- Email: [email protected]
Modelling forest dynamics with vital attributes and fuzzy systems theory
ELSEVIER
Ecological Modelling 90 (1996) 161-173
Modelling forest dynamics with vital attributes and fuzzy systems
theory D a v i d W. Roberts * Department ofForestResources and Ecology Center, Utah State University, Logan, UT84322-5215, USA
Abstract
Vital attributes are the minimal autecological characteristics required to predict the behavior of plants in disturbed environments. In this paper, I modify the existing classifications of reproductive method, establishment requirements, and disturbance resistance to better simulate the behavior of complex vegetation. The vital attributes are coded into a stochastic simulation model for analysis of successional development and disturbance response with varying fire return interval and fire severity. The vegetation composition and dynamics are analyzed with fuzzy systems theory, a fuzzy set generalization of dynamical systems theory. The vegetation composition and structure define a fuzzy state space, and the system dynamics are determined by the simulated trajectory through the fuzzy state space. Model output is validated with respect to vegetation patterns of southwestern U.S. Sensitivity analysis of the model behavior with varying vital attributes is used to analyze the ecological characteristics appropriate to plants in disturbed environments, and implications of the model for plant community diversity are also analyzed. Keywords: Forest ecosystems;Fuzzy logic; Vegetationdynamics;Vital attributes
1. Introduction
Modelling of forest dynamics is an area of active research, with numerous approaches in use and under development. Within the subset of forest models based on ecological mechanism, as opposed to empirical relationships, models derived from JABOWA (Botkin et al., 1972) and FORET (Shugart, 1984) have predominated. These individual tree models are widely available, and have been adapted to a large number of purposes, but possess moderately high complexity with regard to data requirements and computer requirements. The model presented here, Vital Attributes Fuzzy Systems STAND SIMulator
* Fax: (1) (801) 797-4040.
(VAFS/STANDSIM), was designed as a simpler alternative which predicts with sufficient detail to investigate ecological questions of interest. VAFS/STANDSIM is a stochastic simulation model which predicts the composition and age-class structure of forest vegetation on a 10-year time step. VAFS/STANDSIM is based on three elements which will be introduced in turn: (1) vital attributes theory, (2) successional community classification by binomial nomenclature, and (3) fuzzy systems theory.
1.1. Vital attributes theory
Vital attributes theory is a simple, consistent scheme for the characterization of individual plant
0304-3800/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0304-3800(95)00163- 8
162
D. W. Roberts / Ecological Modelling 90 (1996) 161-173
species autecology. Following an analysis of fireadapted species traits by Gill (1975), Noble and Slatyer (1977, 1980) characterized species by three general attributes: method of propagule dispersal or persistence, conditions of seedling establishment, and age of critical life history stages (age of sexual maturity or first production of propagules by vegetative reproducers, longevity, and propagule longevity). Propagule dispersal or persistence was classified into four possible methods: dispersed seed, seed stored in the soil, seed stored in the canopy, or vegetative reproduction. Conditions for establishment were classified into three classes: able to reproduce under any conditions (tolerant), able to reproduce only in the absence of competition (intolerant), and able to reproduce only in the presence of other vegetation (requiring), corresponding to the tolerance, inhibition, and facilitation models of Connell and Slatyer (1977) respectively. Conceptual vital attributes models which produce qualitative predictions have been developed by Noble and Slatyer (1977, 1980) and Cattelino et al. (1979). Kessell and Potter (1980) developed a computer model based on an extension of the same concepts which produces semi-quantitative predictions. Moore and Noble (1990) developed the FATE model by adding life history stages, abundance classes and resource competition to the vital attributes of Noble and Slatyer (1977, 1980).
number of possible successional community types) declines, leading to a pyramid of successional community types (Fig. 1). Given n species, there are n(n + 1)/2 possible successional community types. Comparing the dominant species with the least tolerant species gives an indication of stand structure as well as successional stage. If the dominant species is not the same as the least shade-tolerant, it is likely that the least shade-tolerant species is represented by relatively few individuals in the overstory, with an understory of the more tolerant dominant species. Steele (1984) employed a similar approach to the non-tree understory species, based on the concept of successional vulnerability, but the understory classification is not used in this model.
1.3. Fuzzy systems vegetation theory Fuzzy systems theory is a fuzzy set generalization of dynamical systems theory first applied to vegetation ecology by Roberts (1989). Fuzzy systems theory can serve as a general framework for models of dynamic systems, such as vegetation succession or response to disturbance. In a fuzzy system vegetation model, individual plant communities are assigned membership values in each community type which indicate the degree to which the vegetation meets the definition or ideal of each community type. The distribution of membership values for individual
1.2. Successional community classification ABCO/ ABCO
Steele (1984) developed a simple successional community classification based on the concepts of a successional pyramid (Huschle and Hironaka, 1980). The successional classification scheme employs a binomial nomenclature which reflects the two criteria of classification. The first element of the binomial is the least shade-tolerant species present in the stand, called the indicator species. This species is taken as a partial representation of successional stage, as shade-intolerant species are not present in later stages of succession. The second element of the binomial is the dominant (most abundant) species in the stand. The two criteria together specify the successional class for each stand. As species are considered in order of increasing shade tolerance, the number of possible dominant species (and therefore the
PIPU/ PIPU
PIPU/ ABCO
PSME/ P S M E / PSME PIPU
PSMEJ ABCO
PIPO ~, PSMEJJ PIPU POTR/ POTR
POTR/ PiPO
P O T R / POTPJ PSME PIPU
POTPJ ABCO
DOMINANT
Fig. 1. Successional pyramid diagram. Contours show the fuzzy community type for t~(Pn,O/pipo)(X) = 0.2, P,(PIPO/PSMF,)(X)= 0.3, p,(Pieo/Pmu)(X) = 0.1, t~(PIpO/ABCo)(X)= 0.4, where p,a(x) is the fuzzy membership of a stand x in community type a. POTR = Populus tremuloides, PIPO = Pinus ponderosa, PSME = Pseudotsuga menziesii, PIPU = Picea pungens, ABCO = Abies concolor.
D. W. Roberts~Ecological Modelling 90 (1996) 161-173
community types ranges from [0,1] and sums to 1.0 over all possible community types. The vegetation dynamics are portrayed by the change in membership values with time. Roberts (1989) devised a fuzzy systems generalization of the Steele (1984) classification scheme, where individual stands are potentially partial members of more than one successional community type at a given time. In the fuzzy systems generalization, the representation of each stand is determined by the least shade-tolerant species present and the relative dominance of each species. The membership values for the stand are apportioned among the successional community types according to each species' relative dominance. Fig. 1 presents a simple example. Representing the successional community with a distribution of community type memberships rather than a single community type conveys more information. If two or more species share the relative dominance in close proportion, representing the community type by a single binomial may be misleading. Steele (1984) explicitly did not represent successional pathways on the successional pyramid, arguing that successional development is somewhat stochastic and site specific. However, Roberts (1989) showed that successional pathways could be deduced from the shade-tolerance relations inherent in the pyramid model. In general, shade-tolerant species should increase in dominance at the expense of shade-intolerant species. Shade-intolerant species will fail to reproduce in the shade of more tolerant species and, with time, will become absent from the stand. This produces a general rightward and upward trajectory through the pyramid diagram with time. 1.4. Vital attribute-fuzzy systems simulation model
A stochastic simulation model which produces simple semi-quantitative predictions of plant community succession and response to disturbance was developed by slightly modifying the vital attributes concepts employed by previous workers, and integrating the fuzzy systems representation. The predicted composition of each stand is classified to fuzzy successional community type according to the rules of the fuzzy pyramid model, and the dynamics of the vegetation are portrayed by the trajectories of community type membership with time.
163
2. Objectives The primary objective of this research was to produce a simple, computationally-efficient forest simulation model to investigate the effects of fire regimes on the community composition of forests in the southern Rocky Mountains of the United States. Thus the model must be able to simulate not only forest succession, but also response to disturbance. Historically, fires have been frequent in these forests, and varying the fire return interval and fire severity leads to significant variability in community composition (Weaver, 1974). The secondary objective of this research was to evaluate the suitability of the model to serve as the core of a much larger landscape-scale model (Roberts, 1996). The model must be sufficiently easy to calibrate to be applicable to large areas with only general information available and efficient enough to simulate replicates of hundreds or thousands of individual stands simultaneously. The predicted succession and disturbance response produced by the model can then serve as a base-line for evaluation of the effects of spatial position in the landscape model.
3. Methods 3.1. Model structure
The structure of the model is similar to previous forest composition simulation models such as JABOWA (Botkin et al., 1972) and FORET (Shugart, 1984). The model includes routines for calculating the growth, reproduction, and mortality of trees in the absence of disturbance. Similar to the SILVA (Kercher and Axelrod, 1984) and FIRESUM models (Keane et al., 1990) models, VAFS/STANDSIM also includes a disturbance response routine for calculating the response of different age classes of individual species to disturbance of varying severity. The modelled disturbance regime is stochastic, and the response to disturbance depends on species, ageclass, and characteristics of the stand and environment. Given the objectives of landscape scale simulation, the model is conceptually and operationally simplified when compared to many forest stand sim-
164
D.W. Roberts/EcologicalModelling 90 (1996) 161-173
ulators. Successional development and post-disturbance response may take long periods of time in forest communities, and changes in within-community composition over single years are likely to be small and insignificant when considered from a landscape-scale perspective. Accordingly, the time step of the model was set at 10 years as a compromise of detail and computational tractability. Because of the simplified nature of the model, rather than model individual stems, the model tracks the presence or absence of 10-year age-class cohorts for each species. Species 'abundance' is calculated as the sum of age classes present, °ti = ~ pij X j j=l
where ct i is the abundance of species i, p,, is the presence or absence (0 or 1) of age clas; j for species i with longevity n. The assumption is that size is proportional to age, and that the sum of age classes represents a rough indication of biomass. The assumption does not strictly hold for forest vegetation, but does serve as an index of the importance of a species to the stand total. 3.2. Vital attributes representation
The vital attributes of Noble and Slatyer (1980) were modified slightly to better represent community-level characteristics being modelled and to increase the quantitative information produced by the model. Specifically, changes were made to the reproductive methods classification, the establishment requirement classification, and a new vital attribute was specified for disturbance resistance. Individual species reproduce by: (1) dispersed seed, (2) stored seed, or (3) vegetatively. Because the time step of the model is 10 years, dispersed seed are considered to be viable only in the time step in which they are produced; seeds which do not germinate are lost. Stored seed varies greatly in longevity, and species-specific values are required. The viability of vegetative reproducers is extremely variable, and depends on species-specific characteristics and the history and vigor of individual organisms. In this model I assumed that the ability to sprout depends on stored carbohydrate reserve, which
in tum depends on the recent carbon balance of the individual plant. Carbohydrate storage in the model is calculated as years of remaining carbohydrate, calculated as follows. For species with living stems older than the age of maturity, the storage is incremented every time step that sprouting does not occur, up to a species-specific maximum. For individuals existing only as root systems, the storage is decremented for every time step. Following disturbance, vegetative reproducers sprout (if the shade environment is suitable) and begin to replenish the carbohydrate expended in sprouting. Reproductive maturity for vegetative reproducers is considered to be the length of time required to replenish the carbohydrate expended in sprouting, and carbohydrate storage is decremented every time step until the plants reach maturity. If disturbance occurs when a species has exhausted its carbohydrate storage, no sprouting occurs, and the species goes locally extinct. The establishment classification was modified significantly by employing a shade-tolerance attribute, rather than an establishment attribute. Individual species are ranked for shade tolerance from 1 to 5 (with ties if appropriate). I assumed that species continue to add leaf area until their lower crowns reach their light compensation point, so that species cast shade proportional to their shade-tolerance. All species are assumed capable of reproducing in their own shade or the shade of less tolerant species. Species of shade-tolerance 5 require the shade of less tolerant species to establish (following the facilitation model of Connell and Slatyer (1977) or the R establishment attribute of Noble and Slatyer (1980)). Shade at the forest floor is classified from 0 (full sun) to 5 (full leaf area of maximum shade-tolerant) and is determined by the most shade-tolerant species whose age-classes sum to at least 70. The net effect of the shade-tolerance scheme is to produce a competitive hierarchy (Horn, 1976), where any species with shade tolerance from 1 to 4 can reproduce on open sites, but where more shade-tolerant species eventually shade out their less-tolerant competitors. The shade requirement characteristic of extremely shade-tolerant species produces a time lag (typically 40 years) between the colonization of an open site by intolerant or mid-tolerant species and very shadetolerant species.
D. W. Roberts/Ecological Modelling 90 (1996) 161-173
Species-specific establishment rates are variable, even under ideal conditions. For each species, a probability of establishment under acceptable shade conditions is given which simulates the requirements for restricted seed beds or reproductive sites within the simulated communities.
3.3. Disturbance In the forests of the Rocky Mountains fire intensity varies greatly. Fire severity in the model depends on site-specific characteristics of fuel accumulation rate and the time since the last fire. Fuel is assumed to accumulate after fires at a rate determined by the site productivity and decomposition rate, until reaching a plateau where decomposition equals new fuel production. Severity is classified into five severity classes, which correspond to the species fire tolerance ratings described below. The fuel accumulation rate is specified as the minimum number of years required to accumulate sufficient fuel for each fire severity class. When fires occur, all the fuel is assumed to be burned. In the Rocky Mountains, some species have adaptations such as thick bark and high self-pruning that enable mature individuals to withstand low intensity or moderate fires, while high-intensity fires may kill all individuals. Accordingly, a simple fire tolerance ranking (from zero to five) was employed to characterize the fire tolerance of individual species. If fires of an intensity class lower than or equal to the fire tolerance rating occur, individuals older than X survive the fire, where X is given by:
165
3.4. Species abundance and successional community classification For each species, the 10-year age class cohorts are summed to produce a pseudo-abundance. The least shade-tolerant species present (the indicator) is determined from this pseudo-abundance, and the relative abundance values of all species are used to determine membership of the stand in each of the possible successional community types. The distribution of successional community type memberships is stored for each time step for each replicate, and mean community type distributions for each time step are calculated at the end of the simulation. The values for mean community type memberships are plotted as functions of time.
3.5. Diversity The mean community type distributions for each time step are used to calculate a Shannon-Weiner community type diversity index for each time step. Maximum diversity would be attained if all n(n + 1)/2 possible community types were present with the same abundance, and diversity in the model is scaled relative to maximum possible diversity. Because individual stands may be partial members of more than one community type simultaneously, the index portrays both within-community diversity and stochastic variability between replicates.
X = (6 - (fire tolerance - fire severity)) × l0 If fires of an intensity greater than the fire tolerance occur, all individuals of that species are killed. This fire tolerance scheme results in fire-tolerant species maintaining significant populations of mature individuals under short fire return intervals, where fire-intolerant species are periodically excluded. The fire return interval is estimated as 'fixedprobability independent fire recurrence' (Johnson and Van Wagner, 1985), the length of time required to burn an area equal in size to the modelled area. Because the site-specific occurrence of fires is independent, 63% of the replicates will burn at least once within the fire retum interval; some replicates will bum multiple times within the fire return interval.
3.6. Sensitivity analysis Sensitivity analysis was performed by modifying the vital attribute for a specific trait for each species one at a time and evaluating the variance of model outputs for all modifications of that trait. Specifically, for each species, the shade tolerance and fire tolerance attributes were increased and decreased one unit (where possible), age of reproduction was increased and decreased 10 years, and longevity was increased and decreased 20% (to the nearest even 10 years). This resulted in nine modifications of shade tolerance, seven modifications of fire tolerance, and ten modifications each for maximum age and age of
D.W. Roberts/ EcologicalModelling90 (1996)161-173
166
reproduction, for a total set of 36 modifications. For each modification, 100 replicates were simulated for 500 years at each of six fire return intervals, resulting in 21 600 separate simulations. For each set of simulations with modification to a single attribute, the mean values for species abundance, community type membership, and diversity were used to calculate the coefficient of variation across all modifications of that attribute at each time step. These coefficients of variation were averaged over all time steps to calculate a mean CV. Sensitivity was summarized by simply counting the number of cases (species, community types, or diversity) where the mean coefficient of variation was above 0.30.
derosa to Pseudotsuga menziesii, Picea pungens, and Abies concolor in order of increasing tolerance. Due to thick bark and a habit of self-pruning lower branches, Pinus ponderosa is generally fire resistant in moderate to large diameters. Pseudotsuga menziesii is moderately fire resistant in large diameters. All simulations begin with early seral stands of Populus tremuloides in age classes from 10 to 40 years. Populus tremuloides is assumed to have 80 years of carbohydrate storage for sprouting; the conifer species are assumed to have an available seed source. Simulated stands begin with 40 years fuel accumulation. Fire severity classes are reached at 20, 40, 60, 80, and 100 years for classes 1, 2, 3, 4, and 5 respectively. Simulations were run with mean fire return intervals of 25, 50, 100, 250, 500 years, and absence of fire. One hundred replicates were run for each fire return interval.
3.7. Application The model was tested on a typical mixed conifer forest from Bryce Canyon National Park in southern Utah, USA. This forest type is typical of forests which occupy mid-elevation mesic sites throughout southern Utah, Arizona, and New Mexico (Moir and Ludwig, 1979; Youngblood and Mauk, 1985). The community consists of conifers Pinus ponderosa, Pseudotsuga menziesii, Abies concolor, and Picea pungens, with angiosperm Populus tremuloides. Typical successional sequences begin with Pinus ponderosa or Populus tremuloides (depending on site history), and proceed to mixed compositions of Pseudotsuga menziesii and Abies concolor, with or without Picea pungens depending on site. Table 1 presents the vital attributes of the species as coded for the model. The conifers all reproduce from wind-dispersed seed; Populus tremuloides reproduces vegetatively. The shade-tolerance relation progresses from Populus tremuloides and Pinus pon-
4. Results
4.1. Species abundance Fig. 2 a - f present the species mean abundance trajectories for the six fire return intervals simulated. In the absence of fire (Fig. 2a), the model predicts a simple successional development from pure Populus tremuloides to pure Abies concolor in about 450 years. In the absence of fire, the only stochastic element is the reproduction of species in a particular time step, and the results may be considered a caricature of Clementsian succession. The model assumes within-community homogeneity, and is incapable of simulating gap-phase replacements.
Table 1 Species vital attributes Species name
Longevity
Age of reproduction
Shade tolerance
Fire tolerance
Reproductivemethod
Populustremuloides Pinusponderosa Pseudotsugamenziesii Piceapungens Abies concolor
140 400 300 400 300
10 40 40 40 40
2 2 3 4 5
0 4 3 0 0
V D D D D
Reproductive methods: V = vegetativereproduction, D = dispersed seed reproduction.
D. W. R o b e r t s / E c o l o g i c a l M o d e l l i n g 9 0 ( 1 9 9 6 ) 1 6 1 - 1 7 3
SPECIES ABUNDANCE TRAJECTORIES
. .........? ....
+
60I~
<~
/.,'~"'~'
,./"
40
I--O
20
~
I---
=- _
--
...... .'----- -----.~ ~.--......... ":, 1o8
Z
so
I'-"
60
,<
(b) soo'y.am
"
"
:1
. . . . .
~ ............
z ELI
n-" LLI
(c) 250 years
I
so
60 40
. . . . . .
.~ •"
" ......
~
.-.--
~
.
...... =_..:
.
. ~.-...=
.....
.
_
.
.
..
L"-"L
_
.
.
.
_
-
-'--'":~'~",
.
_
.
.
.
-
• - . -==.
_
.....
0 1 O0
200
300
400
500
YEAR SPECIES ABUNDANCE TRAJECTORIES
,0,00,.-
...1
i1
k0 a z ,< I-"
6O II
180
~.
-" -'''-
60 40
- - - - ~ . . . . .
.
-
-
" ~ -"
2
0
z
tT LIJ
0
100
200
300
400
500
YEAR Fig. 2. Species mean abundance trajectories for six fire return intervals. Fire return intervals: absent (a), 500 years (b) 250 years (c), 100 years (d), 50 years (e), 25 years (f). - - = P o p u l u s tremuloides,
---=
Pinus ponderosa,
ziesii, - • = P i c e a p u n g e n s , - . . . .
---
= Pseudotsuga
Abies concolor.
men-
167
Introducing fire with a mean fire return interval of 500 years significantly affects the successional trajectory (Fig. 2b). While Abies concolor remains the dominant species, its relative abundance is reduced throughout the entire simulation. More importantly, where in the absence of fire all other species became locally extinct within 500 years, with a 500-year fire retum interval no species go locally extinct. With a longevity of 140 years and a maximum of 130 years of carbohydrate storage, some communities burn often enough to maintain Populus tremuloides even on a 500-year mean fire return interval. Halving the fire return interval to 250 years results in a reduced abundance of Abies concolor after 130 years, with a generally increased abundance of all other species, particularly Pinus ponderosa and Pseudotsuga menziesii (Fig. 2c). The composition is similar to a mixed-conifer forest composition on mesic sites. At a mean fire return interval of 100 years a qualitatively different result is obtained (Fig. 2d). Pinus ponderosa emerges as the dominant species throughout most of the simulation period, followed by Pseudotsuga menziesii, and then Abies concolor. With mean fire return intervals of 100 years or less, fire tolerance is more important than shade tolerance in determining abundance. Cutting the fire retum interval to 50 years leads to a clear dominance of Pinus ponderosa with Pseudotsuga menziesii of secondary importance, and Abies concolor reduced to minimal importance (Fig. 2e). Picea pungens goes locally extinct after about 350 years. Populus tremuloides is absent for intervals of about 40 years, but continues to sprout under favorable conditions. Further decreasing the fire return interval to 25 years results in a further increase in the relative abundance of Pinus ponderosa at the expense of Pseudotsuga menziesii (Fig. 2f). Other species have only minimal importance. Each of the fire regimes lead to a unique species abundance quasi-equilibrium within about 450 years. Running the simulations for 1000 years (not shown) does not lead to significantly different results than those obtained at 500 years. Running the simulations from different initial conditions (not shown) ultimately leads to the same quasi-equilibrium dictated by the fire regime. Thus the equilibrium vegetation composition appears to be determined by the interac-
168
D.W. Roberts / Ecological Modelling 90 (1996) 161-173
tion of the fire return interval and the species vital attributes.
COMMUNITYABUNDANCETRAJECTORIES
4.2. Community type membership distribution Of the fifteen possible community types only six occur with a high abundance (membership values > 0.20) during the simulations. Three of the types have Populus tremuloides present as the least shadetolerant species (POTR/POTR, POTR/PIPO, POTR/ABCO), two have Pinus ponderosa present as least shade-tolerant ( P I P O / P I P O and PIPO/ABCO), and one type is pure Abies concolor (ABCO/ABCO). Of the six types, Populus tremuloides is most abundant in one type (POTR/POTR), Pinus ponderosa is most abundant in two (POTR/PIPO and PIPO/PIPO), and Abies concolor is most abundant in three (POTR/ABCO, PIPO/ABCO, and ABCO/ABCO). Community type distributions are strongly affected by the simulated fire regimes, showing quantitative and qualitative changes determined by the underlying species dynamics. Fig. 3a-f show community type dynamics for the six simulated fire retum intervals. In the absence of fire, POTR/POTR (the initial type) rapidly declines, losing dominance after 100 years, and becomes absent at about 160 years (Fig. 3a). After a brief dominance by POTR/ABCO from years 100 to 150, dominance shifts to PIPO/PIPO for a period of over 300 years. In the absence of fire Pinus ponderosa fails to reproduce, however, and dominance shifts to ABCO/ABCO at about 410 years. Generally, only two or three community types occur simultaneously throughout the simulation. With a fire return interval of 500 years, a much more subtle and complex pattern of community types appears (Fig. 3b). POTR/POTR again declines rapidly as species other than Populus tremuloides increase, but remains at low levels throughout the 500-year simulation. While most of the simulation is dominated by the PIPO/ABCO community type, at least five community types are present at all times. Decreasing the fire return interval to 250 years leads rapidly to a nearly equitable distribution of all community types except ABCO/ABCO, which never occurs in simulations with fire return intervals shorter than 500 years (Fig. 3c).
100~ 8 o
(') fire ~ e n t ~
"
._1 6o
O I-LU
4o
'
z li
!
o lo6o 8^o~ (b)soo o y..,, ~ 5
' /"
~. ..... •.......... !...'.: ............... ii
40
]
~'1
-'~
~"...... .
.
ii
O ,o,.o.
z UJ o uJ t3_ 0
.
1O0
.
.
200
t
.
300
400
500
YEAR COMMUNITYABUNDANCETRAJECTORIES 100
(o') 1O0 yeats
80
_J <(
6o
I-0
4o
I"LLI 20 O_ 1o8 <
(o) so y~L,~
"
"
60
._
•
..." " "
:
~."%,'""..
¢.J" ' "'~/ V
40 _1
o
~
.
z 0
~
~,~2,y;,,,
o III
-
~
.....
:i 111 "
40
0
-
..... " " / "
I0
,'~.i '.,/
200
300
400
500
YEAR Fig. 3. C o m m u n i t y t y p e m e a n a b u n d a n c e trajectories for six fh'e return intervals. Fire return intervals: a b s e n t (a), 5 0 0 y e a r s (b) 2 5 0 years(c), 100 y e a r s (d), 5 0 y e a r s (e), 25 y e a r s (f). - - = POTR/POTR, --- = POTR/PIPO, - -- = POTR/ABCO, -. = PIPO/PIPO, - .... PIPO/ABCO, • • • = ABCO/ABCO.
D. W. Roberts / Ecological Modelling 90 (1996) 161-173 GAMMA DIVERSITY
1.0 :~ 0.8 x <
/-...~..-.=.. .... _ "-'~...~... - . . . . . -. '.. . _ . /
0.6
.(-:~'"
O
>_
":.v.-.~...,.~.,..~::::.=:::.~["
0.4
~ 0.~' 0.0
Table 3 Community type sensitivity. Values are number of community types ( m a x i m u m = 15) which showed high variability in response to all modifications of a specific vital attribute at a specific fire return interval. Totals are numbers of community types which showed high variability across all fire return intervals ( m a x i m u m = 90) Vital attribute
"
.
.
.
.
.
.
1O0
.
.
.
.
169
Fire return interval
Total
.
200
300
400
500
25
50
100
250
500
none
0 6 4 9
5 8 1 11
3 9 1 11
2 11 0 9
5 12 I 5
7 10 0 0
YEAR
Fig. 4. G a m m a diversity for six fire return intervals. - - = no fires, - - - = 500 years, - - - = 250 years, - • = 100 years, - • - . = 50 years, • . • = 25 years.
Decreasing the fire return interval again to 100 years results in a qualitative shift (Fig. 3e). After only 70 to 80 years, PIPO/PIPO becomes dominant, and maintains that dominance throughout the entire simulation period. POTR/PIPO is the secondary dominant. Reducing the return interval to 50 (Fig. 3e) or 25 years (Fig. 3f) merely amplifies the same pattern.
4.3. Diversity Mean diversity was calculated for each time step for each of the six fire return intervals (Fig. 4). Because all simulations started off with a monospecific stand of few age classes, diversity in all simulations starts off low and increases for a period of approximately 100 years, as other species begin to invade the single species community. The maximum diversity attained differs, however, and the pattern of diversity following the initial increase is distinct for each fire return interval.
longevity shade tolerance age of reproduction fire tolerance
22 56 7 45
In the absence of fire, diversity increases to moderate levels at about 120 years, and then begins a steady decline, reaching zero at the mono-specific climax attained in about year 460. Introducing fires with return intervals of about 500 to 250 years leads to the maximum observed diversity, and the diversity is maintained at a steady high value throughout the simulation period. Reducing the fire return interval to 100, 50 or 25 years leads to progressively lower maximum diversities, with respectively lower maintained diversities as well.
4.4. Sensitivity analysis The model was analyzed for sensitivity at each of six fire return intervals according to three criteria: individual species abundance, community type membership distribution, and diversity. Tables 2 - 4 present the results of the sensitivity analysis for these three criteria respectively.
Table 2 Species abundance sensitivity. Values are the number of species ( m a x i m u m = 5) which showed high variability in response to all modifications of a specific vital attribute at a specific fire return interval. Totals are numbers of species which showed high variability across all fire return intervals ( m a x i m u m = 30)
Table 4 G a m m a diversity index sensitivity. Values are c a s e s where g a m m a diversity showed high variability in response to all modifications of a specific vital attribute at a specific fire return interval ( m a x i m u m = 1). Totals are numbers of cases where g a m m a diversity showed high across all fh-e return intervals ( m a x i m u m = 6)
Vital attribute
Total
Vital attribute
Fire return interval 25
50
100
250
500
none
7 13 0 16
longevity shade tolerance age of reproduction fire tolerance
0 0 0 1
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
1 1 0 0
longevity shade tolerance age of reproduction fire tolerance
Fire return interval 25
50
100
250
500
none
1 2 0 5
2 2 0 5
0 2 0 4
0 2 0 2
1 3 0 0
3 2 0 0
Total
1 1 0 2
170
D. W. Roberts / Ecological Modelling 90 (1996) 161-173
Significant trends are evident when analyzing the sensitivity of individual species abundance (Table 2). The model is extremely sensitive to fire-tolerance ratings at short fire return intervals, with significant differences in species abundance occurring up to fire return intervals as long as 250 years. This is a reflection of the relative survivorship of mature trees through frequent, low-intensity fires. Additionally, the most fire-tolerant species are relatively shade intolerant, and increasing the fire tolerance of more shade-tolerant species leads to the removal of the shade-intolerant species due to shading. The model is moderately sensitive to the shadetolerance rankings at all fire return intervals. The lack of interaction of shade tolerance and fire return interval is interesting in light of the strong direct effect of fire tolerance on determining the dominant species at short fire return intervals and shade tolerance in determining the dominant species at long fire return intervals. The sensitivity of the model to maximum age of species shows a bimodal distribution with respect to fire frequency. At short fire return intervals, the longevity of the fire-tolerant species affects the relative abundance of species. At long fire return intervals, the longevity of shade-intolerant species affects the relative abundances following the relatively infrequent disturbances. In contrast to the species abundance criterion, community type membership appears most sensitive to shade tolerance, rather than fire tolerance (Table 3). Also, the sensitivity to shade tolerance shows a stronger relation to fire return interval, being relatively more sensitive at longer intervals. At long fire return intervals, increasing the shade tolerance of relatively intolerant species (or reducing the tolerance of the most tolerant species) results in ties for maximum shade tolerance, leading in turn to communities co-dominated by more than one species. Alternatively, at short fire return intervals, increasing the shade tolerance of shade-intolerant species allows them to regenerate beneath the canopy of mature shade-tolerant species which normally suppress them. The distribution of community type membership is moderately sensitive to changes in longevity, and generally insensitive to changes in age of first reproduction except at very short fire return intervals.
In contrast to the sensitivity measures for species abundance and community type, the measure of sensitivity for diversity is relatively crude, being measured on a binary scale rather than a numeric scale. In general, the measure of community diversity appears most sensitive to fire tolerance at short fire return intervals and is sensitive to longevity or shade tolerance only in the absence of fire.
4.5. Validation Stein (1988a) studied the fire history of the Paunsaugunt Plateau in southern Utah, which includes Bryce Canyon National Park. He concluded that mid-elevation sites exhibited historic fire return intervals between approximately 20 and 50 years for individual trees. Fires have generally been absent since the advent of fire suppression around 1910. Stein (1988b) studied the size class distributions and stand structures of forests on the Paunsaugunt Plateau and concluded that Pinus ponderosa dominated these sites under the historic disturbance regime, but that the current Pinus ponderosa size class distribution has too few small trees, and that it is being replaced by more shade-tolerant species, such as Pseudotsuga menziesii and Abies concolor. The lack of large size-class individuals for these species indicates that they were not successful in the historic past. Stein (1988b) attributes this shift to the change in fire regime and possible change in climate. Weaver (1974) describes similar conditions for much of the southwestern U.S. Although the validation data are fewer than would be ideal, the successional dynamics and disturbance response of the modelled community appear to be quite good. Under simulated fire regimes similar to the historic regime, Pinus ponderosa achieves and maintains dominance over the more shade-tolerant species. Eighty years of succession without a fire leads to mixed communities increasingly dominated by the more shade-tolerant species. Simulating a successional development beginning with the historical composition in the absence of fire (not shown) leads to an overstory dominated by Pinus ponderosa with an understory dominated by Abies concolor, similar to that reported for mid-elevation sites by Stein (1988a,b). The model suggests that a critical threshold in fire return interval occurs between 250 and 100 years, as
D. W. Roberts~Ecological Modelling 90 (1996) 161-173
Abies concolor dominates sites with return intervals of 250 years or longer, and Pinus ponderosa dominates sites with fire return intervals of 100 years or fewer. Unfortunately, sites with the appropriate fire histories do not occur in the study area to test this hypothesis.
5. Discussion 5.1. Model behavior Evaluating the species abundance results and sensitivity analyses in an ecological sense, the model identifies critical ecological characteristics for survival and dominance in environments of varying disturbance regime. In rarely disturbed environments, tolerance of competition and the ability to reproduce in competitive conditions eventually confers competitive superiority. In these conditions, age of first reproduction is relatively unimportant compared to longevity. In frequently-disturbed environments, disturbance-tolerance will over-compensate for poor competitive ability and confer dominance. Surprisingly, the model did not identify an early age of reproduction as important in frequently disturbed environments. However, the range of ages considered and the level of modification were both fairly small and may not have been sufficient to exhibit a significant difference. As noted above, each fire regime appeared to lead to a unique quasi-equilibrium. While this equilibrium only holds for the mean characteristics over 100 replicates, and not individual replicates, it is interesting that a stochastic, mechanistic model should exhibit such notable equilibrium behavior. There is no evidence of chaotic or high-order behavior in any of the simulations. Caswell and Cohen (1991) modelled the effects of disturbance, colonization, and competitive exclusion with a two-species non-linear Markov chain. The model employed a strict competitive hierarchy (although with variable rate of competitive exclusion), species had no age-structure, and were both excluded by disturbance. Their results suggested the existence of single stable points for all combinations of parameters, despite the potential for periodic or chaotic attractors. While the model presented here possesses
171
greater ecological structure, the results are consistent with those of Caswell and Cohen. Calculating the community type classification from the pyramid proved very useful. Because the community types are determined in a simple quantitative manner, the classification algorithm can be directly incorporated into the simulation model. By calculating and plotting the community types as well as species, a great deal of information about community composition can be determined. Species which are co-dominant in mean outputs could each occur in single species stands in different replicates, or in mixed species stands during all replicates. Calculating the community types during each replicate distinguishes these conditions simply without maintaining a wealth of detail on each simulation. Additionally, a fair amount of information about community structure can also be inferred. Knowing the shade-tolerance relations of the species, the overstory/understory characteristics of the community types present can be determined approximately. The relatively higher sensitivity values for community types as opposed to species suggests that in some cases the mean species abundances were insensitive to modifications of vital attributes while community compositions were not. This in turn implies a greater between-replicate variability when modifying these traits. Finally, calculating diversity on the basis of community type abundance distributions provided interesting insights on the role of disturbance in forest communities. The model makes clear that maximum diversity is attained under moderate disturbance regimes which allow disturbance-sensitive species to reach large populations but which still produce conditions for reproduction of shade-intolerant species. Interestingly, maximum diversity is attained with mean fire return intervals of roughly the same order as the longevity of most of the species; either the absence of disturbance or too frequent disturbance reduces diversity. The model is too simple to simulate gap phase replacement within communities and thus underestimates the diversity of 'climax' stands, but the general trend of diversity with disturbance is probably not affected by this underestimation. The model's prediction of highest diversity under intermediate disturbance regimes agrees with the intermediate disturbance hypothesis (Connell, 1978;
172
D.W. Roberts / Ecological Modelling 90 (1996) 161-173
Denslow, 1980; Miller, 1982), which relates the role of disturbance periodicity and severity in determining community diversity for a wide range of communities. Malanson (1987) discusses the intermediate disturbance hypothesis in respect to recurrent fires in temperate vegetation, and reaches similar conclusions.
5.2. Efficiency and parsimony The secondary objective of this work was to produce a simple, efficient forest simulator for use in a landscape-scale simulation model. The model presented here meets the objectives very satisfactorily. It is simple to set up and run, and requires minimal computational power. The model will run 100 replicates for 500 years in less than 1 min on a microcomputer. More important than computational efficiency however, is ecological realism. In a sense, the objective is not to find the most computationally-efficient model, but rather the most parsimonious ecological model suitable for simulation. Again, the model appears to largely meet this objective. Using the best-guess estimates of species vital attributes, the model generates realistic patterns of community composition dynamics under a variety of disturbance regimes. Because the model is based on simple species attributes and environmental characteristics, it should be easy to recalibrate for new areas and species.
Acknowledgements
This model was developed over a long period of evolution, and benefited from numerous comments. I would particularly like to thank D.H. Knight, S.L. Collins, S. Glenn, G. Henebry, and S. Will-Wolf. Thanks to G. Cottam and T.F.H. Allen for the facilities at the University of Wisconsin to make publication of this research possible. This work was developed in part through a grant from the U.S.D.I. National Park Service through the University of Wyoming - National Park Service Research Center. FORTRAN code for the VAFS/STANDSIM model is available from the author.
References Botkin, D.B., Janak, J.F. and Wallis, J.R., 1972. Some ecological consequences of a computer model of forest growth. J. Ecol., 60: 849-873. Caswell, H. and Cohen, J.E., 1991. Communities in patchy environments: a model of disturbance, competition, and heterogeneity. In: J. Kolasa and S.T.A. Pickett (Editors), Ecological Heterogeneity. Ecological Studies Vol. 86. Springer-Verlag, New York, pp. 97-122. Cattelino, P.J., Noble, I.R., Slatyer, R.O. and Kessell, S.R., 1979. Predicting the multiple pathways of succession. Environ. Manage., 3: 41-50. Connell, J.H., 1978. Diversity in tropical rain forests and coral reefs. Science, 199: 1302-1310. Connell, J.H. and Slatyer, R.O., 1977. Mechanisms of succession in natural communities and their role in community stability and organization. Am. Nat., 111: 1119-1144. Denslow, J.S., 1980. Patterns of plant species diversity during succession under different disturbance regimes. Oecologia, 46: 18-21. Gill, A.M., 1975. Fire and the Australian flora: a review. Aust. For., 38: 4-25. Horn, H.S., 1976., Succession. In: R.M. May, Theoretical Ecology. Principles and Practice. Blackwell, Oxford, pp. 187-204. Huschle, G. and Hironaka, M., 1980. Classification and ordination of seral plant communities. J. Range Manage., 33: 179-182. Johnson, E.A. and Van Wagner, C.E., 1985. The theory and use of two fire history models. Can. J. For. Res., 15: 214-220. Keane, R.F., Arno, S.F. and Brown, J.K., 1990. Simulating cumulative fire effects in ponderosa pine/Douglas-fur forests. Ecology, 71: 189-203. Kercher, J.R. and Axelrod, M.C., 1984. A process model of fire ecology and succession in a mixed conifer forest. Ecology, 65: 1725- 1742. Malanson, G.P., 1987. Diversity, stability, and resilience: Effects of fire regime. In: L. Trabaud (Editor), The Role of Fire in Ecological Systems. SPB Academic, The Hague, pp. 49-63. Miller, T.E., 1982. Community diversity and interactions between the size and frequency of disturbance. Am. Nat., 120: 533-536. Moir, W.H. and Ludwig, J.A., 1979. A classification of spruce-fir and mixed-conifer habitat types of Arizona and New Mexico. USDA For. Serv. Rocky Mtn. For. and Range Exp. Stn. Res. Paper RM-207, 47 pp. Moore, A.D. and Noble, I.R., 1990. An individualistic model of vegetation stand dynamics. J. Environ. Manage., 31: 61-81. Noble, I.R. and Slatyer, R.O., 1977. Post fire succession of plants in Mediterranean ecosystems. In: H.A. Mooney and C.E. Conrad (Editors), Proc. Symp. Environmental Consequences of Fire and Fuel Management in Mediterranean Ecosystems. USDA For. Serv. Gen. Tech. Rep. WO-3, pp. 27-39. Noble, I.R. and Slatyer, R.O., 1980. The use of vital attributes to predict successional changes in plant communities subject to recurrent disturbance. Vegetatio, 43: 5-21. Roberts, D.W., 1989. Fuzzy systems vegetation theory. Vegetatio, 83: 71-80. Roberts, D.W., 1996. Landscape vegetation modelling with vital
D. W. Roberts/Ecological Modelling 90 (1996) 161-173 attributes and fuzzy systems theory. Ecol. Model., 90: 175184. Shugart, H.H., 1984. A Theory of Forest Dynamics: The Ecological Implications of Forest Succession Models. Springer, New York, 278 pp. Steele, R., 1984. An approach to classifying seral vegetation within habitat types. Northwest Sci., 58: 29-39. Stein, S.J., 1988a. Explanations of the imbalanced age structure and scattered distribution of ponderosa pine within a highelevation mixed-conifer forest. For. Ecol. Manage., 25: 139153.
173
Stein, S.J., 1988b. Fire history of the Paunsangunt Plateau in southern Utah. Great Basin Nat., 48: 58-63. Weaver, H., 1974. Effects of ftre on temperate forests: Western United States. In: T.T. Kozlowski and C.E. Ahlgren (Editors), Fire and Ecosystems. Academic Press, New York, pp. 279319. Youngblood, A.P. and Mauk, R.P., 1985. Coniferous forest habitat types of central and southern Utah. USDA For. Serv. Intermt. For. and Range Exp. Stn. Gen. Tech. Rep. INT-187, 89 pp.
Ecological Modelling 90 (1996) 161-173
Modelling forest dynamics with vital attributes and fuzzy systems
theory D a v i d W. Roberts * Department ofForestResources and Ecology Center, Utah State University, Logan, UT84322-5215, USA
Abstract
Vital attributes are the minimal autecological characteristics required to predict the behavior of plants in disturbed environments. In this paper, I modify the existing classifications of reproductive method, establishment requirements, and disturbance resistance to better simulate the behavior of complex vegetation. The vital attributes are coded into a stochastic simulation model for analysis of successional development and disturbance response with varying fire return interval and fire severity. The vegetation composition and dynamics are analyzed with fuzzy systems theory, a fuzzy set generalization of dynamical systems theory. The vegetation composition and structure define a fuzzy state space, and the system dynamics are determined by the simulated trajectory through the fuzzy state space. Model output is validated with respect to vegetation patterns of southwestern U.S. Sensitivity analysis of the model behavior with varying vital attributes is used to analyze the ecological characteristics appropriate to plants in disturbed environments, and implications of the model for plant community diversity are also analyzed. Keywords: Forest ecosystems;Fuzzy logic; Vegetationdynamics;Vital attributes
1. Introduction
Modelling of forest dynamics is an area of active research, with numerous approaches in use and under development. Within the subset of forest models based on ecological mechanism, as opposed to empirical relationships, models derived from JABOWA (Botkin et al., 1972) and FORET (Shugart, 1984) have predominated. These individual tree models are widely available, and have been adapted to a large number of purposes, but possess moderately high complexity with regard to data requirements and computer requirements. The model presented here, Vital Attributes Fuzzy Systems STAND SIMulator
* Fax: (1) (801) 797-4040.
(VAFS/STANDSIM), was designed as a simpler alternative which predicts with sufficient detail to investigate ecological questions of interest. VAFS/STANDSIM is a stochastic simulation model which predicts the composition and age-class structure of forest vegetation on a 10-year time step. VAFS/STANDSIM is based on three elements which will be introduced in turn: (1) vital attributes theory, (2) successional community classification by binomial nomenclature, and (3) fuzzy systems theory.
1.1. Vital attributes theory
Vital attributes theory is a simple, consistent scheme for the characterization of individual plant
0304-3800/96/$15.00 Copyright © 1996 Elsevier Science B.V. All rights reserved. SSDI 0304-3800(95)00163- 8
162
D. W. Roberts / Ecological Modelling 90 (1996) 161-173
species autecology. Following an analysis of fireadapted species traits by Gill (1975), Noble and Slatyer (1977, 1980) characterized species by three general attributes: method of propagule dispersal or persistence, conditions of seedling establishment, and age of critical life history stages (age of sexual maturity or first production of propagules by vegetative reproducers, longevity, and propagule longevity). Propagule dispersal or persistence was classified into four possible methods: dispersed seed, seed stored in the soil, seed stored in the canopy, or vegetative reproduction. Conditions for establishment were classified into three classes: able to reproduce under any conditions (tolerant), able to reproduce only in the absence of competition (intolerant), and able to reproduce only in the presence of other vegetation (requiring), corresponding to the tolerance, inhibition, and facilitation models of Connell and Slatyer (1977) respectively. Conceptual vital attributes models which produce qualitative predictions have been developed by Noble and Slatyer (1977, 1980) and Cattelino et al. (1979). Kessell and Potter (1980) developed a computer model based on an extension of the same concepts which produces semi-quantitative predictions. Moore and Noble (1990) developed the FATE model by adding life history stages, abundance classes and resource competition to the vital attributes of Noble and Slatyer (1977, 1980).
number of possible successional community types) declines, leading to a pyramid of successional community types (Fig. 1). Given n species, there are n(n + 1)/2 possible successional community types. Comparing the dominant species with the least tolerant species gives an indication of stand structure as well as successional stage. If the dominant species is not the same as the least shade-tolerant, it is likely that the least shade-tolerant species is represented by relatively few individuals in the overstory, with an understory of the more tolerant dominant species. Steele (1984) employed a similar approach to the non-tree understory species, based on the concept of successional vulnerability, but the understory classification is not used in this model.
1.3. Fuzzy systems vegetation theory Fuzzy systems theory is a fuzzy set generalization of dynamical systems theory first applied to vegetation ecology by Roberts (1989). Fuzzy systems theory can serve as a general framework for models of dynamic systems, such as vegetation succession or response to disturbance. In a fuzzy system vegetation model, individual plant communities are assigned membership values in each community type which indicate the degree to which the vegetation meets the definition or ideal of each community type. The distribution of membership values for individual
1.2. Successional community classification ABCO/ ABCO
Steele (1984) developed a simple successional community classification based on the concepts of a successional pyramid (Huschle and Hironaka, 1980). The successional classification scheme employs a binomial nomenclature which reflects the two criteria of classification. The first element of the binomial is the least shade-tolerant species present in the stand, called the indicator species. This species is taken as a partial representation of successional stage, as shade-intolerant species are not present in later stages of succession. The second element of the binomial is the dominant (most abundant) species in the stand. The two criteria together specify the successional class for each stand. As species are considered in order of increasing shade tolerance, the number of possible dominant species (and therefore the
PIPU/ PIPU
PIPU/ ABCO
PSME/ P S M E / PSME PIPU
PSMEJ ABCO
PIPO ~, PSMEJJ PIPU POTR/ POTR
POTR/ PiPO
P O T R / POTPJ PSME PIPU
POTPJ ABCO
DOMINANT
Fig. 1. Successional pyramid diagram. Contours show the fuzzy community type for t~(Pn,O/pipo)(X) = 0.2, P,(PIPO/PSMF,)(X)= 0.3, p,(Pieo/Pmu)(X) = 0.1, t~(PIpO/ABCo)(X)= 0.4, where p,a(x) is the fuzzy membership of a stand x in community type a. POTR = Populus tremuloides, PIPO = Pinus ponderosa, PSME = Pseudotsuga menziesii, PIPU = Picea pungens, ABCO = Abies concolor.
D. W. Roberts~Ecological Modelling 90 (1996) 161-173
community types ranges from [0,1] and sums to 1.0 over all possible community types. The vegetation dynamics are portrayed by the change in membership values with time. Roberts (1989) devised a fuzzy systems generalization of the Steele (1984) classification scheme, where individual stands are potentially partial members of more than one successional community type at a given time. In the fuzzy systems generalization, the representation of each stand is determined by the least shade-tolerant species present and the relative dominance of each species. The membership values for the stand are apportioned among the successional community types according to each species' relative dominance. Fig. 1 presents a simple example. Representing the successional community with a distribution of community type memberships rather than a single community type conveys more information. If two or more species share the relative dominance in close proportion, representing the community type by a single binomial may be misleading. Steele (1984) explicitly did not represent successional pathways on the successional pyramid, arguing that successional development is somewhat stochastic and site specific. However, Roberts (1989) showed that successional pathways could be deduced from the shade-tolerance relations inherent in the pyramid model. In general, shade-tolerant species should increase in dominance at the expense of shade-intolerant species. Shade-intolerant species will fail to reproduce in the shade of more tolerant species and, with time, will become absent from the stand. This produces a general rightward and upward trajectory through the pyramid diagram with time. 1.4. Vital attribute-fuzzy systems simulation model
A stochastic simulation model which produces simple semi-quantitative predictions of plant community succession and response to disturbance was developed by slightly modifying the vital attributes concepts employed by previous workers, and integrating the fuzzy systems representation. The predicted composition of each stand is classified to fuzzy successional community type according to the rules of the fuzzy pyramid model, and the dynamics of the vegetation are portrayed by the trajectories of community type membership with time.
163
2. Objectives The primary objective of this research was to produce a simple, computationally-efficient forest simulation model to investigate the effects of fire regimes on the community composition of forests in the southern Rocky Mountains of the United States. Thus the model must be able to simulate not only forest succession, but also response to disturbance. Historically, fires have been frequent in these forests, and varying the fire return interval and fire severity leads to significant variability in community composition (Weaver, 1974). The secondary objective of this research was to evaluate the suitability of the model to serve as the core of a much larger landscape-scale model (Roberts, 1996). The model must be sufficiently easy to calibrate to be applicable to large areas with only general information available and efficient enough to simulate replicates of hundreds or thousands of individual stands simultaneously. The predicted succession and disturbance response produced by the model can then serve as a base-line for evaluation of the effects of spatial position in the landscape model.
3. Methods 3.1. Model structure
The structure of the model is similar to previous forest composition simulation models such as JABOWA (Botkin et al., 1972) and FORET (Shugart, 1984). The model includes routines for calculating the growth, reproduction, and mortality of trees in the absence of disturbance. Similar to the SILVA (Kercher and Axelrod, 1984) and FIRESUM models (Keane et al., 1990) models, VAFS/STANDSIM also includes a disturbance response routine for calculating the response of different age classes of individual species to disturbance of varying severity. The modelled disturbance regime is stochastic, and the response to disturbance depends on species, ageclass, and characteristics of the stand and environment. Given the objectives of landscape scale simulation, the model is conceptually and operationally simplified when compared to many forest stand sim-
164
D.W. Roberts/EcologicalModelling 90 (1996) 161-173
ulators. Successional development and post-disturbance response may take long periods of time in forest communities, and changes in within-community composition over single years are likely to be small and insignificant when considered from a landscape-scale perspective. Accordingly, the time step of the model was set at 10 years as a compromise of detail and computational tractability. Because of the simplified nature of the model, rather than model individual stems, the model tracks the presence or absence of 10-year age-class cohorts for each species. Species 'abundance' is calculated as the sum of age classes present, °ti = ~ pij X j j=l
where ct i is the abundance of species i, p,, is the presence or absence (0 or 1) of age clas; j for species i with longevity n. The assumption is that size is proportional to age, and that the sum of age classes represents a rough indication of biomass. The assumption does not strictly hold for forest vegetation, but does serve as an index of the importance of a species to the stand total. 3.2. Vital attributes representation
The vital attributes of Noble and Slatyer (1980) were modified slightly to better represent community-level characteristics being modelled and to increase the quantitative information produced by the model. Specifically, changes were made to the reproductive methods classification, the establishment requirement classification, and a new vital attribute was specified for disturbance resistance. Individual species reproduce by: (1) dispersed seed, (2) stored seed, or (3) vegetatively. Because the time step of the model is 10 years, dispersed seed are considered to be viable only in the time step in which they are produced; seeds which do not germinate are lost. Stored seed varies greatly in longevity, and species-specific values are required. The viability of vegetative reproducers is extremely variable, and depends on species-specific characteristics and the history and vigor of individual organisms. In this model I assumed that the ability to sprout depends on stored carbohydrate reserve, which
in tum depends on the recent carbon balance of the individual plant. Carbohydrate storage in the model is calculated as years of remaining carbohydrate, calculated as follows. For species with living stems older than the age of maturity, the storage is incremented every time step that sprouting does not occur, up to a species-specific maximum. For individuals existing only as root systems, the storage is decremented for every time step. Following disturbance, vegetative reproducers sprout (if the shade environment is suitable) and begin to replenish the carbohydrate expended in sprouting. Reproductive maturity for vegetative reproducers is considered to be the length of time required to replenish the carbohydrate expended in sprouting, and carbohydrate storage is decremented every time step until the plants reach maturity. If disturbance occurs when a species has exhausted its carbohydrate storage, no sprouting occurs, and the species goes locally extinct. The establishment classification was modified significantly by employing a shade-tolerance attribute, rather than an establishment attribute. Individual species are ranked for shade tolerance from 1 to 5 (with ties if appropriate). I assumed that species continue to add leaf area until their lower crowns reach their light compensation point, so that species cast shade proportional to their shade-tolerance. All species are assumed capable of reproducing in their own shade or the shade of less tolerant species. Species of shade-tolerance 5 require the shade of less tolerant species to establish (following the facilitation model of Connell and Slatyer (1977) or the R establishment attribute of Noble and Slatyer (1980)). Shade at the forest floor is classified from 0 (full sun) to 5 (full leaf area of maximum shade-tolerant) and is determined by the most shade-tolerant species whose age-classes sum to at least 70. The net effect of the shade-tolerance scheme is to produce a competitive hierarchy (Horn, 1976), where any species with shade tolerance from 1 to 4 can reproduce on open sites, but where more shade-tolerant species eventually shade out their less-tolerant competitors. The shade requirement characteristic of extremely shade-tolerant species produces a time lag (typically 40 years) between the colonization of an open site by intolerant or mid-tolerant species and very shadetolerant species.
D. W. Roberts/Ecological Modelling 90 (1996) 161-173
Species-specific establishment rates are variable, even under ideal conditions. For each species, a probability of establishment under acceptable shade conditions is given which simulates the requirements for restricted seed beds or reproductive sites within the simulated communities.
3.3. Disturbance In the forests of the Rocky Mountains fire intensity varies greatly. Fire severity in the model depends on site-specific characteristics of fuel accumulation rate and the time since the last fire. Fuel is assumed to accumulate after fires at a rate determined by the site productivity and decomposition rate, until reaching a plateau where decomposition equals new fuel production. Severity is classified into five severity classes, which correspond to the species fire tolerance ratings described below. The fuel accumulation rate is specified as the minimum number of years required to accumulate sufficient fuel for each fire severity class. When fires occur, all the fuel is assumed to be burned. In the Rocky Mountains, some species have adaptations such as thick bark and high self-pruning that enable mature individuals to withstand low intensity or moderate fires, while high-intensity fires may kill all individuals. Accordingly, a simple fire tolerance ranking (from zero to five) was employed to characterize the fire tolerance of individual species. If fires of an intensity class lower than or equal to the fire tolerance rating occur, individuals older than X survive the fire, where X is given by:
165
3.4. Species abundance and successional community classification For each species, the 10-year age class cohorts are summed to produce a pseudo-abundance. The least shade-tolerant species present (the indicator) is determined from this pseudo-abundance, and the relative abundance values of all species are used to determine membership of the stand in each of the possible successional community types. The distribution of successional community type memberships is stored for each time step for each replicate, and mean community type distributions for each time step are calculated at the end of the simulation. The values for mean community type memberships are plotted as functions of time.
3.5. Diversity The mean community type distributions for each time step are used to calculate a Shannon-Weiner community type diversity index for each time step. Maximum diversity would be attained if all n(n + 1)/2 possible community types were present with the same abundance, and diversity in the model is scaled relative to maximum possible diversity. Because individual stands may be partial members of more than one community type simultaneously, the index portrays both within-community diversity and stochastic variability between replicates.
X = (6 - (fire tolerance - fire severity)) × l0 If fires of an intensity greater than the fire tolerance occur, all individuals of that species are killed. This fire tolerance scheme results in fire-tolerant species maintaining significant populations of mature individuals under short fire return intervals, where fire-intolerant species are periodically excluded. The fire return interval is estimated as 'fixedprobability independent fire recurrence' (Johnson and Van Wagner, 1985), the length of time required to burn an area equal in size to the modelled area. Because the site-specific occurrence of fires is independent, 63% of the replicates will burn at least once within the fire retum interval; some replicates will bum multiple times within the fire return interval.
3.6. Sensitivity analysis Sensitivity analysis was performed by modifying the vital attribute for a specific trait for each species one at a time and evaluating the variance of model outputs for all modifications of that trait. Specifically, for each species, the shade tolerance and fire tolerance attributes were increased and decreased one unit (where possible), age of reproduction was increased and decreased 10 years, and longevity was increased and decreased 20% (to the nearest even 10 years). This resulted in nine modifications of shade tolerance, seven modifications of fire tolerance, and ten modifications each for maximum age and age of
D.W. Roberts/ EcologicalModelling90 (1996)161-173
166
reproduction, for a total set of 36 modifications. For each modification, 100 replicates were simulated for 500 years at each of six fire return intervals, resulting in 21 600 separate simulations. For each set of simulations with modification to a single attribute, the mean values for species abundance, community type membership, and diversity were used to calculate the coefficient of variation across all modifications of that attribute at each time step. These coefficients of variation were averaged over all time steps to calculate a mean CV. Sensitivity was summarized by simply counting the number of cases (species, community types, or diversity) where the mean coefficient of variation was above 0.30.
derosa to Pseudotsuga menziesii, Picea pungens, and Abies concolor in order of increasing tolerance. Due to thick bark and a habit of self-pruning lower branches, Pinus ponderosa is generally fire resistant in moderate to large diameters. Pseudotsuga menziesii is moderately fire resistant in large diameters. All simulations begin with early seral stands of Populus tremuloides in age classes from 10 to 40 years. Populus tremuloides is assumed to have 80 years of carbohydrate storage for sprouting; the conifer species are assumed to have an available seed source. Simulated stands begin with 40 years fuel accumulation. Fire severity classes are reached at 20, 40, 60, 80, and 100 years for classes 1, 2, 3, 4, and 5 respectively. Simulations were run with mean fire return intervals of 25, 50, 100, 250, 500 years, and absence of fire. One hundred replicates were run for each fire return interval.
3.7. Application The model was tested on a typical mixed conifer forest from Bryce Canyon National Park in southern Utah, USA. This forest type is typical of forests which occupy mid-elevation mesic sites throughout southern Utah, Arizona, and New Mexico (Moir and Ludwig, 1979; Youngblood and Mauk, 1985). The community consists of conifers Pinus ponderosa, Pseudotsuga menziesii, Abies concolor, and Picea pungens, with angiosperm Populus tremuloides. Typical successional sequences begin with Pinus ponderosa or Populus tremuloides (depending on site history), and proceed to mixed compositions of Pseudotsuga menziesii and Abies concolor, with or without Picea pungens depending on site. Table 1 presents the vital attributes of the species as coded for the model. The conifers all reproduce from wind-dispersed seed; Populus tremuloides reproduces vegetatively. The shade-tolerance relation progresses from Populus tremuloides and Pinus pon-
4. Results
4.1. Species abundance Fig. 2 a - f present the species mean abundance trajectories for the six fire return intervals simulated. In the absence of fire (Fig. 2a), the model predicts a simple successional development from pure Populus tremuloides to pure Abies concolor in about 450 years. In the absence of fire, the only stochastic element is the reproduction of species in a particular time step, and the results may be considered a caricature of Clementsian succession. The model assumes within-community homogeneity, and is incapable of simulating gap-phase replacements.
Table 1 Species vital attributes Species name
Longevity
Age of reproduction
Shade tolerance
Fire tolerance
Reproductivemethod
Populustremuloides Pinusponderosa Pseudotsugamenziesii Piceapungens Abies concolor
140 400 300 400 300
10 40 40 40 40
2 2 3 4 5
0 4 3 0 0
V D D D D
Reproductive methods: V = vegetativereproduction, D = dispersed seed reproduction.
D. W. R o b e r t s / E c o l o g i c a l M o d e l l i n g 9 0 ( 1 9 9 6 ) 1 6 1 - 1 7 3
SPECIES ABUNDANCE TRAJECTORIES
. .........? ....
+
60I~
<~
/.,'~"'~'
,./"
40
I--O
20
~
I---
=- _
--
...... .'----- -----.~ ~.--......... ":, 1o8
Z
so
I'-"
60
,<
(b) soo'y.am
"
"
:1
. . . . .
~ ............
z ELI
n-" LLI
(c) 250 years
I
so
60 40
. . . . . .
.~ •"
" ......
~
.-.--
~
.
...... =_..:
.
. ~.-...=
.....
.
_
.
.
..
L"-"L
_
.
.
.
_
-
-'--'":~'~",
.
_
.
.
.
-
• - . -==.
_
.....
0 1 O0
200
300
400
500
YEAR SPECIES ABUNDANCE TRAJECTORIES
,0,00,.-
...1
i1
k0 a z ,< I-"
6O II
180
~.
-" -'''-
60 40
- - - - ~ . . . . .
.
-
-
" ~ -"
2
0
z
tT LIJ
0
100
200
300
400
500
YEAR Fig. 2. Species mean abundance trajectories for six fire return intervals. Fire return intervals: absent (a), 500 years (b) 250 years (c), 100 years (d), 50 years (e), 25 years (f). - - = P o p u l u s tremuloides,
---=
Pinus ponderosa,
ziesii, - • = P i c e a p u n g e n s , - . . . .
---
= Pseudotsuga
Abies concolor.
men-
167
Introducing fire with a mean fire return interval of 500 years significantly affects the successional trajectory (Fig. 2b). While Abies concolor remains the dominant species, its relative abundance is reduced throughout the entire simulation. More importantly, where in the absence of fire all other species became locally extinct within 500 years, with a 500-year fire retum interval no species go locally extinct. With a longevity of 140 years and a maximum of 130 years of carbohydrate storage, some communities burn often enough to maintain Populus tremuloides even on a 500-year mean fire return interval. Halving the fire return interval to 250 years results in a reduced abundance of Abies concolor after 130 years, with a generally increased abundance of all other species, particularly Pinus ponderosa and Pseudotsuga menziesii (Fig. 2c). The composition is similar to a mixed-conifer forest composition on mesic sites. At a mean fire return interval of 100 years a qualitatively different result is obtained (Fig. 2d). Pinus ponderosa emerges as the dominant species throughout most of the simulation period, followed by Pseudotsuga menziesii, and then Abies concolor. With mean fire return intervals of 100 years or less, fire tolerance is more important than shade tolerance in determining abundance. Cutting the fire retum interval to 50 years leads to a clear dominance of Pinus ponderosa with Pseudotsuga menziesii of secondary importance, and Abies concolor reduced to minimal importance (Fig. 2e). Picea pungens goes locally extinct after about 350 years. Populus tremuloides is absent for intervals of about 40 years, but continues to sprout under favorable conditions. Further decreasing the fire return interval to 25 years results in a further increase in the relative abundance of Pinus ponderosa at the expense of Pseudotsuga menziesii (Fig. 2f). Other species have only minimal importance. Each of the fire regimes lead to a unique species abundance quasi-equilibrium within about 450 years. Running the simulations for 1000 years (not shown) does not lead to significantly different results than those obtained at 500 years. Running the simulations from different initial conditions (not shown) ultimately leads to the same quasi-equilibrium dictated by the fire regime. Thus the equilibrium vegetation composition appears to be determined by the interac-
168
D.W. Roberts / Ecological Modelling 90 (1996) 161-173
tion of the fire return interval and the species vital attributes.
COMMUNITYABUNDANCETRAJECTORIES
4.2. Community type membership distribution Of the fifteen possible community types only six occur with a high abundance (membership values > 0.20) during the simulations. Three of the types have Populus tremuloides present as the least shadetolerant species (POTR/POTR, POTR/PIPO, POTR/ABCO), two have Pinus ponderosa present as least shade-tolerant ( P I P O / P I P O and PIPO/ABCO), and one type is pure Abies concolor (ABCO/ABCO). Of the six types, Populus tremuloides is most abundant in one type (POTR/POTR), Pinus ponderosa is most abundant in two (POTR/PIPO and PIPO/PIPO), and Abies concolor is most abundant in three (POTR/ABCO, PIPO/ABCO, and ABCO/ABCO). Community type distributions are strongly affected by the simulated fire regimes, showing quantitative and qualitative changes determined by the underlying species dynamics. Fig. 3a-f show community type dynamics for the six simulated fire retum intervals. In the absence of fire, POTR/POTR (the initial type) rapidly declines, losing dominance after 100 years, and becomes absent at about 160 years (Fig. 3a). After a brief dominance by POTR/ABCO from years 100 to 150, dominance shifts to PIPO/PIPO for a period of over 300 years. In the absence of fire Pinus ponderosa fails to reproduce, however, and dominance shifts to ABCO/ABCO at about 410 years. Generally, only two or three community types occur simultaneously throughout the simulation. With a fire return interval of 500 years, a much more subtle and complex pattern of community types appears (Fig. 3b). POTR/POTR again declines rapidly as species other than Populus tremuloides increase, but remains at low levels throughout the 500-year simulation. While most of the simulation is dominated by the PIPO/ABCO community type, at least five community types are present at all times. Decreasing the fire return interval to 250 years leads rapidly to a nearly equitable distribution of all community types except ABCO/ABCO, which never occurs in simulations with fire return intervals shorter than 500 years (Fig. 3c).
100~ 8 o
(') fire ~ e n t ~
"
._1 6o
O I-LU
4o
'
z li
!
o lo6o 8^o~ (b)soo o y..,, ~ 5
' /"
~. ..... •.......... !...'.: ............... ii
40
]
~'1
-'~
~"...... .
.
ii
O ,o,.o.
z UJ o uJ t3_ 0
.
1O0
.
.
200
t
.
300
400
500
YEAR COMMUNITYABUNDANCETRAJECTORIES 100
(o') 1O0 yeats
80
_J <(
6o
I-0
4o
I"LLI 20 O_ 1o8 <
(o) so y~L,~
"
"
60
._
•
..." " "
:
~."%,'""..
¢.J" ' "'~/ V
40 _1
o
~
.
z 0
~
~,~2,y;,,,
o III
-
~
.....
:i 111 "
40
0
-
..... " " / "
I0
,'~.i '.,/
200
300
400
500
YEAR Fig. 3. C o m m u n i t y t y p e m e a n a b u n d a n c e trajectories for six fh'e return intervals. Fire return intervals: a b s e n t (a), 5 0 0 y e a r s (b) 2 5 0 years(c), 100 y e a r s (d), 5 0 y e a r s (e), 25 y e a r s (f). - - = POTR/POTR, --- = POTR/PIPO, - -- = POTR/ABCO, -. = PIPO/PIPO, - .... PIPO/ABCO, • • • = ABCO/ABCO.
D. W. Roberts / Ecological Modelling 90 (1996) 161-173 GAMMA DIVERSITY
1.0 :~ 0.8 x <
/-...~..-.=.. .... _ "-'~...~... - . . . . . -. '.. . _ . /
0.6
.(-:~'"
O
>_
":.v.-.~...,.~.,..~::::.=:::.~["
0.4
~ 0.~' 0.0
Table 3 Community type sensitivity. Values are number of community types ( m a x i m u m = 15) which showed high variability in response to all modifications of a specific vital attribute at a specific fire return interval. Totals are numbers of community types which showed high variability across all fire return intervals ( m a x i m u m = 90) Vital attribute
"
.
.
.
.
.
.
1O0
.
.
.
.
169
Fire return interval
Total
.
200
300
400
500
25
50
100
250
500
none
0 6 4 9
5 8 1 11
3 9 1 11
2 11 0 9
5 12 I 5
7 10 0 0
YEAR
Fig. 4. G a m m a diversity for six fire return intervals. - - = no fires, - - - = 500 years, - - - = 250 years, - • = 100 years, - • - . = 50 years, • . • = 25 years.
Decreasing the fire return interval again to 100 years results in a qualitative shift (Fig. 3e). After only 70 to 80 years, PIPO/PIPO becomes dominant, and maintains that dominance throughout the entire simulation period. POTR/PIPO is the secondary dominant. Reducing the return interval to 50 (Fig. 3e) or 25 years (Fig. 3f) merely amplifies the same pattern.
4.3. Diversity Mean diversity was calculated for each time step for each of the six fire return intervals (Fig. 4). Because all simulations started off with a monospecific stand of few age classes, diversity in all simulations starts off low and increases for a period of approximately 100 years, as other species begin to invade the single species community. The maximum diversity attained differs, however, and the pattern of diversity following the initial increase is distinct for each fire return interval.
longevity shade tolerance age of reproduction fire tolerance
22 56 7 45
In the absence of fire, diversity increases to moderate levels at about 120 years, and then begins a steady decline, reaching zero at the mono-specific climax attained in about year 460. Introducing fires with return intervals of about 500 to 250 years leads to the maximum observed diversity, and the diversity is maintained at a steady high value throughout the simulation period. Reducing the fire return interval to 100, 50 or 25 years leads to progressively lower maximum diversities, with respectively lower maintained diversities as well.
4.4. Sensitivity analysis The model was analyzed for sensitivity at each of six fire return intervals according to three criteria: individual species abundance, community type membership distribution, and diversity. Tables 2 - 4 present the results of the sensitivity analysis for these three criteria respectively.
Table 2 Species abundance sensitivity. Values are the number of species ( m a x i m u m = 5) which showed high variability in response to all modifications of a specific vital attribute at a specific fire return interval. Totals are numbers of species which showed high variability across all fire return intervals ( m a x i m u m = 30)
Table 4 G a m m a diversity index sensitivity. Values are c a s e s where g a m m a diversity showed high variability in response to all modifications of a specific vital attribute at a specific fire return interval ( m a x i m u m = 1). Totals are numbers of cases where g a m m a diversity showed high across all fh-e return intervals ( m a x i m u m = 6)
Vital attribute
Total
Vital attribute
Fire return interval 25
50
100
250
500
none
7 13 0 16
longevity shade tolerance age of reproduction fire tolerance
0 0 0 1
0 0 0 1
0 0 0 0
0 0 0 0
0 0 0 0
1 1 0 0
longevity shade tolerance age of reproduction fire tolerance
Fire return interval 25
50
100
250
500
none
1 2 0 5
2 2 0 5
0 2 0 4
0 2 0 2
1 3 0 0
3 2 0 0
Total
1 1 0 2
170
D. W. Roberts / Ecological Modelling 90 (1996) 161-173
Significant trends are evident when analyzing the sensitivity of individual species abundance (Table 2). The model is extremely sensitive to fire-tolerance ratings at short fire return intervals, with significant differences in species abundance occurring up to fire return intervals as long as 250 years. This is a reflection of the relative survivorship of mature trees through frequent, low-intensity fires. Additionally, the most fire-tolerant species are relatively shade intolerant, and increasing the fire tolerance of more shade-tolerant species leads to the removal of the shade-intolerant species due to shading. The model is moderately sensitive to the shadetolerance rankings at all fire return intervals. The lack of interaction of shade tolerance and fire return interval is interesting in light of the strong direct effect of fire tolerance on determining the dominant species at short fire return intervals and shade tolerance in determining the dominant species at long fire return intervals. The sensitivity of the model to maximum age of species shows a bimodal distribution with respect to fire frequency. At short fire return intervals, the longevity of the fire-tolerant species affects the relative abundance of species. At long fire return intervals, the longevity of shade-intolerant species affects the relative abundances following the relatively infrequent disturbances. In contrast to the species abundance criterion, community type membership appears most sensitive to shade tolerance, rather than fire tolerance (Table 3). Also, the sensitivity to shade tolerance shows a stronger relation to fire return interval, being relatively more sensitive at longer intervals. At long fire return intervals, increasing the shade tolerance of relatively intolerant species (or reducing the tolerance of the most tolerant species) results in ties for maximum shade tolerance, leading in turn to communities co-dominated by more than one species. Alternatively, at short fire return intervals, increasing the shade tolerance of shade-intolerant species allows them to regenerate beneath the canopy of mature shade-tolerant species which normally suppress them. The distribution of community type membership is moderately sensitive to changes in longevity, and generally insensitive to changes in age of first reproduction except at very short fire return intervals.
In contrast to the sensitivity measures for species abundance and community type, the measure of sensitivity for diversity is relatively crude, being measured on a binary scale rather than a numeric scale. In general, the measure of community diversity appears most sensitive to fire tolerance at short fire return intervals and is sensitive to longevity or shade tolerance only in the absence of fire.
4.5. Validation Stein (1988a) studied the fire history of the Paunsaugunt Plateau in southern Utah, which includes Bryce Canyon National Park. He concluded that mid-elevation sites exhibited historic fire return intervals between approximately 20 and 50 years for individual trees. Fires have generally been absent since the advent of fire suppression around 1910. Stein (1988b) studied the size class distributions and stand structures of forests on the Paunsaugunt Plateau and concluded that Pinus ponderosa dominated these sites under the historic disturbance regime, but that the current Pinus ponderosa size class distribution has too few small trees, and that it is being replaced by more shade-tolerant species, such as Pseudotsuga menziesii and Abies concolor. The lack of large size-class individuals for these species indicates that they were not successful in the historic past. Stein (1988b) attributes this shift to the change in fire regime and possible change in climate. Weaver (1974) describes similar conditions for much of the southwestern U.S. Although the validation data are fewer than would be ideal, the successional dynamics and disturbance response of the modelled community appear to be quite good. Under simulated fire regimes similar to the historic regime, Pinus ponderosa achieves and maintains dominance over the more shade-tolerant species. Eighty years of succession without a fire leads to mixed communities increasingly dominated by the more shade-tolerant species. Simulating a successional development beginning with the historical composition in the absence of fire (not shown) leads to an overstory dominated by Pinus ponderosa with an understory dominated by Abies concolor, similar to that reported for mid-elevation sites by Stein (1988a,b). The model suggests that a critical threshold in fire return interval occurs between 250 and 100 years, as
D. W. Roberts~Ecological Modelling 90 (1996) 161-173
Abies concolor dominates sites with return intervals of 250 years or longer, and Pinus ponderosa dominates sites with fire return intervals of 100 years or fewer. Unfortunately, sites with the appropriate fire histories do not occur in the study area to test this hypothesis.
5. Discussion 5.1. Model behavior Evaluating the species abundance results and sensitivity analyses in an ecological sense, the model identifies critical ecological characteristics for survival and dominance in environments of varying disturbance regime. In rarely disturbed environments, tolerance of competition and the ability to reproduce in competitive conditions eventually confers competitive superiority. In these conditions, age of first reproduction is relatively unimportant compared to longevity. In frequently-disturbed environments, disturbance-tolerance will over-compensate for poor competitive ability and confer dominance. Surprisingly, the model did not identify an early age of reproduction as important in frequently disturbed environments. However, the range of ages considered and the level of modification were both fairly small and may not have been sufficient to exhibit a significant difference. As noted above, each fire regime appeared to lead to a unique quasi-equilibrium. While this equilibrium only holds for the mean characteristics over 100 replicates, and not individual replicates, it is interesting that a stochastic, mechanistic model should exhibit such notable equilibrium behavior. There is no evidence of chaotic or high-order behavior in any of the simulations. Caswell and Cohen (1991) modelled the effects of disturbance, colonization, and competitive exclusion with a two-species non-linear Markov chain. The model employed a strict competitive hierarchy (although with variable rate of competitive exclusion), species had no age-structure, and were both excluded by disturbance. Their results suggested the existence of single stable points for all combinations of parameters, despite the potential for periodic or chaotic attractors. While the model presented here possesses
171
greater ecological structure, the results are consistent with those of Caswell and Cohen. Calculating the community type classification from the pyramid proved very useful. Because the community types are determined in a simple quantitative manner, the classification algorithm can be directly incorporated into the simulation model. By calculating and plotting the community types as well as species, a great deal of information about community composition can be determined. Species which are co-dominant in mean outputs could each occur in single species stands in different replicates, or in mixed species stands during all replicates. Calculating the community types during each replicate distinguishes these conditions simply without maintaining a wealth of detail on each simulation. Additionally, a fair amount of information about community structure can also be inferred. Knowing the shade-tolerance relations of the species, the overstory/understory characteristics of the community types present can be determined approximately. The relatively higher sensitivity values for community types as opposed to species suggests that in some cases the mean species abundances were insensitive to modifications of vital attributes while community compositions were not. This in turn implies a greater between-replicate variability when modifying these traits. Finally, calculating diversity on the basis of community type abundance distributions provided interesting insights on the role of disturbance in forest communities. The model makes clear that maximum diversity is attained under moderate disturbance regimes which allow disturbance-sensitive species to reach large populations but which still produce conditions for reproduction of shade-intolerant species. Interestingly, maximum diversity is attained with mean fire return intervals of roughly the same order as the longevity of most of the species; either the absence of disturbance or too frequent disturbance reduces diversity. The model is too simple to simulate gap phase replacement within communities and thus underestimates the diversity of 'climax' stands, but the general trend of diversity with disturbance is probably not affected by this underestimation. The model's prediction of highest diversity under intermediate disturbance regimes agrees with the intermediate disturbance hypothesis (Connell, 1978;
172
D.W. Roberts / Ecological Modelling 90 (1996) 161-173
Denslow, 1980; Miller, 1982), which relates the role of disturbance periodicity and severity in determining community diversity for a wide range of communities. Malanson (1987) discusses the intermediate disturbance hypothesis in respect to recurrent fires in temperate vegetation, and reaches similar conclusions.
5.2. Efficiency and parsimony The secondary objective of this work was to produce a simple, efficient forest simulator for use in a landscape-scale simulation model. The model presented here meets the objectives very satisfactorily. It is simple to set up and run, and requires minimal computational power. The model will run 100 replicates for 500 years in less than 1 min on a microcomputer. More important than computational efficiency however, is ecological realism. In a sense, the objective is not to find the most computationally-efficient model, but rather the most parsimonious ecological model suitable for simulation. Again, the model appears to largely meet this objective. Using the best-guess estimates of species vital attributes, the model generates realistic patterns of community composition dynamics under a variety of disturbance regimes. Because the model is based on simple species attributes and environmental characteristics, it should be easy to recalibrate for new areas and species.
Acknowledgements
This model was developed over a long period of evolution, and benefited from numerous comments. I would particularly like to thank D.H. Knight, S.L. Collins, S. Glenn, G. Henebry, and S. Will-Wolf. Thanks to G. Cottam and T.F.H. Allen for the facilities at the University of Wisconsin to make publication of this research possible. This work was developed in part through a grant from the U.S.D.I. National Park Service through the University of Wyoming - National Park Service Research Center. FORTRAN code for the VAFS/STANDSIM model is available from the author.
References Botkin, D.B., Janak, J.F. and Wallis, J.R., 1972. Some ecological consequences of a computer model of forest growth. J. Ecol., 60: 849-873. Caswell, H. and Cohen, J.E., 1991. Communities in patchy environments: a model of disturbance, competition, and heterogeneity. In: J. Kolasa and S.T.A. Pickett (Editors), Ecological Heterogeneity. Ecological Studies Vol. 86. Springer-Verlag, New York, pp. 97-122. Cattelino, P.J., Noble, I.R., Slatyer, R.O. and Kessell, S.R., 1979. Predicting the multiple pathways of succession. Environ. Manage., 3: 41-50. Connell, J.H., 1978. Diversity in tropical rain forests and coral reefs. Science, 199: 1302-1310. Connell, J.H. and Slatyer, R.O., 1977. Mechanisms of succession in natural communities and their role in community stability and organization. Am. Nat., 111: 1119-1144. Denslow, J.S., 1980. Patterns of plant species diversity during succession under different disturbance regimes. Oecologia, 46: 18-21. Gill, A.M., 1975. Fire and the Australian flora: a review. Aust. For., 38: 4-25. Horn, H.S., 1976., Succession. In: R.M. May, Theoretical Ecology. Principles and Practice. Blackwell, Oxford, pp. 187-204. Huschle, G. and Hironaka, M., 1980. Classification and ordination of seral plant communities. J. Range Manage., 33: 179-182. Johnson, E.A. and Van Wagner, C.E., 1985. The theory and use of two fire history models. Can. J. For. Res., 15: 214-220. Keane, R.F., Arno, S.F. and Brown, J.K., 1990. Simulating cumulative fire effects in ponderosa pine/Douglas-fur forests. Ecology, 71: 189-203. Kercher, J.R. and Axelrod, M.C., 1984. A process model of fire ecology and succession in a mixed conifer forest. Ecology, 65: 1725- 1742. Malanson, G.P., 1987. Diversity, stability, and resilience: Effects of fire regime. In: L. Trabaud (Editor), The Role of Fire in Ecological Systems. SPB Academic, The Hague, pp. 49-63. Miller, T.E., 1982. Community diversity and interactions between the size and frequency of disturbance. Am. Nat., 120: 533-536. Moir, W.H. and Ludwig, J.A., 1979. A classification of spruce-fir and mixed-conifer habitat types of Arizona and New Mexico. USDA For. Serv. Rocky Mtn. For. and Range Exp. Stn. Res. Paper RM-207, 47 pp. Moore, A.D. and Noble, I.R., 1990. An individualistic model of vegetation stand dynamics. J. Environ. Manage., 31: 61-81. Noble, I.R. and Slatyer, R.O., 1977. Post fire succession of plants in Mediterranean ecosystems. In: H.A. Mooney and C.E. Conrad (Editors), Proc. Symp. Environmental Consequences of Fire and Fuel Management in Mediterranean Ecosystems. USDA For. Serv. Gen. Tech. Rep. WO-3, pp. 27-39. Noble, I.R. and Slatyer, R.O., 1980. The use of vital attributes to predict successional changes in plant communities subject to recurrent disturbance. Vegetatio, 43: 5-21. Roberts, D.W., 1989. Fuzzy systems vegetation theory. Vegetatio, 83: 71-80. Roberts, D.W., 1996. Landscape vegetation modelling with vital
D. W. Roberts/Ecological Modelling 90 (1996) 161-173 attributes and fuzzy systems theory. Ecol. Model., 90: 175184. Shugart, H.H., 1984. A Theory of Forest Dynamics: The Ecological Implications of Forest Succession Models. Springer, New York, 278 pp. Steele, R., 1984. An approach to classifying seral vegetation within habitat types. Northwest Sci., 58: 29-39. Stein, S.J., 1988a. Explanations of the imbalanced age structure and scattered distribution of ponderosa pine within a highelevation mixed-conifer forest. For. Ecol. Manage., 25: 139153.
173
Stein, S.J., 1988b. Fire history of the Paunsangunt Plateau in southern Utah. Great Basin Nat., 48: 58-63. Weaver, H., 1974. Effects of ftre on temperate forests: Western United States. In: T.T. Kozlowski and C.E. Ahlgren (Editors), Fire and Ecosystems. Academic Press, New York, pp. 279319. Youngblood, A.P. and Mauk, R.P., 1985. Coniferous forest habitat types of central and southern Utah. USDA For. Serv. Intermt. For. and Range Exp. Stn. Gen. Tech. Rep. INT-187, 89 pp.