LAASIM: A physiologically mechanistic and spatially explicit forest simulator

Conceptual Outline

Introduction

The leaf area allocation simulator (LAASIM) is a deterministic, spatially explicit forest succession model. A major improvement of LAASIM over stochastic, quasi-mechanistic gap models is the effort to parameterize the fundamental (physiological) rather than the realized (ecological) niche. This is important in so far, as the widely observable realized niche is mostly a function of equilibrium conditions (competitional and climatic. To realistically simulate forest dynamics under transient climate, we need to model the tree species behavior more fundamentally, independent of former equilibria observations. Thus, we must attempt to parameterize the physiological instead of the ecological limits of trees, and to design the competitional model functions from physiological principles as rigorously as possible. Constraints apply due to the fact that the model is intended to run for long time series and on large landscapes. LAASIM is based on a series of ecological theories and concepts, which we present briefly below.

Forest Leaf Area / Site Water Balance Relations

Grier and Running (1977) first observed a strong linear relationship (R²=0.99) between forest ecosystem leaf area (LA) and site water balance (SWB), calculated as the difference between annual precipitation and potential evapotranspiration plus soil storage. Across a range of sites with water balances from approximately -80cm to +10cm Grier and Running observed forest leaf areas from approximately 5 to almost 40 (LAI), respectively. Similar trends for LA/SWB have been reported by Gholz (1982), Jose and Gillespie (1996) and others, prompting Nemani and Running (1989) to develop the hydrologic equilibrium theory which states that ecosystem leaf area is linearly related to site water balance. The theory was tested and shown consistent by comparison of field measured leaf areas, modelled leaf areas (from Forest-BGC: Nemani & Running 1989; Running & Coughlan 1988) and satellite imagery (both thematic mapper and AVHRR: e.g. Elvidge & Chen 1995; Law & Waring 1994; Nemani & Running 1989). Subsequently, the relation was employed by Band et al.(1991) and Milner et al.(1996) to estimate spatially explicit forest leaf areas from climate data for a broad range of sites in Montana (USA).

This relation demonstrates a basic optimization among plants. Leafs are the photosynthetically active organs of trees enhancing growth through carbon allocation. The control of maximum stand leaf area by site water balance can primarily be explained by evaporative demands and photosynthetic efficiency. Supporting leaves in excess of the water available incurs unnecessary carbon costs, generally leading to the decline and mortality of individual leaves (or whole plants), and ultimately to the water induced equilibrium level of leaves. Other factors have been addressed as well. High elevation forest (in cold environment) seem to reveal slightly lower total stand leaf areas than expected from mid- to low elevation regressions with site water balance (Gholz 1982), and several studies have demonstrated the influence of nutrient availability (Cleve & Oliver 1982; Raison et al. 1992; Velazquez-Martinez et al. 1992; Waring et al. 1992) and minimum temperature (Gholz 1982) on stand leaf area. However, none of the latter parameters is as dominating in its overall significance as site water balance.

Individual Tree Leaf Area / Sapwood Area Relations

The physiological functioning behind this relationship was discovered somewhat independently. Beginning with the work of Shinozaki et al. (1964a; 1964b) and others (Grier & Waring 1974; Waring et al. 1977; Whitehead 1978) a body of knowledge has accumulated relating individual tree leaf area to sapwood cross-sectional area. Originally, the work was framed in the ‘pipe model theory’ which characterized the sapwood conducting tissue as a pipe conducting water to leaves. It was hypothesized that for a specific environment every leaf would require a specific amount of transpirational water to maintain open stomates for photosynthesis, and that a specific amount of conducting tissue was required to supply the water. Over the next two decades a large number of studies determined characteristic sapwood area/leaf area ratios (SA/LA) for a broad range of species; Gholz et al. (1976), Waring et al. (1977; 1982), Kaufmann and Troendle (1981), Waring (1983), and Margolis et al. (1995) give an overview of coefficients for conifers and angiosperms. These overviews partly include central European tree species. Other papers specifically list such coefficients for central Europe (e.g. Bartelink 1997; Granier et al. 1996; Hees et al. 1993; Mencuccini & Grace 1995; 1996).

The sapwood area/leaf area ratios exhibit characteristic variability that is ecologically interpretable; species growing in xeric environments require more sapwood per leaf area than do species in more mesic areas, reflecting relatively greater evaporative demands in more xeric areas (Margolis et al. 1995). Individual species growing across a range of environments show similar trends (Callaway et al. 1994; Carey et al. 1997; Long & Smith 1988). Additionally, species specific SA/LA ratios have been shown to be site specific in ways not related directly to evaporative demand, varying with stand density (Long & Smith 1988; 1989), nutrient availability (Brix & Mitchell 1983), and relative canopy position (Dean & Long 1986; Thompson 1989).

In response to limitations of the pipe model theory, Whitehead et al.(1984) proposed the ‘hydraulic model’, which incorporated sapwood permeability and other hydraulic parameters to the basic pipe model. The inclusion of sapwood permeability explains much of the variation in SA/LA ratios between species on a single site (Coyea & Margolis 1992; Whitehead et al. 1984). Pothier et al. (1989) and Coyea and Margolis (1992) related differences in permeability to anatomical characteristics of conifer tracheids, and found that these differences are strongly positively correlated with growth rate and age. Thus SA/LA ratios within a species are reduced on more mesic sites not only because of differences in evaporative demand, but also due to increased sapwood conductivity on more mesic sites.

Clearly, the relation between sapwood area and leaf area demonstrates a basic optimization in carbon acquisition and allocation. Leaves, as the site of photosynthesis, are responsible for all carbon gain, while sapwood is non-photosynthesizing respiring tissue with carbon costs. Plants will support no more sapwood than is necessary to supply leaves with water, as excess sapwood incurs additional carbon cost with no benefit to the plant. Alternatively, plants must have enough sapwood to supply leaves with water or leaves will close their stomates, thereby foregoing photosynthesis and incurring net carbon costs.

Moisture Requirements, Shade Tolerance, and Growth Rates

Smith and Huston (1989) proposed a conceptual model of forest distribution and dynamics based on theoretical considerations about interactions of shade tolerance and moisture demand and its effect on potential growth. Specifically, they proposed a triangular tradeoff model based on the theory that shade tolerance is correlated with moisture demand, and that due to anatomical and morphological characteristics of leaves and canopies shade tolerant species cannot be drought tolerant. Shade intolerant species can be moisture demanding, and this combination is typical of fast-growing seral species. Figure 1 is a representation of the Smith and Huston model adapted to tree species of the Central Rocky Mountains as currently used in a simulation study on the Shoshone National Forest, WY (Zimmermann & Roberts in prep.). At any given moisture level succession proceeds from species along the right margin to species along the diagonal that can exist at the specified moisture level.

Fig. 1: Woody plant strategies for light and water use, illustrating the tradeoffs between adaptation to stress and optimization of growth and competitive ability. The different regions in the triangle represent functional types.

While the diagram does not capture all aspects of forest tree distribution in the study area (ignoring heat and soils), it does represent a basic level of understanding of species biology incorporated into our model.

Temperature, and the tradeoff-model

Biogeographers and ecologist have long recognized the relationship between plant distribution and climate (Candolle 1855; Humboldt 1807; Humboldt & Bonpland 1805; see Woodward 1987). Schimper (1898) was the first to rigorously relate the influence of climate on plant distribution to physiological processes. Temperature in particular was recognized as having a strong influence on plant distribution, primarily through frost frequencies and heat sum. Larcher (1982) and Woodward (1987) discuss the influence of low temperatures on physiological adaptations and natural selection. In general, many biogeographers and ecophysiologists believe that species are limited at their upper elevational or poleward latitudinal limits by climatic effects on reproduction and establishment (Woodward 1992). The limiting effect of high temperature – as observed at the lower elevational or southern latitudinal limit – on the distribution and dynamics of forests is less clear, however. High temperatures do not seem to be directly physiologically limiting (Larcher 1980; Woodward 1987). Ornamental trees have been long noted to grow south of their latitudinal limits in the northern hemisphere (Loehle & LeBlanc 1996), and physiological (Bonan & Sirois 1992), dendrochronological (Cook & Cole 1991), and tree growth data (Larsen 1965) all show that maximum relative growth rates often occur at a species’ southern range limit. Lower elevational or lower latitudinal limits appear to have other causes than temperature. The principal factors responsible for the southern and lower elevation limits appear to be competition and often drought (Hogg 1994).

Decreasing heat sum and increasing frequency of frost is limiting tree growth rates, similarly to the effects of limited supply of water and light. In its general form, this so-called tradeoff-model predicts lower maximum growth rates for a tree species that is better adapted to limited resource availability than for a tree that is generally found under optimal supply (see Fig. 2).

Fig. 2: The Tradeoff-Model explains the relationship between the tolerance to low resource conditions and maximum potential growth rate. Note the inverse relationship in potential growth between the three hypothetical species (red, green & blue) under high and under low resource availability (adapted from Houston & Smith, 1989).

Houston and Smith (1989) discuss the general form of this model, and summarize the mechanism as the "cost-benefit" principle. The principle indicates that tolerance to stress (low temperature/light/water) have to be achieved by plants at the cost of maximized growth, and is a well known consequence of physiological and energetic constraints (e.g. Parsons 1968).

The trade-off model demonstrates the effects of limited availability of resources on maximum growth. It thus makes predictions about the fundamental niche of plants. In terms of temperature, we would assume that the best adapted trees to cold environments would be replaced by faster growing trees at lower elevations (with higher heat availability), even if the latter has the same tolerance to shade and limited water. From the tradeoff-model it also is evident that the point along the (temperature) gradient where the two species are equally competitive is different in its characteristics for the two trees. At higher temperatures, the more stress-tolerant species will soon be outcompeted, even though its maximum potential growth rate high. This is in accordance with physiological (Bonan & Sirois 1992), dendrochronological (Cook & Cole 1991), and silvicultural results (Larsen 1965). On the other hand, it is equally evident that the better competitor is considerably physiologically limited beyond this point of balance. We thus can conclude that the field-observed limits (realized niche) of plants towards stress are relatively close to the physiological (fundamental) limits of the same species, while the same is not true for the limits towards optimal resource availability.

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Last Updated on 4/15/99
By Niklaus E. Zimmermann