions is magnified by the fact that early to mid-seral community

types have been and w ill continue to be a major component of western

Montana forests. Recently, the computer model has become a useful tool

in predicting temporal changes in forest vegetation. Unfortunately,

many current succession computer models were b u ilt for research purposes

and are not oriented to management application. This thesis presents a

quantitative computer model of succession designed to be used in

resource management and planning.

This computer model is empirical in design and based on the

successional community classificatio n system of Arno and others (1985).

Major plant species of the Pseudotsuqa menziesi1/ Physocarpus malvaceus

habitat type (Pfister and others 1977) are individually modeled using

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 2

regression equations derived from an extensive successional data base.

In itia l establishment is based on each species' physiognomic and

morphologic regenerative strategies and subsequent growth in canopy

coverage is determined from empirical equations. Moreover, since a

given stand-removing disturbance in combination with an appropriate

s ilv ic u ltu ra l treatment can create a unique successional community which

progresses towards climax along any one of several pathways, i t was

necessary to s tra tify species regression equations by pathway.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2

LITERATURE REVIEW

Succession Theory

Plant succession has been studied by numerous vegetation

researchers. As a resu lt, many theories on successional processes have

been formulated (fo r review see Drury and Nisbet 1973, Kessel 1 1980, van

Hulst 1978) and diverse conceptual models have been developed (Cattelino

and others 1979, Clements 1928, Connell and Slatyer 1977, Drury and

Nisbet 1973, Egler 1954, Everett and Ward 1984, Gleason 1926, Horn 1976,

Noble and Slatyer 1980, Odem 1969, Peet and Christensen 1980). However,

since Noble (1981) suggests there is no "unifying successional scheme"

but only a multitude of species specific trends (Pickett 1976), it can

be assumed that no conceptual model can be applicable to a ll types of

vegetation communities.

The "initial floristics" model of Egler (1954) generally describes

early mechanisms of succession in western Montana (Arno 1981, Heinselman

1982, Lyon and Stickney 1974). This model asserts that post-disturbance

species dominance is dependent on the survival of intact plants or

regenerating plant parts from the predisturbance community. And, as

succession is essentially a species by species process (Drury and Nisbet

1973) characteristic of Gleason's (1926) individualistic community

theory, multiple successional pathways can emerge depending on

ecological characteristics of the plants (Noble and Slatyer 1980) and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 4

severity of the perturbation (Gardener 1980, G ill 1977, Kessel! and

Fischer 1981). Application of these concepts in the Rocky Mountains is

demonstrated by the m ultiple pathway model of Cattelino and others

(1979) and succession community classification system of Arno and others

(1985). Therefore, the direction of succession in western Montana

forests is dependent on predisturbance plant composition, disturbance

severity, and survival mechanisms of individual plant species (Antos and

Shearer 1980, Debyle 1981, Lyon 1971, Lyon and Stickney 1974 Zamora

1982).

Current quantitative succession models (summarized in Shugart and

West 1980) deal mainly with the tree layer and rarely simulate changes

in the undergrowth (examples in West and others 1981). These models use

a variety of dependent variables to measure successional growth. Bartos

and others (1983) and Shugart and others (1980) used biomass as a

measure to define changes in vegetation over time, while Everett and

Ward (1984) used percent cover as the successional measure. Variables

such as stocking or species frequency (Bella 1970), basal area, and

breast height diameter (Ek and Monserud 1974, Stage 1973, Kercher and

Axelrod 1984, Botkin and others 1971a) are easily measurable for trees,

but prove d iffic u lt to sample for undergrowth species. and herb

compositions are frequently measured in percent canopy coverage because

of cost efficiency (Arno and others 1985, Cholewa and Johnson 1983, Lyon

and Stickney 1976, P fister and others 1977, Stickney 1980). Lindsey

(1956) considers canopy cover "the most important single parameter of a

species in its community relations". The shrub succession model of

Steinhorst and others (1984) and the FORPLAN model of Kessel 1 and Potter

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 5

(1980) have percent cover as the predictive variable.

Forest succession models can be categorized into two approaches;

deterministic or stochastic, based on the nature of the driving

variables. Deterministic models can further be stratified into three

types: mechanistic, theoretical, and empirical. The mechanistic model

uses basic physiologic functions to simulate changes in plant growth

during succession (Botkin and others 1972a, Kercher and Axelrod 1984).

Theoretical deterministic models use estimated or assumed parameters to

drive hypothetical growth equations (Bartos and others 1983), while the

data-intensive empirical models use regression equations created from

substantial data bases to estimate successional growth (Adcard 1974,

Arney 1974, Irwin and Peek 1979, Lin 1974, Stage 1973).

Stochastic approaches simulate successional replacement processes

using Markov chain, Monte Carlo, and other types of probability models

(Binkley 1980, Horn 1976, Leak 1970, Suzuki and Umemura 1974, Wagonner

and Stevens 1970) Frequently, succession models are a combination of

both approach and types within an approach. Steinhorst and others

(1984) modeled succession as stochastic during plant establishment and

deterministic thereafter.

Vegetation Ecology

Succession is directly influenced by the biology of each potential

plant species. Physiognomic and morphologic characteristics of the

vegetation, together with revegetation adaptations or strategies,

dictate perturbation response and subsequent establishment and growth.

A quantitative succession model must be fundamentally based on plant

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 6

species ecology to accurately depict temporal composition changes.

Therefore, it is essential to determine key modes of survival,

establishment, and growth of the major species to be modeled. The

following is an abbreviated summary of principle revegetation mechanisms

for major plants modeled for the PSME/PHMA habitat type (Appendix A).

The two tree species modeled for this habitat type are adapted to

disperse seeds over short distances to gain reestablishment. Larix

occidental is (LAOC), a major component in only the PSME/PHMA, moist

phase, is a rapidly growing, shade-intolerant species whose seeds

usually need a mineral seedbed to germinate and grow into an established

seedling (Shearer 1976, Schmidt and others 1976). The seeds of the

semi-shade-tolerant Pseudotsuqa menziesii (PSME) are capable of

germinating in more diverse seedbed conditions but subsequent seedling

growth is comparatively slower (USDA 1965). Neither species can

reproduce vegetatively and, therefore, rely on o ff-s ite and surviving

seed sources fo r reestablishment (USDA 1965). (PIPO)

and Pinus contorta (PICO) are minor components of this habitat type but,

due to their limited occurrence, were not modeled.

Shrub species show the most diverse response adaptations. The key

indicator Physocarpus malvaceus (PHMA) sprouts from adventitious buds on

the root crown (basal sprouting) after disturbance damage (Crane and

Habeck 1983, Habeck and others 1980, Schmidt 1980). However, recent

studies revealed that sprouting from adventitious buds and nodes on

deep-rooted is also responsible for post-disturbance

revegetation (Bradley 1984). These two adaptations allow PHMA to

regenerate after the most severe disturbances (Bradley 1984, Habeck and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 7

others 1980). Rhizomes account for the most regeneration in Spiraea

b etu lifo H a (SPBE), which revegetates with high fecundity under certain

environmental conditions, and Symphoricargos alba (SYAL), which needs

large diameter rhizomes to insure adequate carbohydrate reserves for

resprouting (Bradley 1984, Crane and Habeck 1983, Habeck and others

1980). Both plants can reestablish after moderate to severe

perturbations. Vaccinium qlobulare, having its perennating rhizomes

nearer to the soil surface, is more susceptible to disturbance damage

(Antos and Shearer 1980, Bradley 1984, Crane and Habeck 1983, M ille r

1976,1977). The major basal (root crown) sprouters in the PSME/PHMA

h.t. are the shade-tolerant Acer qlabrum (ACGL), the ubiquitous

Amelanchier a ln ifo lia (AMAL), and the somewhat shade-intolerant Salix

scouleriana (SASC). SASC can also reproduce from numerous, wind-borne

seeds but the dry seedbed conditions associated with this habitat type

generally inhibit successful establishment via seed germination.

Two shade-intolerant have the unique adaptational advantage

of reproducing from seeds which remain viable in the soil for long

periods of time. The nitrogen-fixing Ceanothus velutinus (CEVE)

produces seeds which may remain viable for 400 years or more and need

heat treatment to stratify the seedcoat for initiate germination

(Cholewa and Johnson 1983, Lyon 1971, Lyon and Stickney 1974, Morgan and

Nuenshwander 1984, Mueggler 1965, Quick 1959). Although CEVE also has

the capability to resprout basally, it is usually absent in stands with

greater than 50 percent canopy closure, thus relying on the soil

seedbank for creating the dense CEVE shrubfields evident on western

Montana landscapes (Arno and others 1985, Lyon 1971, Stickney per.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 8

coram.). The bird-disserainated seed of Prunus virqiniana (PRVI) remains

viable in the soil for shorter periods of time but expansion is often a

result of basal and rhizoraatous sprouting (Habeck and others 1980,

Mueggler 1965).

Two disturbance response mechanisms are exhibited by the three

subshrubs in this habitat type (Appendix A). Linnaea borealis (LIED)

and Arctostaphylos uva-ursi (ARUV) are repent, mat-forming shrubs

expanding vegetatively by creeping stems with little or no regeneration

from seed (Bradley 1984, Crane and Habeck 1982, Flinn and Wein 1977).

Since the majority of plant parts are very close to the soil surface,

these species are extremely sensitive to disturbance (Arno and others

1985, Rowe 1977, Bradley 1984). Conversely, Berberis repens (BERE) has

moderately deep-rooted rhizomes (10-15 cm) that regenerate after light

to moderate disturbances (Bradley 1984, Crane and Habeck 1983, M ille r

1976).

A ll grasses listed in Appendix A, with the exception of Aqropyron

spicatum (AGSP), regenerate prim arily from deeply buried rhizomes.

(Antos and Shearer 1980, Lyon 1971, Mueggler 1965). However, Crane and

Habeck (1983) found that the most abundant grass, Calamaqrostis

rubescens (CARU), expands equally from seeds and rhizomes and can

potentially double in cover after a disturbance. AGSP can resprout from

rhizomes but the “bunchgrass" or tufted form of this perennial protects

meristematic tissue from f ir e , allowing regrowth from the original plant

(Stickney per. comm.). The sedges, Carex qeveri (CAGE), Carex rossii

(CARO), and Carex conncinnoides (CACO), are usually not mat-forming lik e

CARU but seem to possess the protective traits of the tufted grasses.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 9

Resprouting from rhizomes, stolens, and caudexes are the

morphological adaptations to disturbance for forbs in Appendix A.

Arnica co rd ifolia (ARCO), Aster conspicuus (ASCO), and Thalictrum

occidental is (THOC) regenerate mainly from rhizomes and are capable of

surviving low to moderately severe perturbations (Crane and Habeck 1983,

Habeck and others 1980, Lyon 1971, Lyon 1966, Mueggler 1965). Forbs

having shallow-rooted rhizomes that are extremely susceptible to

disturbance include the shade-tolerant plants Chimaphila umbel lata

(CHUM), Goodyera oblonqifolia (GOOB), and Mitel la stauropetala (MIST)

(Antos and Shearer 1980, Arno and others 1985, Rowe 1979). Adventitious

buds on stolons account for expansion in Fraqaria vesca (FRVE) and

Fragaria virqiniana (FRVI), but due to the close proximity of the

stolons to the soil surface, Fraqaria coverage is somewhat reduced by

moderate to severe disturbances (Rowe 1977). The colonizer Epilobium

anqustifoilurn (EPAN) is capable of resprouting from rhizomes providing

the intolerant plant is present on post-disturbance sites. However, the

major mode of establishment is through production of copious, lig h t

seeds that are dispersed over great distances by wind (Arno and others

1985, Crane and Habeck 1983, Flinn and Wein 1977). This la tte r

adaptation is also present to some degree in Hieracium albiflorum (HIAL)

and Achillea millefolium (ACMI), although the seeds are usually only

locally distributed. The warm, dry seedbed conditions of this habitat

type are apparently the cause of reduced germination success for EPAN,

HIAL, and ACMI resulting in low post-disturbance coverages (Arno and

others 1985, M ille r 1976, Rowe 1977) In addition, HIAL and ACMI can

resprout from a fisberrot caudex. The taproot caudex of Balsamoriza

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 10

sagittate (BASA) is capable of resprouting after low to moderate

treatments while the stout, s u rfic la l system of Xerophyllum

tenax (XETE) can resprout if left intact after disturbance (Antos and

Shearer 1980, Bradley 1984, Habeck and others 1980).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3

STUDY OBJECTIVES

At present, forest managers use q ualitative procedures to assess

s ilv ic u ltu ra l impacts on succession dynamics. Successional

classification systems such as Arno and others (1985) and Steele (1984)

relate successional pathways to silvicultural treatments and wildfire

but magnitudes of compositional changes are absent. This study was

in itia te d to provide quantitative estimates of successional shifts in

species coverage to facilitate evaluation of management actions.

Therefore, the objective of this modeling study is:

To develop a management-oriented, quantitative succession

computer model that would predict post-disturbance plant

species' response in the PSME/PHMA successional community

types of Arno and others (1985).

11

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4

METHODS

Study Area

Data for the succession computer model were collected on the

PSME/PHMA h.t.'s of the Lolo and Bitterroot National Forests, the

southern half of the Flathead National Forest, and parts of the Flathead

Indian Reservation (Figure 1). This area is composed of rugged, heavily

forested mountains bordered by grasslands and agricultural valleys at

low elevations and slow-growing, "upper subalpine" forests at the high

elevations (Pfister and others 1977). The surface geology is mainly

from the Precambrian Belt Series consisting primarily of quartzites and

argillites. However, the Bitterroot National Forest is largely granitic

in origin. Soils are medium to course-textured and generally shallow

and rocky, but deeper mantles sometimes occur on north and east slopes

due to deposits of volcanic ash and loess. Cryochrepts and Cryandepts

are the major soil great groups of the area. The climate is described

as inland maritime with short, warm-dry summers and cold snowy winters.

Mean annual precipitation is approximately 15 to 25 inches for this

habitat type.

The PSME/PHMA h .t. consists of two phases. The dry phase is more

abundant and occurs predominately on moderate to steep, south and

west-facing slopes with presence on north and east aspects restricted to

drier portions of the study area. Elevation ranges from 3200 to 5800

12

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 13

ü_

CO CO

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 14

fe e t. The more productive moist phase of this habitat type occupies

moderate to steep, north and east-facing slopes between 3400 and 5300

feet in elevation. The moist phase is not as abundant as the dry phase

being absent from the B itterroot National Forest south of Stevensville

and from the Lolo National Forest east of Rock Creek. The moist phase

is distinguished from the dry phase by having LAOC as a forest component

(Arno and others 1985).

Study Design

The data base used for model construction was created by pooling

data collected for the review draft of the Arno and others (1985)

classification system with data subsequently collected for an evaluation

of the classification system (Keane 1984).

In these studies, potential study sites were selected using the

USDA Forest Service Northern Region timber data base and National Forest

Ranger D is tric t compartment maps. A study site was often composed of

several, different-aged stands, and typ ically a combination of a

disturbed stand with an adjacent control or mature stand. This multiple

stand sampling was designed to minimize the three main sources of

vegetation variation: 1. site variability within a habitat type, 2.

geographic variations in the vegetation, and 3. variations in stand

histories prior to treatment.

A circu la r, 375 square meter macroplot was established in a

representative portion of each stand in the study site. The

representative area was selected as displaying average vegetation

compositions and uniform treatment severity across the stand. This

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 15

procedure, described by Muener-Oorabois and Ellenberg (1974) as

"subjective without preconceived bias", is sim ilar to that employed by

Pfister and others (1977) for the Montana forest habitat type

classificatio n . Canopy coverage for a ll woody and herbaceous species on

the macroplot was ocularly estimated in cover classes (Table 1) as

outlined by P fister and Arno (1980). In addition, tree species cover

was stratified into two diameter classes; coverage of trees less than

and greater than four inches diameter at breast height (DBH). Other

variables recorded on the macroplot were:

1. Elevation (feet above sea level + 100 feet). 2. Slope (percent + 5%), 3. Aspect (degrees or azimuth + 5 degrees). 4. Plot location (Township, Range, Section). 5. Treatment type (Table 2) from stand records. 6. Treatment intensity type (Table 3) ocular estimation. 7. Percent exposed bare mineral soil (percent) ocular estimation. 8. Total tree cover (nearest five percent) ocular estimation 9. Average stand DBH (inches + 1 inch). 10. Stand basal area (square feet per acre + 5 sq. f t . ) prism. 11. Stand age since treatment (years + 1 year) from stand records and field evidence. 12. Successional community type as defined by Arno and others (1985).

The sampling design of the evaluation study differed from that of the

original classification study in that only one stand per study site was

sampled. This allowed the freedom to sample a wide range of communities

within the study area in a lim ited amount of time. As a consequence,

sampling was concentrated on the highly variable early-seral

cormnunities. Additional tree data were collected during the

classification study but these were not used in the modeling study. A

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 16

Table 1

Cover classes used to estimate cover on sample plots.

Cover Class Cover Range in Percent (%)

T or trace less than 1 1 1 to 5 2 5 to 25 3 25 to 50 4 50 to 75 5 75 to 95 6 95 to 100

Table 2

Sampled treatment types implemented in the model.

Treatment type Abbreviation

Wildfire WF Clearcutting with broadcast burning BB Clearcutting with mechanical scarification MS Clearcutting with no site preparation NP

Table 3

Sampled severity types implemented in the model

Severity type Abbreviation

Low or light L Moderate or medium M High or heavy H

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 17

to tal of 225 stands were sampled with 146 in PSME/PHMA, dry phase and 79

in PSME/PHMA, moist phase habitat types.

Model Construction

The construction of the computer model of succession was done in a

stepwise process. First, field data was inspected to determine

appropriate species to model and then analyzed to assess ecological

modeling c rite ria . Regression analyses were then performed on the data

to compute equations which would approximately replicate species

successional trends. Next, a computer program was w ritten to

incorporate equations and ecological modeling criteria into a scheme

which simulates succession on a community basis. The model was then

tested with additional fie ld data to determine accuracy and precision of

predictions and the test results were then used to further refine the

model. These steps w ill now be presented in d e ta il.

The data were entered into computer data files in a format

compatible with existing statistical and vegetation analysis programs

(Gauch 1977, SPSSX 1984). Synthesis tables (Mueller-Dombois and

Ellenberg 1974) were produced to select the most important or frequently

occurring species to be modeled. These species (Appendix A) constitute

the majority of cover in any succession community type. Also selected

from these plants were the most dominant or the species that directed

successional progression in any of the community types. (Table 4 ).

These dominant plants are the species used in the succession

classification key (Arno and others 1985).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 18

TABLE 4 Major plant species u tilize d in the regression analysis with th e ir cover as independent variables. These species were the same for both moist and dry phases.

Species name. Common name

1. Pseudotsuga menziesii and Douglas-fir and western Larix occidental is larch (PSME + LAOC)

2. Physocarpus malvaceus (PHMA) Ninebark

3. (CARU) Pinegrass

4. Carex geyeri (CAGE) Elk sedge

5. Ceanothus velutinus (CEVE) Evergreen Ceanothus

6. Amelanchier a ln ifo lia (AMAL) Serviceberry

7. (ACGL) Mountain maple

8. (SASC) Seouler's willow

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 19

Two types of numerical analyses were employed to create the

succession computer model. Ordination techniques were used in the

formation of species response groupings and regression analyses were

u tilize d to estimate parameters for the prediction equations associated

with the succession computer model.

Ordination is the process of arranging species (or samples) in

relation to one or more environmental gradients using vegetation

coverage data (Whittaker 1973). Numeric or graphic representation of

species sim ilarity along the gradients can be obtained from any of the

current ordination programs (Gauch 1977). Using Polar and Reciprocal

Averaging Ordination methods (Gauch 1982, 1977) on the data collected

for species in Appendix A, s im ilarity between plants along possible

succession gradients was indirectly identified and response group

clusters were delineated (Huschle and Hironaka 1980, del Moral 1983).

Examples of ordination by species for both phases are shown in Figures 2

and 3. Ordination results were used to fin a liz e the response groups

defined in the next paragraph.

To simplify model construction, plant species were categorized into

response groups using methods of reestablishment, response to

disturbance, and tolerance to shade as criteria. Formulation of

response groups was fa c ilita te d by classifying species according to

Raunkiaer's lif e forms (Chapman and Crow 1980, Mueller-Oombois and

Ellenberg 1974) Plant Strategy Types (Grime 1979), and Vital Attributes

(Noble and Slatyer 1980,1977). The results of the species

classification and the ordination were used to create 24 response groups

(Appendix B). These groups were designed to permit inclusion of

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 20

O o

T3

a.

V) Q. (U CO X s. < o

c o

I

CSJ 2i 3 c n

o

3 8IXV

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 21

00

Ou

LU to Q.

(V

&_ o

CL v> >> j O c o to c -o L. o 0> s tofO

I

r o t i.

Z 8IXV

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 22

additional species as more habitat types are incorporated into the

model. With species response groups as guidelines, modeling decisions

could be based on ecological attributes of plants.

The model was created empirically using multiple regression

analyses. For each phase of the PSME/PHMA h .t., a multiple regression

analysis was performed for each species using only data from plots of

the community types in each of the successional pathways depicted in

Figure 4 and 5. These pathways were identified from the classification

system (Arno and others 1985) as explaining the greatest portion of

successional variation. The multiple regression analysis was repeated

for each successional pathway. The dependent variable fo r the

regression analyses was percent cover fo r every plant species, and DBM

and basal area fo r the stand. The independent variables included stand

age, percent total tree canopy cover, dominant species cover (dominant

species are presented in Table 4 ), elevation, aspect, slope, treatment

type, and treatment severity. Predisturbance cover, assumed to be the

cover in the control or untreated stand on the same site as the

disturbance stand, was often used as an independent variable. However,

this eliminated the evaluation data from the data base because the

multiple stand sampling technique, which sampled an undisturbed stand

adjacent to the disturbed stand, was not employed in that study. All

regression equations generated from the regression analyses were

developed to be descriptive as well as predictive in the successional

sense. Cover class values recorded for a ll vegetation variables were

transformed to percent cover using the percent midpoint for each cover

class.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7) ■DCD O Q. C g Q.

■D CD PSME/PHMA, DRY STRUCTURAL STAGES

C/) C/) SHRUB-HERB SAPLING POLE MATURE SERAL THEORETICAL CLIMAX FOREST FOREST

CD 8 3 PHMA ( I I PSME/PHMA (SI PSME/PHMA (9) PSME/PHMA (121 PSME/PHMA (15)

PHMA-CARU (2) PSME/PHMA-CARU (6)’------— PSME/PHMA-CARU (10) ------— PSME/PHMA-C ARU (13) PSME/PHMA-CAflU (16) 33" / CD

CD T3 O AMAU-PHMA (3) PSME/AMAL-PHMA (7)' PSME/AMAL-PHMA (11) ------PSME/AMAL-PHMA <14) Q. aC 3o T3

O CEVE-PHMA (4) PSMC/ceVE-PHMA (8>

CD Q. SUCCESSIONAL PATHWAYS

■D CD 1. (1) — *(5 )----*(9) ----'(1 2 )-----'(15 ) 4. (3) —'(7 ) — '(11)----'(1 4 )-----'(16) 7. (4)—*(8) — -(9 ) (1 2 ) .(15)

C/) C/) 2- ( 2 ) -----'( 6 ) ---'( 1 0 ) -----(13)—'(16) 5. (3)—-(7)— '(11)-—.(13) — '(16) 8. (4) —.(8) -----'(10)— '(13)__ .( i 6) T3 0» 3. (2) '(6) ---'( 9 ) ----.(12) -*(15) 6. (3) — (7)--(ID —*(12)------(15) 9. (4) —*(8) —(11) ^(14) ----.(1 6) (O n> wPO Figure 4 - Successional diagram and pathway lis t fo r PSME/PHMA, dry phase 7J ■DCD O Q. C g Q.

■D CD PSME/PHMA, MOIST STRUCTURAL STAGES (/) W o ' 3 SHRUB-HERB SAPLING POLE MATURE SERAL THEORETICAL CLIMAX FOREST FOREST CD 8

tQ- PSME/PHMA-CARU (6) 3" PSME/PHMA-CARU (4) PSME/PHMA-CARU <11) ------— PSME/PHMA-CARU (13)

i PHMA-CARU <1) 3 CD

PSME-LAOC/PHMA-CARU (5)-—PSME-LAOC/PHMA-CARU (»> -«-PSME-LAOC/PHMA-CARU (12) 3. 3" CD ■DCD O PSME-LAOC/AMAL-PHMA (6)-— PSME-lAOC/AMAl-PMMA (10) Q. AMAI.-PHMA <2) C a o SUCCESSIONAL PATHWAYS 3 ■D O PSME-LAOC/CeVE-PHMA (7) CEVE-PHMA (3) 1. (1) — »(4) — >(8) ■— (11) — (15)

CD Q. 2. (1) —*(5) —49) —'(12) — (13) NOT MODELED 3. (2) — (6) -—do) —*( 11) — (13) CESA-PHMA ■D — p s m e - l a o c / c e s a - p h m a CD 4. (2) -->(6) -—do) — (12) -(1 3 )

C /) Figure 5- Successional diagram and pathway lis t (/) 5. (3) — (7) -^ (9 ) 412) -—(13) for the PSME/PHMA, moist phase 6. (3) - 4 7 ) - -CIO) — (12) — (13) T3 IQCU (D r\3fa. Page 25

Various transformations were performed on the independent variables

of stand age, total tree canopy cover, aspect, slope and elevation to

compensate for curvilinear trends in the data and variable Interactions.

Sigmoid and asymptotic transformations were of the form described by

Jensen (1979, 1973), Jensen and Homeyer (1970,1971), and Dolby (1963)

while interactive transformations were formulated using ecological

judgement. A summary of the transformations used in the regression

analyses is shown in Appendix C.

Some species cover regression equations may have dominant species

cover predictions as an independent variable. To eliminate confounding

effects of related predictions for dominant plant species (Table 4 ), a

priority system (Figure 6) was utilized during the regression analyses.

In this system, each species was p rio ritized according to its

successional importance or its re lative dominance in any successional

pathway. Species of a lower p rio rity were not used to predict cover of

a species with a higher priority. For instance, CARU coverage is not

used to predict PHMA coverage but PHMA coverage is used to predict the

coverage of CARU. Since successional importance is based on pathway,

CEVE received a p rio rity higher than PHMA, CARU, or CAGE along any of

the CEVE pathways.

Regression analyses were performed using the REGRESSION procedure

in the SPSSX (1983) statistical software package on the University of

Montana DEC 2060 computer. Regression coefficients associated with each

pathway prediction equation were estimated by a stepwise process known

as "backward elim ination". All independent variables were entered into

an equation and then each was tested for removal using s ta tis tic a l

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 26

FIGURE 6

P rio rity system for species cover variables used in the regression analysis for model development. Cover fo r species with higher p rio ritie s are not used as independent variables in building regression equations for species of lower priorities. This priority system is for both PSME/PHMA, dry and moist phases.

FIRST PRIORITY — Total tree canopy coverage

SECOND PRIORITY — PHMA

THIRD PRIORITY — CARU and CAGE

FOURTH PRIORITY — CEVE (except in CEVE pathways where i t is SECOND PRIORITY)

FIFTH PRIORITY — AMAL and ACGL and SASC

SIXTH PRIORITY — All other plants

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 27

significance criteria (F value, tolerance). Once all insignificant

variables were removed, each would again be entered to determine i f the

variable accounted for additional variation. Combinations of seventy

variables or variable transformations were used in the stepwise

procedure with each combination selected to best represent successional

trends for a given species. The estimated coefficients for each

equation, along with the standard deviation about regression at mean Y,

number of observations, and coefficient of determination were stored in

an external data f i l e to be accessed by the computer program.

The programming requirements for the model were that i t had to be

easily implemented on the new Forest Service FLIPS mini computers

produced by the Data General Corporation and i t had to be in a

programming language compatible with many Forest Service compilers.

Since large storage requirements fo r programs b u ilt on mini computers

consume valuable computer time, it was decided to store all parameters,

output labels, and simulation results in external files to be accessed

by the program when appropriate.

Model Assumptions

Since models are simplifications of reality, certain assumptions

must be made to compensate for data lim itations. The assumptions for

this model are: 1. If a vegetatively reproducing plant is not present in the predisturbance community, it will not be present after disturbance.

2. The pathways displayed in Figures 4 and 5 represent succession on the PSME/PHMA habitat type.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 28

3. There is always a seed source for the tree species.

4. The dominant plants in the p rio rity system affect coverage of species with lower p rio ritie s ,

5. Presence of CEVE or EPAN on a predisturbance site or in an immediate area indicates CEVE seed in soil or EPAN seed source.

6. Basal sprouting is the main method of expansion after disturbance for SASC in the PSME/PHMA h.t.

7. Cover class is an adequate measure of species composition dynamics.

8. Any plant species has only one main method of expansion, a ll others are considered to be insignificant.

Model Validation

The model was tested with actual fie ld data to assess the accuracy

of postdisturbance cover class predictions. During the summer of 1984,

20 new disturbance sites (13 in PSME/PHMA, dry and 7 in PSME/PHMA, moist

habitat types) were sampled as previously described using the multiple

stand sampling technique. Measurements for the control or untreated

community adjacent to the disturbance stand were used as inputs to the

model. Cover class predictions for each species from the computer model

were then compared with the corresponding values recorded for the

sampled disturbance community using regression techniques and frequency

tables.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 5

RESULTS

Model Structure

The computer model was structured in modular form, using a main

driver to direct control to subroutines that perform unique tasks. A

simplied flow chart is presented in Figure 7.

At the start of a simulation run, the defaults and flags

initialized in the driver. Subroutine GREET is then called to

interactively describe the model and ask for the title of the simulation

run and habitat type phase to be modeled. Using habitat type phase as a

key, the number of species, major species (in the priority system), and

transformation parameters are determined. External device numbers are

also set to access proper files. MAJNAME is then called to read

the major species names from an external f i l e . These names are stored

in an array in order of decreasing successional p rio rity so that the

current year's coverage of high priority species can be used to predict

coverage for lower p rio rity species. The input data entry routine is

then activated by calling IREAD.

The data entry routine is an interactive subroutine with a variety

of features for entering input values. Two skill levels are available

to the user. The Novice skill level explains in detail the input value

to be entered, while the Advanced level expedites data entry by printing

a short, one line prompt or query with minimal input value description.

29

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 30 START INTERACTIVE ROUTINE

ENTER INPUT VALUES

START SIMULATION ROUTINE

KEY OUT PATHWAY

DETERMINE MAJOR SPECIES COVER

CALCULATE OTHER SPECIES COVER

NO LAST SIMULATION YEAR 7

YES

PRINT TABLES AND/OR GRAPHS

YES ANOTHER DISTURBANCE ?

Figure 7 - Simplified flowchart NO for the successional computer

END PROQRAM model.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 31

Once the input value has been entered, the subroutine scans for entry or

data boundary violations. Data boundary violations occur when the entry

is not within the range of data used for model construction. The

following is a summary of data boundary errors.

1. Succession cannot be modeled past year 300.

2. Succession can only start on or after year five. Stands younger than fiv e years old were not used in model construction because of the inherent v a ria b lity within early-seral communities.

3. Elevation boundaries range from 3500 to 5800 feet.

4. Canopy coverage can never exceed 100 percent for any species.

5. The number of individual simulation years cannot exceed f i f t y . This is a limitation of the program not the data. The number of simulation years can be determined by dividing the maximum year to model by the age increment.

6. Slope cannot exceed 100 percent.

7. Aspect must be between zero and 360 degrees.

If the program detects an error, subroutine ERROR is called and a

message describing the type of error is printed. The user has the

option of entering cover class or percent cover for predisturbance plant

coverages. However, model output is always presented in cover classes.

A summary of all entered values is printed at the conclusion of the

entry session and the user is then able to change any of the input

values. An example of an entry session is presented in Appendix D.

Two unique situations occur during entry of predisturbance plant

coverages. If the user enters zero cover for either CEVE or EPAN, a

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 32

message 1s printed asking the user i f there is evidence of these plants

o ffs i te . I f so, the model assumes, based on response groupings, that

viable propagules of these species are either on site (CEVE) or can

disperse onto the site (EPAN). The predisturbance cover is then altered

to reflect this potential.

After data entry, the successional pathway is determined in

subroutine PATHWAY. This procedure is the most sensitive component of

the model since failure to predict the correct pathway results in

calculating cover from wrong regression equations. The successional

pathway is assessed from predisturbance composition using a modified

Arno and others (1985) classification key for each phase (Figures 8 and

9). These keys attempt to predict pathway before disturbance actually

occurs.

Successional simulation commences once the pathway is established.

Species cover for each simulation year is calculated in a two staged

process. F irst major species' coverage is calculated in subroutine

MAJOR in order of decreasing successional p rio rity . Cover for remaining

species is then calculated in subroutine COVER. To calculate coverage,

both subroutines pass regression parameters obtained from external data

files to REGRESS. This subroutine creates regression equations from

seventy variables or variable transformations using the regression

parameters as selection criteria. Response groups are used to decide

how to model a species that does not occur on the predisturbance s ite .

I f the species is from group 1 or 2 (Appendix B), or occurs o ffsi te and

is from groups 8 or 17, its coverage is calculated via regression

equations. I f the species is a member of any other group, the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 33

FIGURE 8 Successional pathway key implemented in the model fo r the PSME/PHMA, dry habitat type phase. The cover requirements are for predisturbance conditions. Start at the top of key and stop at the first requirement that f it s .

1. CEVE greater than 5% canopy cover (cc) and treatment is

WF or BB at moderate to high se v e rity ...... la

la . AMAL* greater than 5% cc ...... PATHWAY 9

lb. CARU** greater than 25% c c ...... PATHWAY 8

Ic . Not as above ...... PATHWAY 7

2. AMAL greater than 5% cc ...... 2a

2a. AMAL greater than 15% cc ...... PATHWAY 4

2b. CARU greater than 25% cc ...... PATHWAY 5

2c. Not as above...... PATHWAY 6

3. CARU greater than 25% cc ...... 3a

3a. CARU greater than 37.5% c c ...... PATHWAY 2

3b. PHMA greater than 60.0% cc and low severity

treatment ...... PATHWAY 3

3c. Not as above ...... (assumed) PATHWAY 2

4. PHMA greater than 15% cc ...... PATHWAY 1

5. Not as above ...... (assume depauperate) PATHWAY 1

* AMAL = AMAL + ACGL + SASC * * CARU = CARU + CAGE

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 34

FIGURE 9 Successional pathway key implemented in the model for the PSME/PHMA, moist habitat type phase. The cover requirements are fo r predisturbance conditions. Start at the top of key and stop at the first requirement that f i t s .

1. CEVE greater than 5% cc and treatment is WF

or BB at moderate to high severity ...... la

la . AMAL* greater than 5% cc ...... PATHWAY 5

lb . CARU** greater than 25% cc and LAOC greater

than 5% cc ...... PATHWAY 6

Ic . Not as above (assumed) PATHWAY 6

2. AMAL greater than 5% cc ...... 2a

2a. LAOC greater than 5% cc and moderate to high

severity treatment ...... PATHWAY 3

2c. Not as above ...... PATHWAY 4

3. LAOC greater than 5% cc andmoderate to high

severity treatment ...... PATHWAY 2

4. Not as above ...... 4a

4a. PHMA greater than 15% cc ...... PATHWAY 1

4b. Not as above ...... (assumed) PATHWAY 1

* AMAL = AMAL + ACGL + SASC * * CARU = CARU + CAGE

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 35

successional coverage is assumed to be zero. REGRESS also scans

computed coverage for negative values and values over 100 percent and

adjusts to zero or 100% respectively.

Subroutine REGRESS also contains equations that were not

em pirically developed. Data for some plant species were so poorly

represented along a successional pathway that a statistically sound

regression equation could not be constructed. In these cases,

successional coverage estimates were based on a qualitative assessment

of the limited data, or, more simply, equations were designed to

represent a plant's successional trends in general terms from visual

inspection of the data. Three types of variables were used to

qualitatively assess cover changes as a result of disturbance, namely

treatment severity, tree canopy cover, and age. Species in obligate

climax (21), stoloniferous shade intolerant (20), and repent mat-forming

climax (12) (Appendix B) response groups were assumed to be eliminated

from the site afte r moderate to severe disturbances, but retained

predisturbance coverage a fte r lig h t treatments. Species in response

groups 17 and 8 were assumed to be absent from the site afte r 50 percent

canopy closure. These assumptions were incorporated into the model in

equation form by using treatment severity or canopy coverage as

parameters. Calculated species coverages for each simulation year are w ritten

to an external output file in subroutine OUTFILE. This file is accessed

by subroutines which display simulation results.

The user can print results on the terminal or the line printer in

two types of formats. Successional coverage can be presented in tabular

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 36

format using subroutines TABLE (for line printer) or SCREEN (for

terminal). Graphic display is also available for individual species.

Subroutines GRAPH (for line printer display) or DISPLAY (for terminal

display) are used for this task. These two subroutines create graphs

with percent cover on the Y axis and succession years on the X axis.

Since succession is modeled using only cover classes, the graphs depict

only trends in coverage rather than actual percent and should be

interpreted as such.

Statistics associated with each pathway regression equation may be

displayed to indicate the reliability of the prediction. These

regression equation statistics are read from an external file in

subroutine STATS and printed either on the line printer or terminal.

The printed statistics are coefficient of determination (R squared),

standard deviation about regression at mean Y (Sy.x), and total number

of observations (n).

After the output is displayed for a particular simulation, the user

has the option of implementing another disturbance on the same s ite .

There are two ways by which an additional disturbance can be modeled.

The user can model a new disturbance after the old disturbance in which

case the coverage of species during the last simulation year is used as

the new predisturbance plant cover. Or, the user can implement a new

disturbance in place of the old disturbance and the original

predisturbance coverages are used. If an additional disturbance is not

modeled, the program execution ends and a ll output file s are erased.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 37

Model Specifications.

This computer model was programed in FORTRAN 77 and executed on a

Perkin-Elmer 1200 mini computer located at the Northern Forest Fire

Laboratory, Missoula, Montana, The code can be easily transfered to the

FLIPS system now available at many National Forest district offices.

The program has low storage requirements (88 kilobytes) because a ll

parameters, results, and output labels are stored externally. Twenty

one subroutines, using 2100 lines of structured code, are accessed by

the driver, A copy of the code is presented in the User's manual (Keane

1984), The average entry session requires approximately seven minutes

at the Advanced skill level. There are currently seven external files

which are accessed by the program including two temporary output file s .

Parameter Estimation

A list of all regression equations with respective coefficients is

presented in Appendix E. For each equation, the following statistics

are also listed: coefficient of determination (R squared), standard

deviation about regression (Sy.x), and the total number of observations

(n). Of the possible 603 regression equations (312 regression equations

for the dry phase and 213 for the moist phase of the PSME/PHMA habitat

type), 78 are qualitative estimates. The R square values range from

0.44 to 0.99 with standard deviation about regression from 0.010 to

18.000. This large variation associated with these statistics is a

direct consequence of poor data representation in some of the less

sampled pathways.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 38

Simulation Runs

Outputs of a simulation run are presented in Appendixes F and G.

Information printed for the user includes a description of the site, the

keyed successional pathway, and the predicted coverage (in cover

classes) for each species by simulation year (Appendix F). Graphic

output (Appendix G) displays plots of species percent cover on the Y

axis versus stand age on the X axis. S tatistics associated with the

user-specified species regression equations are also printed to

indicated r e lia b ility of the predicted coverages. All outputs may be

printed on the terminal or line printer.

Model Validation

The validation data for the undisturbed stands were used as model

inputs and the simulation predictions were then compared with the actual

cover estimated on the adjacent, disturbed stand. The model averaged

63% accuracy in predicting cover class for a ll species, with dry phase

simulations more accurate than moist phase simulation results (Table 5)

probably due to the more extensive data base for the dry phase. Tree

species proved to be the most d iffic u lt to model (55% accurate) when

compared with the undergrowth (65% accurate). The PSME-CARU and CEVE

pathways had the highest predictive ability (63% and 67% respectively),

but this may be due to low validation sampling frequency in the

remainder of the pathways (Table 6). Accuracy by treatment type is

presented in Table 7. Species cover is best predicted on the

mechanically scarified stands (65%), but treatment type accuracy is

d ifficu lt to compare due to frequent sampling for this disturbance.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 39

TABLE 5 Results of model validation by habitat type phase.

Percent correct {%) Phase Range Average Number of plots

Dry 45-74 65 13 Moist 45-74 59 7 Total 45-74 63 20

TABLE 6 Results of model validation by successional pathway.

Percent correct (%) Pathway Range Average Number of plots

PHMA 45-45 45 1 PHMA-CARU 50-74 63 11 AMAL-PHMA 45-74 64 5 CEVE-PHMA 60-71 67 3

TABLE 7 Results of model validation by treatment type.

Percent correct (%) Treatment Range Average Number of plots

WF not sampled 0 88 50-71 62 8 MS 45-74 64 10 NP 54-64 59 2

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 40

In addition to comparing species cover, predicted successional

pathways were compared with observed pathways to test pathway key

r e lia b ilit y . The nwdel determined the correct successional pathway in

all 20 cases.

A common procedure fo r evaluating the accuracy of a model is to

regress predicted values as dependent variables with observed values as

independent variables and s ta tis tic a lly test for a slope of 1.000 and a

y-intercept of zero. The slopes for this model were 0.79 for the moist

phase and 0.88 for the dry phase of the PSME/PHMA habitat type.

However, s ta tis tic a l tests on the slopes (t value) show that they both

were not significantly different from 1.0 with alpha or level of

significance equals 0.05 (null hypothesis: beta = 1.0, alternative

hypothesis: beta not equal to 1 .0 ). Y-intercept values for the phases

are 1.28 (moist) and 0.78 (dry) with both these values not significantly

different from zero. The results of the validation regression analyses

show the model is over-estimating cover in the lower cover classes and

underestimating cover in the higher cover classes. These results were

used to refine the model a fte r validation analysis was completed.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 6

DISCUSSION

Model Structure

The program was designed to easily accept additional habitat types.

However, because ecological relationships between habitat types are not

identical, new transformations, different major species, and other

pathway keys w ill be required when new habitat types are added in the

future. A procedure for implementing habitat types into the model is

presented in the User's Manual (Keane 1984).

Parameter Estimation

The regression coefficients were estimated according to species

response groups. Equation parameters for species regenerating

vegetatively (response groups 4 thru 6, 9 thru 16, and 18 thru 24) were

estimated using only plots in which the species was present. This

assumes that species which are not present before treatment w ill never

become established after treatment, and conversely, species which are

represented in the predisturbance stand will never be eliminated from

the site. However, a species could possibly be eliminated from the site

as a result of a severe treatment, p articularly i f the species is in

response groups 12, 18, 20, 21, or 23. In these cases, a ll plots were

used in regression equation construction, but only if the pathway was a

result of a severe treatment as described by Arno and others (1985).

41

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 42

Regression analyses for species in groups 1, 2, 7, 8, and 17 had every

plot added to the regression data base because i t was assumed these

species could potentially become established on the site regardless of

predisturbance cover.

The use of predisturbance cover as an independent variable was also

governed by response group. Regression analyses for groups 1, 2, 7, 8,

and 17 never integrated predisturbance cover as an independent variable

in the equations because these species either did not occur in mature,

closed-canopy stands or th e ir method of revegetation was not dictated by

surviving members. Equations fo r species in the remaining response

groups employed predisturbance cover as an independent variable whenever

it was statistically significant.

Predisturbance cover proved invaluable as an independent variable.

This confirms concepts presented in past studies which describe

succession in terms of the predisturbance composition (Lyon and Stickney

1974, Stickney 1983, Steele 1984), Moreover, magnitudes of the

predisturbance cover coefficients, approximately 1.0 or slig h tly less

(Appendix E), indicate postdisturbance cover w ill be as much as

predisturbance cover or slightly less depending on severity of

treatment. Predisturbance coefficients associated with the equations

used to predict SASC cover were sometimes greater than 1.0 indicating a

gain in coverage as a result of disturbance. This gain could be

explained as expansion via seed, but is more lik e ly due to aggressive

sprouting from severely suppressed plants. Unfortunately,

predisturbance cover was rarely used as a predictor in the moist phase

equations because few multi pie-stand sites were sampled by Arno and

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 43

others (1985). Future modeling effo rts should sample mature stands

adjacent to disturbed coiranunities so predisturbance cover can be

Incorporated Into regression equations.

In some Instances, regression equations only explained data

characteristics rather than describe successional tendencies. This was

a consequence of Inadequate pathway plot representation coupled with

high species cover v a ria b ility between sites. This situation was

especially prevalent In the PSME/PHMA, moist phase. Some successional

pathways were poorly represented because they were rarely observed In

natural situations. For example, the dry phase PHMA pathway (Pathway 1

in Figure 4) had inadequate plot representation because silvicultural

and natural disturbances seldom create proper conditions for development

of this pathway. Data In these poorly represented pathways were often

combined with data from sim ilar pathways to more adequately explain

variation in successional communities. For Instance, dry phase Pathway

9 (Figure 4) did not have enough observations for some species to

adequately build re lia b le regression equations, so parameters were

estimated using additional data from Pathways 7 and 8. These pathways

are similar in that all are CEVE dominated during early serai stages.

Certain age groups are absent In the data base for similar reasons.

Disturbed stands between the ages of 35 to 64 years are uncommon In

western Montana because of fir e suppression policies and the fact that

early logging activities were usually partial cuttings rather than

clearcuts. This limited age distribution in the data base could explain

underestimations in species cover predictions.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 44

Even in mature stands, plant species cover can vary greatly between

sites of the same habitat type phase. Past disturbance histories such

as underburning and thinning, and subsequent seed germination success

rates are factors which might explain cover variations. For example,

frequent surface fires might enhance seed germination of an otherwise

sprouting plant eventually resulting In Increases In cover. Another

site, similar In physical site climatic characteristics, but

experiencing l i t t l e understory burning might have comparatively less

cover for the same species because of the absence of reproduction by

seed. The model cannot account for these differences In stand histories

because light surface treatments were not Incorporated Into the

regression equations. As a result, there Is Inherent variabllty In the

coverage data due to these and other unknown factors and this variablity

strongly affects regression equation form and precision. Initial

regression analyses produced equations containing transformations which

apparently made no sense ecologically but explained the greatest

proportion of variation. In such Instances, equations were reformulated

so that only transformations which reflected known successional

processes were used. Unfortunately, standard deviations about

regression usually Increased as a result of this reformulation, as would

be expected.

The error of the cover estimate Is often compounded when

predictions are used as Independent variables In the regression

equations. Since major species cover predictions are commonly used as

Independent variables In minor species cover equations, additional

variation is bound to be introduced. Yet, the compounded error of the

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 45

minor species cover estimate is hopefully absorbed in the conversion of

cover percent to cover class.

Validation and Refinement

This "brute force" validation procedure (described by Shugart and

West 1980) is limited in scope because site and vegetation conditions

are not constant between disturbance and untreated stands. A mosaic of

species cover between stands on the same site influences the reliab ility

of the model predictions. Differences in microsite and dispersal

patterns are factors affecting the spatial distribution of species

cover. The model can not handle a vegetatively regenerating species

which is present in the disturbance stand but not in the adjacent

control or mature stand (Assumption 1 in Methods). This situation was

often evident in the validation data. If these cases are eliminated

from validation data base, accuracy increases by 3% to 5%,

An important ecological measure of model validity is the magnitude

of difference between predicted coverage values and observe values. It

makes little difference ecologically if a species occurs at a trace

(0.1% to 1% coverage) or cover class one (1% to 5% coverage), unless of

course the species is rare or endangered which is not the case in this

model. If these two classes are combined and validation data again

analyzed, the average accuracy increases to 85% correct.

An important result of the validation process was the inability of

the model to predict tree species cover reliability. This was probably

due to the establishment of trees from a seed source in or adjacent to

the disturbed area. The amount of seed (seed crop) and subsequent

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 46

dispersal is dictated by highly variable weather conditions. The

stochastic nature of these weather variables makes it extremely

d iffic u lt to model tree establishment determ inistically. Regression

equations only predict average species cover regardless of current or

past weather influences. Therefore, coverage predictions for individual

tree species should be interpreted as averages.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 7

CONCLUSIONS

Empirical models do have th e ir lim itations. Regression equations

do not indicate cause and effect relationships, therefore, changes in

species cover are modeled as "black boxes" which produce desired outputs

but give no insights as to why these changes occur. Basic successional

processes such as nutrient allocation, microclimate alteration, and

competition are not addressed in this empirical model. On the other

hand, mechanistic models which simulate these basic processes rarely

produce outputs that can be used in resource management because

dependent variables are not of the form useful in management planning.

Future modeling effo rts should bridge the gap between the empirical and

mechanistic designs to produce management-oriented succession models

which are founded on fundamental ecological interactions.

Model Improvement

The data base fo r the model could be improved by sampling

successional communities along the infrequently observed pathways at the

same intensity as the other pathways. Although these communities are

less common in west-central Montana, they must be adequately represented

so that statistically reliable regression equations can be built. A

more evenaged plot distribution is also needed to accurately describe

shifts in species coverages.

47

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 48

Additional pathways within a habitat type phase could Improve model

accuracy. Successional variation In species cover could be more

accurately assessed by the Inclusion of more successional pathways

s tra tifie d by new community types. However, a larger data base w ill be

required to properly represent each of the new pathways.

An alternative modeling design is to simulate successional changes

by response groups rather than by species. If collective cover of a

species within response groups could be used as the dependent variable,

perhaps the high v a ria b lity between plots could be decrease. Of course,

this assumes species within response groups occupy approximately the

same ecological niche. Another modeling approach involves the use of

factor analysis on the dependent variables. Since data is collected in

discrete categories (cover classes). Is converted to percent for

analysis, and then reconverted back to categories. I t might prove

beneficial to use Factor analysis on the cover classes categories to

more accurately predict successional compositions.

Impl1cations

This model can be used for any phase of management planning where

the major emphasis is on the vegetation component. W ildlife managers

might need to assess the effect of two alternative treatments on the

cover of a major browse species. Timber specialists could determine the

natural regeneration success of LAOC after two types of cuttings.

Recreation planners might wish to evaluate the consequence of

clearcutting with respect to visual quality. The outputs of this model

could be used as an evaluation tool for each of these concerns.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 49

LITERATURE CITED

Adcard, P.G. 1974. Development of an empirical competition model for individual trees within a stand, p. 22-37. In J. Fries (Editor) Growth Models fo r Tree and Stand Simulation. Res. note 30. Dept, of Forest Yield Research, Royal College of Forestry, Stockholm, Sweden.

Antos, J .A ., and R.C. Shearer. 1970. Vegetation development on disturbed grand fir sites. Swan Valley, northwestern Montana. Forest Service, U.S. Dept. Agric. Res. Paper INT-251. 26 p.

Arney, J.D. 1974. An individual tree model for stand simulation in Oouglas-fir, p. 38-43. In J. Fries (Editor) Growth Models for Tree and Stand Simulation. Res. note 30. Dept, of Forest Yield Research, Royal College of Forestry, Stockholm, Sweden.

Arno, S.F. 1981. Classifying forest succession on four habitat types in western Montana, p. 54-62. In J.E. Means (Editor) Proc. of a Symposium on Forest Succession and Stand Development Research in the Northwest. Forest Research Lab., Oregon State Univ., C orvallis, Oregon.

Arno, S.F. 1976. Historical role of fir e on the Bitterroot National Forest. Forest Service, U.S. Dept. Agric. Res. Paper INT-187. p. 21.

Arno, S.F. 1980. Forest f ir e history in the northern Rockies. J. For. 78:460-465.

4f(Arno, S .F ., D.G, Siimnerman, and R.E. Keane. 1985. Forest succession on four habitat types in western Montana. Forest Service, U.S. Dept. Agric. Gen. Tech. Report INT-177.

Bartos, D .L., F.R. Ward, and G.S. Innis. 1983. Aspen succession in the Intermountain West: a deterministic model. Forest Service, U.S. Dept. Agric. Gen, Tech. Rep. INT-153. 60 p.

Bella, I.E. 1970. A new competition model for individual trees. For. Sci. 17:364-372.

Binkley, C.S. 1980. Is succession in hardwood forests a stationary Markov process. For. Sci. 26:566-570.

Bledsoe, L.J. and G.M. van Dyne. 1971. A compartment model simulation of secondary succession, p. 480-511. In B.L. Patten (Editor) Systems Analysis and Simulation in Ecology. Academic Press. New York, New York.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 50

Botkin, D.B., J.F. Janak, and J.R. W allis. 1972a. Rationale, limitations, and assumptions of a northeastern forest growth simulator. IBM J. Res. and Development. 16:101-116.

Botkin, D.B., J.F. Janak, and J.R. Wallis. 1972b. Some ecological consequences of a computer model on forest growth. J. Ecol. 60:849-872.

Bradley, A.F. 1984. Rhizome morphology, soil distribution, and the potential fire survival of eight woody understory species in western Montana. Master's Thesis, Univ. of Montana, Missoula. 184 p.

Cattelino, P.J., I.R. Noble, R.O. Slatyer, and S.R. Kessel 1. 1979. Predicting multiple pathways of plant succession. Envir. Man. 3:41-50.

Chapman, R.R. and G.E. Crow. 1980. Application of Raunkiaer's lif e form system to plant species survival after fire. Bull. Torr. Sot. Club. 188:472-478.

'i^olewa, A.F. and F.D. Johnson. 1983. Secondary succession in the Pseudotsuga menziesli/Physocarpus malvaceus association. Northwest Sci. 57:273-283.

Clements, F.E. 1916. Plant succession: an analysis of the development of vegetation. Carnegie Inst. Publ. No. 242, 512 p.

Clements, F.E. 1928. Plant succession and indicators: a d efin itive edition of plant succession and plant indicators. H.W. Wilson Co., publishers. New York, New York. 453 p.

Connell, J.H. and R.O. Slatyer. 1977. Mechanisms of succession in natural communities and th e ir role in community s ta b ility and organization. Amer. Nat. 111:1119-1144.

Crane, M.F. and J.R. Habeck. 1982. Vegetative responses afte r a severe w ild fire on a PSME/PHMA habitat type, p 22-29. In Proc. of a Symposium on S ite Preparation and Fuels Management on Steep Terrain.

Crane, M.F. and J.R. Habeck. 1983. Early postfire revegetation in a western Montana Douglas-fir forest. Forest Service, U.S. Dept. Agric. Res. Paper INT-319. 29 p.

Day, R.J. 1972. Stand structure, succession, and use of southern Alberta's Rocky Mountain forests. Ecology 53:472-477.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 51

Debyle, N.V. 1981. Clearcutting and fire in the Larch/Douglas-fir forests of western Montana: a multi-faceted research summary. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. INT-99. 74 p.

del Morel, R. 1983. Vegetation ordination of subalpine meadows using adaptive strategies. Can. Jour. Bot. 61:3117-3127.

Dolby, J.L. 1963. A quick method for choosing a transformation. Technometrics 5:317-325.

Drury, W.H. and I.C .T . Nisbet. 1973. Succession. Arnold Arbor. J. 54:331-368.

Ek, A.R. and R.A. Monserud. 1974. T rials with program FOREST: growth and reproduction simulation for mixed species, even or uneven aged stands, p. 56-73, In J. Fries (Editor) Growth Models fo r Tree and Stand Simulation. Res. note 30. Dept, of Forest Yield Research, Royal College of Forestry, Stockholm, Sweden.

Egler, F.E. 1954. Vegetation science concepts; 1. In itia l flo r is tic composition - a factor in old fie ld vegetation development. Veg. 4:412-417.

Everett, R.L. and K. Ward. 1984. Early plant succession on Pinyon-Juniper controled burns. Northwest Sci. 58:57-68.

FI inn, M.A. and R.W. Wein. 1977. Depth of Underground plant organs and theoretical survival during fire. Can. J. Bot. 55:2550-2554.

Gardener, C.J. 1980. Tolerance of perennating Stylosathes plants to fire. Aust. J. Exp. Agric. Husb. 20:587-593.

Gauch, H.G. 1982, M ultivariate Analysis in Community Ecology. Cambridge Studies and Ecology; 1, New York, New York. 298 p.

Gauch, H.G. 1977. ORDIFLEX — a fle x ib le computer program for four ordination techniques: weighted averages, polar ordination, principal components analysis, and reciprocal averaging. Release B. Ecology and Systematics, Cornell Univ., Ithaca, New York, 185 p.

G ill, A.M. 1977. Plant tra its adaptive to fire s in Mediterranean land ecosystems, p. 17-26. IN Proc. of a Symposium on the environmental consequences of fir e and fuel management in Mediterranean ecosystems. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. WO-3.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 52

Gleason, H.A. 1926. The ind ividu alistic concept of the plant association. Bull, Torr. Bot. Club 53:7-26.

Grime, J.P. 1979. Plant Strategies and Vegetational Processes. J.P. Wiley and Sons, New York. 222 p.

Habeck, J .R ., P.P. Stickney, R. P fis te r, and N. Noste. 1980. Fire response classification of Montana forest species. In house paper presented at an Ad hoc Vital Attributes committee meeting, Univ. of Montana, Missoula. 15 p.

Heinselman, M.L. 1982. Fire and succession in the conifer forests of northern North America, p. 379-406. In D.L. West, N.H. Shugart and O.B. Botkin (Editors) Forest Succession: applications and concepts. Springer-Verlag, New York.

Horn, H.S. 1974. Succession, p. 187-204. In R.M. May (Editor) Theoretical Ecology: Principles and Applications. Blackwell Scientific Publications, Oxford.

Horn, H.S. 1976. Markovian processes or forest succession. In: M.L. Cody and J.M. Diamond, (Editors) Ecology and Evolution of Communities, pp. 196-211. Belknap Press of Harvard University, Cambridge, Mass.

Huschle, G. and M. Hironaka. 1980. Classification and ordination of serai plant communities, J. Range Management 33:127-129.

Irw in, L.L. and J.M. Peek. 1979. Shrub production and biomass trends following five logging treatments within the cedar-hemlock zone of northern Idaho. For. Sci. 25:415-426.

Jensen, C.E. 1973. MATCHACURVE-3: multiple-component and multidimensional mathematical models for natural response studies. Forest Service, U.S. Dept. Agric. Res. Paper INT-42. 22 p.

Jensen, C.E. 1979. EXP(-k), a function for the modeler. Forest Service, U.S. Dept. Agric. Res. Paper INT-240. 9 p.

Jensen, C.E. and J.W. Homeyer. 1970. MATCHACURVE-1 for algebraic transformations to describe sigmoid or bell-shaped curves. Forest Service, U.S. Dept. Agric. 22 p.

Jensen, C.E. and J.W. Homeyer. 1971. MATCHACURVE-2 for algebraic transformations to describe curves of the class X to the n power. Forest Service, U.S. Dept. Agric. Res. Paper INT-I06. 40 p.

Keane, R.E. 1984. Evaluation of a successional classification system. Unpublished Cooperative report on f i le at Northern Forest Fire Lab, Drawer G, Missoula, Montana.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 53

Keane, R.E. 1985. User guide to FORSUM: a FORest Succession Model. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. (in press).

Kercher, J.R. and M.C. Axelrod. 1984. A process model of fire ecology and succession in a mixed-conifer forest. Ecology 65:1725-1742.

Kessel 1, S.R. 1980. A review and evaluation of successional modeling approaches. On f i le as a Cooperative agreement fin a l report. Northern Forest Fire Lab, Drawer G, Missoula, Montana. 45 p.

Kessell, S.R and W.C. Fisher. 1981. Predicting postfire plant succession fo r fir e management planning. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. INT-94. 19 p.

Kessell, S.R. and M.W. Potter. 1980. A quantitative succession model of nine Montana forest communities. Envir. Man. 4:112-115.

Leak, W.B. 1970. Successional change in northern hardwoods predicted by birth and death simulation. Ecology 51:794-801.

Lin, J.Y. 1974. Stand growth simulation models for Douglas-fir and western Hemlock in the northwestern United States, p. 102-118. In J. Fries (Editor) Growth Models for Tree and Stand Simulation. Res. note 30. Dept, of Forest Yield Research, Royal College of Forestry, Stockholm, Sweden.

Lindsey, A.A. 1956. Sampling methods and community attributes in forest ecology. Forest Sci. 2:287-291.

Lyon, L.J. 1966. In itia l vegetal development following prescribed burning of Douglas-fir in south central Idaho. Forest Service, U.S. Dept. Agric. Res. Paper INT-29. 25 p.

Lyon, L.J. 1971. Vegetal development following prescribed burning of Douglas-fir in south central Idaho. Forest Service, U.S. Dept. Agric. Res. Paper INT-105. 41 p.

f Lyon, L.J. 1976. Vegetal development on the Sleeping Child burn in western Montana. Forest Service, U.S. Dept. Agric. Res. Paper INT-184. 19 p.

Lyon, L.J. and P.F. Stickney. 1976. Early vegetal succession following large northern Rocky Mountain wildfires. Tall Timbers Fire Ecol. Conf. 14:355-375.

/ Miller, M. 1977. Response of Blue Huckleberry to prescribed fires in a western Montana Larch-Fir forest. Forest Service, U.S. Dept. Agric. Res. Paper INT-188. 21 p.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 54

M ille r, M. 1978. Effect of growing season on sprouting of Blue Huckleberry. Forest Service, U.S. Dept. Agric. Res. Note INT-240. 8 p.

/ Morgan, P. and L.F. Neuenschwander. 1984. Modeling Shrub succession following clearcutting and broadcast burning. Presented at Northwest Science, Fire Effects on W ild life Habitat Symposium. 26 p. Morgan, P. and L.F. Neuenschwander. 1984. Shrub response to high and low severity burns. Can. Jour. For. Res. (in press).

Morgan, P. and L.F. Neuenschwander. 1984. Seedbank contribution to shrub regeneration following clearcutting and burning. On file at Nat. Forest Fire Lab. 33 p.

Mueggler, W.F. 1965. Ecology of serai shrub communities in the cedar-hemlock zone of northern Idaho. Ecol. Monog. 35:165-185.

Mueller-Dombois, D. and H. Ellenberg. 1974. Aims and Methods of Vegetation Ecology. John Wiley and Sons, New York. 547 p.

Noble, I.R . 1981. Predicting successional change, pp. 278-301. In: Fire regimes and ecosystem properties, Proc. of the Conf. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep.

Noble, I.R . and R.O. Slatyer. 1977. Postfire succession of plants in Mediterranean ecosystems, p 27-36. IN Proc. of a Symposium on the environmental consequences of fir e and fuel management in Mediterranean ecosystems. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. WO-3.

Noble, I.R. and R.O. Slatyer. 1980. The use of vital attributes to predict successional changes in plant communities subject to recurrent disturbances. Vegetatio 43:5-21.

Noste, N.V. 1982. Vegetation Response to spring and fa ll burning for w ild life habitat improvement. In D.M Daumgartner (editor) Proc. of a Symposium on site preparation and fuels management on steep terra in .

Odum, E. P. 1969. The strategy of ecosystem development. Science 164:262-270.

Peet, R.K. and N.L. Christensen. 1980. Succession: a population process. Vegetatio 43:131-140.

P fis te r, R.E., B. Kovalichik, S. Arno, and R. Presby. 1977. Forest habitat types of Montana. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. INT-34. 174 p.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 55

P fis te r, R.O. and S.F. Arno. 1980. Classifying forest habitat types based on potential climax vegetation. Forest Sci. 26:52-70.

P ickett, S.T.A, 1976. Succession: an evolutionary interpretation. Am. Nat. 110:107-119.

Potter, M.W., S.R. Kessell and P.J. Cattelino. 1979. FORPLAN - a FORest PLANning language and simulator. Envir. Man. 3:59-72.

Rowe, J.S. 1979. Concepts of fire effects on plant individuals and species. In: Fire in Northern circumpolar ecosystems, Proc. of a Symposium, Fredericton, New Brunswick.

Schmidt, W.C. 1980. Understory vegetation response to harvesting and residue management in a 1a rc h -fir forest. In: Environmental Consequences of Timber Harvesting in Rocky Mountain Coniferous Forests. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. INT-90

Schmidt, .W.C., R.C. Shearer, and A.L. Rowe. 1976. The ecology and silvicu ltu re of western larch forests. Forest Service, U.S. Dept. Agric. Tech. Bull. No. 1520. 56 p.

Shearer, R.C. 1976. Seedbed characteristics in western larch forests after prescribed burning. Forest Service, U.S. Dept. Agric. Res. Paper INT-167. 26 p.

Shugart, H.H., T.R. Crow and J.M. Hett. 1973. Forest succession models: a rational and methodology for modeling forest succession over large regions. Forest Sci. 9:203-212.

Shugart, H.H., W.R. Emanuel, D.C. West and D.L. Deangel is. 1980. Environmental gradients in a simulation model of a beech-yellow poplar stand. Math. Biosciences 50:163-170.

Shugart, H.H. and D.C. West. 1980. Forest succession models. Bioscience 30:308-313.

Shugart, H.H. and J.M. Hett. 1973. Succession: sim ilaritie s of species turnover rates. Science 180:1379-1381.

SPSS Inc. 1983. SPSSX User's Guide. McGraw-Hill Book Co., Chicago, Illin o is . 802 p.

Stage, A.R. 1973. Prognosis model for stand development. Forest Service, U.S. Dept. Agric. Res. Paper INT-137. 32 p.

Steele, R. 1984. An approach to classifying serai vegetation within habitat types. Northwest Sci. 58:29-39.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 56

Steinhorst, R.K., P. Morgan, and L.F. Neuenschwander. 1984. A stochastic-deterministic simulation model of shrub succession. Ecol. Model, (in press).

Stickney, P.F. 1980. Data base fo r post fir e succession, f ir s t six to nine years, in Montana 1arch-fir forests. Forest Service, U.S. Dept. Agric. Gen. Tech. Rep. INT-62. 133 p.

Suzuki, T. and I. Umemura. 1974. Forest Transition as a stochastic process II, pp. 358-379. In: J. Fries (Editor) Growth Models for Tree and Stand Simulation. Res. note 30. Dept. of Forest Yield Research, Royal College of Forestry, Stockholm, Sweden.

USDA. 1965. Fowells, H.A. (E d ito r). Silvics of forest trees of the United States. Agric. Handbook 271. Forest Service, U.S. Dept. Agric. 762 p.

van Hulst, R. 1978. On the dynamics of vegetation: patterns of environmental and vegetational change. Vegetatio 38:65-75.

Waggoner, P.E. and G.R. Stephens. 1970. Transition probabilities for a forest. Nature 225:1160-1161.

West, D.C., H.H. Shugart and D.B. Botkin. 1981. Forest Succession: Concepts and Applications. Springer-Verlag, New York. 517 p.

Whittaker, R.H. (E d ito r). 1973. Ordination and Classification of Communities. Dr. W. Junk, the Hague. 737 p.

Zamora, B.A. 1981. Understory development in forest succession: an example from the Inland Northwest, p. 32-44. In J.E. Means (Editor) Proc. of a Symposium on Forest Succession and Stand Development Research in the Northwest. Forest Research Lab., Oregon State Univ., Corvallis, Oregon.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 57

APPENDIXES

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 58

APPENDIX A

List of the species which were modeled.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 59

APPENDIX A

List of the most frequently occurring or the most dominant plant species on the PSME/PHMA habitat type. Also included is the common name and the four letter abbreviation for that species.

TREES GRASSES

Larix occidental is Agropyron spicatum - AGSP (western larch) (Bluebunch wheatgrass) Diameter classes: Calamagrostis rubescens WL<4-less than 4 " dbh (pinegrass) - CARU WL>4-greater than 4" dbh Carex concinnoides - CACO WLAL-total cover a ll dbh (northwest sedge) Pseudotsuga menziesii Carex geyeri - CAGE (Douglas-fir) (elk sedge) Diameter classes: Carex rossii - CARO DF<4-less than 4" dbh (Ross’ s sedge) DF>4-greater than 4" dbh DFAL-total cover a ll classes SHRUBS FORBS

Acer glabrum - ACGL Achillea millefolium - ACMI (mountain maple) (yarrow) Amelanchier a ln ifo lia - AMAL Antennaria racemosa - ANRA (serviceberry) (woods pussytoes) Ceanothus velutinus - CEVE Arnica cordifolia - ARCO (snowbush) (Heart-leafed arnica) - LOUT Aster conspicuus - ASCO (Utah ) (showy aster) Physocarpus malvaceus - PHMA Balsamorhiza sagittata-BASA (ninebark) (arrowleaf balsamroot) Prunus virginiana - PRVI Chimaphilla umbel lata -CHUM (chokecherry) (prince's pine) Rosa gymnocarpa - ROGY Epilobium angustifolium-EPAN (rose) (fireweed) Salix scouleriana - SASC Fragaria vesca - FRVE (Scouler's willow) (strawberry) Spiraea betulifolia - SPBE Fragaria virginiana - FRVI (spiraea) (Virginia strawberry) - SYAL Goodyera oblongifol1a -GOOB (snowberry) (rattlesnake plantain) Vaccinium globulare - VAGL Hieracium albertinum and (blue huckleberry) albeflorium (hawkweed)-HIAL

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 60

APPENDIX A (c o n 't)

List of the most frequently occurring or the most dominant plant species on the PSME/PHMA habitat type.

SUBSHRUBS FORBS (con't)

Arctostaphylos uva-ursi - ARUV M itella stauropetala -MIST (kinnickinnic) (starry mitrewort) Berberis repens - BERE Thalictrum occidentale (creeping Oregon grape) (meadowrue) - THOC Linnaea borealis - LIBO - XETE (twinflower) (beargrass)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 61

APPENDIX B

Species Response Groupings

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 62

APPENDIX B

Species Response Groupings for the 33 species in the PSME/PHMA habitat type.

TREES

Group 1 - Shade tolerant (climax) Pseudotsuga menziesii

Group 2 - Shade intolerant (serai) Larix occidental is Pinus ponderosa*

Group 3 - Serotinous serai Pinus contorta*

SHRUBS

Group 4 - Root-crown sprouting serai Prunus virginiana Salix scouleriana**

Group 5 - Root-crown sprouting climax Lonicera utahensis Rosa gymnocarpa

Group 6 - Root-crown sprouting meso-seral Acer glabrum Amelanchier a ln ifo lia

Group 7 - Light-seed producing serai Salix scouleriana**

Group 8 - Soil dormant seed producing serai Ceanothus velutinus

Group 9 - Rhizomatous climax Vaccinium globulare Symphorocarpus albus Spiraea betulifolia

Group 10 - Rhizomatous meso-seral Rubus p arvifo lia

Group I I - Root-crown sprouting and rhizomatous climax Physocarpus malvaceus

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 63

APPENDIX B (c o n 't)

Species Response Groupings for the 33 species in the PSME/PHMA habitat ty p e.

SUBSHRUBS

Group 12 - Repent mat-forming climax Arctostaphylos uva-ursi Linnaea borealis

Group 13 - Rhizomatous climax Berberis repens

GRASSES

Group 14 - Mat-forming rhizomatous climax Calamagrostis rubescens

Group 15 - Tufted rhizomatous climax Carex concinnoides Carex geyeri

Group 15 - Tussocked or bunched climax Agropyron spicatum Carex rossii

FORBS

Group 17 - Widely-dispersed. lig h t seed producing serai Epilobium angustifolium

Group 18 - Locally dispersed lig h t seed producing serai Achillea m illefolium ** Hieracium albertinum

Group 19 - Rhizomatous climax Arnica cordifolia Antennaria racemosa

Group 20 - Stoloniferous serai Fragaria vesca Fragaria virginiana

Group 21 - Obligate climax Chimaphilla umbel lata Goodyera oblongifolia

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 64

APPENDIX B (c o n 't)

Species Response Groupings for the 33 species in the PSME/PHMA habitat type.

FORBS (con't)

Group 22 - Rhizomatous serai Thalictrum occidentale Mitel la stauropetala

Group 23 - Caudex perenniatinq serai Balsamorhiza sagittata Achillea millefolium

Group 24 - Stout rhizome climax Xerophyllum tenax

* Species was not modeled but used to create a response group to facilitate addition of new habitat types.

* * Species demonstrates duel revegetation mechanisms

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 65

APPENDIX C

Transformations and Interactions used in Regression analyses

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 66

APPENDIX C

Transformations used in the regression analysis for model construction.

TRANSFORMATIONS

VARIABLES Elevation (feet) PHMA (%) Aspect (degrees) CARU (%) Slope (percent) CEVE {%) Severity type (categorical) AMAL+ACGL+SASC (%) Treatment type (categorical) (CAGE+CARU) (%) Age (years) DBH (inches) Tree canopy cover (CC) (percent) Predisturbance coverage (percent)

SINGLE VARIABLE TRANSFORMATIONS (Agemax - Age)**5.0 CC**2 (Agemax - Age)**3.0 Age**2 (Agemax - Age)**(0.15) Age**3 Age / (1.0 + Age**2) 1 / Age 1 / CC INTERACTIONS Elevation / Aspect CC / Age Slope / Aspect CC**2 / Age**2 POWER TRANSFORMATIONS Age**(0.15) Age**(-0.20) Age**(0.40) Age**(-0.30) Age**(0.35) Age**(-0.40) Age**(0.65) Age**(0.50) Age**(0.10) Age**(-1.50) Age**(0.25) Age**(-2.00) CC**(0.40) CC**(0.30) CC**(-0.01) CC**(0.25) CC**(-0.20) CC**(-1.50) CC**(-2.00) CC**(-0.40) CC**(-0.60) CC**(0.15)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 67

APPENDIX C (c o n 't)

Transformations used In the regression analysis for model construction.

TRANSFORMATION

SIGMOID TRANSFORMATIONS EXP( 1.0-Age/Agemax) /O.7 )**5 .0 )) EXP( 1. 0-Age/Agemax) /O.6 )**6 .0 )) EXP( 1 .0-Age/Agemax) /O.9 )**8 .0 )) EXP( 1.0-Age/Agemax)/O.7)**8.0)) EXP( 1 .0-Age/Agemax) /O.8 )**8 .0 )) EXP( 1.0-Age/Agemax)/0.8)**9.0)) EXP( 1.0-Age/Agemax) /O .8 )**1 0 .0 )) EXP( 1.0 -Age/ Agemax) /O.6 )**4 .0 )) EXP( 1.0-Age/Agemax)/0.9)**10.0)) EXP( 1.0-CC/CCmax) /O.8 )**5 .0 )) EXP( 1.0-CC/CCmax) /O.6 )**6 .0 )) EXP{ 1.0-CC/CCmax) /O,8 )**1 0 .0 )) EXP( 1.0-CC/CCmax)/0.7)**8.0)) EXP( 1.0-CC/CCmax)/0.9)**8.0)) EXP( 1.0-CC/CCmax)/0.7)**5.0)) EXP{ 1.0-CC/CCmax)/0.7)**8.0)) EXP{ 1.0-CC/CCmax)/0.8)**9.0)) EXP( 1.0-CC/CCmax)/0.6)**4.0))

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 68

APPENDIX D

Sample Interactive Data Entry Session.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. r* 'iN f OR<;uM

ExtxUTIUtl Cir kOHSUn FOLLOWS i PSQG 69

FOR,St succession ftotiel

iS a CQnoHter nodel which predicts the c « ver of ma j or plant speciws eai^tino on é habiter tvpe over time.

I>o vov wish fvrther information on the operation of this model? u l f «se answer Y :

This computer model reads input in fo rm atio n qiven by the user «no u t i l ties the input in fo rm a tio n in a number of m v Ifip le re g ressio n e o u atm n s. These regression equations predict the coverages of the major soecies in .« habitat type phase over a user-spec if led time spun , The succe'ssional '-imiUation starts on the fifth year after the stand renoving dis i vrp*»nce

The user w ill be ashed a variety of questions per t am mq to; t. The s i t e to be modeled. 2. The tin e p e rio d and in te r v a l to model. T, The post-disturbaoce coverages of the major plant species. 4. The types of outputs to be generated

It IS important that the user input only one value per prompt (question) and end the e n try w ith a c arrag e re tu r n . I f there are any Questions concerning ifie data e n try p ro ced u res, p lease consul, t ttie USER'S GUIDE b e fo re proceeding .

DATP ENTRY PROCEDURE

Please enter « title for vour simulation run :

The title cannot exceed 60 characters and should describe the unique 4Soect5 of T h is s im u la tio n . ( e i: BIG FORK CREEK TIMBER UNIT P'JhE/PHMA, DR Y > 'DEMO RUN PSME/PHMA. DRY BOB KEANE

Please enter the number corresponding to the h a b ita t type phase which you wish to model I f you d e s ire more in fo rm atio n on which habitat type phase yeor land area keys to, please consult th e p u b lic a tio n "FOREST SUCCESSION ON FOUR HABITAT TYPES IN WESTERN MONTANA" to obtain the necessary information.

The phases implemented in this model are: 1 - PSHE/PHNA«DRY 2 - PSNE/PHHA,MOIST 4 - ABLA/XETE,VACL 5 - ABIA/XETE,VASC

Please enter the habitat type phase number: fern An entry of "2" would cause the model to simulate succession on the PSME/Phm a , MOIST habitat type phase.)

THE INPUT OF SITE VARIABLES

Please enter the elevation of the disturbance site in feet ( e i : > 4500)

Enter the .i ^.pec t of the site in degrees: ( ex : >350 - th is would be a n o rth e rly aspect)

Please enter the slope in percent; (exi>as>

INPUT OF PRE-DISTURBANCE VEGETATION COVERAGE

You w ill now be presented with the latin name for each of the ma)or species occurring on this habitat type phase. After the name, please enter the coverage (cover class or percent) for that plant species. (e : I Acer qlabrum >45)

There are two ways to e n te r p re -d is tu rb a n c e c o verag es. you Can enter coverage classes or the actual percent of canopy coverage.

5o you wish to enter cover classes? (Please e n te r "Y" ' yes) or "N" (no>>

The Cover Tlasses implemented in th is model are:

D - zero or no canopy coverage T - trace or 0.1 to 1.0 % can. c o v . 1 - 1.0 to 5 0 % can. cou. 2 - 5.0 to 2 5 .0 Z Can. cov 3 - 25.0 ta SO.O X can. cov. 4 - 50,0 to ? 5 . 0 %can. cov, 5 - 75,0 to 95.D % can. cov. 6 - 95 0 to lOR.O % Can cou.

Please use only these values for canopy coverage codes.

Fnter the coverage for all tree species :

Enter the average Diameter at breast height 13

Enter the average Basal Area of the stand in square feel per acres

nnter the coverage for DouglaS-fir less than 4 inches DBh ( DF(4)

Erttwr The coverage for Dsuglas-fir greater than 4 inches DBH (DF>0):

E n ter the coverage fo r a l l D o w g la s -fir

E n ter the coverage fo r Acer glabrum (ACGL) or mountain maole;

Enter the coverage fo r Arnelaneh ie r a l n i f e l i a lAMAL' or serw iceborry:

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. With nn vi^iblv evidence of Ce*othvs »n me site. H«wewer, p re sen ce of Ceenothws seed on s i t e c jn w. n«iri econd, are there many senescent Ceanathvs 0 l*nts in the stand which do r»ot constitute great coverage? If the answer* is yes t u either one of these questions please enter "Y", otherwise enter "N* .,.

( The cvveraqe far Lonicera vtahensi* (LOUT) or Utah honeysuckle:

E n te r the coverage f a r PhysoCarpvs nalw aceus (PHMA) or n ih e b a rk :

Enter the coverage far Prvhws virginiana (PAVl) *r chokecherry:

Enter the coveraoe far Rasa gynnoearpa or wild rose: >T

Gtitpr the coverage far Salim scowleriana or Scouler's willow:

Entpr the coverage far Spiraea betviifolia *r white spiraea:

Enter the coverage far Synphoncarpas altvs ( 5YAL ) or snowberry;

Enter the coverage far Vaccinivm globulere or blue huckleberry:

Elites the coverage for Arctostaphylas uva-ursi (ARVV) or hinnikinnic:

Entt*r the coverage fo r B e rb e ris repens < BERE) or c re e p in g Oregon qpripe;

Enter the coverage for Linnaea boreal is (LIB0> or twmflower: >0

Eiit(?r the coverage fo r Agropyron s p ic a iv n (ACSP ) or blwebvnch wheatgr js s :

Enter the coverage for Calanagrostis rwbescens (CARU) or pinegrass :

Enter the coverage far Carei coneinnoides (CACO) or northwestern sedge:

E n ter the co verage f a r Carem g e y e ri or e lk sedge: >2

E n te r the coverage f a r C a re t r o s s i i (CARO) or Ross sedge : >0

Enter the coverage for Achillea millefolium (ACMl> or yarrow: >T

Ent»r the coverage far Antenneria racemose (ANRA) or wood's pvssytoes

E n ter the coverage fo r A rn ic a c o r d l f a l i a (ARCQ) or h e a r tle a fe d arn ic a :

E n te r the coverage f a r A s te r eonsplcuus (ASCO) or showy a s te r: >0

Enter the coverage for Balsamorhita sagittate (BASA) or arrowleaf balsamr<,#t >r

Enter the coverage for Chimaphila umbel lata (CHUM) or pipsissewa: >T

Enter the coverage for Cpilobiun anguslfolium (EPAN) or f ireweed : >0

Elf ewewd (EPAN) has the potential to disperse many light seeds over wide rannc Is there evidence of Fireweed in areas that are off-site? Please enter yes or no (N).,.

Enter the coverage for Fragaria vesca (FRVE) or strawberry: )T

Ent»?r The coverage for Fr agar ia virginiana (FRUI> or Virginia strawberry : >0

Enter rhe coverage for Goodyera oblongifolia (GOOB) or rattlesnake plant.tm: >0

Enter the coverage for Hieracium spp. or hawk weed :

Eotcjr the coverage for M itella stauropetala (MIST) or starry mi trewor t : >T

Enter the coverage for Thallctrum occidentale (THOC) or western meadowrye; >T

Enter the coverage for Xerophyllum tenax (XCTC) or beargr.:ss : >0

THIS IS THE END OF THE FRE-DISTURBAHCE VEGETATION COMPOSITION ENTRY PROCEOURf

INPUT OF MANAGEMENT VARIABLES

Please enter the number corresponding to the treatment type which w ill be implemented on the disturbance site. The treatment types and their respective numbers are:

1 ' WILDFIRE ? - BROADCAST BURN 3 - MECHANICAL SCARIFICATION (in c lu d e s p i l e and burn) 4 - NO SITE PREPARATION

Plonte enter the treatment type number: (ex : an entry of 2 wuvld result ifi modeling a broadcast burn treatment disturbance)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. riK'ase »«'r rho number cerrf.Bonding the inT«'f«sjtv or .Mvit i;v , «1 rhe r.Brfrment. The s^eventv Type^ with rhe i r r t-spvc t i vi-' niinbtr--, n .

1 - LIGHT OR LOW SEVERITY Page 71 i? - MODERATE SEVERITY 1 - HfGH OR HOT SEVERITY

RI e : s e enter the 'Severity type number : ( e m : an entry of 2 r u 1 1 s in the modeling of a noderately severe treatment) >2

INPUT OF THE TIME CONSTRAINTS Too W ill be ashed to enter two time variables to model accession. The first time variable is the total amount of time ( m vi-. you wish to model. The second time factor is the tine irurum-nt •»t which von wish t# examine the successional cover ai#ms For example, if you wi-ihed to model a disturbance sire from wear 5 to year ?00 ( a f t e r d is t u r b a n c e ) and you want to lonfa at thf %pecles coverages every 10 years, simply enter 20D after the first prompt and 10 after the -second. There is, howevw, , one rule which you must remember : the model can only handle ®-n t , ne intervals. This means that the time span < in this examp Im 200 ) t h i s c a s e 20 0/10 = 2 0 ) .

Piea-ie enter the time span which you wish to model succession. (e*; an entry of 200 would result m ttte prediction of the major species coverages wp To the 200th ye.jr after disturbance) >200

Ple»'-.e enter the time interval at which you wish to view success n»n . (e*: an «ntry of 20 would allow you to examine the coveraoes □ f the major plant species every 20 wears wp to the maumum year you spec ifled above)

Would you like to see the results of your successional u 1 a 1 1 0 n If. tabular form? (Please enter "Y“ (yes) or "N" (no)) )G

»*mx» ERROR «»»»»

A *’ Y * or a was not entered. Please try again ...

Would you like to see the results of your svccessional simulation in tabular form? (Please enter "Y" (yes) or "N" (no)) )Y

liuvld you like response graphs for the major species? (P le a s e e n t e r "Y" ( y e s ) or "N" ( n o ) ) >Y

SUMMARY OF THE DATA INPUT SESSION THE FOLLOWING ARE THE VALUES WHICH WERE ENTERED: <1> EtE V (F T )» 4 800. <2) ASPECT ( OEG)= 160. ( 3 ) SLOPE (ï)-= 45. <4) TREATMENT TYPE <1-W F , 2 - 8 8 , 3-M S , 4-WP) = 1 TIME SPAN TO MODEL » 200 YRS (7) TIME INTERVAL * 25 YRS <«) TABLE FORMAT (O-NO. l-Y E S ) » 1 (9> g r a ph g e n e r a t io n (O -NO , I-Y E S ) = 1

If you wish to change any of the input values, ,please enter the nnmbi^r (in parenthesis) next to the input valve which you wish to change, If y»u are satisfied with the entries, enter zer n ( (I ) to continue, 'ex: if you wish to chahae the elevation value, enter the n u mbef I i )0 PREDISTURBANCE PLANT SPECIES COVERAGES THESE VALUES ARE PECENT COVERAGE EXCEPT DBH 6 BA;

MOTE : The m ;dpoini$ of the ic over classes w ill be presented. f I ) CCAL) 6 2 ,5 ( 2 ) DBH > 13. Q ( 3 ) BA > 1 3U . < 4) DF (4 ) 3 , n ( 5 > DF>4> 6 2 .5 ( 6 ) DFAL > 6 2 .5 ( 7) ACGL) 3 .0 ( 0 ) AMAL> .5 . 0 < 9 ) CEVE) 0 . 0 LOUD 0 .0 ( I D PHMA) 0 .5 (1 2 ) PRVI ) 0. n ( I 3 > HOCY) 0 .5 (1 4 ) SASC) a 5 (15) SPBt) 15.0 (1 6 ) SYAL > 7 . 9 (1 7 ) VACL) 0 .0 ( Ifi) ARUV) 0 .0 ( 19) BERE) 3.0 (20 ) LIBD) Q . 0 (21 ) AGSP> 0 .5 CARU) 1 5 .0 (2 3 ) CACO) 0 . 0 i2 4 ) CA(,F> •15.0 (2 5 ) CARO) 0 .0 (2 6 ) ACMI ) 0 .5 (2 7 ) ANPA) 0 . 5 <28 > ARCO) CHAN) -,. Ü (33) FRVE) 0.5 (3 4 ) F RVI > 0 0 (3 5 ) GOOB) Q . U (3 6 ) H iAI.) 0 . L ( 37 ) Miy T) 0 .5 (3 8 ) THOC) 0 .5 < 39 ) XETE) 0 . 0 [ 40 )

It you wish to change any of the pre-disturbance coverages, please 4 ntnr the number (in parenthesis) next to the plant name whose coverjos’ you wish to alter. If no corrections are necessary, ootmr lero (O' «Ex; to change the total coverage of all tree spt-cies (CCAl ) , <»n ter the number I) )1 1

En tor the coverage for Physocarpus malvaceus (PHMA) or n tneb.ir k : >4 PREDISTURBANCE PLANT SPECIES COVERAGES THESE VALUES ARE PECCNT COVERAGE EXCEPT DBH & BA:

MOTE : The midpoints of' the cover classes w ill be pre'tented . ( 1 ) CCAL) 6 2 .5 ( 2 ) DBH > 13.0 < 3) BA ) 130. < 4> DF<4> 3 ,0 ( 5 ) DF>4> 62.5 t 6) DFAL) 62.5 ( 7) ACGL) 3 .0 I 8 ) AMAL> 3. 0 < 9 ) CEVE) 0 .0 (1 0 ) LOUT) 0 . 0 (1 1 ) PHMA) 62 . 5 ( 12> PRVI > 0 . 0 ( 1 .i > ROGY) 0 .5 (1 4 ) SASC) 0.5 (15) SPBf > 15 D (1 6 ) SYAL ) 3, n (1 7 ) VAGL) 0 . 0 < 18) ARUV) 0 . 0 (1 9 ) BEPE) 3.0 <20 > LIPO) 0 .0 (21 > ACSP ) 0 .5 (2 2 ) CARU) 15. 0 (2 3 ) CACO) 0 . 0 (24 > CALF) ■I . 0 (2 5 ) CARO) 0 . 0 (2 6 ) ACMI > 0 .5 (2 7 ) ANRA) 0 . 5 (2 9 > AHCÜ) 0 . 5 (2 9 ) ASCO) 0 . 0 (3 0 ) BASA) 0 ,5 <31 ) CMUM) 0 . 5 ( 32 ) EPAN) 5 .0 (3 3 ) FRVE) 0 ,5 (3 4 ) FRVl ) 0 . 0 (3 5 ) GOOB) 0 . 0 (3 6 ) HI A D 1 . 3 ( 37 ) M IST) Ü .5 (3 0 ) THOC ) 0 ,5 < 39) Xl:TF> 0 . Ü ; 40 ) ) (1.0

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. îf V (#1 wish to Chang* ,*ny of ihp ore-disturbance coverage*-, piDa'.i* t*nter the* n«mb*r ( m parenthesis) next to the pl.int name who*\e vow wi to alter. If no corrections are necessary, enter zero CO). Page 72 \E<; to r hatiQ* the total coweraue of ail tree spec le*, et»ter>0 the nwmher I)

foü ttav* the option of either prir>ting th* output on this terminal or on the line printer. Do you wish to view the output on this t ermin.» I Please answer yes .

DATA i n p u t SESSION NOW CONCLUDED. SIMULATION WILL COMMENCE,

CURRENTLY SIMULATING YEAR 25.

CURRENTLY SIMULATING YEAR 5 0 .

CURRENTLY SIMULATING YEAR 75.

CIIRRFNTLVSIMULATING YEAR to o .

CURRENTLYSIMULATING YEAR 125.

CURRENTLY SIMULATING YEAR IS O .

c u r r e n t l y SIMULATING YEAR 1 7 5 .

CURRENTLY SIMULATING TEAR 2 0 0 .

X»XXX«*KXXXXX»K»«»»•«»X- T IT L E :DEMO RUN PSME/PHMA, DRY BOB KEANE

D ESCRIPTIO N OF THE S IM U LA TIO N AREA: ELEVAT(ON : 4800. FEET TREATMENT TYPE ; WILDFIRE ASPECT : 160. DEGREES IN T E N S IT Y TYPE : MODERATE Si OPE ; 45. (DEGREES) HABITAT TYPE PHASE : PSMF/PHMA.DRY

SUCCESSIONAL PATHWAY DIAGRAM: AMAL-PHMA -) PSME/AMAL-PHMA PSME/AMAL-PHMA -> PSME/PHMA-CARU PSME/PHMA-CARU

xxxx-xxaxx x xi x

Press "C" to continue the display of output

SPECIES COVERAGE (CLASSES) AT VARIOUS AGES (YEARS) Spp name 25 58 7 5 100 125 150 1 75 200

CCAL 3 4 4 4 4 4 4 4 DBH 2 5 8 11 13 14 15 16 BA 22 67 105 136 159 177 190 J V9 DC (4 0 0 0 0 0 0 0 0 DF >4 2 3 3 3 3 4 4 4 DFAL 3 4 4 4 4 4 4 ACGL 2 2 2 2 2 2 2 2 AMAL 5 3 3 3 3 3 3 3 CCVE 0 Q 0 0 0 0 0

P r e s s "C" To continue the display o f OMtPUt )C

SPECIES COVERAGE (CLASSES) AT VARIOUS AGES (YEARS) Spp name 2 5 50 75 100 125 150 175 200

ARUV 0 Q 0 0 0 n 1) BERE T T T 1 1 L fB O 8 0 0 0 0 0 u 0 ACSP 0 0 Q 0 0 0 0 fl CARU 2 2 2 2 2 2 J CACO 0 0 0 0 0 1) 0 Ü CAGE 2 2 2 CARO 0 0 0 0 0 ■' ACMI r T r T T T r 1 ANRA 0 0 0 0 U 0 Q 0 ARCO » 0 0 0 0 0 0 n ASCO 0 0 0 0 0 u ;t BASA T T T T T r r CHUM T T T TTT r r EPAN f 0 0 G 0 0 (i 0 FRVE 1 r 0 0 0 0 0 0 FRV C 8 0 0 0 0 0 a (1

P re s s C ' to continue the d i s p l a y o f o u tp u t )C

SPECIES COVERAGE (CLASSES) AT VARIOUS AGES (YEARS) Spp name 2 5 SO 75 too 125 150 175 2 1)0

GOOB 0 0 0 0 0 0 0 II HIAL r T T T T T T r HIST T T T TTTT r THOC T T T T T r T XETE 0 0 0 0 I) 0 0

P r e s s "C to continue the display of )C

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. F lf ? 4 s e en t e r the soec ies abbreviation for the plant wh i c h y o u w ish a auccessional graph. If vou wish to see a list of the abbreviat ions with the plant names, singly enter a question nark (?). Page 73 To terminate the graphing sequence, enter END.

XCOVER* 4Ü 9» 120 160 2<‘U ( AtL IN fLAPS Enter species abbreviation (type END to terminate or ? for species litut); >CCAL 10 0% *

90% + I 80% 1 70% I 60% I 50% I 40% I 30% I 20% I 1 0% Î

%COVER* 40 80 120 160 200 < AGE IN YEARS Enter species abbreviation END

The coverage, D&H and basal area estimates were derived from regression equations. Three important regression statistics are available for each equation: 1. Standard error of the regression line (s). 3. Coefficient of détermination (R square). 3 Degrees of freedom (N). However, regression equations for some species could not be estimated due to inadaguacies in the data set or site variablities within the plant species. In these cases, the three regression statistics are preseofed as zeros.

Do you wish to examine The regression statistics for any species eg ua 1 1 on ? E n te r Y ( y e s ) or N Y

To examine the i^ta t isf ics you must enter the four letter abbreviation for the ’-'.oecies which that equation concerns. Enter a question mark < ? > to receive a list of ail ihe species with the abbreviations or enter "END" to terminate this routine.

Enter The four letter abbrevia1 1 on : ( ex :PHMA> )PH#1A

t h f 'i I H I 1 -, t I (, I, i ij / f’ HMA flr ; Sfjiidard Error 13 . : 1W R suvare - 76 Dir'tir of Frei'din - 17

Enter The four letter abbrevlation : (exiPHMA) >CCAL

Tlie S t a t i s t i c s f o r CCAL a re : Standard Error = 20.852 R square = 54 Degrees of freedom = 50

Enter the four le tte r abbrev ia t i on ; < ex :PHMA) )END

Would you like to implement another treatment on the same land area, but>N after the previous treatment? Please enter "Y" or "N" ...

Would you like *o implement another treatment on the same disturbance area under the same site and time conditions') Please>N enter "Y" or ”N" ...

TUTc; mnnn tmc crcctnw mac wm.i rwhrn uahc a hirrc aav

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 74

APPENDIX E

List of the Pathway Regression Equations.

This appendix is composed of many tables containing regression equations stratified by pathway for each species. Each variable in the equations has been assigned a fo u r-le tte r abbreviation to condense the format. A key to the abbreviations is presented at the beginning of the appendix. The appendix is also s tra tifie d by the two phases; PSME/PHMA, dry and PSME/PHMA, moist. Equations that were formed q ualitatively (not from regression analyses) have zero values for the coefficient of determination (R squared), number of observations (N), and standard deviation about regression (STD DEV).

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ABBRevlflTION KEY FOR TRANSFORMATIONS Page 75 AOBkEVIATION TRANSFORMATION FORM ELEV ELEVATION / 100.0 ASPT ASPECT SLOP SLOPE SVRT SEVERITY TRMT TREATMENT TYPE AGE! AGE TREE TREE CANOPY COVER(CC) CCPl CC**2.0 /lOO.O AGE2 A6E**2.0 / 100.0 AGE3 A6E*»3,0 / 100000.0 PHMA PHMA CARU CARU CEvE CEVE SHR3 ( AMAL ♦ ACGL + SASC > GRSS ( CARU ♦ cage ) CCAG CC / AGE CCA2 CC**(2.0) / AGE**(2.0) AGEA A6C**<0.1S) AGES AGE**(-0.01I AGES A6E**(0.90) EXPl EXP<(<1.0-AGE/AGEMAX)/0.7)••(5,0)) EXP2 EXP<((1.0-AGE/AGEMAX)/0.6)^«(6>1/10000 EXP3 EXPiM 1.0 - A6E/A6EHAX»/0.9)^^(e.0)) EXP4 eXP<(<1.0-A6E/AGEHAX)/0,7)**(6> »/10E06 EXPb EXP I(I 1.0 - AGE/AGEMAX>/O.S)^^ia.O)) EXP6 CXPt(< 1.0 - AGE/AGEMAx)/0.e)^*(9.0)) EXP7 EXP< <(1.0-AGE/AGEMAX)/0.S)»»(10))/1000 AGE7 AGE^^(0.35) EXP8 EXPMd.O - AGE/AGEMAX)/0.6)**(4.0) ) CCP2 CC*^<-0.A0) AGE8 (AGEMAX - A6E)*»«5.0) / lOElO AGE9 (AGEMAX - AGE)**(3.0) / 10E6 AGIO AGE**<-0.30) AGll AGE**(-O.A0) AG12 AGE**(0.2S) CCP3 CC**(0.90) CCP4 CC*^(-0.01) COPS CC*^«-0.2) CCP6 CC*^(-2.00) / 1000.0 CCP7 CC*^(-0.60) EXP9 EXP(((1.0 - CC/CCMAX) / 0.6)**(9.0)) EXIO EXP(((1.0-CC/CCMAX)/0.6)**(6)J/10E6 EXll EXPC((1.0-CC/CCMAX)/0.8)**(10))/10000.0 EX12 EXP(((1.0-CC/CCMAX)/0.7)**(6))/1000000,0 EX13 EXP(((1.0 - CC/CCMAX)/0.9)**(10.0)) 1/CC 1.0 / CC 1/AG 1.0 / AGE AG13 AGE /(l.O + AGE»^2.0) CCP8 CC**(0.30) PREO PREDISTURBANCE COVERAGE SLAS SLOPE / aspect CCP9 CC**(0.2S) Dt)H DIAMETER BREAST HEIGHT (DBH) ELAS (ELEVATION / ASPECT) / 100000.0 AG14 AGE ••(-1.50) EX14 EXP(((1.0-CC/CCMAX)/0.6I**(9) • 1000,0 AGIS AGE ••(-0.90) EX15 EXP(((1.0 - AGE/AGEMAX)/0.9)**(10.0)) A616 (AGEMAX - AGE)**(0.15) AG17 (SQRT(AGE)) CPIO (CC**(-1.50)) EX16 (EXP(((1.0 - CC/CCMAX)/0.9)••(8.0)) AGIS (AGE**(-2.00)) EX17 (EXP(((1.0-CC/CCMAX)/0,7)••(5.0)) AG19 (AGE*«(0.60)) AG20 (AGE**(0.10)) EX1Ô EXP(((1.0 - CC/CCMAX)/0.7)**(8.0) EX19 (EXP(((1.0-CC/CCMAX)/0,6)••(9))/1000.0 AG21 AGE**(-0.20) CPU CC**(0.15) OUMY (DUMMY VARIABLE) TSEV «< SEV. TYPE TO ELIMINATE SPECIES TAGE «< AGE WHICH SPECIES DIES FROM STAND

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 76

APPENDIX E (con't)

Regression equations for PSME/PHMA, dry phase. Nine successional pathways.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pflfHW*» RFUHfSStON EQUATIONS FOR CCAL OR t o t a l iR rC CAfiCPY COVE® Pag

P»TH w E n n rs !::o h E o u a T ic fi Fo&M Rsa 371 DEV

1 C C A ts lHl.7<»A*j-.l3.9*i»»t*ElfP3+ ( • ! I ,327) «SVh T a . 74 24 l b . * ! 9

? CCAL = ( *1 P . ? * 6 > « Ek H34 1 5 . 9 3 8 » «TR>.T 0.9 0 Ifc 2 3 .0 9 5 i CCAL = 7 3 .0 8 “ * < - n . <*0 71 «E xp 3 C.51 68 2 0 .7 9 2

CCAL: -lU,t»6n*l-ll,«€xP3 n.S h 63 1 9 .1 0 5

h CCAL? 7?,FT7*«-.H,229»*EXP3 3.5 3 14 2 2 .4 9 6

7 CCAL: 6S.IR4*) -9,970WexP3 0 .5 7 32 2 0 .1 0 *

h r c A L * I2S.S90*l>tl»*i93l«CXP>*< -0.i31)*ASPT7f -0.9H2I«ELEV C. 71 52 1 6 .9 5 3 9 cents 69,630*(-XO.S79>«exP3 0 .5 9 J7 2 0 .1 3 9

• • • • • PA fM MA r REGRESSION EQUATIONS FOR OBM OR AVERAGE O0H OF STANO 4 INCHES)

P a fH P F 6RC S SI0K COUATIOrt FOPM »SQ .. STD oe v

I ie.0C7»l -O.GGSI•AGES*« -O,ItS)*StCP 5.93 26 1 .6 0 5

12,295*) -0.67GI«A8E8*{ 0.699T«SVHT 0 .9 1 36 1 .3 4 6

11,9)5*1 •0,62*i)*AGC8*< 0,e33)#SVkT 0 .9 0 Î * 1 . 5 ) 5

** 1 7 . 1 2 2 * ) ’ 6 . 7 6 A I «AGC9 0 .0 9 34 1 .’835

17.319*4 -6.886 1*AGC9 fl ,B8 52 2 .5 1 3

13.284*1 .0,63Cl#AGER n .86 34 1 .8 3 5

n n n z 13.906*4 -O.G99l*ACE8 0 .8 6 52 2 .6 6 3

-î.ii* = 1 7 ,9 1 1 * 4 - 7 . 0 l l» « A f i E 9 r ,97 50 2.<^62

ritiM - 16.960*4 •6,7931*AGE9 0.9fl 37 1 .8 7 5

* * PATHWAY REGRESSION EQUATIONS FOR F)A OR AVE STAND BASAL AREA [SO FT )

Pa Th hCCAfS SlON FOUATIOI* FOh R I'SO 37 0 OEV

L 4A 3 239,559*4 -8,27fl»*ASE8*4 -2.3721“SLOP 0 .9 0 25 3 5 .0 9 4

i. 19P.0 7G*(>10.ilG9) «AGta 0 .8 6 57 3 5 ,6 1 8

s 233.889*4 -8.775l*AGE6*4 *2.3011#SLUP 0.89 39 2 9 .0 6 0

« 161.889*4 -e,aO7t«A0C6 0 ,8 2 36 2 8 .9 6 3

5 209.562*4«83.9261•AGE9 fl.B 3 52 3 8 .2 3 9

133.326*4 •7.G69)*AGEa 0 .7 3 34 5 4 .7 3 9

7 = 156.169*4 -7.667) c a g e a 0 ,7 0 32 î 9 .? 6 1

(?A = 209.595*1-89.9951•A6E9 0 .8 1 50 4 2 .2 2 6

HA S 181.102*4-72,8561*A6E9 ij.T g 36 51.464

PATHUAT REGRESSION EQUATIONS FOR 0F <9 OR PSCuOOTSuGA M EN21ESII 4< 4 TN. 1

PATH REGRESSION EQUATION FOAM R5C STU OEV

t n F < „= 16.349*4 •5.201I*EXP3 0 .8 5 25 1 2 .9 0 4

C .73 0 .9 2 3 2 riF<4s 9.503*4 -3.5861 *tFM3*4 9,74)6 ) «SLAS* 4 5,dSl)*SVRT 20

3 OF

-25.677*4-10.018)*EXP5*4 0.706 )*ELEV*4 2.327 ) «AGE8*4 6,013>*SVRT 0.70 31 14.236

Û.7C 31 1 . 2 ) 8 S OF<‘*s 63.939*4 2.51A)*AGEa*4 -1,049I*CLCV*4 -6.302)*SVRT*t -9.917)»EKP3

6.699)*SVRT 0 .5 6 35 1 9 .2 9 4 6 0F<*»? -23.349*4 -8.857)•C»P5*< 1.073)«EtCV*) 0.119)#AGE6*4 1 6 .9 5 3 7 OF<**s 68.127*4-11.595)*EXP3+< -0.131)«ASPT*< -0*942>«ELEV*1 2.0G7)*AGE8 0 .7 1 32

0 .7 1 32 1 6 .9 5 3 PF<**a 68.127*4-11.S93>»CXP3*< -0.13l)»ASPT*4 -0.942 > •CtEVi ♦ ) 2,067)*ACE8

57 1 7 ,4 6 6 9 A F < *= 11.651*4 -9.9731#EXP3*4 2.358>*A6E8 0 .5 ?

* • • • • p a t h w a y r e g r e s s i o n EQUATIONS FOR 0F >4 OR PSCUOOTSUCA M E N Z IC S II (> * n . )

RSQ STO d Ev PATH «EGRESSION EQUATION FORM ■'

ll.404)*TRMT 0 .8 5 25 1 2 ,9 0 4 I OF >4= 75.204*4-10.5261*exP3*4*22.487)«SVRT*! -0.025)*EtA$*4 0 .5 8 57 1 6 .9 1 2 2 0 F > 4 : 4 3, 7 2 9 * 4 - 2 , 2 1 6 ) • AGE8 0 ,7 1 38 1 4 .5 8 9 3 Ü F>“*s 60.620*4-13.506)*CXP3 0 .7 1 34 1 3 .8 9 2 t OF>As -18.774*4 •2.S27)*AGE8*4 1.116)*ELEV*I 6.013)«SVRT

o .? o 31 I * * . 238 5 OF)**: -10,012*4 -2.518 ) •AGE8*4 1.4)44)*ELLV*4 6.302)«SVRT

0 .5 a 53 1 6 .2 4 7 6 0F>*«« 30.812*4 -2,114)*AGE8*4 6.699)*SVRT n.SO 50 1 8 .- 3 6 OF>»*s 4 2 . 4 2 5 * 4 - 2 * 0 6 7 ) zAGEO

o.'-o 50 1 8 ,7 9 6 OF>Rs 42,423*4 -2,067)*A6E8

n ,5 6 37 1 6 .- 6 8 GF>'*s 48.565*1 -2.35A1«AGE8

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * ** paTwLAy ftcskcssrow ravarro^s «-pm p fac cm «■sccpctsug a '-Efrrrsri ♦t o t a l ) Page 78

p a t h PlGP^SSIO^ FC'ATICN F OH" . . . «. wau \ - ' •'5.V

I rrA Ls 1 0 1 .T9A*( -1 5 .8 9 9 I«LKP3* C -1 ),5271«SUMT 0.7« 29 16.5 56 2 1FAL% -10.302»*LXP3*r 57.691)*SLaS*( -0 .3 1 1 1.PMF4 + t -0.2S6)«eLAS h.97 36 •»1.263 1 CFALs -n,633»*ExP3 n.9 7 57 OFALs -2G*951*< -10,(tl8»*iXP9+c 1.9081+ELLV 0.66 36 17.120 5 3FAL = 69.9??*< -9.917».£XP3 C .50 63 19.105 6 PFAL* 6.963*1 -0.857l:tXP3+C l.073)*ELEV 0.56 35 19.299 7 HFALs 110.550*1 .11.593>«EXP5+I -0*1311«ASpr*< -0.992»*ELEV 0.71 32 16 .«^53 8 pFALs 110,550*< -11.593>*eXP3+< -0.13I)*A$KT*( -0.992)*ELEV 0.71 32 16.953

9 PFAL* 6 0 .2 l6 * ( -9,973>»Ex PS 0.57 37 19.773

* * • • • PATHWAY REGRESSION EQUATIONS FOR ACGL OR ACER GLARRUM PAtM PCGPCSSIOr CQUATTON FORM RSC N STD OEv

1 ftCGLa - e . 139*4 0.959»*PRCO+4 -D.129»»EX12*4 2.727)*SVRT 0 .97 11 0.552

AC6Ls 2 -0.852*4 9,etO|*PRE0+c •1.05e)*EXP9*( 3.266)+SVHT+4 -2,060I*TRHT 0,75 29 1.093

Î ACGL* C ,262*4 0.759 I•PREO 0.59 17 1.376

ACGL: 12.001*4 10.9a2l*CEve*| -0.179I*GRSS 0 ,5 " 21 6. *69

5 ACGL: ? b ,728*4 l0.758l«CEVE+i -0.219)*GRSS+4 •0.13ll«ASP7 0 .73 16 6. . '1

6 ACGL* 9.796*4 0.257UCCP1 + 4 1.090»»CCA2 0.92 23 6.84*5

ACGLs -2,200*4 0.39R}*CCP6+I g.OB9)*PH4iA 0.53 17 3.798

6 ACGL: -7.776*4 0,392)«CCPG+4 1.319>*PRtO*| 0.169)«El EV 0.79 38 1.935

9 ACGL: -0.019*4 a,602»«CCAQ+4 1.037»*PR£U -0.9? 1* 6.556

•• * « * PATHWAY REGRESSION EQUATIONS FOR AMAL OR AMFl ANCHICR a l m f o l ia

PATH PCGf’ rSSIOA ESUATtON FOHH »SQ N STu OEV

1 AMAL = 0.008*4 1,OOOI*PREO*4 -S.250»«SVRT 0.6? 11 1.615

2 AMALs 17.538*4 -0.232 »*eLCv*( -0.079»*GRsS+4 1.966>*1/CC 0 ,7w 17 1.973

3 AMAL: -e .6 « 7 *( *0,306I*ELEW*4 0.213>«ASPT+4 2 9 .3 S 2 )é SLAS*4 l,975>*l/CC+< -O.OOe)»EXP2 0.8? 18 1.279

f* AMAL: 18.04*9*1 0 .6 8 1 >*PRCO*f •5.2961*SVRT 0,99 21 9.250

5 AMAL: 70.737+4 -2,16i»>0BH +C -5.2994#EXP9+< -0 .8 2 2 )* El EV 0.63 17 8.582

6 AHALs 144.959*4 -7.355»*TRMT*< -0.35l>»PMMA+< 1.216)*PReO*4 1.099»*SLOP 0.78 21 6.905

' 30,977+4 4J,306»«6PSS*4 -D.605)#ELLV 0.5? 28 6.290

« 31,520*4 0.650»*PREO94 0.19«»*GRSS*< -0.199)*CAPU+( -0 .9 2 1 )*ELEV+( -0.3Î2JASL0P 0,66 37 6.639

31.520*4 0.650)*PREO*4 0.198>*6RSS*4 •0.199)«CARU*< -0.921)"ELEV*f -0.352)*SL0P 0.66 37 6.639

#"* * PATHUAT REGRESSION EQUATIONS FOR CEVE OR ceakothus ve lu tin u s

path FCGflCSSlOK EQUATION FORM RSC FT? oEv

I crvE s 4).500*4 2«000)*TSEV*4 50.000|:TAGE 0. 0 0 0.000

3 ccve= 0.500*4 2.000*#7SEu*f SO.OOO>*T46£ 0, 0 0 0,000

i CEVE: 1,000*4 2.000»*TStv*i 50.000)«TAGE 0. 0 0 O.OflC

M CCVC: 1.136*4 -4>.l109»«ASPr*< 7 0 .0 0 0 )*T a GE 0.65 10 1.096

5 CEVE: 3.000+4 2.000»«TSCV*4 S0*04)0»«TAGC 1. 0 0 0. 300

6 CEvts 3.COO+4 2,000»#TSEv+( SO«OOOl*TAGE 0. c 0 0.300 10.5**2 , 7 CEVE: -95.996+4 2.328>«£l EV*4 -0 -5 0 9 t«PHMA*! ll,759)*SVRT*4 6.10? » *CCAG+4 80.0001 + TAGE 0.83 21 12,379 4 CEvE: -53.921*4 -ll.SQ9>«A6E3*4 l,390)*ELCV*4 -0,397>*PHMA+( 8.152I+TPHT+4 6.555) •CCAO+4 ' 0 ,00 0 t+TAGE 0.83 29 11.316 9 CEVE: •61.070*4 • 19.160 >"AGE3*4 2.200I*CLEV*C -0 ,3 1 2 M P hmA*( 6 .7 6 9 )+TRMT*( 6.980 » •CCAG+4 0 0 .000 >■TACC 0.3? 2k

*« + •• PATHWAY REGRESSION EQUATIONS FOR L^UT OR LONICERA UTAHCLSIS

RSO \ STO CEv PATM REGRESSlOA' EQUATION FORM

0.95 S 3.233 1 lo u t * 0.226*4 0,n9TI*CaRU*4 -0.0D2l«CCPl 0 o.OT-n 2 LOUT: 0.500*4 l.O00l*PREO*4 S.OOO»*TSEV 0. 0 0 5.00C 3 LOUTs 0.000*4 1.000I*PREO 0. 0 99 0.267 9 LOUT: -0.089*4 0,865)*PRE0*4 q.009)*TREE*| -0.023)#D8M 0.95 0.63 11 1, 800 5 LOUTs 0.732*4 0.036)*CCP1 13 I .*«6 6 LOUT: •3 ,011*4 D.0611«CCP1+I 10-S97|«A611 0.5? 3,126 7 LOUT: -o .o a o *( 0.001}«AGei*( 0.325)«PREO 0.50 I** 23 0.101 a LOUT: -0.097*4 D,9961*PHE0+4 0.005)«5LOP 3.75 O.:oo 9 LOUT: 0.000*4 1.000I*PAE0*43.000)*TSCV 0. 0 0

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • • • • r>ATMWAY REbHE

1 3 b .C 9 m *l 1 .2 1 5 #SLOP*< •>a.943»*CCMC' 2? 1 .6 AM 9 Ü.77t»»PREÛ*f .a.l98»"CC/'w4( -0.0491 *Err>? ■‘.79 ll. F O r

9 b 9 2 ,0 2 S *< O.A73»«PRED4( -1.142I*THLE4# • • • * • • * ► i CCP44( 11. 32#’ 1 «SV" T 4 31 17.*=>*0

^)93.Cam*< 0*e73)«PRC04( -1.142l«TRte*C >*CCP4*< ^ 1 . S 2 r \ #5VhT r'. be 21 l7.Dk,C 5 P 9 3 ,0 2 P + ( -1.142f#TRCE4f 0.8?jl#PREO*< |*CCP44( 11.32:>«SVHT '^.53 21 17.940 b - l b . 9 b S * ( 0.589J4PHEO*# l.324l#SLUP n .< 7 21 1 9.215 7 PHFA= - a i0 .7 ? A + ( 5.387#*ELEV4#-12.131|*CCA2*# -0 .2 7 » t *E X P 5*I 0 .3 7 P t*P R F n C.?h 1-» 1 3 . I l f

a pm « a = - a i o . 7 ? o * i 5« 3 8 7 )« C l EV4( -l2.131)«CCA24f - 1 .2 7 » ► *f «PS4# 0.376 1 •Pt'Cr 0.7& 17 u . i i é y 2 X 0 .7 S 0 *( 5,387>.tLEv*# -l2.13l>*CC/-a4< -0.274 ►#L*P54I 0 .3 7 * ) •P?" r, 17 13.119

• • • • « PATHWAY REGRESSION EGU«TlOHS FOR P»VT OH PPgfiiJS VIH61rjlA*'A

PATH P»F.K£SSIOr» EwUATIOH POHfi i#S'J 9T- oEV

1 PPWls 0.000-f ( 1.000>«PRE0 b 1 0 O.PQO

a PHVlA 0.00041 1 .0 0 0 I« P k CO 1 . 0 0.0-30

3 FRVI* 0.00041 l.OOOIaPRCO 0 . 0 0 P. 000

b nftvis C.OOO+l 0.200l«CCP64l 4.250|*PREC> 4 .6 0 IF 1 . 7=.0

b PPVts 0 ,0 0 0 4 ( 0.200>*CCP64( 4.2S0>*PRED n ,60 1» 1 ,7eP

6 PPVts 0.4SO*( 0.169I-CCP6 n.47 21 1 .744

7 r n v l s o .5 o r 4 t 0,113)*CCP6 4 1 .0 00

9 PPVCs 0 ,? o 0 4 { 0.113J4C C P6 ') .99 4 l.C-niO

0.*.(-04 ( I . " nij 9 p n v is #l.llil»CCP6 “

. PATHWAY REGRESSION EQUATIONS FOR ROGY OR ROSA GY^riOCAOPfl

PATH BEGPESSÏON fOUATrOtJ FOH« n ST-' nEv

1 ROtrTB 0.0004C l.O O O XPREO p 11 3 .001

? HOtits »n,09b4f 1.755I*PRE04< 0.411»*CCA2 34 3 .355

H0 6 T« 4 .b 9 S * ( -0.l2l)#Sl0P*f - 0 . 0 2 1 ►•CAHU 0 . 7 r 12 0 ,0 24

4 nOGTs -1 0 .9 2 6 4 1 D.696I*PREQ4# S.963>*AG£4 4.71 11 Û.530

b ROGTs 1 .9 4 9 *1 0.991I*PRE04( -57.554>«1/CC 0 .9 7 31 I . *4?

4 ^OGTa - e . '? 4 * < 0 .6 9 b 1«PRE04( 5,963t«AQt4 '*.71 11 Cl. 5 n >J

7 fiCiGTs O .G 44*( 0,l0St*EYP7*{ 0.9U1)*PREO % 6 7 I ? U.151

0 . l « 2 4 t 0,994t*PREO 17 0 .4 4 5

floGT* 0 . « l ‘»4i 0,992 >#PREO*( -0.648»*EXP34# 0.104»*CCP6 3b

SASC OR S n tr v SCOULERlAhA

PATH PCGPKSSICA LOUATIOr; FQOH wSC STi -'Ey

1 Sf.i»Cs 1 .î"« *f -0.012l#P##MA*f-0.02Sl*SLùP 11 0 . 1 ' “ -'.94 17 1.246 ? VAbCs 0 .1 6 2 *1 I.S90i«CCA24f 1.200)*PRE04( -1 .3 5 0 >*CCAG*{ 0.002»*ASPT 1 . --0 j SASCs 0,000*1 1.500I+PREO "

4 SAbC= -0 .5 2 9 4 # 1.640I-PRCÛ 0.68 2 .900

0.6P 3. = 7" 5 SASCs -0.5234( 1.640;#PRED

O.hP ■,9 2 . " o : 6 SASCs - 0 . 5 2 3 * f 1.6401*PRE0 0,^9 0 ,4 1 9 7 SASCz -0 .2 6 « 4 t H«>.a07)*l/CC4< 0.05S»«GRSS 7.4« " .-*1 * b SASC: -n,260*{ 46,807>*1/CC*< 0.0S5l*GRSS 7.99 3.41« 9 TASCs -0 .2 6 P *# <46.807)*1/CC4I 0.0S5l«GPdS

.•••• « « *« * PATHWAY REGRESSION EflOATIOHS POR SPBF OR SriRAFfl '^ETULlFOLla

= S0 c T : - r 1 PATH HCGPfSSIOK EOUATIOW FOHM

O .tl 11 12.U ?* 1 spe£= 1 0 .6134# 0.6lO)*PRE04t •25.915>*CCA2 -0.054)#ASPT*( 3,i26t*syRr 0 .8 ? 17 5 .6 9 8 a S P B t* -8.3164# a.967»«PRE04< #).l34»*EXP54f 0 .5 1 23 IC .^5 ": 5 spec= 2 .7 5 1 *# 0 . 6 5 4 ►•PREO 4 .0 4 9 -9,e72»*l/CC*l 3.974 »«a GE6 n.94 21 4 SPBC: 6.943*1 a.977»*PR£ü4# -4.253»*TRMT*< 0 .1 6 3 1 •PHMA*# 8.O20 -6.l67>*TRhT o . n 22 5 SPfiC = 23.8694# Q.9981*PRE0*< ".6 9 21 «.5eo 6 SP9E* 2 4.6 6 1 4 # 0.9au»*PAE0*| -7.999|*SVHT 7.49 2«* ?, **9 7 SPBE: 3.1124# 17.200I*1/CC*( 0.745l*PRE0 I ' 11 . 7.734»*EXH44# -4 .0 2 3 } »CCP2 ' ,92 8 SPBEs n .ü T Î* # n.949>*pReo*i - 5 , 4 4 " ►•SVRT 0.93 3 Ï 3 . 634 9 sp ees 17,0304# Q.969I#PRED*I a.094,#EXR44| -4 ,0 3 0 }*CCP2*#

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PfttMUftT QCGRESSIOU P CUA1 I JUS P 0» .1 &l 0^ f-,vD., 'UC: Page 80

4= ATM 'rGficss :oi. rottftTic.i foiJH 'T-' "F

I >r AL* • 2 t . V V 4 * 4 " . 9 9 ^ )* E K l 2 * f 1 ,0 1 3 ) •PRC-J* ( «.6S1 ) . F V T 11 . .74,7

2 tTALs 0 . 6 lT>*prt£o Zt- 9 , t . 7

5 6 2: 6 . r 5 ?TAC = 32.29T»#l/CC** 0,799»*PRC0** -0.736)*tLEW IS 6 ,f Ac* 29,186»,1/CC** O,740)*PRtU*f -0.4l7)*Eufv 0 . 6 » 2? 6 ,:5 ® ? »CCi’ 6 ** 0 . a i i l , P R E P C 77 1 7 5 . : 01 TYAL* m .L 0 6 + < ll.e71 Ml/CC* * -7.32C)*CC4G C .C ' 36 0 .

iYALs 1- .CA6 + t H.97H.1/CC** - 7 . 3 2 ô J*CCAG 1 =

PATHWAY HEQ'^FSSIO» EUUATIGNS FO*» vAGl 0» VfiCCIMU'l GLOftuLARE .....

PATW htGHtS«lCK t'JUiTTÜfl FOHM sT'i :Ev

1 'J AGL* Q . POO*( l.OCOïwPREO ft

O .h in * ! 9 VAGL* 0.40n »#PRE3** S.OOO)«T5l V 0 C , FtftO

i VAGL* C.POO*t 0.9nu)«PRE0** 2,000)*TSLY 0 . ' ? 0

(# -C,PAC *1 ' AGL* J. 0CC**AGE2* f 0.032)«SLAS*r 0,140),PREO 21 ; . 1Î 4

-O .U 3***t 0,00UI#AKG2** 0.032)«SLAS*( 0.340)•FREn .66 ?1 '. 11*

'■AteLs - 0 .0 5 A + ( o,r)oo»«Aoc2*< 0 .0 3 2 ) * S L m S*( 0.340>*PREn 1? 4 66 21 n . 114

r VAGL* 0 .4 7 S * I 1.01U»«AGG3 0 .9 9 7 0 . 0/6

4 >/ iC L * 0 .4 ? = + , 1 .0 1 0 >*AGE3 0 .9 4 7

9 v&GL* 0 .4 4 7 * ( *'.n29i*CCPl*< -0.003)*AGE3 '.6 6 1C J.19*.

• • * * « PATHWAY HFGHE^SJOM GOUATIONS FOR ARUV OR APTOSTAPh YLOS I'VA-LPSI

Pf.TH MEGRESSlOA' fOltATION FOPr rs<3 '1 STl OF :

I 1.40T)*CCA2*( -O.S26)«SLOP O.ftJ 25 '*.944

? b.4ifU#PRE0** fl,on2 ) * c x r 2*« - 0 . 0 6 0 ) , 1 / C C * ( 0 , 0 0 6 ) *SLOP 0 ,9 9 24 0 .0 76

3 i-i-UV* 5.4 lO I# P flE O ** 0 . 0 0 2 »*F)(M2*( -0.060),1/CC+* O.OOf«>*SLOP 1,49 54

*i..UV = A.50A+< 0.1?«*t*SLAS*« -0.027)*SLUP 0 .4 7 21 0 .511

9 r^MV* 0 ,Gf.A*< 0 .0 3 4 1 *T n fE 0.57 11 0, = 14

4 A 'UV = h * Fôfi♦( C.034l«rPEE -.. = 7 11 0 ,9 1 *

T A<>UW = 5,l65t*TR4r '’.f ? 6 . 166

« A. ,V : ■5.1A9»»TmMT n .S 2 6.1 b6

- I 0 . ü j 9 + t '’.134 f*ccve*« 3 .0 6 4 )* T R iiT C . =■ = ID - .|?13

• •• « • Pr-.fHHflT r CGr ESSXON EOLATIONS FOR 0CPC OR 0EP9ERIS REPELS

PATH BEGRESSIC^ raUATIC'f FÛAX FT' ^Ev

1 nCRE* 15.963I*CCAG 12 '• . 3?C

I .6 *5 2 u ra c s •A .32?*1 U.04«i**AGEl** O.O10)*ASPT*« 0.173l,ELfV*l - n .150 ) "SLOP 0 . 6 ? 2b

3 . Oag 3 PCRLs O .b c T tt 17 .3 0 0 > *C C A 2 *( .0.73e>*PRGO ^ .7^

** r^rOC* 5.ht»p*» - 0 . 1 3 4 |«C l EV* * a .o o 9 )*t/cc** 0.079),SLOP *:. 55 I . 44 I

5 (>E«Cr -2.0b3+< O.OS4)*AGE3*I 0.054)»ELEV ’ .R-" 16 r .653

0.5 + 27 I .+94 6 I f l,&* «4.072*1 -0.1271*£L£W*I o.ooe>*i/cc*i 0.095»«SLOP .47 ! » 5 . T t-FRfs *0.««?G*I l.*96l#CAHU*( -5.639»*E)* h 7 2! 4 • F?L* G .7 2 3 *t 0,04iJ*AGEt+* -18.950)*5L* iS ■j.fe 5 0 5 . . . e 9 HERE* < .0 5 4 *1 0.66b)#PPCO

, * PATHWAY r e g r e s s io n EQUATIONS FOR l ISO OR LlLNAEA RORE a l IS

psi; ST- CE'. PATH REGRPSSIOr- LOUAtlOf: F0«f-I

0 0 : ^ I LIPO* 0.0G0*< 1.0Q0l*PRED*t 2.000»*TSLV 0 .99 5 0 .6 2 4 9 L l» 0 » 5 .9 ? 6 *< -3.e4ll*TRPT*l 0.402),SLOP 1 . e 5 i L I BO* 9 .5 7 6 + * -3.A4H+TRHT** 0.402»*SL0P 0,5? 21 0.4A6 LiflOs 0 .2 6 6 * * 0.1S6)*SLAS*( -0.009),PHMA

3,5? 31 0.**»5 S LIBO s 0 .2 6 6 * * 0.196)«SLAS*r -*}.009),PHMA

-O.009),PMKA ''.52 21 :.*** 6 L |6 0 * 0 ,2 6 6 *1 0.196**SLAS*(

0.125),AG12 ''.65 5* ' . I l l T L ie o = . 0 . 3 w 3 *1 0,430)*PRGC*t .65 0 L I 30* - 0 .3 4 3 * * 0.43d»*PREO*C 0.125)«AG12 27 : . 111 9 LiBOs - 0 . 3 4 3 * * O.430>4PREO*f 0.12S),AG12 0,65

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATMWAt RKGPCSSIOM CQUATtOKS FO? ftC SP OH flrHO»rHO( liPîCATu Page 81

PATH pf k*p»:ss rc» ifjHATiOM ponr ■:T [V

1 ARUrs -C ,U o O *f 0.5*»3 ••l/CC*i 0.002:*AGLl*( 0.020),CCA2

S A&SP* 5.i*2ai*l/CC*< •O.203)*CARV*( -0.565).ELEV I"" 2 . ■’77

s AûSPs 3** 5,«*2fe>*l/CC*» • 0 . 20 3 t «C AAV*» - r . 5 6 5 » ,ELEV .«■: (* AOSPb 0 . 1@3*( 0,30 5 > » C C P 7 *f 0.199>«PREU*f - 0 .0 5 9 » * T R k T T , a a 21 0 . lA * 5 AOSP = 0 .M 1 5 *| 0.32e>*CCP7*4 -0.007)*CAHV*( -» > .0 0 7 )*S h RP ' .9 r c 1

6 ACSP» 0,R lR +< 0.32ai»CCP7*t •0.007)«CAhU*» -o.onT»,SHPn 21 : .2 r3 y (* ,A 9 9 * f AvSPs 0,GS3)*PREO*( -0.01S(*CCHl*l -0.0a7i.ELEV I"» A A&SPs «*.ô99*t 0,653î*MPE0*f -0.015)*CCkl*( * 0 . 0 0 7 ) *E l CV 17 - _

9 A&SPs O.GS3I«PREO*( •0.01Sl«CCPl*( -»l,O0T)*tLf V 3. Tr 1'*

PATHWAY REGRESSION C0VAT1 ONS FOR CAKU OR CALAMAGROSTlR PllRCSCFi

PATM PE6RPSSI0A COVATION FOPH 7 1 • r

1 -1 1 .0 5 3 + C CAi;v= t«£50i*PRED*( 0.2e3)«Pt»hA*( -0.030)*AGE1 I.:"" 1 2 1 .7 f8

t CAHUs t0«l6 5 « -( 0 .6 7 ? » « P h CC*4 0.29G}*TREE ?4 17.172

% Ca PV* 53e.9el*i -?.»59I*ASPT*» *«•••*•)«s l a S*» * , * * * * * ) « C E v E * ( 1 2 .5 0 1 ) *SVPT*» -O.E^'R) ■ T'Jt C 17 “ . 4 1,-ïl

f APV* m .3 : 2 + < 0.6?lf*PRE0*» *6.901>«1/CC*< -0.307),CCPl 10.312

5 CA»U = 0.S71f*PH£0*» -6.W0l>«l/CC*< - 0 . 3 0 7 1 , CCPl '♦ l u . ‘ l “

é CAHUs 0.871f*PREO*(-G.H01)*1/CC*(-0.307l*CCPi 44 10, 312

T CARUs 1 .7 9 3 *1 Q.789»«PRED*( 0.155)«CCP6 1 7 5 . 2 i«

a CAKU: %0.912*C 0,67St*PPED*» -2T.759»*l/CC*| - 0 . 4 6 8 ) , PHMA*» -0.192 »•ASPT*» -0.533)*rCVF*» •0.435 ) •THf f ''.9" ‘ 7 b , '■Oi'

9 CAPUs l«*,fe93*C 0.783)*PRE0*I -8*6ia>*exp3*« 0.8 9 7 ),C C P A O .é ' 23 11 .*’ 64

« « * « • PATHWAY r e g r e s s io n EOVATIONS FOR CACO OR C"KE% CONClNNOlPf.S

PATH PCGRCSS ION EOVATION FORM ■>T'' rrv

I CflCOs Û.GOO*( 1«000)*PREO A. ^ 0 0, '•) ",

3 CACO: 3 .1 7 ? * ( -0.276%,Exit*» -»Ï.103»*CC a 2 *( -0.556)»3VRT n.5P 0.-r»4

5 CACO: 0.i)00*i 1.000),PRED V. C h . n^n

CACO: • 0 .2 2 6 * C 1 .615)*P R E D U.7fi 1 .1 3 3

5 Ca CD s ft.6S 7+( -0.160)#SL0P+I -0.054)#C A R U : .51 1 .♦ : *

6 CACO: o .o o o *t 0.900)«PREO 0. r n .030

7 CACO* 0,3 9 5 )*C C A 2 . 1.« f‘

a CACO* -1 .9 Q 3 *» l.R30)«C C A G *» 0.084),SLOP 0 , 447

9 caCOs 2.57fl*< 0.ni9}«CCA6«( -0.770)*SVHT 'I.V3 : . 74

• * * • PATHWAY REGRESSION EGVATtONS FOR CAGE OR CARE* GEVERI

PATH ACGDESStON EOVATION FORM “ SC. STr n f ,

2 . 4 A ? I CAGE: u a .2 9 G *f l.52«»*PR£D+< •0.7G1>«£LCV*( -0,093)*TREE f .F7 tl.C A b d CAGE* 3 .21*9*1 0.t*92)«PRE0*< 1 2 . 3 5 3 ) , CEvE

3 CrtOC: 3.21» 9*1 0,»»92)«PREO*C 12.333),CEVE 1.5b 1 1 .4 *3

".6g 21 1 5 .r =« H CA6E: i r .12«**( 0.A05)*PRE0 0,47 15.554 5 CA6E: • 2 . 7 7 2 * ( O.G52)*PREO*( 39.849),1/CC

a CAGE* 10.1 2 ***! 0.809)*PRED*I •l3.000)«CXP4*r -0.405),CCPl r .6 = n I * . •’- *

0 .Î'- 17 1 5 . " - “ 7 CAGE: ? 0 .G 2 3 *( - 2 .6 2 2 l* S L Q P * ( 0.539»*PHMA*c -0.317),TREE C.P? Z ? 1 1 . 1:"" A CAGE: 5 .5 0 0 *1 a.6871*PHE0*» -9.43ni«CCA2*( -1.290),CCP7*» - 2 ,3 2 3 » *SLAS 1.A? 1 1 .1 7 ' 9 CAGE: 5.500*» o.aa7i*PREO+e -9.438),CCA2*» -1.294),CCP7*f -2,523 »*SLAS

. • PATHWAY REGRESSION EOVATIONS FOR C^'RO OR CARE* HÛSSII

A s: ST" ''F. PATH REGRESSION EOLATION FOHh

0. : : . : ? c t CAPO: 0 .0 0 0 *» 1»000)«PRCO 0 .9'' 3.163 2 CARO: n.i»2R*(626.000>«CCPG 0 . d 0 3.0CC CARO: 0.000*» 1.000)*PREO 0.50 21 1 5 . AaO CARO: 1 0 .2 1 0 *» 0.6001*PREO 0. r C 0 .C"C CAPO: o .ooo*» l,000)*PREO c CARO: 0 , ooo*( 1.000)*PRED 0. c 0, 0 CARO* 0 .0 0 0 *» 1.000)«PREO 0 . ? c e CARO: O.OOO*» 1 .0 0 0 1 *PREO 0 . 7 c : . : : : 9 Ca ROs 0 .0 0 0 *1 L.OOO)*PPEO

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. $ # . . FATrtWAV AECWESSlÛ*' ECuA TlO ^S FOA aCMJ OR ACh ÎLLCA I t L t F OL I ü K Page 82

p a Th AEGRESJIOa f Qt'ATiC^ FCn*' esc ST rZj

i ACPTs 0,304+{ 0.02CI«CARU il '. tPC 2 ACf [ = I.Con*( 70 .000 )«fAGE n S l.bwb*( ACKl: -C.4J20)*Ph MA c ,6* 22 :.?8j 4 • 1 ,499+1 ACPI5 l«6b6l*l/CC*4 0,043)*ELEV y,95 1* 0.230 5 ACHls -T.498+< 1.666I+1/CC+4 0.043)*ELLV f ,9! 14 0.230 (» AC**ts -l.775+( l,672)*l/CC*4 0.040)«ELLV 14 0,2*2 ACPI = 7 S,042*1 -0,093>»CLEV*4 0.127)«CCA2*4 0,f>13)»GRSS n.64 16 -14 .090+ t 9 A C H U -l>.Q99)«CtEV*4 20,549)«AGE5*( Û.451>«CCA2*4 -0.950)*CCAG 0 .96 20 0.ÎA3 9 A C I = 6.522+( -P.105I+CLEV+4 -Q,009)«GRSS+f 0.?94MCCA2*( -l,23j)*CCAG D.ÇJ 16 c.;i=>

•»••• PATHWAY REGRESSION EQUATIONS FOR ANRA OR a n t e m n a r i a r a c e m o s a

PATH PEOPfSSÏON fOWATîON FCWM esc - STC rCv

I AkPA: 1.962*4 1,126»*CCA2 0.7? 13 3. 469

2 A jRAe 0,794+4 4>.3e9)*PReO*4 •1,3S7)*CCa 2 0.59 24 1.556

5 ANRAs im.696*4 -0,155)*ASPT*4 0,712)»PRiO*f-13.465)*SLAS f.^0 16

ANRA: .2.6S2+4 l,l23>+PR£r}*4 0.077>«CAKU 0,70 II 1,965 5 Af,RA = •2,652+4 l,123)»PREO*4 0.077)*CAKU 0,70 11 1.^45 b AMHA: 1.3P9+4 1,012)+Pk C0*4 1,739 )*SLAS*4••••■••P*EUAS*I A,000)*SLOP 0,96 22 n.967 7 Af.RAr 0,4400+4 a.900)*Pr4CC*4 2.000)«rsev f'. 0 0 C.r^O 6 A/.riA = -2,102* 4 0,079)+Ph RA+4 0,033)*CCP1 0,77 8 1,371 9 ANKA. -n.643+4 24.900 >*CLAS+4 -0.052>«SLu P*I 0,01ê)«A5PT 0,90 23 0.555

«•••• PATHWAY REGRCSSION EQUATIONS FOR ARCO OR ARNICA COftOlFCLIA

PATH bfGRrsAiOA couurrON f o r h - RSG f.

1 ftPCOs 4),26**4 O.S20)«PREO*I -4).193I#AGE9 0.«5 A3 0,465 2 *r CU = 0.207+4 0.636)*CCAG*4 0.002)«AGE3 Ü.42 ?4 0.84,5 5 0.274+4 l,01.3)«PREO*4 •0.113)«SVPT 0.95 17 0.200

<4 4).274**4 t,013)*PRCO*4 •0.113)*SVMT 3.95 1? D.200 5 ARCO= •Ü.936+4 0.942)+PREO*4 -0,204 1 «SVRT*( -4).009)*CCP6*4 -0.005)*PHMA 0,97 17 0.156

b AHCOs -0,956*4 fl.942)«PRED*4 -0,204)*SVHT*| -4),009>*CCP6*( -O.005)*PHMA 0.97 17 0.156

7 rtwCO = • C,2l?+ 4 0.945)*PRCO*4 -0,229l«CCA2*| 1,9?3»*CCAG 0.9*1 19 ^.191

A &r«PR€0+4 -0.226)«CCA2*( 1.923>*CCAG 0.99 19 0.151

9 a h COs -0.212+f 0.94S)*PRE0*4 -0,229)aCCA2*| 1,9?3)*CCAG 0,9^ 0.Î51

• ••• PATH4WAY REGRESSION COOATIONS FOR ASCO OR ASTER CONSPICUUS

PATH b f &Re s s ION COUATION f o r m 9SC ÇT- CEV

1 asCO= 1,396*4 Q.3354+CCP6+4 0,OS2)+CARÜ 0.86 13 1.707 2 ASCOs -0,300*4 %.032:*PREO*4 2.400l*eKP7*4 0,074)«GRSS 3.57 24 0.7î?

3 ASCOs •44.364**4 1.230)«etCU*4 1,769)«CCA2+< -4,924)*CCP3 0.4? ?4 ll.lflÛ

ASCOs 0,257*4 0,072)#1/CC*4 Û,970)«PRLÜ 0.95 59 Û.“is

9 ASCOa 0.257*4 6.I)72)#1/CC*( 0.970>»PR£0 C.8h 59 0.91»

b ASCOa 0.257*4 0.072>*1/CC*( 0,970)#PRE4) 0.89 59 0.818 n. 0 C . OnO 7 ASCCa 0.000+4 1.10U>+PREO 0 . 0 3 ASCOa 0.000+( 1.100)«PREO 0 0 0.000 n o.ono 9 ASCOa 3,4)00+4 VOO.OOO>*TAG£ 0. C

, PATHWAY REGRESSION EQUATIONS FOR RASA OR ftACSftf'ORHlZA SA6ITTATA RSQ N .T-; ncv PATH REGRESSION EQUATION FORM

3. C o . c a 1 BASAa 0.04)0*4 l,0QO)«PREO ° 0’,9l 24 1.1 56 2 BASA: -0,095*4 0.747)*PREO*< 0.271)*CCP7 0.91 24 1.156 3 QASAa •4),095*4 0.747)*PRCO*< 0,271)*CCP7 0.65 0.69 5 4 BASA: 1,677*4 0,042)aCCP6*4 •0.023)«PHMA 11 3.64 11 O.SâS S BASA: 1.679*4 0.042)«CCP6*4 -0,023)«PHrtA 3,60 13 0 .646 6 BASA: 1.590+4 0,042)«CCP6+( -0,019)«PhMA 3.9f :. ?2fe 7 BASAS 0.467*4 0,003)«ASe3 10 0.84 « : .386 9 BASA: 0,594*4 0.111)«CCP1*I .0,044|«TRLE 3.«=-6 15 0.391 9 BASA: 0.433*4 -0,422)*SLAS

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. >•««• HiTiMAr REGRESSION EQUATIONS POM C»-UR PR CHI"'fiPHlUL« L'^HEll «TA Page 83

R A T H O E î R r s s r O f C O O A t l C N F0R|4

1 CMOMa 1.00n)*PHLD+4 2.U00I+TSLV U«OOQt < 0. n „ a Doo 2 ruuMa 0,000+( 1.000t«PRCO+l 2.OO0l*TSLV f', tl 0 O.OoO

3 CPUM* a . 600+1 l.OOO>*PPEO*4 2.ü00i»TSfW ?, n V

CMUrts o,ortO+( 1, 000»•PREO*( 2.000)«TStV ** c 0 C.OoO S CH'Jrts 0,U 90*< l.O0O»*PPEO*l 2.000»*T$i.V 0 O.OOO 6 ri.ijMa O.OOQ+t i.Aon»«pREo*r 2.ooo>*Tsev r . 0 0 0 . 000 7 CHUtts 0 .0 0 0 * ( 1.000»«PRtO*t 2.000l#TSLV 0, c 0 O.OOC a THU#: 0,000+t 1.000»+PRE0+< 2.00D»*TSCV h. f) 0 0 .000 9 CHUM: O .uo0«( ).OQO»*PREO*f 2.000)*TSi.V n. 0 0 0. oor

• * * PATh WAT RC6ACSSI0N EQUATIONS POP [PAM OR CPILOHIUH ANGUSTIFOl I u M

OATH MFGRfSSJOf EOUAltON FORM MSO ?T0

1 rpANs O.&OO+t 5 0 *0 0 0 > +TAGC 0 , n 0 0. 300 2 f pAt*a •>0.£Ql+( 0.l9St«CXP3*T •0.229>*l/CC+( •0«OOt)*£XP2 0 .68 2X 0.130

5 rPAMa -U .2 A l+ ( 0.192»#EXP3+( •0.229I*1/CC+| •0«OOil*EXP2 0.68 2X 0.150 I'PANs * - u . a o i * t 0.192l+£XP3+« .0.229>*l/CC+4 - O .O O lc C XP2 Q,6e 2x O.IJO

5 EPAfiéS - 0 , 2 û t + f C. !«*.;»+exP3 + < - 0 . 2 2 9 ) * l / C C + < - 0 . 0 0 1 »«Ex p 2 L, 6f 24 0.150

a rPANs •C .201+< a.l92»:£XP3+4 -4>.229»#l/CC + < -o.ooi)*exP2 0.6A 2x 0 .1.SO

? FPANs ♦0,201+ < 0,19?»*EXP3*4 •0.229»«l/CC+< -0.001»*CXP2 0.6? 2X 0 .130

a EPANz -0 ,2 ilJ + t 0.l92»*CxP3*4 •4>.229»*l/CC + t •O.OOL)«eXP2 0 .6 6 0.130

9 EPANZ 0.19?)«£XP3+f .4).229»*l/LC + < *0.04»l)«ExP2 0 .6 0 24 0 .1 3 0

• PATHWAY REGRESSION CQUATlOIvS FOR FRVE OR FRA6ARIA VESÇA

PATH PTGWrgRlCN rPU^TrON FOHM RSQ H STO QEV

1 F:-»WEs -? ,3 S 5 *< 0.?a2>*CARu*4 •3.S27»*CCA2+4 1 1 .A 6 x »*CCAG*( -0.112)*CCP1 0 .7 7 27 4.8X 6

2 0 ,7 0 5 *< 0 * 5 7 2 )+ E vP3+( .4).068)=CCFa*f 0.596»«SVRT*I •0.052»*ELEV " .8 2 27 0 .5 6 7

3 FHVCs 0 .2 9 9 + t <*.S63»«exP<* 0.9X 24 0.791

» FwvCs 0 .7 0 5 * ( 0.573)*bXP3+4 •O.Oaa»«CCP6+( 0.5A6)«SVRT*| -0,052»*ELEV 0 .8 2 27 0 .5 6 7

5 PFtVC: 0.9MP4 < 0 .9 5 6 t «CXP3+4 *4».069»«CCPG+4 0.5a2>*SVRT«-< -0.0S71*FLEV O.f 12X 0.596

6 f F«€s n.dSM+t a.SSl»*CXP3+4 .0.069»*CCPG+4 0.590»*SVRT*4 - 0 . 0 5 x »*El EV 0 .6 2 2P 0 .5 5 9

7 FFVCz 10.025*1 . 0 . 1 X 1 |«C l EV+4 -0.iG2»«CCpi+| 5.6l2»*CCftG*4 .C.023>*CEV£ C.72 20 1 .0 *0

A PKWCs IU.Q25*( -a.tXll«CLEV*4 -0.162)«CCP1*4 5,aH2)*€CA6+< -0.023)*CEVE 0.72 20 i . " * n

) FkvE = 1 0 ,0 2 5 * t -0.1X1».CLEV*4 •4».162>«CCP1«4 S.692)*CCAG*4 -O,023»*CEVE 0 . 72 20

pathw ay r e g r e s s io n EQUATIONS FOR PRVI OR FRACARIA vlRGlNlANA

pa th REGPeSSrOfI EQUATION FOHM RSQ N STO or.v

1 F H W I s 0 .9 5 9 *1 0 .4»?X »*l/C C + 1 *0.015> *E L C Y 0 .9 9 1 .2 3 9

3 r ijv ls a.l33J-CKPX o.eo

3 FPV 1 = 0 ,0 0 0 *1 1.900l*PReO*( l.OOO»*TSEV 0 . '1 O.OOO

M r x v l = 0 ,0 0 0 + t t.OOO>*HRCa+4 1«000>*TSEV 0 , 0 0 .OftO

5 F P V l: l .9 5 0 + t 0.072>«l/CC+4 .0.09S)*SLOP*l •0.168)«TRMT 0 .8 ! 59 0 .8 9 2

0 . “ ! 59 0.5X2 6 FM V Ï: 1 .9 3 0 * ( O,072»»l/CC+4 -0.033I#SL0P*4 •0.l6aJ»TRMT 59 -. = ^2 7 FrtVix 1 .9 3 0 * t 0.t>72»*l/CC*4 -0.033>*SL08+4 - 0 , 1 6 6 ) •TRMT i 0, 0 0 0.C31 8 F ft V Ï r 0 .900+1 2 . AhO >»Tsev Q, 5 c J.O 9 F Ptfla O .500+ « 2«00n>«TSCV

* pathway regression equations for GOOe OR GnODYERA OBLONGIFOLIA «S5 \ ST? OEV PATH f>fGRESSION EQUATION FO«H

0 . 0 0 .0 0 : 1 C JC0: 0 .0 0 0 + ( 1.00 0 » *P « E P *4 2 .0 0 0 »#TSEV c 0 . 0 0 o.ooc 2 0008 = 0.000+( 1,000>«PREO*1 2,000)*TSEV 0. 0 0 0 .0 " 3 J 6008= 0 .0 0 0 + ( l.OOO»«PRED*4 2.000»«TSCV 0 . 0 0 Q.OOO 4 GOOHs D.OOO+t 1.000»«PRCQ+C 2.000»#TSEV 0 . Ii 0 0 . 'loO 5 6008 = 0 .0 0 0 + f l.QQO)*PRED*C 2.000»*TSEV 0 . 0 0 0 .0 )0 6 3 0 0 8 : 0 .0 0 0 + r l.OOO»*PRED+C 2.000)«TSLV 0. Q 0 .0 0 0 7 GOCBs 0 .0O 0+( 1.000l«PREO+4 2.000|aTSCV 0 0 , : )c 9 6000 = 0.000+4 1.000»*PREO*4 2,000)«TSEY O.OOQ 9 6008= Q.000+4 1.000»«PREC+< 2.000»*r$EV

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. «•••• p a t h w a y r EA h E'nSION EQUATIONS EOp h IAL 04 HlpOACIUW &l Ü FB TIN U H A CTI'OGLO Page 84

p a t h ^rGPESSlCK ECiMTIOn EOKII RSC

1 HlALa O .b O O *!1 0 0 .0 0 0 1 «T4CC 0 . 0 u o.ooo 2 M A L a 0. 300 + 1 • •• •• •• ) *TASC 0 , 0 0 0 .0 0 0

3 HlALa 0,500+1 •n.002>«A6E3+( 0.000)«AGL2 0 .9 9 12 O.Oill HIAL: 0.500+1 >0.00t.)«AGE3 0 . 9 * L ■j .001

3 HIAL: 0 ,5 O 0 + ( -0.001I+AGE3 n .9 9 3 0 ,0 0 1 6 HIAL: a . joo+< -O.OnU+AQPt 0 .9 9 -- 0 . 301 7 HlALs 0.535+< 0.002)*PHMA 0.4Ô 9 0 .0 3 2

i HIAL: 0,5i3+< o.oozi+PHmA 0.4') 0 .0 3 2 9 ^lA Ls G .5T 3+ t 0 , 002 > +PH/A 0.4ft 9

PATHWAY r e g r e s s io n EQUATIONS FOR m IST OR MITCLLA STAUn OPe TALA

p a Tm PEGflFSS ION EOUa TION FOPh (SC Str) oEv

L FJSTs 0 . 4 2 9 + « 0.002I+CXP9 0 .7 9 11 0 .2 0 7

2 Î-IS T : 0 .4 29+1 0.002)«EXP9 0 ,7 9 11 0 .2 0 7

3 •'TST: 0 ,4 2 9 + ( 0.002)«CXP9 0 .7 9 11 0 .2 0 7

4 M jS T : 0.4 ? 9 + < 0 . 0 0 2 ) «EXM9 n. 79 11 0 .2 0 7

5 *t%Ts 0 .4 2 9 + 1 0 0 2 )*C X P 9 f . 79 11 3,2r>7

b MIST: 0 . 4 2 9 * ( 0.0Û2)+ExP9 0 .7 9 11 4.207

7 HIST: 0 .4 2 9 *1 0.0O2I+EXP9 0.7 m 11 0 .2 0 7

6 "1 S T : 0.4 2 9 + 4 0.U02I+CXP9 P . 79 1 ^ 0.?r'7

? ttlSTs 0.429+C U.002I+EXP9 0 .7 9 11 0 .2 0 7

•« •** PATHWAY REGRESSION EQUATIONS FOR THOC Oft THALICTRUM OCCIDENTALE

PATH REGRESSION EQUATION FORM 450 SfO DEv

1 THOC: l.l4l+( -0.317»*TRNT+< -0.2O6)*CCP5+) -0.002»+GRSS+< 0,Oaô>*SVRT 0.9S 17 0 .0 6 5

2 IndC: 1. i4l+I -0.317)wTft«T+f «0.2«G)*CCP5+< •0.002)«GR$S+I o.o e a > » s v « T 0 .93 17 0 .0 6 5

S THCCx 1.1 4 1 + 1 •n,3X7)*THMT+( -0.2S6t«CCPS+( «O.OOdl+GRSSX 0.08A)#SVAT c .9 “ IT " .0 3 9

» THOC: n .? 5 l*( 0.45l»*PRCO 0 .46 12 0 .5 6 9

3 THOC: n.t.oT+c n.779l#PRE0+( •0.462):SLAS+| «O.OOGl+TREE 0 .99 10 0 .0 * 2

b THOC: 0 .6 O ? + ( 0,779l+PREO+< .0,4a2)«SLAS+( •O.OOG}«TREE 0 .99 10 0.OQ2

7 THOC: 0,000+< 1.000)+PHC[) r. 0 C),?DO

3 THOC: 0 . ooo + < l.OOOJ+PREC 0 . 0 0 . 000

9 THPCs 0 ,0 0 0 + 1 l.O O R »*P R tU 0 . 0 0 .0 0 0

«« • • • PATHWAY r e g r e s s io n e q u a t io n s FOR XETC OR XEROPMYLLUM TENAX

PSD STr- iJEV PATH REGRESSION e q u a t io n FORM

0 0 .0 0 0 I y f TEs 0 ,0 0 0 + ( 0,900>*PREO+< 2.G00)#TSLV ", "

r>. " 0 3 .000 2 -tCTC: 0,1)00*1 0,900>*PHEn+) 2.000)«TSfcV . 0 0 0 . m n Î XETE: 0.000+Ï 0.90n)+PHEO+€ 2.000)«TSCV n. 0 0 o.ooo *t XETE: 0.000+( 0.900)*PREn+* 2.000i:TSeV Û 3. 'ino 3 XETE: 0 . 000 + ) 0,900)*PREO+< 2 . 0 0 0 ) * T S l V

0. 0 0 0.000 6 At TE: o.ooo+i 0.90R)*PREO+( 2.000)*TSEW

0. 3 0 . : ^ 7 XETE: O.OOO+f 0.900)+PflEO+< 2.000)wTs£V

0. 0 o.ooo a xtTCs 0.000+( 0.900l*PRED+( 2.000)*TSbV

0. 0 0,000 9 XETE: 0.000+) 0.900)«PREO+( 2,QOOI*TSEV

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 85

APPENDIX E (con't)

Regression equations for PSME/PHMA, moist phase. Six successional pathways.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PATHWAY BfTGRLSSIOf* (GUAT TOUS *'0« CCAL 0» TOTAL T R tf Cû'vrPY CCVF.» Page 86

MATH *;i.GHFSSlOA CullATICri FORI: ^T- cEV

I CCAL? 6,é«A*1•49.A69 » wCtP3*(737.428>*AG11 O.é^ 15.4^6 ? CCALs 14.525*t•44.4 021•EXP3*1659.276»*AGll G .55 3 14.525*1•44.4 02>*EXP3«I6 75.2T6»*AG11 CCAL# 7.5!: ’ C . C4l

4 CCALs 19.525*4 *43.4021*C fP5 *1665.276»*AGll 7.55 2 0.04: 5 CCAL# 1 2 0 .1 2 0 *1 -1 0 ,9 8 3 » «EXPS*1 - 2 1 .382»*SWRT*4 -0.136»«ASPT Cl.fil 14.F?9

6 CCAL# 124.297*4 -4.2561#AGE8 0.75 17.400

* 4 PATHWAY r e g r e s s io n e q u a t io n s FOR Q8h OR AVERAGE 06H OF SÎANO

PATH REGRESSION E q uatio n FOPft hso sTr dev

Ll'H = t 1 7 ,4 0 3 *( -0 .4 2 2 1 #AbEa*t -0 .0 6 5 » «ELLV 0.97 le u. 2 CbH s 17.177** •5.760l*AGC9 rt.97 20 C .637

COM = -35.321** £7.834I*A020 17.95 20 1,239

■* P'BH # -4.9D8** 1.S29I4AG17 ',8 9 20 1.305 C0N s 5 23.008** -0.4211*AGE8** -Q.111 »«ELEV*( -0 .12»»«SLOP*i -0.855»»SLAS 0.96 20 0.730

OPH 5 -22.014** 26.526)«AS20*| -0 .146>*ELEV*( -0.1S2>«S l OP 0.92 14 0.973

* • * • « PATHWAY re g r e s s io n EQUATIONS FOR QA OR AVE STAND BASAL AREA « SO FT)

HATH REGRESSION e q u a tio n FORM 9SC f. STr ?EV

1 14 7.1 9 3 * * -2 6 .3 6 9 » *CXP3 0.61 36.034

? 229.H19** -8.5181*AGE8 0.93

J 131.6 06 * * - 2 5 .6 7 3 ) *EKP3 0.50 20 "7.774

-34 7.e96*(240.749»«A6E4 0.60 20 40.963

320.623** -4.473 »*ASC6** - 0 .961»«ASPT*1 - Î.4 9 0 » *SLOP 0,94 20 21.761

PA 14 5.368**-16.674)*EAP3** 39.556 I«SLAS** -2.514)#SLOP 0.90 17.732

PSEUOOTSUGA MCNZItSll l< 4 IN,) "

REGRESSION EQUATION FORM RSO N STQ n€v

t 0F<4= 10.6 7 » * 19.406CCXPa*( 1.401)«A6L6 0.52 18 19.020

2 OF<*is 4.50!»*( "3.3e6 )# E X P 3 *( 706 »«SLAS* I S.aStlwSVRT 0,73 20 4.923

3 CP(4= 5.639*1 1.6S2)«CCA0*C 0.000»«SLAS 0.40 21 15.6&A

*» UF<4s 5.639*« 1«652)*CCA6 0,40 21 t3.6«iH

5 L:F<4± -2.304*1 0.20A:#CAAu 0,52 IT 6."13

6 0F<4x a 5 .7 l5 * ( 0 .524 : *GLAS*f "? 6 .S 1 2 )*S L A S *i -0 .0 6 6 > aCLCV* f 5.546XAGC3 A .9? 19 3,514

« * • • • PATHWAY PCGrESSION EQUATIONS FOR uF>4 OR PSCUOOTSUOA M CNjIESII

PATH hrG«E9SlON ÊCUa T î ON FORM

1 6 .6 8 8 * f -49.809»*CxP3*i717.4281«AG11 ?.69 19.45*.

2 0F>4s 43.074** •0,980)«AGCa*1 -6.336)«SVHT 0.59 9.940 10.791 J QF>4a 95.143** -l.l51)*AGCa«* -l.300)*ELEtf

4 f?F>4S "6 .6 7 9 ** -9.66SI*AGE8*< -1.544)«ELEV 11.4=3 9.764 5 0F>4 = 62.1102** -1.1191«A6C8**-12.649)a SVKT 20

6 nF>4 = -4 5 .5 9 7 *1 0.513)•AGE2*( -9.623)VELAS*(106.487)«SLAS*( i.02e»«CLCw .... 19 6.512

« • • • PATHWAY REGRESSION EQUATIONS FOR DFAL OR PSEUOOTSUGA MCNZIESII (TQT^LI «

sT : oev PATH REGRESSION EQUATION FORM

26 DFAL# Z .6 0 9 * 1 -4 9.809»«EXP3*I727.4 28)VAGll 0.35 20.0*1 CFAL# 5 .525*1 .4 4.402»«EXP3**625.276)*AGll ".7 0 14.35! OFALs 140.525*1 -9.Ql9lw£XP3+* -1.823>*ELEV 0.51 20 11.853 OFALs 8 6 .679*1 -0,68SI«AGC8** -1.544»#CLLV 0 .e* 20 1 0.7*4 5 DFAL# 5 9 .4 4 2 ** -7.203»*E*P3*C 0.072»*SLAS**-12.925)«SVRT 0.95 19 5 ,P J “ OFALs 6 8 .5 7 5 ** -0.484l#ASPT*f -0.96S)*SLOP*I 7.536*«AGE3

, PATHWAY REGRESSION EQUATIONS FOR WL<4 OR LARIX QCCIOENTa l IS l< 4 I'lC^TS» •

RSfl 'f STO QEV r e g r e s s io n EQUATION FORM

0.44 1.141 1 WL<4= 6 .7 9 5 * * -0. 026)«PHMA*1 -0.099»*CLtV 11.334 -5.379>*TRMT 0 .!5 2 ML<9s -3 1 .9 0 5 *1 0.556»«TREE*( 4.346»«EXPS** -9.379t«TRMT : ,5c 7 0 : 1 . i Î 6 3 WL<'»- -2 9 .0 0 8 *1 0.@56)#TREE** 4.556»#E%P3*f 0.62 20 10,493 LL<4* -5 5 .1 6 0 ** 0.5aO)«TRCE*< 1.789)«AGE8 0.42 17 I , =16 WL<9# 9 .0 5 5 *1 •0 .3 1 9 )« S l OP 0.33 ? l «.941 4L<9 s -0 .7 8 i* C 0,095>*TREE

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • •••* (JATMk,AV HrOfieSSION COVATtOi.S POn C‘‘'Sft( CCC lüEr'Tfli. £ s (> Page 87

RCGKCSSTOt f 3M/-.TlQf. POHi, FS43 r STû 3EV

1 *L>'*s 1 0.03l>*TRCe*4 0.4)25|*GR sS*4 0.4)A9)*ELEV 18 :. e ; I “*•3. 762* i 1.696>*FLLV -1.372)»AG£8*4 %70 ?n 9.2?S 3 i-.L>'*s 0.1564-THEF j . i t 17 e.o;-» l> 4 = 0.228)*A6E1 a .51 20 3.562 5 WL>»: -•>.696)«EXP9 0.25 20 13. -<06 4).207»*T,*EC*4 4J.332J«PNMA C.61 21 7.233

• PATHWAY REGRESSION EQUATIONS FOR wLAL OR LARIX OCCIOC n TALIS 4 TOTAL :

pa Th REG«ESSICf tOUATIOig POBH RSC STr

1 .'LAL = t . 7 9 9 * ( •0.02ei*PHMA*! -O.Q99)*ELEV 0.32 lf> 1 . l<4l 2 WLALs -t.372)«AGCa*4 1.696)«ELCV*( 1.396).CKP;*4 O .0 0 0 )*E l EV 0.70 20 9.225 5 -L 4 ts *2 3 .5 9 0 *4 0.738)*TPEE*4 7*3691«CXP5*| -4).2l6 J «SRSS + t -4.813)«TRMT C .50 20 10, f,-* «LAL = 9.S9A*< 0«n>79>*TReE*( •5.6551,TRMT 0.55 20 13.7^2 9 ■«LAC* 2 f .011*1 •*.ail)«EXP3 0.45 20 143 . 222 6 .L *L = 33.392*1 *4).9881*8068 o.*»? 19 1(3.2b9

• • • • • PATHWAY REGRESSION EQUATIONS FOR ACGL OR ACER GLAORUM

p &T m PtGRPSSlCr L'jtJAllCh FORM RSQ ST.. igv

X ACGLs 1 .1 0 3 1 « E X F **( ■ « * • « • • |«CCP8 O.ÎÎ 17 0.31? 2 0.992+< ACGL2 1 .OeSI■EXF9*4 **•••■ •)*CCP6*4-16.l391«EKt1*4 -0.0Q6)«GRSS 0.91 20 0,246

ACGL» 5 * I1 1 * ( 0.199»«CCP6 0.21 l i 6.431

ACGL» 0.199)*CCP6 n .3 l 15 6 . ‘•01

ACGL» 1.135*1 7.398)«EXP9 0,56 10 2 .13?

6 ACGL» S,135*« 7.39e)*EXPW 0.56 10 2,132

• * • « * pathway r e g r e s s io n e q u a tio n s FOR AMAL OR AMCLANCMIER ALMFOLIA

PATH MLCRCSSlOH EQUATION PONM RSO 'J STO oEv

1 AnALs l.G 7 0 *( 1.213}*PRE0 0.52 19 6.216

AHAL» l..i? 0 *4 1.213»*PRE0 ft.52 19 6.209

AHAL» 1«.099*4 Q.66t)«PREO*4 -S,236)*$VMT 0.44 21 9.PS0

AMAL» l A . 099*4 0 .6 8 1 1 *FRE0*4 •S .2 3 6 |,S V R T 0,4*. 71 9.250

6 AMÛL» 3 .621*4 2.

6 .HAL» F-.621*4 ^.'*a•*}mCCAZ*^ 5 ,9 6 7 1 «CCA6* 4 -0.4)62 ) *CEVE 0.72 17 2 .3 0 *

• • • * « PATHWAT REGRESSION EQUATIONS FOR CtVC OR CEANOTWUS VELUTINUS

path KEGPfSSiCA eq u a tio n FQWM flSO STO oCv

I CEVE» 2,04)0*4 50,000»*TA6E 0. " O.CgO

2 CEVE» 2,000*4 50.4304)1,TAGE C . 0 0

3 CEVE» 0.379*4 0.022 I«PHMA* 4 1.079»«£XP7*<-ll.689)*EL4S+4 60.000)«TAGC o.5e 27 ).4T 8

CEVEs 0 .3 7 **4 0,022>«P h MA*4 1.4Ï79),CXP7*<-11,889)*ÊLAS*4 80.000),TAGE 0.58 30 0.47«

5 CCVE» 112.263*4 •61.386}«CP11*4 -O.0S6),CXPS 0.71 20 15.636

CEvE» 115,563*4 -60.601)«CPll*l -0.05SI,EXP5 0.69 19 15.9,2

» ••• PATHWAY r e g r e s s io n EQUATIONS FOR LÛÜT OR UOMCERA UTAh ENSIS

HEGRCSSrOA EQUATION FORM «SC ST; r.cv

LCUT» •2 .3 7 8 *4 C.015)*EXP5*4 0.083l«ELLV " . 67 -.''45 0 .«9 2 LOUT: -0 .7 9 7 *4 0.006>«EXP6*( I.S55)«CCA2*( O.7 05t*SvftT*i - 0 . 2 6 1 )«TRHT r .* ? 12 : .4^5 3 LOUT» 0 .377*4 0.Q151«CARU 0.4) 13 3.445 LOUTa 0.377*4 0.aiS>«CARLI 0 .97 10 ) . 1 3 1 LOUTs 0,508*4 9.023>«CCP1*4 - 0 . 0 1 9 ) « tr ee * t 0.04)8 >*GRSS*{ - 0 . 0 1 3 ) , AGE) O .fl 12 3.219 6 LOUT» 0 ,570*1 0.4>181*CCPI*4 -4).D11I«TRC£*4 0.005)"GASS

PATHWAY REGRESSION EQUATIONS FOR PHMA OR physocarpus MALVACEUS

RSQ STO CCV PATH REGRESSION EQUATION FORM '•

19.03 3)«EX12*t -0.119 J,E%P9*l -l.it90»*ELEV :.7 ? I* S .S 'l 1 PHMA s 78.569*4 0.565)«PREO*4 L9.033|*EX12*I -0.1161,EXP9*4 -1.990)*ELEV 1. 7-* 5.801 2 PHMA: 78.568*4 0.363>*PR£0*1 ' . C ic 3 0,4)00*4 1 .0 0 0 1 «PRED*4 Q,220)«EX12 0 ." l0 4 PHMA» 0.000*4 1.000i*PRED*4 0.220)«LX12 -3,391 )*SLAS*t****««*>«CCP6*( -0,»*S‘t)*CARU*4 -0.612)*Ar;l = 0.9U :? - .6 3 “ S PHMA s 35.668*4 -8.590)*CCA6*4 -3 ,391>»SLAS*f• •• •• * • >,CCP6*( •0 . t*5« 1 «CARU* 4 - 0 .6 1 2 » * ’4 17 6 PHMA» 35.668*4 -a.59a»*CCAG*4

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. h a t h w a t p r OffCSSJO^ F.QUrtTTO'vS FOP FKVI 09 PH'.' li', VIP&I' lifiA Pag

PATH PEGPrssiCA tou.'TrCf- pohh ■»s:

I O .O flO *) l.0004*CCP9*f l.ODOtvTSLV 0 0 .0 0 0

? OoO«( 1.0C&>*CCF«*4 1 . C 0 9 ) « T s l v : . c :.w o o 0.000*1 1 .0 0 0 »*CCP9*4 i.OOO)*TSEV 3 0 . 0 0 : . c 1 c PJtVls 0 . 0 0 0 * ( l,O00»*CCH9*4 1.04)0 4 mTSLV A. 0 c

5 HPVls 0 .0 0 0 *{ i.ooa>*ccp9*4 1.0DO)«TSev 3 . 0 Q 0 .0 0 0 6 P ftV ls 0 .000*1 I.OOO>*CCP9*4 1 .004)):TSCV c 0 .0 0 9

* • • • pathway REGRESSION EQUATIONS FOR ROGY Off ROSA hYMNOCARPA

Pa Tm RCGHrS&IOL CgUATICN FORM RSO i: 'ITJ DEV

I @.716*4 a.032laa0E2*l -0.166»»ELCV 0 .5 3 15 Q .975 2 MAGYs # .7 1 6 * 4 0.0321«A0C2*( 1 -0.168>«£LLV 0 .5 3 15 Û, 975 } pgOT* •0 .2 7 0 *4 0 .0 2 8 1 * c rc p l 0.66 12 U .67 0

fiOGTs •0.296*4 0.0501*CCP1*( 9.C9G>*GRSS*1 •0 .022)«T P E E *( -0.0291*CARU 3 .7 * 21 0 .6 5 9

0 , ^ 9 2 * 4 POGTP 0.026)*CCP1*( -0.01T)*CARU 0 ,6 9 11 0 . 2 * 5

6 h OGTs 0 . 9 1 9 * 4 0,099)*CCPl+4 •0.28a)*CCP3 0 .6 9 IS "1.439

• • • • • Pa t h w a y r e g r e s s io n EQUATT4)NS FOR s a s c or SALiX SCOULCRIflNA

path MtGRCSSlOA' eq u a tio n FOHM 9SC FT"

1 sa?Cs ft.C & P *l o.oo6}*exP6 0 .3 9 20

2 SASC: O.Cr5,8*f 0.006)«CKPG C . 3 ' 20

3 Sa SCs •0 .3 5 9 *1 0.120)*A6E«*4 1.077l«PREO r . 9 î 0 .5 0 5

** 3ASC = •0 .3 5 9 *4 0.120»#AGE8*4 1.077)*PRCO C.91 0 .5 0 5

SASC: - t . t 9 S * 4 0.3C5)«GRSS 0.90 5.4S«*

SASC: - 1 . 0 . 5 * . 0.305l*GfiSS " • * 0 5 .*6 9

« * • * • PATHWAY REGRESSION EQUATIONS FOR SP0E OR SPIRAEA aCTULlFOLlA

PE^RcsslON Eq u a tio n FOfi.i RSC ST") oEV

1 spcrs 4.V09*4 0.1W2)«AGC5*4 . 1.SA9»«CCA2*4 •0.125)«CCP1 0,95 17 3.287

2 .,Pf Cs 9 4 .6 4 2 * 4 3.R371«CCA2*4 -1.063>*ELEV*4 0.916)«SLOP 0.66 19

5 S P 0E : -25.453*4 0.691J*PREO*4 l.O02)*SLOP*< 6.905)«SVRT 0 .6 3 13 7 .9 0 5

SFBEs 5 2 .t5 Q *4 D.i39)«AGE3*{ -0.936}*CLEV 0.75 15 fl.u a e

S cpQE: -2 ,9 5 5 *4 4) .‘14)11 «AGES* 4 -0.257l*PHNA*4 0.716)«SLOP 0.66 29 7 .5 1 ?

6 speea 92,709*4 0.099)*«GC3*( -0.160»*TREE*4 •0.699I«EL£V 0.60 35 *.72%

*### pathway REGRESSION EQUATIONS FOR SYAL OR SVMPHOfflCARPOS ALPUS

PATH HfGRESSIOh EQUATION FORM RSQ r t v

1 SYAL: •1.259*1 l.l3l>*PRE0+f 1.6 2 8 I» C e v E 0.9 A 13 3 .1 3 9 0,2T81*PMMA 0.96 19 12.7(43 2 St AU: •19.329*1 0,3991«TRCE*f 5 . 0 7 9 ) * C £ v C*I

3 SYAL: 1 . 0 2 7 * 1 0.192>«CCPI*i - 2 .9 5 7 1 *ACeS n . 9 *

SYAL: -0 .3 9 0 *4 0.029>*GRSS 0.75 fi 0 .5 5 2

0.69 13 5 .5 7 6 5 s y a l = 3 .7 0 B + I 0.909):CCP1*4 •0.282I9CARU

O .an 15 5 .5 7 6 6 S rA L a 3.74 )0 *4 Q.94)9>«CCP1*( -0*282I«CAPU

* • * « • PATHWAY REGRESSION E4)4JATI0NS FOR vAGL OR VACClHtUM OLoeULAHE

5T^ CL. PATH •«EGRtSSrcr. EQUATION FORM

Û.96 0.6,46 1 V»SL= - 6 . 9 7 0 * 4 2.HSe)*CEVC*4 0.019)*ELEV ? 1 .5 6 VAGL: - 6 , 9 7 0 * 4 2 . 9 s a » «c c v c * i 0.019)#EL&V

. 0 VAGL: 0.000*4 1.000i*PREO+4 2.4)00)«TS£W 0 0 . r O.C'O 4 VAGL: 0,000*4 1 .0 0 0 i*P R tD + 4 2.000l«T5LV if. 0 o .'co 5 VAGL: 0.000*4 1 .00O)«PRCC*< 2,4)00)«TSEV

2.000>«TSLV d . 0 0 0.0 :0 6 VAGL: 0.000*4 I.OQ0)«PREO*C

PATHWAY REGRESSION EQUATIONS FOR ARUV OR artostapmylos u v a - u r s t RSC < T } CEv PATH REGRESSION EQUATION FORM

fl .7 7 20 2 . «95 1 ARUV: - 2 . 9 6 1 * 1 0.Q09I#EKP2*1 0 . 0 6 6 ) «ASPT 0 .7 7 3 . «07 2 ARUVS 9 .9 6 8 *4 6.0T1)*EYP9*4 -5.S23)*SLAS 11 ? .9 9 6 : . 3 * i i AHUV: 19.539*1 0.079»*AGE3*I -0 .2 7 6 1 #ELLV 0 .9 6 21 % 5J9 M 0.959*4 0,076)*AOE3*1235.8811*AG18*( -0.030>aPHPA 0 .9 2 * . ''52 i @ 7.13 7*4 - 1 . 5 3 7 i «Cl Ev * i -0 .2 0 7 1 a C£vC*4 0 .0 9 1 1 «ASES 11 0.9U 3 . 9 * 7 6 96.082*4 - 1 . 9 1 2 ) * C l Cv *I - 0 . 2 3 2 ) *CCVL*4 -5 .8 6 0 1 *Tfl*'T 10

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. • « • • « t'RTi'kAT e»fG » rs 9 I0 f CCuATIfJ..S FO® nf »r 0» ••r J s uEPP’ S Pag fjrt»Ffsstc* ( ju'TiO L FOff-»' F I T ' "I,/

1 ' I '♦Cs , A '* ft * ( *Q. 156> *SLLP* < 0.2-901.CCA2 <'.AC 1* l . 2r 2 z -'tr'Cs '►0.1635 «SLOP* 1 0.26RJSFLLW o .t* 2C 1 .-1 2 PERFs C .

• P fl Tk WA i tJ rr..ir'C..^ T fthl rnnA T m tic cr»n . ta<. rva LlN"aAEA MOHEa l TS

‘^ICRCSSÎÜN tCC T1 OK FGkr*

. L J üO: (*.77'5J«rRrE

' ■ L I 'Cs - 15 . On?*< <*.îfl3»«AÛtS*< Q.3&7t*GMSS*i 3 . 4 9 * » *CCa 6 0 . 9*

: L 1 4 0 : • Ifr. • 20 *{ n,'3H6)»CARt.'*< C.217l*TPLE 11 5 .6 - r

L ld C * Û, 366 .CARU*( S,20ai-Svf

5 LI'JOs 0 . r. 0 0 ♦ t 0 . ‘JOO > *PHCC* ( 1 . DC 01.TSEV 1. Ô Cj c .-o o

6 LinO s 101.5 1 ^*( 0 .6 3 7 )» C A R U *< *« « ****l*C j{P 9 *( 0.000 t -SLOP 6 2 .-3 6

a . . . dAtlfUA* arr: BC c c * n.i ...... a ^narum r . «- araa. v . fl&SOPTRON SPlCATUM

k-mTH *»eîRCSSiCN FCjfiTlCN FORM .. STC rev

iCS^’ E 0 , C r, 0 *-1 0,75Pt*PRED*( 2.DQ0)*CXP9 0 0.900

acSPs Q.OOtt*-! 0,TS0t*PREr*< 2.DOOJ.EXP9 0 C .000

fl C- J F s 0 . ORft*( 0,750t*PHEO*< 2.000l«CxP9 7 . C 0 0.000

' flüSPi 0 .0 0 0 *1 0. 750 I •PREO + < 2.0tt01*CXP'a C. 0 o .tfiû

■5 ibSP* 0 .00 0+( 0.71:0 1 #PREC*I 2,OOOi.CxP9 (I. " o.ooc

6 flbSPs O.CnO*< C.7ÎU».PMEC*< 2.000)*EXP9 C. A P . C r 0

CAl AMa SROSTIS RuaESCEN-S

RCCRESSICN ECUATTON FOKrt R$â STP c tv

, CflRUt «ll,C«5*t l.2501*PRE0*( 0.285iaPNf*A*f -0,030).AGEl 0.95 12 1 .758

- n .t'5 3 * f 1 .250> *PfiEO*f O.SeSisPHHA.t -0.030).*&£l 0.95 12 - -58

CARL'S 0 .8 7 1 )«PHED*< -6 ,007».1/CC*( -0.307)*CCPt Û.IÎ7 1J.312

» CflPUE 0.fl711*PREP*< -6 .0 0 7 » a l/c C * ( - 0 . 3 0 7 * . CCPl ft,6T 10.312

5 CAHL-S 0,77br#TREE*t le.aSSJaTRMT 6 .-3 i? i 5 . ; * 4

CtKCs 0.77bJ*TREE*( tO.»35l*THMT 0.Ô3 17 1 ! . Î4 *

f%BpMuaA F % t iT ur#AN F s A4yu*" j fl T1 4Tftuc JrVo *UK Cns L Fflrn * L V A# VW C/ REF COflC INtJOTCES

»ntH nCGf'f’ sSICK fCUATIOfi FORM OSC -, :T1 DEV

CACOS 2.97S*( -0,101>#SLCP*< 0.869»*1/CC 10 C . 4u5 O.U.? Ca COs 3 ,5 te * « - p . i d s »*Slcp 10

CaCOs - 3 . ? ) A * 1 ê.752)*txP7*J 0,164).SLOP - . 6 = 6

CaCOs -?C.*J73*< 0 .2 2 9 » "SLO P*4 C.253l*ELLV*t 1 . 2 7 3 * . TRMT*, 0,03 2 )*r»'^tr 1.168 ? .c -r 5 caC fs o.SAn*< 0.1R2l#ealO

O.b0O*< 0.142>*CX10 2.99 - CfCua

• • « * • PATHNAT «LORCSStCH CGuAtlOKS FOR CAGE CP CARE" GEtCRI

RSO GT- lEv I-CCRESSIOK CCUAT ION FOKM '■

*2.C ftO *( rt.993)»FPEC»( . 0 . 0 3 6 ) *A0C2 13 I C . - l > CnCts * 2. t- e 0 + c 0.99 3 >,PRED*f •>0.036)*ACC2 21 l i . 059 CAGES I 0 , i : 4 * ( 0.e05i*PPE:*i -1 5 .OOO J.EXP4*1 -Q.109)*CCPl 21 15 .5 *4 CAGES 0. e 05J*PP£C*l -1 3.0Q O ).E X P 4*( - 0 . 4 0 9 ) . CCPl 20 4.3-.^ s Cfl^Cs 1 3 . ?■»•**< 7.50a>*E*PH#t - 0 .2 7 7 |* E l LV 3.277 CAGES 8.61?I.EXP7*( 0 .2 6 2 ) “ PhMA*< - 0 . 4 5 5 ) . ELEV

ONS FOR CARO 04 tra A aM rvt S "p Vnc a ^t *T .% IT? nPi, SI OK ECWATJOf. FORM PSC ■-

p. " ” P ,"Z' 1 CAROS 0 . r> 0 0 * 1 0 .9 0 0 1 .PREO C. 0 : . : DC ? C ARCS O.Ot'O*! 0.900l*PftCO Z.-it 15 : . 3* 5 CARÔS 0 . C 30#( O.OOLt.AGES 15 u. CAROS 0.030*1 0.001)*ACC3 '. -«

•; BHÛS 0 , OOO* < 0.9Q0l*PPCO : C

r APO = 0.020*1 0 . 9 0 0 ( «PPED c ■. : -'f

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. . \rM»AT prr.wts^ior^ inu&TTOf.^ con rCMl a c h l l c a r t l Ju> Page 90 ICf » iiUATIC ! f-OHR KTPPESr <•5. 'TO rjt J

ACPIs L . 14^*1 0.31U>*iXll :.5i 2b 0.1L9 AC"I = 0.3inf,tjiii ■'.51 26 r . l^ Q 4C«Is I ,W24*t •O.Ol.M «TPCe '.•4P 20 ' . 7*5 ACHIs X.324*1 •0.013»«TP1E 0.4P 20 0.795 5 2,4fl*i*.I •0,070 #PHKA n C "I» 4 0.944 6 AC"Is 2.4AS*t -0,070l#r*.*A 0 .54 u.«54

• * • • biftTuwAv err.Bffeernfti ranm*TA,±A con . .,a. n— AflTCNKAHiA RACEMOSA

PftfH MCSHfSKtCA Lt)UATU:i FOItH «SC STO OCV

1 A'lHA: -1 5 .1 5 3 *1 2.520)«CEVC*( -3.433)«CXP9*4 0.361l«Ctrv 0.7* 12 2 .*1 5

i Af.ttAs 0 .T 3 3 *( 0.752>*PRC0 1.74 15 2 . 972 5 at.RAs •3 .1 2 4 *1 9 .»= 2 »«EXP4* 4 0.1445»«SLOP*I -1.7S0>*CP10 >'j 1 .0 *4 ANMAi ** -2,77®*{ 7,2@9l#[KP9*| -0.004»»*exp5*| 0.1361 «SLOP 0.66 21 1.067

Ar.ftAs 0.025*1 0,036>*CARU 0.59 € '‘ .«04

Af,PA = 0 .0 2 5 ** 0.O2«4«CARg 0.59 0.604

• * * PAFHbAY RCGRCSSION eOUATIONS POR a RCO OR ARNICA COROIFOl IA

P'ATH MLCRCSSION EOUATXON FORM RSC -, STn rjcv

X anCO* 0,44(3*( 0.032)«TReC 0.99 t 3.002

7 ARCOs -0 .9 2 9 *4 0 .2 1 1 >*CCPt 0.91 9 2.174

i -0.557*4 0. 449>*CCPX*I S.146l*ThtE 0.5? f

** -0,594*4 0.061> «SEAS*1•«•«••«1«CCP6*( 0.0021«ASPT*i -0 .1 6 0 » «TRMT 5.96 13 0.0«6

- G . “ 2A*4 0.123)«CCP1 0.46 29 3.0?1

6 -0.9,6*4 0.123»«CCPl 0.46 3 ,0 ? l

• * * PATHWAY REGRESSION ecUATTONS FOR ASCO OR ASTER CONSPICUUS

PATM hEGRPSSlQIV fOUAlICN FCHH RSG N STO dev

1 ASCOs 2.716*4 0.1251*CAKU*4 - 2 .9 0 6 )«SVf(T 0,36 21 5.193

2 ArSCO* •2 .0 2 5 *4 « • • * • * • ) *CCP£* 4 0.0

A!àCOs - 1 0 . «77*4 0.1A7I«SU0P*4 0.15at«ELEV*f 0.038(«SHRB*i - 0 .0 1 1 1 «GRSS n.t.4 15

ASCOe •0 ,0 7 1 *4 O.OAtl*SLOP 0.33 20 1,040

S 55.6JP*t -l,19U«SLOP*4 5.34)2)«SLAS 0.76 11 2.915

h ASCO* 36.747*4 -3.349> *T5M T*i -0.9201«SLOP*! 4.6aat*SLAS 0.66 15 5.643

, PATMWAT REGRESSION eOUATIQMS FOR RASA OR 8ALSAM0RHI2A SAGITTa TA

Path MfGRCSSrOK EQUATION FORM RSC r. STi oEv

1 FASfts 0.000*1 0,900>«PRE0+4 2.000)«TSEV 0. 0 0.3C0

2 BASA: 0.000*4 0.900 f«PRED*4 2,OOOl«TSev n, 0 o.ftoo

3 IIASAS 0.000*4 0,9OOf*PR£t)*4 a.OOOIeTSEV 0. 0 O.DOO

4 DASA* 0.000*4 O,90r>) •PREO+4 2 .0 0 0 1 «TSEV 0, 0 0.000 Û.O0O b hASAs 0.000*4 0,900»*PRCO*I 2.00D1«TSEV 0. 0 O.QOA 0.000*4 0,900t*Pf»CO*< 2.0001«TS£V 0. 0

• . « * * PATHWAY r e g r e s s io n EQUATIONS FOR CHUM OR Ch im a p m I l l a uneCLLATA RSC ST' cCV PATh RtGRtSSlCM tCUATICM FORK

0. " 0 . ■'oc I chum: 0.000*1 0.750 1 •PPteO* 4 2.000>«TSCV 0. 0 0 3,"00 2 CMUMs 0.000*4 O,750J»PhCO*I 2.000t«TS4bV 5.74 20 5 CHUM* -4,343*4 rt.n22>«CARU*4 0 .0 2 6 } «TREE*4 -0 .0 2 4 I «C C P l*4 0.071 J.ELEV*4 0 .2 31 MTRMT 0,74 20 0.296 4 CHUMa -4.343*4 0.022i«CARU*4 0 .026l«T R E C *f -0 .0 2 4 1 «CCPl«e 0.07tl«CLtV*4 0»231)«TRMT 0.97 7 0 .2 0 " 5 CHUM: 6 .0 0 0 *1 -2.500)aSVRT 0.9? 0 . 0>5tt 6 Cf UMs 6 .0 0 0 *4 •2.500>»SVRT

««*« PATHWAY REGRESSION EOVATIONS FOR £PAN OREPILOSIUM ANGUSTIFCl IUP

RSQ STO OEV PATM REGRESSION LGUATlOAi FORM

0.9C 0.243 1 EPAN: 0.010*1 3.030»«1/CC 0.90 3.243 2 CPAN* 0.010*4 3.030>«1/CC 1,7? 10 1.241 S EPANa 6.66 3 *EXP4*( -1 .5 6 7 }« C £ v C*4 70.OOOi.TAGC 1.24-= 4 EPANz - 2 . «75*4 2.07Rl«SVRT*( 4.297»«EKP4«i 7 0 .0 0 0 ) .TAGE 0, 72 = 1.206 s EPAN: 0.401*4 -0,0051«TREE n.36 21

EPAU= -3 .6 3 4 *4 i.776l«CCP4 0.40 I * : .205

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. fATMtaftY nf&!<çssio*i CQLATroi-s FOR rnvr om vesca Page 91

r.'TH prcHFSSiflK roiJATTCn fo*<. 9T -E-.

1 6.3ftft)«SVRT*4 O.R56i«CCA2*r 9.19l)*CAPU 11 2.TYO 2 Ff.VEs - iO .722*» 0.201I*ASPT*4 0,029»«ELAS 0.1Ô 17 1.522 FRVE* 0.b2*j4*P«En h.?3 PHVEs 0.101*4 0.&25>*PPEO 0.75 0. ICS ) - o . ; s 3 * ( 1 .6 6 7 ) «PREO 0.99 0 .0 0 : 6 FPVCs -0.333*1 1.6A7)#HHEu 0.99 0.001

• FATHWAT REG•fCSSION EOLATIONS FOR On FPAGARIA VIRGINIANA

PûTH OfGPCSSIÜA roUATIOht FORn RSO 'i STD DEV

1 0.000*4 0.900I«PRCO*( 1.000)«TSev 0. 0 0

2 0.000*4 0.94>0)«PRC0*( 1.000l*TSEV 0. n 0 c . f'qn Î 0 .1 0 1 * 4 0.625»«PHE0 0.73 « C.10«

9.113*4 1.S12I«EXP1 G.M? 19 I . 292 r p v ls 5 O .b T ltt 0.010}*CCP1*( •0.016)«GRSS 0.4*5 10 0.390

6 FRVI* 0.900*4 • 0 .0 0 1 )«A6E3+4 0.000)«AGE2*| o.ooo)«SHRe 0.99 15 0.300

•« •« • PATHWAY REGRESSION EQUATIONS FOR GOOB OR GOODYERA CPLONGIFOLIA PATH KEGHESSIOK e q u a tio n FOHM RSU ■J ST? -.fv

1 GOOOs 0,000*4 0.900>«PRCQ*4 l.604))«TSEV 0. 0 0 0 . r, 0 w 2 fiCOBs 0 ,000*1 0,900)«PNEO*4 i.oooiaTsev 0. n 0 o.ono

3 4ooe= 0 .000*1 0 .9 0 0 1 *PREO*l i.ooo)*rsEv 0. n 0 o.nno

•* iOCHs 0 .ro o *( 0.900»«PRCO*( 1.000)«TSEV 0. 0 0 0,000

5 GOOBs 0 .000*1 0,9CO>*PREQ*( i.ooo)«rsev 0. 0 0 0.000

6 GCOB* 0 .000*4 0.900I*PRCO*1 l.OOOiaTSev 45.000 0. n =

* *•*• PATHWAY REGRESSION EQUATIONS FOR HlAL OR HIERACIUM ALBERTINUM » CYNQGLO

PATH HCGRCSSIOft F.CUATi ON FOHM PSQ rj STri OEV

I hlAUS O.ïOO+l 0,COO)*OUMT 0, C G 0.000

2 HIALS 0 .500*1 0.000>*OUPT 0. 0 0 o.fifid

5 MlALs •1.209*1 0.031)*ELEV*( •0.012)«PHMA*r 0.012l*5HRei< -0 .092)*CCAG 0.6a 20 0.162

** ^|AL = •1 .2 0 a *< 0 ,0 3 1 I* C l Cy*1 •0.012l«PHMA*f 0.012)«SHRe*4 -C ,092)«CCAG o.âû 20 0.162

? H|AL3 0.bO 0*( 0.000>*OUHT 5. 0 0 o.oon

MlALa 0.500*1 0.000)*OUMV 0. 0 0 O.QOfl

.«••• PATHWAY REGRESSION EQUATIONS FOR HIST OR HITpLLA STAUROPETALA

OftTH REGRESSION EQUATION FORM RSQ N STn oEV

I M iS ta 0 ,*T 3 *4 Q.215)«CX12 0.98 12 0, 392 0.98 2 MiSTa 0.173*4 0.2I3>«EX12 12 0.092

Î WIST* 0 ,173*4 0.2I3I*EX12 0.96 12 0.C9Z 0.092 >» MISTa 0 ,173*4 0.215)*EX12 0 .9 * 12

"tST = 0 .173*4 0.215}*EX12 0,99 12 0.092 12 0.092 -IS T a 0 .1 7 3 *4 0.2l3)«exl2 0,9a

, **•* PATHWAY regression equations for THOC OR TMALICTRU" OCCIDENTALE RSO PATH REGRESSION EQUATION FORM STO SEV

1 THOCs 0 .2 9 **4 3,570I«CCA2 C.9,* o .a i 2 THOC a •ft.053*4 0.166)«ElEV*( •0.021>*PHMA T .99 o.ono i THOCa 0.000*4 1.000)#PREO C .99 0,000 THOCa 0.000* 4 I.00O)*PR£O 0. 0 0 c.aoo 5 THOCa 0.500* 4 0.900)«PREO*4 1.000)«TSEV 0. 0 0 O.OnO 4, TMOCa 0,500*1 0.900>«PRCO*< l.OOO»«TStV

« •« * * PATHWAY REGRESSION EQUATIONS FOR XETE OR XCPOPMYLLUM TENAX ST? OEV REGRESSION EOUATION FORM RSO

26 3 . d ll KETEs -2.151*1 3,500l«exPR*4 0.07R)*ASPT 0 .1ft

xCTEa •2 .1 3 1 *4 3.5S8)»CxP4|*| 0.071>*ASPT 0.16 28 3 .A ll

XtTEs 6 .0 4 7 *4 •1.293I*TRMT*( D.603>«CCA2 0.63 10 2 . 1*3

4» XETE: 5,195*4 0 ,0 5 2 1 #ASPT*4 -i.l«i)*TRMt*4 •0.136)«SUDP 5.59 20 1 . 9ft? 5 xEfEa •1.865*4 0.099)«CARu*1 0.160)«SHRB 0.93 ? I . O i l ft xCTEs 9.220*4 -0.3Q3)«SUOP*| •O.OaOlvPHMA 5.15 19 1.6-*i

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 92

APPENDIX F

Sample of Tabular Output Generated by the Model.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 93

▼TT^E OF TmÇ SIMULATION RUf": Su CCESSIONA l S Î’Mjla TIO" HUN

OESCRIPTlOn oF TmE SlhULATlON AREA ; ELEVATION : J500. FTFT TREAT*>CfT TYPE : W IL O flP E ASPECT : 190. CCOAcr*; i n t e n s i t y Trrc : -nnEP/iTE Slo pe : «**. % ip e r c e n t i M&eiTAT TYPE PHASE : PS‘^E/Pw“A .D«T

OI&GRAM Or THE modeled SUCCES^î IONAL RAT hw AY

S"RUB-HEHA SAPLING pc ll MATURE SEPAL I*Ak

PuNA ------> PSMC/PHKft - - - - > rSME/PwMA PSME/PMMA ------> ?S "E/PMMA

PERCENT Cov C"AGE OY SPECIES F or SeCrIFICC AGES

SPECIES NAME 5 30 55 #0 105 130 155 acift

TOTAL TWEE CANOPY COvER 0 26 . 50 51 - TÇ 51 - 75 51 - 75 51 - ?5 51 - 75 51 - 75

AVERAGE OSm of STAND « INCHES) 0 9 a 10 12 l i I" !>.

AtfF STAhO OASAL AREA (SO FT) 0 46 96 129 ISO 163 170 1?6

PSCuOUTSUGü •‘f . Z î t S U (< 4 I N . I 3 6-25 6-25 6-25 6-25 6-35 6-25 E - 2*

PSEuOOTSUGA mENZTESlI l> *♦ IN . I 0 6-25 6-25 26 - 50 26 - 50 26 - 50 26 - 50 26 - «3

- PSEUDOTSUCa « E N Z ltS ll (T0T4L» 0 26 - 50 51 - 75 51 - 75 51 - 75 51 - 75 -1 . 75 51 7 =

ACER 6LA9RUM 0 0 1 0 L-

AMELANCHlER ALMFOLtA G - 25 6-25 6-25 6-25 6-25 6 - i>5 6-25

CCANOTh u S vELUTImUS T c (J J

l o n ic e r a UTAHENSIS T T T 7 7 7 26 - 50 26 - S.. PMTSOCfiRPUS MALWACEUS 26 . 50 26 - 50 26 - 50 26 - 50 26 - SO T PRtJNUS VIRGINIANA TT T TT

ROSA GYMNOCARPA T TT T 7 T SALIX SCOUl EWIANA T T 7 T 7 7

SPIRAEA BETULIFOLU 6 * 25 0 0 0 T - S T - 5 6-25 T - « St"PHOPICAHPOS ALDUS 6-25 T - S T - * T - 5 T - S T - 5 T - • r - 5 T - 5 VACCINIUM OLODLLAPE T - 5 T - 5 T - 5 T - 5 T - 5 T - 5 T - 5 r - 5 T - 5 ARTOSTApHfLOS UVA-UHSi T - 5 6-25 T . 5 T - 5 6-25 6-25 T - 5 ^EPREHIS «EPENS T - 5 6-25 6-25 6-25 6-25 T T LINN&EA BOREALIS t T t T 7 T AGROPYPON SPïCAÎyM T 0 0 0 7 6-25 6-25 6-25 6 - 2. calamagpostis rupcscens 6-25 6-25 6 25 0 0 0 CASE* CONCIN- jOICES 0 0 0 6-25 6-25 6-25 6 - 5« CARE* GETEWI 26 - 50 6-25 6-25 6-25 26 - 50 26 - 50 26 - 50 26-50 CARE* ROSSII 26 - 50 26 - 50 26 . 50 26 - 50 T ACHILLEA MILLEFOLIUM T TT T 7 T T - 5 T - 5 A'lTENUARIA RACEMOSA T - 5 T - 5 T - * T - 5

0 ARNICA COPCIFO l IA 0 0 T - 5 T - = ASTER CONSPICUUS T - 5 T - 5 T - ! T - 5 T T 7 RALSAMCRH12A SAGITTATA T T T 7

6-25 6-25 6-25 6-2% C m IMAR p I L L A u m s e l l a t a 6 • 25 6 - 2S 6-25 6 a s

1 0 CPILORIUM ANGUSTIFOLIUM r T 0 1)

FRASARia VESCA T - 5 6-25 T - 5 r : T FPftGAHIA VlPGIt;IAUA T T T ’’ T T GDOOT l h a OPLOUGlFOLlA T 7

HlERACIUM ALPCRTTNUM I CYNDGLO T 0 5

MITELLA ST auf^ORLTALA T - 5 T T

ThALICTRUH CCCICENTALE T 7

XEROPHYLLUM TfNAR T T 7

R SOUARC s 7<* OCGREES of FREEOOM s 24

R SOUARC P SO OCGREES OF FREEDOM = 27

:...... r:.» R SQUARE » 6% DEGREES OF PR E C Û C s U

A SQUARE : At< OfQREC' OF F9EECC*' a. 43

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Page 94

APPENDIX G

Sample of Graphic Output Generated by the Model.

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f TTLC : ' ■ i r L L . î î : Page 95

io HO 60 «0 lOO l?0 l**0 160 lOO 2fO

AGE IN TEARS

the V-AKIS IS I« PE9CFNT COVER <»>

TIT LE : SUCCESSIOr.AL SlKULflTrOf- RUN FOR s p e c ie s : PF>H

HO 60 60 100 120 IH?

AGE IN TEARS

TME r-ollS IS IN PEPCE'T COVER («)

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.