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Graduate Student Theses, Dissertations, & Professional Papers Graduate School
1984
Predicting successional plant composition on a Pseudotsuga menziesii/Physocarpus malvaceus habitat type in western Montana
Robert E. Keane The University of Montana
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Recommended Citation Keane, Robert E., "Predicting successional plant composition on a Pseudotsuga menziesii/Physocarpus malvaceus habitat type in western Montana" (1984). Graduate Student Theses, Dissertations, & Professional Papers. 7419. https://scholarworks.umt.edu/etd/7419
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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
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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.
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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 plants. 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.
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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
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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
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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
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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
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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.
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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
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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. Shrub 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
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(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
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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). Pinus ponderosa (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 rhizomes 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
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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 shrubs 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.
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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.
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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
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sagittate (BASA) is capable of resprouting after low to moderate
treatments while the stout, s u rfic la l rhizome system of Xerophyllum
tenax (XETE) can resprout if left intact after disturbance (Antos and
Shearer 1980, Bradley 1984, Habeck and others 1980).
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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
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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
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ü_
CO CO
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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
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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
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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
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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).
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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. Calamagrostis rubescens (CARU) Pinegrass
4. Carex geyeri (CAGE) Elk sedge
5. Ceanothus velutinus (CEVE) Evergreen Ceanothus
6. Amelanchier a ln ifo lia (AMAL) Serviceberry
7. Acer glabrum (ACGL) Mountain maple
8. Salix scouleriana (SASC) Seouler's willow
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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) Lonicera utahensis - LOUT Aster conspicuus - ASCO (Utah honeysuckle) (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) Symphoricarpos albus - 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 Xerophyllum tenax - 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 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 ( 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 Gtitpr the coverage far Salim scowleriana Entpr the coverage far Spiraea betviifolia Enter the coverage far Synphoncarpas altvs ( 5YAL ) or snowberry; Enter the coverage far Vaccinivm globulere 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 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 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. 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 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 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 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, 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 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 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. 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