SCOPE 35 - Scales and Global Change

 INTRODUCTION

The current discussions of biospheric dynamics and global ecology (Risser , 1986) come at a time when there is a renewed interest in time- and space-scales in ecological systems. An appreciation of scales is a clear prerequisite to unifying the dynamics of atmospheric and oceanographic process with the dynamics of ecosystems on the terrestrial surface. Of particular importance is a knowledge of the patterns of dominance (in the sense of controlling pattern) of particular causal factors at particular scales. The categorization of controlling factors important at different space and time scales in particular ecosystems has been the topic of several reviews (Delcourt et al., 1983; Pickett and White, 1985). In 'hierarchy theory' (Allen and Starr, 1982; Allen and Hoekstra, 1984; O'Neill et al., 1986; Urban et al., 1987), one sees a focus on expressing relevant mathematical developments in a manner that can provide insight into the ways ecosystems are structured at different scales.

Historically, the complex unravelling of ecological interactions was evident in A. S. Watt's (1925) early work on beech forests and elaborated in his now classic paper on pattern and process in plant communities (Watt, 1947). When one inspects Tansley's (1935) original definition of the ecosystem, one finds the same concepts that one sees in hierarchy theory, today.

Of course, the Watt/Tansley ecosystem paradigm has been reintroduced as a major ecosystem construct in ecological studies. One conspicuous re-introduction of these concepts was Whittaker's (1953) review which used the Watt pattern-and-process paradigm to redefine the 'climax concept'. These same ideas are also found in ecosystem concepts developed by Bormann and Likens (l979a, b) in their 'shifting-mosaic steady-state concept of the ecosystem' as well as in what Shugart (l984) called 'quasi-equilibrium landscape'.

The essential idea behind the Watt (l925, 1947) paradigm is that in ecosystems controlled by sessile organisms, the temporal dynamics at the scale of the individual organism are almost by necessity non-equilibrium dynamics. This is most apparent in forest systems where the spatial scale of the individual organisms (the canopy trees) is relatively large. Considering forests as an example, the space below a canopy tree has reduced light levels and a considerably altered microclimate due to the influence of the tree. These conditions determine the species of trees that can survive beneath the canopy tree. Upon the death of the canopy tree, the shading is eliminated and the environment is changed. In cases in which the canopy tree dies violently (e.g. broken by strong winds), the changes in the microenvironment are extremely abrupt. The death of the canopy tree initiates a scramble for dominance among the smaller trees that were persisting in the environment created by the canopy tree and seedlings that establish themselves in the high-light environment. Eventually, one of the trees becomes the canopy dominant. The establishment of a new canopy dominant represents the closure of the death/birth/death cycle that can be thought of as the typical small-scale behaviour of a forest.

In ecosystems other than forests but still dominated by sessile organisms, one would expect the same sorts of dynamics. This nonequilibrium behaviour at fine spatial scales has been noted in a diverse array of ecosystems including coral reefs (Connell, 1978; Huston, 1979; Pearson, 1981; Colgan, 1983), fouling communities (Karlson, 1978; Kay, 1980), rocky inter-tidal communities (Sousa, 1979; Paine and Levin, 1981; Taylor and Littler, 1982; Dethier , 1984), and a wide range of heathlands (Christensen, 1985).

The ecosystems that are both historically and currently the most studied in this regard are forests. For this reason, it is worthwhile to elaborate the details of the death/birth/death process in forests. In forests, the non-equilibrium dynamics are quasi-periodic with the period a function of the growth rates and potential longevities of the individual organisms (Shugart, 1984). This 'cycle' can be modified by a variety of factors. One important consideration is the manner of death of the dominant tree.

Some trees typically die violently catastrophically and the attendant alterations of environmental conditions at the forest floor (and thus the effect on the regeneration of potential replacements) are very abrupt. Typically these abrupt changes are associated with exogenous disturbances but there are some species of trees that are 'suicidal' in that mature trees flower but once and die to release canopy space to their progeny (Foster, 1977). Some trees tend to   'waste-away' after they die so that the changes in the microenvironment that they control are more continuous. Some trees tend to snap at the crown when torn down by winds; others are heaved over at the roots exposing mineral soil. All of these modes of death (and others) influence the stochastic regeneration success of the trees that form the next generation.

It is an open question as to whether mode of death or mode of regeneration is the strongest determinate of pattern of diversity in forests. Both are attributes of the various tree species and may be strongly interrelated. One aspect of the mortality of canopy trees and the associated opening in the forest canopy ('gap formation') is the size of the gap that is created. Several authors (van der Pijl, 1972; Whitmore, 1975; Grubb, 1977; Bazzaz and Pickett, 1980) have discussed species attributes that are important in differentiating the gap-size-related regeneration success of various trees. The complexity of the regeneration process in trees and its stochastic nature makes it nearly impossible to predict the success of an individual  tree seedling. Most current reviewers recognize this and tend to discuss regeneration in trees from a pragmatic view that the factors influencing the establishment of seedlings can be usefully grouped in broad classes (Kozlowski, 1971a, b; van der Pijl, 1972; Grubb, 1977; Denslow, 1980).

In models of forests and other sessile-organism dominated ecosystems, the death and replacement of large individual organisms creates a cyclical, non-equilibrium response. There are good reasons to expect such dynamics to prevail in natural ecosystems as well (Whittaker and Levin, 1977).

In the next section we will review the functioning of several of the extant computer models of ecological section. These models all operate on the assumption that the landscape can be considered a dynamic mosaic of element at the scale of a single dominant plant-an approach that we have called the Watt paradigm and whose historical antecedents and importance in ecology we have already discussed. Following this review and some examples of ecological models at different resolutions, we will discuss the atmospheric influences on ecological dynamics. The focal ecosystems in these discussions will be forests.

ECOLOGICAL SUCCESSION MODELS

Over the past two decades there has been a remarkable development of computer models designed to simulate the dynamics of ecological succession. Many of the basic concepts used in these models originate in the works of Clements (an emphasis on dynamic interactions, 1916), Tansley (the ecosystem concept, 1935), Gleason (the importance of species attributes in dynamic systems, 1939), and Watt (the relationship between internal dynamics and spatial patterns, 1947). The theories that were developed by these early ecologists proved difficult to apply in a formal mathematical fashion to the complex natural systems (with a multiplicity of potentially important temporal dynamics) for which they were intended. The eventual development of mathematical models based on these concepts was clearly catalysed by the increased availability of computers.

Not only have computers become widely available to ecologists over the past several years, but there has also been a great reduction in the cost per computational unit operation. At present, there are several hundred succession models of forest ecosystems alone (Shugart, 1984). This set of succession models includes examples that have proven capable of predictions that can be used for purposes of application. Other models have inspired a continued theoretical development of ecological concepts. One of the conceptually important aspects of the use of succession models in both theoretical and applied contexts has been the emphasis that the developers of the models have placed upon 'scaling-up' the consequences of natural history of plants, physiology and demography.

Succession models take on a wide range of mathematical forms. Their richness in formulation originates to an extent in the diverse objectives and training of the model designers. These differences may also originate from different theoretical constructs as to what is important in the functioning of a given ecosystem. In this sense, the models represent a complex set of a priori hypotheses about the function and behaviour of ecosystems. The limitations, failures, and successes of these models potentially reflect functional patterns in the real systems that they represent.

We will review several of the more successful modelling paradigms used in succession models and to describe the underlying assumptions and thus the theoretical implications of these models. We will also discuss what we feel is a logical next area of development in succession models as tools for understanding global change. This is a more explicit consideration of the dynamics of the abiotic systems that drive ecosystem succession.

Most succession models have been developed for forested systems (Munro, 1974; Shugart, 1984). This is in part due to a simultaneous (and relatively independent) interest in modelling forest dynamics that developed in forestry and ecology in the early 1970s. In ecology, this was a period of great interest in systems approaches from engineering sciences and was also a period when several large coordinated research programmes used computer modelling as a way to organize a diverse array of studies of ecosystem processes. The most conspicuous of such programmes were associated with the International Biological Programme (IBP).

Many of the ecological succession models in use originated from models developed in the early 1970s. The development of these models occurred at a time when research institutions were obtaining large fast computers, when there was strong motivation to increase the quantitative nature of ecology and when there was a considerable interest about the temporal dynamics of ecological systems.

At about the same time, there was also considerable interest in modelling, 'computerization', and quantitative methods in forestry (Munro, 1974). There were several new forestry practices being considered, such as the fertilization of forests and the development of genetically improved trees for plantations. These new and relatively untried practices were potentially beyond the prediction range of the forest yield tables that formed the backbone of predictive forestry. This was because yield tables had been calibrated with data based on more conventional forestry practices. Questions such as, 'How many trees per unit area should one plant to produce a maximum yield of pulp wood, if these trees grow 20% faster than the present stock?' provided an incentive for the development of models that could provide stand yield predictions based on tree growth.

Many of the forestry models were (and are) designed for the projection of tree size, tree density, timber yield, and other similar state variables for forests in which the regeneration of trees is controlled. For this reason, most of these models are not able to simulate the dynamics of a forest beyond one tree generation and are not succession models in the sense that most ecologists think about succession. However, the models are important in their role in the historical development of succession simulators and because they often contain a level of realism in the representation of the growth and competition processes that is rarely found in succession models.

A REVIEW OF SUCCESSION MODELS

There are several hundred computer models of ecological succession and a rich array of approaches. Reviews of the forestry literature are found in Munro (1974) and a compilation of examples from forestry in Fries (1974). Shugart (1984) reviews several ecological models of forest dynamics and explores the theoretical implications of gap models in particular. In the present discussion, we will review four different modelling approaches that are arranged along a spectrum according to the dimensionality of the interactions among the simulated plants. In this spectrum, Markov models simulate the change in state of a simulated area in time; gap models simulate plant-to-plant interactions in the vertical dimension; transect models simulate pattern in one horizontal dimension; spatial models simulate in two and, in some cases, three spatial dimensions.

Markov models

Markov models of succession are mathematically and conceptually the most straight-forward of the succession models that are presently in use. The models share obvious relationships to other quantitative approaches used in plant ecology. The models can be solved by hand (or on a small computer). Markov  models are constructed by determining the probability that the vegetation on a prescribed (usually relatively small area) will be in some other vegetation type after a given time interval. It is an essential requirement of these models to have a scheme for classifying the vegetation into identifiable categories.

The manner in which the vegetation states are classified has varied across applications of Markov models. Horn (1975a, b; 1976) used the species of a canopy tree as the states of a well-known Markov model developed for a forest near the Institute of Advanced Studies in Princeton, New Jersey. The time interval of this particular model was the generation time of canopy trees. Waggoner and Stephens (1971) categorized the forest types according to the most abundant species (in terms of individual trees over 12 cm Diameter at breast height-DBH) on 0.01 ha plots located on the Connecticut Agricultural Experiment Station and applied the model over uniform time intervals. These two approaches for identifying the states of the forest (categorization by attributes of a dominant individual as in Horn's (1975a, b; 1976) model or by attributes of an aggregate of an individuals as in Waggoner and Stephens (1971) model) represent most of the applications in ecology although a variety of other schemes could possibly be used. For example, one could categorize a small plot of land by both the species of the largest individual and by the number of individuals (e.g. highly-stocked White Oak dominated type, understocked Loblolly Pine Stands, etc.). Hool (1966) used this approach in developing a Markov model of stand change over a large area.

In a Markov model, the number of model parameters is a function of the square of the number of states (or categories in the model). Thus, in the development of a Markov model, one is forced to trade-off between the increased resolution in being able to enumerate many different system states and the parameter estimation problems that attend this greater resolution. In Waggoner and Stephens' (1971) simulation, a 40-year long record of 327 regularly remeasured sample plots was used to compute the model parameters. This means that the change in state of about 16 plots on average was used to estimate each of the transition probabilities. One feature of Markov models is that the relatively uncommon transitions from one state to another need to be estimated with equivalent precision to that of the other more common transitions. This feature creates a need to observe the frequency of occurrence of rare transitions between states and causes an emphasis on large remeasurement data sets as necessary to parameterize a Markov model that has very many states.

An alternative to direct measurement to determine the parameters of a Markov model is to develop theoretical constructs that allow the estimation of the model parameters on some other basis. For example, Horn (1975a, b; 1976) assume that the proportion of trees of a given species found growing below a canopy tree indicated the transition probabilities. Noble and Slatyer (1978, 1980) have developed a concept called the 'vital attributes' concept which uses regeneration, response to disturbance, and longevity of plants to determine the parameters of a Markov model. They currently have an 'expert-system' under development on a small 'personal computer', a computer programme that queries the user as to the ecological attributes of the species in a successional system and then develops and implements a Markov model of the system. The development of these theoretical methods of estimating the transition probabilities creates the possibility of developing larger Markov models in which parameter estimation from data would normally be proscribed due to logistic difficulties (Cattelino et al., 1979; Kessell, 1976; 1979a, b; Potter et al. , 1979; Kessell and Potter, 1980). The theories are based on biological attributes of the species and this approach is also found in the more complex models discussed below.

Gap models

Gap models are a subset of a class of forest succession models called individual-tree models (Munro, 1974) because the models follow the growth and fate of individual trees. The first model of this genre was the JABOWA model developed by Botkin et al. (1972); a similar modelling approach has been applied to several forests in different parts of the world (see Chapter 4 of Shugart, 1984, for a review of several of these applications, also see Kercher and Axelrod, 1984).

Gap models simulate succession by calculating the year to year changes in diameter of each tree on small plots. The plot size is determined by the size of the canopy of a single large individual. Forest succession dynamics are estimated by the average behaviour of 50 to 100 of these plots. The growth of each tree is determined by the average competitive influence of the neighbouring trees on a plot. Due to the small size of plots, gap formation events (the removal of canopy trees through mortality) strongly affect the resource availability on a plot which in turn affects tree growth.

The exact location of each tree is not used to compute competition in these models. Tree diameters are used to determine tree height, and then simulated leaf area profiles are computed to devise competition relationships due to shading. These models are spatial in that competition is computed in the vertical dimension. There is an implicit assumption that within a plot of a certain size the horizontal spatial patterns of the individual plants do not affect the degree of competitive stress acting on an individual to significant degree beyond that accounted for by the plants height (i.e. tree biomass and leaf area are considered to be homogeneously distributed across the horizontal dimension of the simulated plot).

The regeneration of seedlings on a plot and their subsequent growth is based on the silvicultural characteristics of each species, including site requirements for germination, sprouting potential, shade tolerance, growth potential, longevity, and sensitivity to environmental factors (water and nutrients). Under optimal growth conditions, the growth of a tree is assumed to occur at a rate that will produce an individual of maximum recorded age and diameter . This curvilinear function grows a tree to two-thirds of its maximum diameter at one half its age under optimal conditions. Modifications reducing this optimal growth are imposed on each tree based on the availability of light and, depending on the specific model, other resources. In most gap models, tree growth slows as the simulated plot biomass approaches some maximum potential biomass observed for stands of the given forest type. Growth is further reduced as climate stochastically varies. Death of individual trees is a stochastic process. The probability of an individual tree's death in a given year is inversely related to the individual's growth and the longevity of its species.

Gap model dynamics are based on information concerning the demography and growth of trees during the lifespan of species. The models have a capability to predict the sequence of replacement of species through time and other dynamics on the scale of the average tree generation time (Figure 8.1). At this scale, the success of a tree at growing into the canopy is more related to the opportunity for inseeding into a plot and the relative growth rate compared to other seedlings than it is related to the distribution of distances from other competing individuals.

The relationship of the height of the individual to the distribution of heights of competitors is assumed to be sufficient to determine the level of competitive stress experienced by an individual in relation to other trees on the plot. This implies that the distance of a tree to its competitors has no significant influence on the amount of light and other resources available to a given tree. In terms of implementing these models, these assumptions lead to a requirement that the dynamics of a large number of plots be averaged to better estimate the mean rate of success of canopy invasion of each species.

Because regeneration, growth, and death are modelled on a per-tree basis and the silvics of individuals vary among species, gap models are particularly useful tools for exploring the dynamics of mixed-aged and mixed-species forests. The models have been tested and validated against independent data (Shugart, 1984; Chapter 4). For these reasons, gap models can also be used to explore theories about patterns in forest dynamics at time scales that are sufficiently long to prohibit direct data collection. Such applications have been instrumental in developing a theoretical basis for understanding the coupled effects of tree death and regeneration in forest systems (Shugart, 1984).

One gap model that has been used in a large number of applications in complex, mixed-species, mixed-aged forests is the FORET model, a derivative of the JABOWA model (Botkin et al., 1972). The JABOWA/FORET modelling approach has been the central topic of a pair of books on the dynamics of natural forests (Bormann and Likens, 1979a; Shugart, 1984). The FORET model and other analagous models have been modified and applied to simulate the dynamics of a wide range of forests: mixed hardwood forests of Tennessee (Shugart and West, 1977), montane Eucalyptus forests of Australia (Shugart and Noble, 1981), upland forest of Southern Arkansas (Shugart, 1984), eastern Canadian mixed species forest (EI-Bayoumi et al., 1984), the arid western coniferous forest (Kercher and Axelrod, 1984), a western coniferous forest (Reed and Clark, 1979) and northern hardwood forests (Botkin et al., 1972; Aber et al., 1978, 1979; Pastor and Post, 1985).

Figure 8.1 Example output from a gap model (The BRIND model of succession in Eucalyptus forests in the Brindabella Range, Australian Capital Territory, Shugart and Noble, 1981).  The plots are drawn to scale (distance across each plot is 32m) from model output for a single 1/12 ha.quadrat.  The  simulation time step of the model is one year but the output is displayed here on 50-year intervals.  Trees shown are various species of Eucalyptus particularly E.delegatensis (the trees with half white and half black trunks) and E. dalrympleana (the trees drawn with white trunks)

Transect models

The extension of the approaches used in gap models to the spatially explicit case is conceptually straight-forward and involves a reformulation of the competition function. Unfortunately, the increases in computer storage and computational time are significant. Gap models are based upon a computer- driven compilation of the birth, growth and death of each tree on a small plot. The interactions between trees in this formulation are spatially lumped. This lumped representation loses validity in cases in which the quadrat size is no longer small relative to the zone of influence of the individual plants. Thus, to extend model formulations that follow the fates of individual organisms to the spatially explicit case, paired interactions between individual simulated plant trees must be calculated. This has the effect of squaring the number of calculations; often making the cost of simulation prohibitive. There are, however, several approximations to the absolutely spatially explicit case that can reduce computation costs. These simplifications are often justified, independent of cost savings, because the data available for validation is not of sufficient resolution to justify a more detailed simulation.

One simplification of the spatially explicit case is the consideration of only one horizontal dimension, that is, a transect model. If the between-plant interactions can be ignored when the plants are more than a certain distance apart and the determination of which plants should be included in the determination of the competitive effects on a given target individual can be determined rapidly, then the consideration of spatially explicit interactions becomes less computer-time limited. Computational efficiency can be improved in a transect model because the search for individuals within the zone of influence of the target plant only need be in one direction. If the individuals are catalogued based upon their location along the transect, then this search can be made even more efficient. Shugart and Rastetter have developed a transect model of a mangrove community that is based on a gap model of the same system. The resultant model uses the same parameters as the gap model from whence it was derived and differs only in the formulation of the competition equations.

Transect models are most applicable to situations where the community is strongly zoned along some environmental gradient. Ecosystem/environment interactions are frequently conceptualized as responses of transects to gradients (see, for example, the illustrations in Watt's classic 1947 paper). It is surprising that transect models are not more in evidence given the interest that is manifested in transect representations of ecosystems processes.

Many dynamic physical processes that contribute to the pattern and responses of ecosystems over time can be simulated by models that are considerably simpler in a single horizontal dimension. Shugart et al. (1987) have developed a transect model that maintains the computational efficiency of a Markov model but also incorporates both a mechanistic formulation of the important population processes and the realism of spatial heterogeneity. The model is based upon a Markov chain representation of the life stage development of each plant species at intervals along a transect. If a species has 'n' life stages that are ecologically important, then that species is represented at each interval by an n-bit word, each bit signifying the presence or absence of a respective life stage and there are, therefore, 2ⁿ possible simulation states for the species. In its current implementation on the computer, the number of life stages represented for the various species and the spatial resolution (interval width) along the transect can be defined by the model user. This allows the adjustment of the resolution of spatial patterns and life history detail to optimize detail and computational efficiency.

The state transition probabilities in the Shugart et al. (1987) model are calculated based on seed availability and environmental factors affecting sprouting, growth and mortality. There are 2ⁿ (n = number of life stages) possible state transitions for each species at each location during any particular time step. For large n (n > 3), the dimensionality of the problem can be reduced by considering each life stage individually. This also facilitates a more mechanistic formulation of the transition probabilities incorporating the growth characteristics of the species.

There are four possible transitions for the individuals of a particular life stage at a particular location:

1. they can all die

2. they can all remain unchanged

3. some can mature to the next life stage and some remain the same

4. they can all mature to the next life stage.

Three other possibilities involving some plants dying, and some either remaining the same and / or maturing are indistinguishable from possibilities 2, 3, and 4 because only the presence or absence of individuals in each life stage is followed in the model. Since these four transitions represent all possibilities, the probabilities associated with them must sum to one. It is therefore only necessary to calculate three of the probabilities, the fourth can be calculated by difference. Possibilities 3 and 4, however, do not exist for the oldest life stage, consequently only two probabilities must be calculated for this last life stage and one of these can be calculated by difference.

Figure 8.2 Example output from a computer model (Shugart et al., 1987) simulating the pattern and dynamics of vegetation along a transect through a barrier island such as might be found along the Atlantic coast of North America. The open ocean is to the right of the figure. Over the time of the simulation the island moves landward and the water table on the right side of the island forms a brackish marsh with scattered shrubs. Trees and shrubs occupy a position behind the sheltering dune and the dune flattens

In addition, a recruitment probability must be calculated. Thus, a total of 3(n-1) + 2 = 3n-1 probabilities must be calculated at each time step, for each species, at each location. The 2ⁿ state transition probabilities can be calculated from these life stage transition probabilities by cross-multiplying the probabilities associated with each life stage with those of each of the other life stages and summing the probabilities of all redundant outcomes.

The model has been implemented to simulate the vegetation dynamics of coastal dune ecosystems (Shugart et al. , 1987). Because of the transect formulation of the model, several important physical variables can be simulated dynamically-notably the height of the water table, the height of the sand mass at any point and the salinity of the water table at each point. The model is driven by the position of the O height beach front. The successional dynamics of an example simulation (Figure 8.2) features the development of a horizontal gradient of vegetative pattern, a reduction of the height of the sand dune due to aeolian erosion, a landward displacement of the dune system (a consequence of vegetation-mediated aeolian transport of sand) and the eventual development of a back-dune marsh as the water table moves to the surface behind the dune. This particular model is presently in a prototype form but the example (Figure 8.2) is indicative of the richness of behaviour that can be developed from transect models.

Spatial models

Like gap models, spatial forest models simulate forest dynamics by modelling the establishment, growth, and mortality of individual trees within a defined area. Spatial models of other ecosystems tend to be developed as spatially extended Markov models of a form like the transect models discussed above (van Tongeren and Prentice, 1986). The spatial forest models differ from gap models in their explicit consideration of tree position in the horizontal plane. An inherent difference between gap models and spatial forest models is in the form of the competition functions. Because of the explicit consideration of horizontal position, spatial forest models generally use a measure of competition that is a direct function, of the proximity and size of neighbouring individuals.

Although the competition indices used in spatial models vary greatly in their design, they can be classified into three major categories:

1. Distance-based ratios

2. influence-zone overlap indices

3. growing-space polygons.

Distance-weighted size ratios (Hegyi 1974; Daniels, 1976) define the degree of competition between a given tree and a neighbouring individual as a function of the ratio of the sizes of the two trees (competitor subject tree) multiplied by the inverse of the distance between the two individuals.

The influence-zone indices (Gerrard, 1969; Bella, 1971) are based on the assumption of a circu1ar zone of influence around every tree, wherein direct competition occurs (Staebler, 1951). The extent to which this area overlaps the influence zone of neighbouring trees represents a measure of encroachment and crowding of a tree's optimal functional environment. These indices vary with regard to the type of overlap expressions used (i.e.linear, angular, areal).

Growing-space polygons (Brown, 1965; Moore et al., 1973; Alard, 1974; Pelz, 1978; Doyle, 1983) represent geometrical designs to calculate non-overlapping crown area of a tree as limited by the proximity and size of neighbouring individuals.

Figure 8.3 Simulated growth of the crowns of five trees from Mitchell's (1975) model of Douglas-fir (Pseudo- tsuga menziesii). Tree 3 is subjected to active competition and eventually dies in year 25. The crown of tree number 2 has grown outside of the simulated plot by year 20 and is 'wrapped' to re-enter the plot on the right side. This is a typical device used in spatially explicit models to eliminate the effects of plot boundaries. The Mitchell model simulates the interaction of the trees by branch pruning as the crowns overlap

Although each of these indices is based on the relative horizontal position of individuals on the plot, they vary in the methods that are used to determine which neighbouring individuals to consider as potential competitors, in defining the size of the zone of influence for a given individual, in consideration of size of competing individuals relative to the target tree, and in their consideration of potential differences in competitive ability among species.

With the exception of Doyle (1983), the above-mentioned competition indices are based on statistical models and the calculated values of the competition indices are regressed against observed growth rate of individuals to determine the functional relationship between competition and growth. As a result, the functional form of the relationship between the competition index and the growth rate is site specific (i.e. related to site factors such as nutrient and moisture availability) and data intensive. For these reasons, most spatial models have been developed for managed forests (e.g. Mitchell, 1975 and Figure 8.3) and, with the exception of the Ek and Monserud (1974) FOREST model, simulate monospecific stands.

FUTURE APPLICATIONS AND CHALLENGES

The development of simulation models initially resulted from an interest in forecasting the patterns of change in plant communities. Over time this interest in forecasting has matured into a more theoretical focus of understanding the scaled-up consequences of various physiological and ecological processes. This shift in interest from forecasting to theory testing is a consequence of several factors:

1. The actual data base for our understanding of succession is extremely sparse and the goal of forecasting in such situations is often unrealistic

2. Successional studies are frequently based on inferences used to piece together data sets that relate important features of ecosystems into a rational pattern. One frequent method to organize successional data is to order systems sampled at the same time but over a large space into an inferred chronosequence

3. The rate of addition of new data-rich studies of succession to the ecological literature has decreased over the past several decades

4. An increased interest in the non-equilibrium nature of ecosystems requires a data base that is beyond the spatial and temporal scale of most data sets that are available and has created an arena for theorization about ecosystem dynamics.

A potentially important class of theoretical investigations to which models can be usefully employed regards the response of ecosystems to the dynamics in the systems that drive them. The problem is one of understanding which scales of dynamics in the driving system interact with the ecosystem to produce responses. There is also a related problem of understanding how changes in ecosystems in response to the environment are feedback to alter the environment. In some cases these problems are global in their scale.

Cowles (1899) once characterized succession as 'a variable approaching a variable' and thus conceptualized ecosystem dynamics as a system perturbed away from-but moving toward-an equilibrium that was itself changing. The present problem is to understand both of these 'variables' and the interaction between them. Successional models are the tools to investigate the responses of systems such as those conceived by Cowles. In the following discussion we will focus on atmosphere ecosystem interactions to provide what we feel is an important example of this class of problem. The emphasis on these interactions stems from the implications of terrestrial ecosystem dynamics to the global scale, from the important and unique role of models in understanding these interactions, and to the degree to which including these interactions challenges our understanding of ecosystem function.

The addition of realistic climatic factors to forest succession models

It is interesting to note that most of the classical static climatic classifications, such of those of Koeppen (summarized in Oliver and Hidore, 1984) were originally subdivided by biotic unit. Their use in climate biota research therefore ensnares the investigator in a circular trap of guaranteed results.

Only rather recently has climatology evolved, from such endless series of tables and classifications, into a much more dynamic science based upon physics and theory. Dynamic climatology is the spatial and temporal integration of the dynamic meteorology evident on the daily surface and upper atmospheric maps, where fronts, airmasses, and cyclones are modulated by complicated dynamic processes. Like ecosystems, these phenomena exhibit discontinuous and preferred scales of motion. Many of these are characterized as aggregations of physical variables that have quantifiable impact on tree mortality and consequent community distribution.

Thompson Webb III, in his doctoral dissertation (1971), used multivariate statistical techniques to relate both standard climatic variables and more integrative airmass durations and frequencies (i.e. a rudimentary dynamic climatology) to arboreal pollen assemblages over North America. The result was a partial specification of holocene atmospheric circulation patterns related to and predicted from community migration. The implication is that one can indeed quantitatively relate atmospheric circulation systems and community distribution. Thus the prospect of defining functional relationships between the dynamic climate and changing ecosystems seems attainable.

Yet, atmospheric perturbations-weather, climate, and their moments of variability-have traditionally been parameterized in simplistic fashion in most successional models. Further, these variables are assumed to exert primarily first-order effects rather than acting through intermediaries such as defoliators or herbivores. Concurrent with the development of successional modelling has been a substantial increase of our understanding of climate and its variability. It remains an important research focus in understanding global change to interface these two developing fields.

Barry and Perry (1973) have written what remains the standard text on comprehensive analyses of climatic data; it describes a number of methodological and theoretical considerations that should be considered in the interface of climate and successional models. Fujita (1981) has written an interesting contextual background, which details the scales of atmospheric motion. However, neither of these works are directed to an ecological audience.

The heart of the research problem is the discrimination between weather and climate events that have significant successional effects and those that do not. This is one of the important scale questions that was mentioned in the introduction. Verified successional models are appropriate tools to determine the dimensions of those events. This is true in particular because the historical (non-proxy) record of climatic variability is insufficiently long to relate directly to successional impact. However, the more sophisticated classifications of the nature and parameters of climatic variability can be used with successional models to isolate the successionally important climatic events.

For an atmospheric process to exert a significant successional effect, it must impact the ecosystem in a manner that directly allows for the alteration of local community composition. Some processes-including gap openers such as windfalls, lightning strikes, and ice-induced crown damage-appear as prominent and persistent. Others, such as differential mortality resulting from unusual temperatures, are much more subtle.

Fujita (1981) provides strong evidence for five relatively discrete scales of atmospheric motion (Figure 8.4), some of which can influence succession. The dynamic nature of successional models can be used to quantify that influence. Fujita's five scales are each separated by approximately two orders of magnitude in spatial extent, with the largest, or 'A' scale, corresponding to the planetary and synoptic circulations. The planetary scale circulations do not directly impinge upon forest community processes. Rather, it is generally the 'E' ('mesoscale') circulations that are more ecologically active.

The planetary scales of motion dissipate a substantial portion of their energy in the form of the more familiar secondary scales-mid latitude cyclones, their associated fronts, and the anticyclones that comprise the airmasses that are separated by frontal discontinuities. The secondary scales have embedded within a variety of mesoscale phenomena whose effects, temporal, and spatial characteristic should be input to successional models.

Figure 8.4 Atmospheric scales of motion according to Fujita (1981)

One exception to this general scheme is the planetary-scale intertropical convergence zone (ITCZ), a region of relative upward motion that roughly corresponds to the earth's thermal equator. The ITCZ produces only ill-defined secondary circulations that tend to be confined to the Asian Subcontinent. Instead, the primary mesoscale circulations of ecological import are directly produced by the ITCZ and are in the form of strong thunderstorms with attendant downburst winds and lightning strikes.

It is noteworthy that the ITCZ takes on several forms, some of which bear no strong relation to seasonality. In fact, its position and conformation from day-to-day is surprisingly unpredictable (Chang, 1972), negating the common misconception that its movement is one of the primary predictable forcing functions that stabilizes tropical forest systems. It therefore seems appropriate that tropical successional models (e.g. Doyle, 1981; Shugart et al., 1981) be modified to investigate the ecological implications of this phenomena.

The occurrence or non-occurrence of thunderstorms should be treated as a random variable within broad seasonal limits. However, the ecologically significant effects-immediate gap opening resulting from downbursts, and slowly opening gaps resulting from lightning-induced mortality-should be given exponentially increasing likelihoods related to a relative relief and topography.

As noted above, the primary successional disturbances are generated by mesoscale meteorological phenomena embedded in the macroscale. Those which may have considerable successional significance include tropical cyclones, mesoscale convective complexes ('MC Cs'), severe thunderstorms, and frozen precipitation. Temperature effects are dealt with separately below.

1. Tropical cyclones

Tropical cyclones are warm-core eddies that develop primarily as embedded disturbances within the trade wind regime, which itself is the return flow that maintains the mass continuity of the ITCZ. Winds often exceed 100 km/hr , and one-minute velocities at landfall as high as 300 km/hr have been noted. While their most obvious damage is done primarily by storm surge waves impinging upon pericoastal regions, they also produce broad areas of up-rooted trees and mid-crown damage within 200 km of landfall.

Ecologists interested in exogenous disturbances and successional response, particularly in North America, should be aware of the historical climatology of tropical cyclone tracks produced by Neumann et al. (1981) for the previous 110 years. Also, attention should be paid to a paper by Shapiro (1982) that details secular change in the track regime through the 20th century. The combined analyses suggest a significant nonstationarity in the time series over the fire-stabilized extensive Oak-Pine forests of the southeastern United States. This indicates that using simple mean and variance estimates for climatic input into succession models may be an inappropriate simplification if a high level of realism is the modelling goal.

Tropical cyclone movement is primarily related to the strength of upper-tropospheric winds which are subject to secular changes associated with hemispheric temperature fluctuations. For example, it is quite plausible that the relative cooling of the late 1950s and 1960s, compared to the earlier three decades, as noted by Diaz and Quayle (1980) would have resulted in stronger mid-atmospheric westerlies and a concomitant increasing northward deflection of tropical systems up the east coast of North America observed during that period. Attempts to include prospective climatic change in succession models should include such phenomena.

2. Mesoscale convective complexes and severe thunderstorms

Mesoscale Convective Complexes ('MC Cs') and severe thunderstorms are two notable E-scale phenomena that tend to occur in preferred regions of A-scale fronts and cyclones. MCCs are concentrated areas of intensive convection, approximately 10000 km², often accompanied by intense cloud-to-ground lightning. They are only sometimes accompanied by heavy precipitation. The synoptic climatology of MC Cs, including tracks and background conditions, have been documented by Maddox (1983). Approximately 30 occur per year over North America east of the Rocky Mountain system, and they tend to appear ahead of northward moving thickness patterns ('warm fronts').

The synoptic climatology of MC Cs, which were initially detected from weather satellites, has only been documented for recent years (see Maddox, 1983). Further, a preferred track analysis, similar to that for tropical cyclones in Shapiro (1982) or for temperate cyclones (Hayden, 1981) has yet to be generated. But it seems reasonable to conclude that their association with frontal situations would also suggest a nonstationary time series forced by hemispheric climatic change.

Severe thunderstorms, which produce frequent lightning and are accompanied sometimes either by strong downburst winds exceeding 150 km/hr (Fujita, 1981), or by tornadoes, are primarily a factor during the transition from winter to summer, over most regions, although they have been noted in all seasons over eastern North America. As yet, no objective synoptic climatology of either severe thunderstorms or tornadoes has been generated, so it is impossible to state the broad parameters of temporal and spatial variation. However, as is the case for all lightning and wind generators, it is likely that the most significant effects will tend to be concentrated over the high elevations in areas of relatively high relief. Thus, similar to the case for ITCZ thunderstorms, it would seem appropriate to apply some exponentially increasing risk function for gap opening in such areas. Canham and Loucks (1984) recently detailed the community alteration resulting from a strong downburst in a severe thunderstorm.

Tornadoes are sufficiently uncommon over most of the forested areas of North America as to exert only a minimal effect. However, this is not true for some of the forested regions extending from Alabama to East Texas, where calculations based upon average track length of 2 km² suggests a return period of about 2000 years at a given point, based upon data from the National Climatic Data Center (1979).

3. Frozen precipitation

The synoptic climatology of frozen precipitation, primarily in the forms of snow or freezing rain, may have particular bearing upon successional transformations. For example, it is generally noted that boreal coniferous species shed snow more efficiently than their deciduous counterparts. Thus Bryson's (1966) conclusion that the mean southward (winter) and northward (summer) position of the polar front circumscribes the boreal zone seems logical, as it is between these areas that substantial precipitation is likely to fall as snow.

Freezing rain can induce substantial and extensive crown damage. It can occur over extensive regions where shallow layers (less than 2 km) of cold air are trapped either because of dynamic or topographic processes. It is thus a phenomenon confined primarily to the excursionary regions of the wintertime polar front, and accentuated by topography. Regions such as the eastern slope of the Appalachian mountains and nearby piedmont, from approximately 30° to 40° North, are unusually subject to this phenomenon. It is also likely, but undocumented in the western literature, that the same problem occurs along the eastern slope and piedmont of the Ural Mountains. As a mix of coniferous and deciduous vegetation dominates these regions it would appear that the coniferous species, with their more extensive surface area during the cold portion of the year, would be more substantially impacted.

4. Temperature

The previous discussion ignores the effects of changing or unusual temperatures on successional phenomena. Successionally important temperature fluctuations are primarily controlled at the' A' level in Fujita's scheme, denoted by either warm anticyclonic conditions at the subtropical level or by cold anticyclonic weather associated with the export of shallow airmasses from arctic regions.

Overlaying the entire temperature picture are the scenarios for increasing trace gas-related warming, noted with perspective by the US National Research Council (1983) Report. The caution with which that report was tendered cannot be understated; however, it is clear that some hemispheric warming should be expected over the coming decades. Predictive successional models should therefore be conditioned with temperature data suggestive of both increased variance and increased mean temperature values, if both the findings of Karl et al. (1984) and the National Research Council Report are accepted.

CONCLUSION

As noted above, resolution of the relationships between tree mortality, distribution, and the dynamic atmosphere can be approached at a number of levels. Signal progress will be achieved when the atmospheric circulation system regime, rather than its derived physical variables, serves as the climatic input to dynamic models of the forestscape.

Given the diversity of climatic phenomena that can affect succession and the current debate with regard to future climate, an important future challenge is to make succession models become more responsive to changes in their base atmospheric input. This includes the design of models with appropriate local climatology. The greatest need appears to be realistic input of the synoptic climatological variables that are probably associated with successional disturbance.

It is important to determine what degrees of climatic fluctuation are necessary to affect successional change. This can be accomplished by examining the responses of ecological models for significant differences in the simulated communities that result when differing climatic data are used as input in realistic ecological models. We have only provided some general guidelines here concerning the important phenomena. To properly answer this question will take a long-term interdisciplinary effort in ecology and climatology.

In developing this review we initially discussed scales of controlling external phenomena and scales of ecosystem response as both a present issue in ecological studies and as a classic historical topic in ecology's history. The understanding of resolution of scale problems in ecological systems is clearly a central problem in understanding global change. In this review one sees that there exist a considerable number of modelling tools for projecting the long-term dynamics of forest systems and these tools have analogues for other ecological systems. However, when one considers the scales at which atmospheric phenomena can affect the dynamics of forests, for example, one quickly realizes that the effects can occur at a wide range of time and space scales.

What this all implies is that the use of models to project ecosystem response to climatic change will be considerably more complex than simply taking a model 'off the shelf' .The models will need to be honed to the task of interfacing with projections from atmospheric models to a considerable degree. The present generation of ecosystem models has been developed to meet a diverse set of problems and objectives. As a result, even a well tested and seemingly reliable model will not necessarily contain the responses to critical driving variables that might be effected by a change in atmospheric systems. The development and testing of models either created or modified to project forest (or other ecosystem) response to change in the atmospheric systems is not a solved problem by any means. The richness of scales of the abiotic driving variables may proscribe use of a single model for these purposes. One approach is the application of several models that are internally consistent in their basic assumptions but designed to operate at different time and space scales to problems of interfacing ecological and atmospheric systems. 

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