George Perkins Marsh, 1864

In the previous chapter I described the growth of an individual tree as a function of inherited characteristics under non-limiting environmental conditions. Under those conditions growth rate changes only with age or size, as illustrated in Chapter 2, Figure 2.1. Actual growth can range from zero to the value calculated from the fundamental growth equation, depending on competition with other trees, which determines the light each tree receives, and on other environmental conditions, that is, on the availability of resources (soil water and soil nitrogen) and the thermal conditions of the environment. A tree responds to all environmental conditions, and a fundamental question is how this total response integrates the individual effects of separate environmental factors. Does each factor act independently on the tree or do factors act together?

In the history of the study of plants, the classic answer is Liebig's Law of the Minimum, which states that the single factor in least supply will limit plant growth. In this sense, there are no interactions among limiting factors. For example, if a soil is low in phosphorus and this limits plant growth, the addition of nitrogen to the soil will have no effect on tree growth.

(An alternative is that resources interact. For example, since enzymes require nitrogen, addition of nitrogen might allow a tree to produce more enzymes involved in the uptake of phosphorus, improving its efficiency in the use of phosphorus. Additional fertilizer would lead to an increase in tree growth even if phosphorus were the limiting factor. Although the latter is possible, most plant ecologists and agricultural scientists have accepted Liebig's law.)

Mathematically, the response of a tree to each environmental factor can be expressed as a function that takes on values between 0 and 1 (or in some cases slightly more than 1), which affects the fundamental growth equation (2.1). Each of these relationships will be called a response function. To follow Liebig's law of the minimum, one would calculate the value of each response function and then choose the one with the smallest value and multiply the fundamental growth equation by that value, ignoring all others. Formally,

_D/_t = _D/_t*MIN{f₁, f₂,....f_j} (31.a)

where _D/_t is the change in diameter (the actual diameter growth); f₁,...,f_j represents the response functions; and MIN{ } is the function that becomes the minimum of the values contained in the brackets. The approach expressed in equation (3.1), which is an expression of Liebig's law of the minimum, is called an additive approach; the functions are said to be chosen additively.

A second approach assumes that the functions continue to influence the growth simultaneously and independently. The simplest expression of this is to assume that the fundamental growth equation is multiplied by each response function, so that

_D/_t = (_D/_t)_opt*f₁*f₂* . . . f_j (3.1b)

where (_D/_t) opt is the fundamental growth equation (2.1).

In this case the tree responds to each factor independently, but responds to all independent factors simultaneously. The tree's calculated response to a specific level of nitrogen is the same whatever may be the level of phosphorus, the temperature of the air, or soil moisture conditions. Its total growth is the product of these independent responses.

The reader should understand that the resulting total response may resemble synergistic curves. I define a synergistic relationship as one where one environmental factor influences another and then the combination of two factors acts on tree growth as a single function to produce a new, single response curve.

The important point here, worth repeating, is that the total growth response of the tree is the product of all environmental factors, though each factor operates independently through its own response function on the tree. I emphasize this point because some colleagues have urged me to apply multiple regression analysis to data about the response of trees to two environmental factors, and then to use this integrated response in the model. As an example, tree ring analysis (the study of the correlation between past climates and diameter increments in trees) often employs multiple regression analysis. A single function is generated relating diameter increment to air temperature and rainfall. With the structure of JABOWA, such analysis cannot be used directly. The relationship must be decomposed into two separate ones: diameter increment as a function of precipitation and diameter increment as a function of temperature. Then these studies can be used to improve JABOWA.

The assumption that the response functions operate independently means that they are graphically orthogonal; each plot of growth versus a response function will lie 90 degrees from each other plot (Fig. 3.1). This approach is called multiplicative. JABOWA operates under the multiplicative assumption (equation 3.1), but it is simple to convert it to a model that operates under the additive assumption (equation 3.1).

In the original formulation of the model, we chose to use multiplicative interaction to capture the possible interactions among factors and because it seemed intuitively preferable. It may interest the reader to know that we compared the additive and multiplicative interactions in a model of an algal community within a freshwater ecosystem. We found that both methods ordered species dominance correctly, but the multiplicative approach was quantitatively closer (the multiplicative model was more accurate) than the additive model (Lehman, Botkin, and Likens, 1975a,b).

An obvious question raised about multiplicative interactions is what happens when there are many factors and all of them are at suboptimal levels? Can any tree grow? For example, if four factors, temperature, light, soil drought, and soil nitrogen, are at 50% of maximum, then the actual diameter growth will be (0.5)⁴_D_opt or 0.0625_D_opt; the tree would grow at a little more than 6% of its maximum. This suggests that, if multiplicative interactions exist in nature, then only a few factors actually determine tree growth, or only a few are much less than optimal at any one time, or trees can withstand very suboptimal conditions. Operation of the forest model (that is, using the forest model), as discussed in chapter four, provides some insight into a possible answer.

From the point of view of mineral nutrition of plants, one might believe that many factors could limit tree growth. On the order of 20 chemical elements are required by green plants. If ten were characteristically below 50% of their maxima and interactions were multiplicative, most of the time plants would grow little. As I will discuss later, there is a connection between the concept of multiplicative interactions and niche theory (see chapter four). This provides additional insight into the question I have raised here.

Graph of the light and temperature responses functions in three dimensional space. This graphs shows two dimensions of the fundamental niche of tree species. The graphs are part of the assumptions of the model. (Reproduced from Fig 5.2b Botkin, D.B., 1981, Causality and Succession, Chapter 5, pp. 36-55, In: West, Shugart and Botkin, eds., Forest Succession: Concepts and Applications, Springer-Verlag, NY.)

The totality of the effects of environmental conditions on tree growth, also referred to throughout as totality of "environmental response functions" and denoted in the general form by f(environment) in equation (2.6) is a product of several factors:

f(environment) = f_i(AL)*Q_i*s(BAR) (3.2)

for a tree of the ith species, where f_i(AL) is the light response of the species and s(BAR) is a function of the maximum basal area that the plot can support (similar to the forester's idea of a site index). For each site, the value of each response function is computed for each species. In JABOWA-II, Q_i is the product of response functions for thermal properties of the environment, drought (wilt factor), soil-water saturation (soil wetness factor), and soil fertility. (This approach follows Botkin and Levitan, 1977.) Q_i will be referred to as the "site quality" for species i. For each species i,

Q_i = TF_i x WiF_i x WeF_i x NF_i (3.3)

where TF_i is the temperature function. WiF_i is the "wilt" factor (an index of the drought conditions that a tree can withstand). WeF_i is a "soil wetness" factor, an index of the amount of water saturation of the soil a tree can withstand. NF_i is an index of tree response to nitrogen content of the soil. The calculation of each environmental factor was described in Chapter 2. The next sections describe how these factors change growth and regeneration. (In JABOWA-I, Q_i consisted only of the temperature response function.)

Earlier I described some aspects of photosynthesis and growth. During the twentieth century, hundreds of experiments have been conducted to measure photosynthesis as a function of light (see, for example, Botkin, 1969; Botkin, Woodwell and Tempel 1970; Woodwell and Botkin, 1970; Vowinckel, 1975; Kozlowski, Kramer and Pallardy, 1991). The general shape of the curve relating net photosynthesis to available light is an upward-sloping asymptotic curve (Fig. 3.2). At low light intensities there is a rapid increase in net photosynthesis as light increases. Eventually other factors, including intrinsic (genetic) capacities, become limiting. The photosynthetic rate becomes "light saturated" - additional light has a smaller and smaller effect on growth. Eventually increases in light fail to increase net photosynthesis.

The general form of the light response function can be written as

(A₂AL - A₃)

f(AL)_L = A₁{1 - e } (3.4a)

where A₁, A₂, and A₃, are empirically derived constants and AL is

the light available to a tree, and L is the light tolerance class (class one is intolerant of low light, two is intermediate in tolerance, and three is tolerant of low light.)

Although there have been hundreds of studies of the response of growth and photosynthesis of vascular plants to light intensity, few exist for tree species and fewer still for individual mature trees under natural conditions. When the model was first developed, very few measures were available, and in the original version of the model, species were put into one of two light response categories, tolerant or intolerant, whose response functions were

-1.136(AL - 0.08)

f(AL)₁ = 2.24{1 - e } shade intolerant (3.3b)

-4.64(AL - 0.05)

f(AL)₃ = 1 - e shade tolerant (3.3c)

(In versions I and II, light tolerance class two has the same equation as class one). The parameters in these equations were obtained from data in Kramer and Decker (1944) and others (Kramer and Kozlowski, 1960). These continue to be the light response functions in the model, but the computer code allows three categories of response functions: tolerant, intolerant, and intermediate. The code also allows each species to have a unique light response. Some evidence suggests that each does have a unique light response curve (Botkin, 1969). It is even conceivable that genotypes within a species might have distinctive curves. However, experience with the model shows that, at least for trees with C₃ photosynthetic pathways, we can limit the responses to two categories, shade tolerant and shade intolerant. A shade-tolerant species is comparatively efficient in using light when little is available, but it becomes light saturated at comparatively low light intensities. A shade-intolerant species has comparatively low growth rates under low light conditions but responds more rapidly to increases in light and reaches saturation at a much higher light intensity than a shade-tolerant species (Fig. 3.2). Foresters sometimes talk about a third category, intermediate, with light response curves between the tolerant and intolerant. As I mentioned earlier, JABOWA allows for three shade tolerance classes, but in the existing version intolerant and intermediate species share the same light response function. Regeneration algorithms separate shade-intolerant and intermediate species from each other, as I will discuss later. The accuracy of such shade-tolerance classification has been discussed (Lorimer, 1983).

The relationships shown in Figure 3.2 are for near-instantaneous measurements of net photosynthesis of tree leaves. Of course the net photosynthesis of individual tree leaves will vary with changes in light, temperature, and soil water availability during the day, and there are differences in the instantaneous photosynthetic rates of different leaves in different parts of the same tree, some of which will be shaded and some will be sunlit. Thus one cannot expect a one-to-one correspondence between instantaneous net photosynthesis of a single life and total tree growth. However, measurements of net photosynthesis over an entire growing season from a surprisingly small sample of leaves give a reasonably good estimate of net forest production (Botkin, Woodwell and Tempel, 1970). The assumption of the model is that the shape of the photosynthetic curve (either shade tolerant or shade intolerant) will correspond reasonably well to the response of a whole tree to annual insolation.

To summarize, parameters in light response equations derive from laboratory measurements of shade-tolerant and shade-intolerant trees (Kramer and Kozlowski, 1960), and the simplifying assumption was made that two categories could represent the growth of all species. It was expected that, as more information became available for specific tree species, species-specific parameters would be substituted. I have been surprised through my own use of the model and use by others to find that the general categorization has been adequate.

Al is available light. The curves are solutions to equations (3.4a) and (3.4b).

There is a strong empirical relationship between tree growth and climate, especially between tree growth and temperature or degree-days. This relationship holds for long-term records, over thousands of years. It is used as one basis for reconstruction of past climates, and the relationships between tree growth and climate are used to determine ages of archeological sites and past climate-vegetation relationships. The study of these long-term relationships is so soundly based empirically as to develop into its own field of study, dedrochronology (Cook and Kairiukstis, 1989; Fritts, 1976; Jackoby and Hornbeck, 1987).

We can put these relationships on a conceptual and theoretical foundation. The rate of an enzyme reaction within a cell increases with temperature to a maximum and then decreases. Such unimodal curves are biologically universal and typically fall within a range between O and 50^oC. The sum of metabolic activities within an organism also leads to a similar unimodal response of total growth rate as a function of temperature. The temperature of a tree depends on external environmental conditions mediated by the ability of the tree to increase evaporation of water to cool leaves under warm conditions and to reduce this evaporation under cooler conditions, and by other factors as discussed in Kramer and Kozlowski (1979) and in Gates (1980). The general relationship between net photosynthesis of woody plants and temperature is shown in Figure 3.3(A). Trees from widely different habitats and environments have temperature response curves of the same shape, roughly a parabola with the peak response at higher temperatures for tropical trees than for temperate ones. For example, Pinus cembra reaches a peak net photosynthetic rate at approximately 18^oC, whereas tropical Acacia carspedocarpa reaches a peak at 40^oC (Larcher, 1969). It has been suggested that this parabolic curve is the result of three interacting physiological responses: an exponential increase of gross photosynthesis that occurs at low temperatures, an increase in dark respiration that at first lags gross photosynthesis but increases at a more rapid rate as temperature rises; and an inactivation or destruction of the photosynthetic apparatus at high temperatures (Kramer and Kozlowski, 1979; Kozlowski, Kramer and Pallardy, 1991). Regardless of the specific form of the function, there is a strong empirical relationship observed between tree growth and temperature or tree growth and degree-days. For example, Fuller, Reed, and Homes (1987) reported that the most important variable related to tree growth was cumulative air temperature degree-days.

From this we can propose that the general form of the temperature response of a tree is parabolic, as shown in Figure 3.3(A). However, that response is to the instantaneous temperature. The actual response over a longer period - a month or a year - is a response to the integrated thermal properties of the environment. These can be represented by growing degree-days, discussed in Chapter 2, which I remind the reader is the sum above some minimum of the average temperature of a day over a month or a year. The minimum growing degree-days is the value below which tree growth ceases. This may be a species-specific factor that has evolved over long periods of time as an evolutionary adaption of trees to regional climate. For trees in boreal and northern hardwoods forest, the minimum growing - degree-days value is assumed to be 4.4^oC (40^oF). To my knowledge, this base has been used in all versions of the model. As discussed in Chapter 2, where actual local weather records are not available one can assume that the temperature profile is sinusoidal and estimate degree-days for each month from January and July average temperatures, as discussed by Botkin et al. (1972a, 1972b) from equation (2.11):

DEGD = 365(T_july - T_jan) - 365 {40 - (T_july + T_jan)/2}

2pi pi

+ 365[40 - (T_july + T_jan)/2)]²}/(T_july - T_jan)

Pi

(2.11)

where temperature is in Fahrenheit.

The temperature derating factor, TF_(i) is a parabolic function of the growing- degree days. For species i,

TF_i = max(0, TDEGD_i) (3.5)

TDEGD_i = 4(DEGD - DEGD_min(i))(DEGD_max(i) - DEGD) (DEGD_max(i) - DEGD_min(i))² (3.6)

where DEGD = growing degree-days during the current year at site as discussed in Chapter 2

DEGD_min(i)= value at northern end of range of species i

DEGD_max(i) = value at southern end of range of species i.

In theory, the values of DEGD_min(i) and DEGD_max(i) could be determined from laboratory experiments in which the rate of photosynthesis was measured over a range of temperatures, as has been done in some cases, primarily for seedlings (Ledig and korbobo, 1983). This is the preferred method. However, there may be considerable differences in this response for seedling, sapling, and mature stages in an individual tree and among individuals and ecotypes within a species, so that the determination of an average value for these parameters for a species might require measurements of many individuals known to be representative of the variability within the species. Unfortunately such extensive measurements are generally not available. Lacking such measurements, DEGD_min(i) and DEGD_max(i) can be estimated from species range maps and lines of temperature isotherms for January and July, as shown for yellow birch in Figure 3.4. The development of a program for direct estimation of these parameters following methods of Ledig and Korbobo (1983) and others and using standardized environmental conditions, would be useful.

The temperature derating factor, TF_(i) is a function of the growing degree days. For species i,

TF_i = max(0,TDEGD_i) [3.5]

TDEGD_i = 4(DEGD - DEGD_min(i))(DEGD_max(i) -DEGD) (DEGD_max(i) - DEGD_min(i))²

[3.6]

where

DEGD = growing degree days during the current year at the site as discussed in chapter 2;

DEGD_min(i)= value at the northern end of the range of species i;

DEGD_max(i) = value at the southern end of the range of species i.

In theory, The values of DEGD_min(i) and DEGD_max(i) could be determined from laboratory experiments in which the rate of photosynthesis was measured over a range of temperatures. However, there can be considerable differences in this response for seedling, sapling, and mature stages in an individual tree, and considerable variation among individuals and among ecotypes within a species in this response, so that the determination of an average value for these parameters for a species would require measurements of many individuals known to be representative of the variability within the species. Such extensive measurements are generally not available. Lacking such measurements, DEGD(i)_min and DEGD(i)_max can be estimated from species range maps and lines of temperature isotherms for January and July, as shown for yellow birch in Figure 3.4.

(Fig. 5.17, p. 196, from P.J. Kramer and T. T. Kozlowsi, 1979, Physiology of Woody Plants, Academic Press, N.Y., adapted from Larcher (1969)).

The temperature derating factor, TF_(i) is a function of the growing degree days, as explained in the text.

Temperature Isotherms Correspond to Geographic Limits of Yellow Birch. The January minimum temperature isotherm that gives 2000 growing-degree days closely approximates the northern limit of yellow birch, while the July maximum that gives 5300 growing-degree days closely approximates the southern limit. This gives an approximation of DEGD(i)_min of 2000 and DEGD(i)_max of 5300 for this species. Because of the lack of detailed experimental data, this method has been used as the general estimation procedure for these parameters (From Botkin et al., 1972b).

The parabolic curve representing the response of tree growth to temperature imposes certain stringent assumptions, the most important of which are: (1) photosynthesis and growth become zero at specific degree-day values, and (2) the temperature response curve is symmetric, falling off at equal rates above and below the peak. In reality the curve could be asymmetric, especially with a steeper decline toward higher temperatures above the peak than the rise at lower temperatures before the peak, which might result from rapid destruction or deactivation of the photosynthetic apparatus as proteins and therefore enzymes became denatured. Such asymmetries have been observed for algae, and we applied that asymmetric relationship in a model of a phytoplankton community (Lehman et al., 1975a). However, available data do not support this choice of a curve for woody plants.

It is possible that growth declines gradually toward the geographic limits of the range of a species, so that the growth would decline asymptotically with temperature toward zero instead of ceasing abruptly at one temperature. This gradual approach to the thermal limits can be represented by a bell-shaped or Gaussian curve. One could justify the use of this curve for a species with high genetic diversity. Local genotypes near the limit of the range could have different temperature response functions than genotypes in the center of the range. Although individual trees would reach zero growth at specific temperatures, net population growth would decline gradually because individuals would reach zero growth at different temperatures.

Such a Gaussian response curve is represented by

TF_i = exp {-(DEGD-r)²/2_²} [3.7]

where TFⁱ is the temperature response function for species i, DEGD is the celsius degree-days as defined in Chapter 2, r is the average of the maximum and minimum degree-day limits, and _ is an estimate of the standard deviation of degree-days (Woodby, 1991). It is straightforward to substitute the Gaussian curve for the parabolic and find which gives the more realistic results.

The growth of a tree changes with too much and too little water. Unfortunately, studies of the response of total biomass increment of an entire tree to soil water have been qualitative and do not provide a solid basis from which water response functions can be developed. Existing studies suggest that tree growth is insensitive to the exact value of soil water except near the extremes of drought and saturated soil (Kozlowski, 1968; 1970; 1972; 1982a; 1982b) Although much is known about anatomical, morphological, and physiological details of water transport in a tree, including the forces, pressures, and sources of energy and the cellular processes in leaves, xylem, phloem, and roots (Kramer and Kozlowski, 1979), and although models exist that project water use and transport by individual trees, such as the models of Jarvis (1981) Running (1984), and Waring, Schroeder, and Ore (1982), less is known about the response of total net biomass increment to soil-water conditions. The observed, general shape of the response to drought is shown in Figure 3.5.

Drought conditions for a tree occur when energy available for evapotranspiration greatly exceeds the amount of water available in the soil for that evaporation. Remember that the amount of water that could be evaporated and transpired given the available energy is known as potential evapotranspiration. When potential evapotranspiration is much greater than the calculated actual evapotranspiration, the net amount of water stored in the tree declines. If this continues long enough, leaves wilt and eventually the tree dies. There are two ways in which a drought effect has been calculated in the model. In the first method, too little water is represented by the difference between potential evapotranspiration, E₀, and actual evapotranspiration, E, normalized by the potential evapotranspiration, so that

WILT = (E₀ - E)/E₀ (3.8a)

WILT is a dimensionless quantity that ranges from zero in swampy sites to about 30 percent in thin interior soils with a low till depth (Botkin and Levitan, 1977). The wilt factor measures the lack of a positive property of soil moisture for plant growth. Note that since E can never exceed E_o. WILT can never be less than zero. WILT can also never be greater than one. (For an example of the size of the wilt factor for two different soil conditions, see Table 3.1.).

In the second method, the wilt factor is calculated as the difference between the field capacity and the normalized actual water storage, so that

WILT = w_k - w/w_k (3.8b)

In either case, the effect of drought on tree growth, WiF_i, is

WiF_i = max{0,1 - (WILT/WLMAX_i)²} (3.9)

where WLMAX_i is the maximum wilt tolerable by species i. WILT and WLMAX_i are dimensionless quantities. In practice, the value of WLMAX_i has been estimated as a relative factor, with species known to be characteristic of very dry or very wet sites given extreme values and other species given intermediate values consistent with the known habitats. This approach to the derivation of WLMAX_i is less satisfactory conceptually than the derivation of other parameters in the model, and remains a subject for which improvement is desirable, both from experimental studies to specify the shape of the relationship between tree growth and drought, and from theoretical analyses of tree-soil-water flux. As discussed earlier, available information suggests that trees grow reasonably well in relation to soil moisture except at the extremes - that the curve relating tree growth to soil moisture is level except at the extremes, where a rapid decrease occurs. If WiF_i were made a function of WILT/WLMAX_i to the first power, the slope would be too gradual. Raising this ratio to higher powers steepens the slope. The ratio WILT/WLMAX_i is raised to the second power to provide a realistic steepness to the slope of the decrease in tree growth with soil dryness.

Unless otherwise stated, results presented in this book use the first method, but both methods are available in the model available for use with this book. The shape of WiF_i is shown in Figure 3.5(B) for several species. This function has the general shape observed for trees (Fig. 3.5A). Note that when WLMAX = WILT, that is, when the maximum drought tolerable by a species equals the current site conditions, then WiF_i is zero and individuals of the species cannot grow.

Soil texture affects the amount of water stored, thus affecting site quality (the function Q_i in equation [3.2] and in [3.3]). The effect of soil texture on site quality can be seen in Table 3.1 for a clay-loam soil (soil moisture-holding capacity 250 mm depth of water/m depth of soil) (Table 3.1[A]) for a sandy soil (soil-moisture holding capacity 50 mm/m) (Table 3.1[B]). Texture has a large effect, which varies with species. The wilt factor for sugar maple drops from 0.592 to 0.394 and the site quality, Q_i from 0.171 to 0.114. Here the site is dry - the soil is comparatively shallow and the water table deep, so that the site quality favors upland species adapted to dry conditions, including jack pine. The difference between sites is sufficient to allow yellow birch to persist marginally in the clay soil (site quality = 0.054), but to fail (site quality = 0) in the sandy soil. Inspection of Table 3.1 shows which species will be favored during competition for specific site conditions. A user of the software available as a companion to this book can inspect the table, list species that he believes should dominate, and then run the model using site conditions in Table 3.1 or for other cases and observe the quantitative projections of the model for these two habitats.

Effect of soil texture on site quality for two locations near Mount Pleasant, Michigan weather station - a coarse sandy site and a clay soil.

Symbols in column headings not given below are explained in the glossary and text. The wilt factor is calculated according to the first method:

WILT = E₀ - E/E₀ (3.8a)

and evapotranspiration is calculated as discussed in Chapter 2:

E₀ = 16(10T_m/I)^a (2.15)

(A) Clay soil (soil moisture holding capacity 250 mm/m)

(^oC) (mm) Storage(mm) Storage (mm) degree-days

1 -7.59 54.86 100.00 161.80 0.00 0.00 31.16 1.00

2 -6.88 42.16 100.00 203.96 0.00 0.00 31.16 1.00

3 -1.65 60.20 100.00 117.96 146.20 54.15 31.16 1.00

4 3.66 102.62 100.00 0.00 117.96 211.80 31.16 1.00

5 12.69 65.02 63.19 0.00 0.00 498.89 31.16 1.00

6 15.73 66.04 42.79 0.00 0.00 573.80 31.16 1.00

7 19.29 97.54 43.89 0.00 0.00 703.49 31.16 1.00

8 17.23 90.93 47.74 0.00 0.00 639.60 31.16 1.00

9 12.78 118.11 69.28 0.00 0.00 485.47 31.16 1.00

10 8.90 143.26 95.58 0.00 0.00 381.44 31.16 1.00

11 -2.69 47.75 100.00 0.00 47.75 21.40 31.16 1.00

12 -4.95 59.18 100.00 59.18 0.00 0.00 31.16 1.0

Totals 947.67 311.91

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 17.24 146.20 0.00 0.00 0.00 128.96 17.24 -0.00 4 19.05 220.57 0.00 21.41 21.41 180.11 19.05 0.00 5 -36.81 65.02 0.00 84.62 83.64 18.19 0.00 -36.81 6 -20.40 66.04 0.00 106.36 76.28 10.16 0.00 -20.40 7 1.10 97.54 0.00 131.87 82.00 14.44 0.00 1.10 8 3.85 90.93 0.00 108.15 71.67 15.41 0.00 3.85 9 21.54 118.11 0.00 68.56 59.97 36.61 0.00 21.54 10 26.30 143.26 0.00 42.36 42.35 74.60 0.00 26.30 11 9.34 47.75 0.00 0.00 0.00 38.41 4.92 4.42 12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Totals 41.21 995.43 0.00 563.33 437.32 516.90 41.21 0.00

SPECIES PWT W_iF W_eF TDEGD NF

Sugar maple 0.171 0.592 1.000 0.848 0.342

Beech 0.173 0.592 1.000 0.857 0.342

Yellow birch 0.054 0.166 1.000 0.958 0.342

White ash 0.006 0.166 1.000 0.377 0.093

Mountain maple 0.102 0.334 1.000 0.892 0.342

Strip.maple 0.097 0.334 1.000 0.848 0.342

Pin cherry 0.060 0.650 1.000 0.991 0.093

Choke cherry 0.139 0.650 1.000 0.626 0.342

Balsam fir 0.041 0.166 1.000 0.450 0.545

Red spruce 0.057 0.166 1.000 0.628 0.545

White birch 0.234 0.650 1.000 0.660 0.545

Mountain ash 0.119 0.405 1.000 0.860 0.342

Red maple 0.181 0.753 1.000 0.441 0.545

Scarlet oak 0.000 0.753 1.000 0.000 0.545

Hornbeam 0.071 0.753 1.000 0.276 0.342

Green alder 0.000 0.000 1.000 0.000 0.545

Speckled alder 0.000 0.000 1.000 0.926 0.545

Chestnut 0.000 0.753 1.000 0.000 0.545

Black ash 0.000 0.000 1.000 0.989 0.093

Butternut 0.005 0.444 1.000 0.131 0.093

White spruce 0.007 0.166 1.000 0.479 0.093

Black spruce 0.000 0.000 1.000 0.552 0.545

Jack pine 0.406 0.822 1.000 0.906 0.545

Red pine 0.409 0.800 1.000 0.938 0.545

White pine 0.352 0.753 1.000 0.857 0.545

Trembling aspen 0.255 0.753 1.000 0.993 0.342

White oak 0.047 0.753 1.000 0.182 0.342

Red oak 0.114 0.753 1.000 0.443 0.342

White cedar 0.000 0.000 1.000 0.581 0.093

Hemlock 0.061 0.166 1.000 0.678 0.545

Silver maple 0.000 0.000 1.000 0.547 0.093

Tamarack 0.000 0.000 1.000 0.517 0.342

Pitch pine 0.000 0.822 1.000 0.000 0.545

Gray birch 0.313 0.753 1.000 0.762 0.545

American elm 0.007 0.166 1.000 0.481 0.093

Basswood 0.030 0.405 1.000 0.795 0.093

Bigtooth aspen 0.000 0.000 1.000 0.857 0.342

Balsam poplar 0.050 0.650 1.000 0.839 0.093

Black cherry 0.000 0.650 1.000 0.000 0.342

Red cedar 0.075 0.753 1.000 0.182 0.545

TABLE 3.1 (Continued)

(B) Sandy soil (soil moisture holding capacity 50 mm/m)

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

3 4.99 146.20 0.00 0.00 0.00 141.22 4.99 0.00 4 4.76 220.57 0.00 21.41 21.41 194.40 4.76 0.00 5 -10.93 65.02 0.00 84.62 63.55 12.39 0.00 -10.93 6 - 1.40 66.04 0.00 106.36 59.52 7.93 0.00 -1.40

7 1.13 97.54 0.00 131.87 81.97 14.44 0.00 1.13

8 0.88 90.93 0.00 108.15 74.11 15.94 0.00 0.88

9 6.64 118.11 0.00 68.56 66.91 44.56 0.00 6.64 10 6.41 143.26 0.00 42.36 42.36 94.49 2.74 3.67 11 4.26 47.75 0.00 0.00 0.00 43.49 4.26 -0.00 12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Totals 16.74 995.43 0.00 563.33 409.82 568.86 16.74 0.00

TABLE 3.1B (Continued)

SPECIES PWT W_iF W_eF TDEGD NF

Sugar maple 0.114 0.394 1.000 0.848 0.342

Beech 0.115 0.394 1.000 0.857 0.342

Yellow birch 0.000 0.000 1.000 0.958 0.342

White ash 0.000 0.000 1.000 0.377 0.093

Mountain maple 0.003 0.011 1.000 0.892 0.342

Strip.maple 0.003 0.011 1.000 0.848 0.342

Pin cherry 0.044 0.480 1.000 0.991 0.093

Choke cherry 0.103 0.480 1.000 0.626 0.342

Balsam fir 0.000 0.000 1.000 0.450 0.545

Red spruce 0.000 0.000 1.000 0.628 0.545

White birch 0.173 0.480 1.000 0.660 0.545

Mountain ash 0.034 0.117 1.000 0.860 0.342

Red maple 0.152 0.633 1.000 0.441 0.545

Scarlet oak 0.000 0.633 1.000 0.000 0.545

Hornbeam 0.060 0.633 1.000 0.276 0.342

Green alder 0.000 0.000 1.000 0.000 0.545

Speck. alder 0.000 0.000 1.000 0.926 0.545

Chestnut 0.000 0.633 1.000 0.000 0.545

Black ash 0.000 0.000 1.000 0.989 0.093

Butternut 0.002 0.175 1.000 0.131 0.093

White spruce 0.000 0.000 1.000 0.479 0.093

Black spruce 0.000 0.000 1.000 0.552 0.545

Jack pine 0.363 0.736 1.000 0.906 0.545

Red pine 0.359 0.703 1.000 0.938 0.545

White pine 0.296 0.633 1.000 0.857 0.545

Trembling aspen 0.215 0.633 1.000 0.993 0.342

White oak 0.039 0.633 1.000 0.182 0.342

Red oak 0.096 0.633 1.000 0.443 0.342

White cedar 0.000 0.000 1.000 0.581 0.093

Hemlock 0.000 0.000 1.000 0.678 0.545

Silver maple 0.000 0.000 1.000 0.547 0.093

Tamarack 0.000 0.000 1.000 0.517 0.342

Pitch pine 0.000 0.736 1.000 0.000 0.545

Gray birch 0.263 0.633 1.000 0.762 0.545

American elm 0.000 0.000 1.000 0.481 0.093

Basswood 0.009 0.117 1.000 0.795 0.093

Bigtooth aspen 0.000 0.000 1.000 0.857 0.342

Balsam poplar 0.037 0.480 1.000 0.839 0.093

Black cherry 0.000 0.480 1.000 0.000 0.342

Red cedar 0.063 0.633 1.000 0.182 0.545

Change in elevation affects both evapotranspiration and temperature, but the effect is much larger on the temperature factor (Table 3.2). For example, at 500-m elevation, the boreal species including balsam fir, red spruce, and white birch have a sufficient site quality to allow growth, but at 100-m the temperature quality is 0.0 for fir and spruce and 0.048 for white birch; fir and spruce cannot grow at 100 m elevation and white birch will do poorly. In contrast, the northern hardwoods, such as sugar maple and beech, have a considerably improved temperature quality at 100 m in comparison to 500 m. Although these species can grow at both elevations, their growth will be much better at 100 m.

Species PWT W_iF W_eF TDEGD NF

1 0.499 0.776 1.000 0.992 0.648

2 0.501 0.776 1.000 0.998 0.648

3 0.339 0.542 1.000 0.965 0.648

4 0.139 0.542 1.000 0.593 0.431

5 0.410 0.634 1.000 0.998 0.648

6 0.408 0.634 1.000 0.992 0.648

7 0.339 0.808 1.000 0.972 0.431

8 0.415 0.808 1.000 0.793 0.648

9 0.000 0.542 1.000 0.000 0.718

10 0.000 0.542 1.000 0.000 0.718

11 0.028 0.808 1.000 0.048 0.718

12 0.031 0.673 1.000 0.072 0.648

13 0.380 0.864 1.000 0.612 0.718

Species PWT W_iF W_eF TDEGD NF

1 0.427 0.835 1.000 0.789 0.648

2 0.429 0.835 1.000 0.793 0.648

3 0.392 0.664 1.000 0.913 0.648

4 0.092 0.664 1.000 0.320 0.431

5 0.400 0.731 1.000 0.844 0.648

6 0.374 0.731 1.000 0.789 0.648

7 0.361 0.859 1.000 0.975 0.431

8 0.323 0.859 1.000 0.581 0.648

9 0.281 0.664 1.000 0.589 0.718

10 0.362 0.664 1.000 0.760 0.718

11 0.467 0.859 1.000 0.758 0.718

12 0.464 0.760 1.000 0.943 0.648

13 0.257 0.900 1.000 0.397 0.718

(A) Net Photosynthesis of sweetgum (S) and loblolly pine (L) with decreasing soil moisture(Fig 5.21, p. 203 in Kramer and Kozlowski, Physiology of Woody Plants; data on sweetgum from Bormann (1953); on loblolly pine from Kozlowski (1949).

(Effect of soil drought on Tree Growth)

This is a plot of the function WiF for balsam fir, showing the effect of a error of plus and minus 10 percent in the estimation of this parameter on the response function.

Too much water in the soil has negative effects on tree growth, principally because water-saturated soil lacks oxygen that is necessary for root tissue respiration. Cessation of root growth has several effects. Uptake of chemical elements takes place at the growing, actively metabolizing ends of roots, and a lack of oxygen suppresses nutrient uptake. Suppression of growth renders roots more vulnerable to fungal or bacterial diseases. Trees with a poor root structure are more vulnerable to physical damage from wind. Again, although much is known about the details of these mechanisms at the cellular level, less is known about how biomass increment of an entire tree responds quantitatively to soil-water saturation. As a first approximation of these effects, we have chosen as our measure of site wetness simply the reciprocal of the water table depth (Botkin and Levitan, 1977).

The factor for site wetness is calculated as

WeF_i = max(0,1 - DTMIN_i/DT) (3.10)

where DTMIN_i is the minimum distance to the water table tolerable for species i

and DT if the depth to the water table. The shape of this response curve is shown in Figure 3.6. In the absence of numerical data in the literature, we provided values for parameters reflecting the hydrological environments that each species is known to tolerate (Table 3.4).

This is a plot of WeF_i for several species.

For readers not familiar with chemical cycling and vegetation, the following background material may be helpful. Every organism exchanges chemical elements with its environment. Each organism is made up of many chemical compounds, as it grows it must accumulate more chemical elements to make more compounds. In addition, some chemical elements inevitably are lost, and these must be replaced. Some loss occurs in the elimination of wastes - for example, green plants give off oxygen to the atmosphere as a waste product of photosynthesis. Some occurs through loss of tissue as, for example, when roots or the inner, living part of the bark dies and the material is sloughed off.

There are 24 chemical elements required by at least some kinds of organisms, and each must be available at the right time, in the right concentrations, and in the right ratio to other elements. Trees can store a certain amount of some chemical elements for later use, but storage has limits, which vary seasonally. In deciduous angiosperm trees, nitrogen can be transported out of leaves in the autumn before leaf fall and transported to roots, where it is stored until spring. A tree must obtain the right amounts of all the elements needed, though these elements vary in abundance and availability over time - with seasons and among years - and they are distributed in a patchy way throughout their environment.

Chemical elements required by living things can be separated into three categories: (1) macronutrients, nutrients required in large amounts by all life forms; (2) micronutrients that are used in small amounts by all life forms; and (3) micronutrients that are used in small amounts by some, but not all, life forms. Macronutrients are the "big six" elements: carbon, hydrogen, nitrogen, oxygen, phosphorus, and sulfur. These are the basic building blocks of organic compounds. Carbon, hydrogen, and oxygen make up carbohydrates, fats, and oils. These three plus nitrogen form proteins. Phosphorus and sulfur are required for compounds that control many cell functions. Phosphorus is the energy element, acting in the compounds adenosinetriphosphate (ATP) and adenosinediphosphate (ADP) to store and transfer energy within cells. Sulfur occurs in enzymes that control important cell activities.

Chemical cycling in ecosystems has been the subject of considerable study during the last two decades, as exemplified by analyses of eastern deciduous forests of North America (Bormann and Likens, 1979; Bormann et al., 1974; Likens et al., 1977). There has been an emphasis on changes in nutrient storage at the ecosystem level (Schlesinger, 1991; Waring and Schlesinger, 1985), as discussed for example by Vitousek and Reiners (1975) and Gorham, Vitousek, and Reiners, (1979). Volumes of research exist about the effects of limitations of each chemical element on plant growth (Kozlowski, Kramer and Pallardy, 1991), especially for crops (Kramer and Kozlowski, 1979).

These studies provide a picture of the general response of a plant to the concentration of a required chemical element in the soil. The shape of this curve is like the growth response of a tree to available light (equation 3.3) (Figs. 3.1, 3.2). This is known as a dose-response curve. Dose-response curves characteristically show sensitivity to low concentrations and insensitivity to high concentrations. At low concentrations of a chemical element in the soil, a unit increase causes a large increase in growth; at high concentrations, the same unit increase causes a small increase in growth, and when concentrations are sufficiently high, additional increases in the soil lead to no growth increase and eventually to a suppression of growth (although this final negative effect occurs at levels not usually found for macronutrients and micronutrients in nature). From this background we know that the general shape of the growth response of a tree to the concentration of any required chemical element will resemble that shown in Figure 3.2.

We need to consider another factor before we can arrive at a model of growth response to chemical nutrients. Plants do not grow in direct response to the abundance of a chemical element in the soil, but in response to the internal stores of that element. There are two steps in the utilization of molecules of a nutrient: uptake and growth. We might try to simplify the representation of these processes by devising a dose-response curve that relates growth directly to external concentration. Experience with models of other photosynthetic organisms, including freshwater algae (Lehman, Botkin and Likens, 1975a; 1975b) and salt marsh grasses (Morris, 1982; Morris, Botkin and Houghton, 1989), suggests that greater realism is obtained in model output if the two stages are retained. With this background, we can set down the nutrient response function of the forest model.

In theory, one could introduce into the model a nutrient response function for each required chemical element. This would require approximately 40 additional equations (one each for uptake and one each for growth from internal stores for approximately 20 elements). This is unnecessary in practice because (1) some elements vary together so that the variation in one would represent for purposes of a model, the variation in the other; and (2) some elements are rarely limiting, and where they are a specific response function could be added. Data are insufficient to develop a complete set of nutrient response functions. It is not an overstatement to say that nitrogen may be the only element for which the response of trees under natural conditions is sufficiently well studied to develop a function. Even for this element data are sketchy. A model with 20 or more chemical elements would be computationally clumsy, requiring parameters for which data are poor or lacking. Such a model would provide little additional realism at the cost of great effort. In the long term there are situations for which additional nutrient response functions will be important. However, given the paucity of data for any chemical element, we have developed algorithms only for nitrogen. In Chapter 4 the success of this simplification of the model can be examined.

Green plants cannot use molecular nitrogen directly, but they can use either nitrate or ammonia, and some evidence suggests that these are used equally efficiently (Morris, 1982; Morris, Houghton, and Botkin, 1984). As is well known, nitrate and ammonia are made available by various bacterial reactions. Readers unfamiliar with the nitrogen cycle and interested in these reactions can refer to a number of standard references, such as Waring and Schlesinger (1985) and Schlesinger (1991) and other recent papers discussing nitrogen cycling in forests, such as Aber, Melillo, and McClaugherty (1990); Stevens et al. (1990); Hendrickson (1990); Van Miegroet, Johnson, Cole (1990); Nohrstedt (1989). When nitrogen is low in concentration in the soil, the addition of a small amount produces a relatively great increase in plant growth, if other factors are not limiting. As the concentration of nitrogen in the soil increases, the addition of each new unit of nitrogen results in a smaller increase in plant growth. As a result, the generalized response of a green plant to soil nitrogen concentration is a curve that increases to an asymptote an with increase in soil nitrogen, a curve of the same form as the light response function (equation 3.4).

Although hundreds of studies have been done on the response of plants in greenhouses to changes in concentration of a specific chemical element, there are few studies of the response of trees in a forest to changes in the soil concentration of a single element. Such studies require long periods - for forest trees results might not be evident in fewer than 5 or 10 years. There are many confounding variations in natural forest soils. And until recently there were few funds for such studies. One of the few classical studies of the response of a forest to fertilization was that done in New England by Mitchell and Chandler (1939). This study provides the basic shapes of the curves and the definition of the gradient. Mitchell and Chandler measured the growth response of trees against the amount of nitrogen added in fertilizer. The study has one serious limitation: the authors did not measure the nitrogen concentration in the soil prior to the addition of fertilizer, so the absolute concentration of available nitrogen is not known.

Mitchell and Chandler were not alone in having difficulty in dealing with the concentration of nitrogen in soils. Although there have been a number of recent studies of the nitrogen cycle and of concentrations in the soil, the connection between a measured amount of nitrogen in a soil and the amount actually available for uptake by trees remains unclear. Most measurements of soil nitrogen give the total amount (Federer, 1984; Huntington, et al., 1988), and suggest that total nitrogen can be as much as 1,000 to 10,000 kg/ha, but most of that is bound in complex organic compounds not available to plants. In a review of nitrogen cycling by Waring and Schlesinger (1985) report that nitrogen concentrations in the forest floor ranged from approximately 600 to 700 kg/ha in boreal and temperate forests is less than 400kg/ha in temperate deciduous forests, and is approximately 200 in tropical forests. Total nitrogen concentration in organic and inorganic fractions of the soil, typically measured to depth of 20 to 100 cm, ranges up to more than 8,000 kg/ha.

Plants can take up nitrogen as nitrate or ammonia, but these are produced by bacterial action, through the fixation of atmospheric molecular nitrogen, or the decomposition of organic compounds, processes that can vary comparatively rapidly with changes in soil temperature and moisture. Nitrate and ammonia are reactive and relatively volatile, so that they have a short residence time in the soil, which means that even a perfect measure of the status of these compounds would have to be done frequently (or monitored continuously) to provide an exact measure of available nitrogen. In spite of these limitations, considerable progress has been made in recent years in obtaining measurements that correspond to nitrogen levels that can be taken up by plants, and these suggest that nitrogen becomes available for plant uptake at a rate generally less than 100 kg/ha/yr (Aber, Melillo and McClaugherty, 1990; Hendrickson, 1990; Van Miegroet, Johnson and cole, 1990; Clark and Rosswall, 1981; Pastor et al., 1984; Pastor et al., 1987;). Available nitrogen is highest in forests with a high abundance of trees that have symbiotic nitrogen-fixing bacteria in root nodules; in these, the nitrogen fixation can approach 100 kg/ha/yr (Bormann and Gordon, 1984). Nitrogen fixation by free-living bacteria seems to be much less, on the order of 0-3 kg/ha/yr (Roskoski, 1980; Waring and Schlesinger, 1985). Further field research is needed to resolve the question of the relationship between nitrogen measured in the soil and nitrogen available to a tree.

Thus in part the problem is one of measurement: it is still not clear what measurement method corresponds to the level of nitrogen available to trees. In spite of these limitations, Mitchell and Chandler's study provides a basis from which a dose-response curve can be derived, and their study is a basis for the following discussion. The factor for nitrogen tolerance, NF, is based on work by Aber, Botkin, and Melillo, (1978; 1979). NF is a function of the available nitrogen in the soil, AVAILN, and the nitrogen concentration in the leaves, _. Different curves for responses to the nitrogen gradient are used for each of three classes - tolerant (1), intermediate (2), and intolerant (3). Here, "tolerant" means tolerant of low levels of available nitrogen.

This analysis leaves one question unanswered: What is the correspondence between the quantities derived from the Mitchell and Chandler study and measured amounts of nitrogen reported in the literature? Woodby (1991)followed Aber et al. (1979) and normalized the results from the Mitchell and Chandler study to represent kilograms per hectare to give amounts of the same order of magnitude as nitrogen available by biological fixation on an annual basis. The nitrogen content of the leaves is computed for each tolerance class, N, using the following equation:

__N = _₁[1-10^{-_2(AVAILN+_3)}] [3.11]

and the response of the trees calculated as:

NF_i = (_₄ + _₅ x __N)/_₆ [3.12]

where _ is the concentration of nitrogen in leaves of tolerance class N; AVAILN is the concentration of available nitrogen in the soil, NF_i is the nitrogen response function, and the coefficients (_₁ through _₆) are given in Table 3.3 and some resulting nitrogen values are given in Figure 3.7.

Conceptually, the two equations (3.11) and (3.12) create a two-step nitrogen response, with nitrogen first taken up by the leaves and then leaf storage affects tree growth. This conforms more realistically to cellular and physiological processes. If a lag effect in nitrogen response were observed in forests, then this is a location in the model where, by modification of the form of equation (3.12), that lag could be represented. Arithmetically, however, as presently formulated, equation (3.12) simply normalizes the relationships from Aber et al. (1978) so that NF_i ranges from slightly less than zero to a small positive number for each tolerance class within a reasonable range of expected concentrations of available nitrogen.

From Figure 3.7, you can see that nitrogen tolerance species have a greater response than the other classes at all nitrogen concentrations. There is a cross-over point in the responses of intermediate and tolerant classes, which occurs at approximately 30 kg/ha/yr. Below this level, tolerant species have a greater response; above this level, intermediate species have a greater response.

________________________________________

intolerant 2.99 207.43 0.00l75 -5.0 2.9 3.671

intermediate 2.94 117.52 0.00234 -1.2 1.3 2.622

tolerant 2.79 219.77 0.00179 -0.6 1.0 2.190

________________________________________

This is a plot of the function NF_n for the three nitrogen tolerances classes: (1)

intolerant of low concentrations of available nitrogen; (2) intermediate in tolerance; and

(3) tolerant.

(Note table (A) also appears as Table 2.1, it is repeated for convenience)

SPECIES MAXIMUM MAXIMUM MAXIMUM B2 B3 G C

AGE (n) DIAMETER HEIGHT

Sugar Maple 400. 170. 3350. 37.8 .111 118.7 1.570

Beech 366. 160. 3660. 44.0 .137 87.7 2.200

Yel. Birch 300. 100. 3050. 58.3 .291 143.6 .486

White ash 150. 150. 2440. 30.7 .102 147.5 1.750

Mtn. maple 25. 14. 500. 53.8 2.000 72.6 1.130

Strip.maple 30. 23. 1000. 76.7 1.700 109.8 1.750

Pin Cherry 30. 28. 1126. 70.6 1.260 227.2 2.450

Choke cherry 20. 10. 500. 72.6 3.630 233.3 2.450

Balsam fir 200. 86. 2290. 50.1 .291 102.7 2.500

Red Spruce 400. 60. 2290. 71.8 .598 50.7 2.500

White birch 140. 76. 3050. 76.6 .504 190.1 .486

Mtn.Ash 30. 10. 500. 72.6 3.630 155.6 1.750

Red Maple 150. 150. 3660. 47.0 .156 213.8 1.570

Scarlet oak 200. 30. 3050. 194.2 3.230 128.7 1.750

Hornbeam 150. 30. 1520. 92.2 1.530 144.4 .486

Green alder 30. 5. 300. 65.2 6.520 143.3 2.000

Speck. alder 30. 8. 400. 65.8 4.100 196.9 2.000

Chestnut 200. 122. 2740. 42.7 .175 195.2 1.750

Black ash 70. 60. 2130. 66.4 .554 96.2 1.750

Butternut 90. 91. 3050. 64.0 .352 192.2 1.750

White spruce 200. 53. 3350. 121.2 1.140 91.8 2.500

Black spruce 250. 46. 2740. 113.9 1.240 32.0 2.500

JackPine 185. 50. 3050. 116.5 1.160 142.0 2.000

Red Pine 275. 91. 3050. 64.0 .352 156.4 2.000

White pine 450. 101. 4570. 87.8 .435 141.2 2.000

Tremb. aspen 100. 100. 3050. 58.3 .291 173.7 .486

White oak 600. 122. 3050. 47.8 .198 72.0 1.750

Red oak 400. 100. 3050. 58.3 .291 107.7 1.750

White cedar 400. 100. 2440. 46.0 .230 35.7 2.500

Hemlock 600. 150. 3660. 47.0 .156 86.0 2.000

Silver maple 125. 122. 3960. 62.7 .257 164.8 1.570

Tamarack 200. 85. 3050. 68.5 .403 86.3 2.000

Pitch pine 200. 91. 3050. 64.0 .352 86.5 2.000

Gray birch 50. 38. 910. 40.7 .535 119.5 .486

Amer. elm 300. 152. 3840. 48.7 .160 180.0 1.600

Basswood 140. 137. 4270. 60.3 .220 169.8 1.600

Bigt. aspen 70. 60. 2130. 66.4 .554 176.7 .486

Balsam popl. 150. 100. 2440. 46.0 .230 232.5 .486

Black cherry 258. 91. 3050. 64.0 .352 166.7 2.450

Red Cedar 250. 60. 1520. 46.1 .384 88.7 2.000

SPECIES ITYPE NTYPE DEGDMAX DEGDMIN DTMIN WLMAX

Sugar Maple 3 2 6300. 2000. .567 .350

Beech 3 2 6000. 2100. .489 .350

Yel. Birch 2 2 5300. 2000. .600 .245

White ash 2 1 10947. 2414. .400 .245

Mtn. maple 3 2 6300. 1800. .489 .274

Strip.maple 3 2 6300. 2000. .567 .274

Pin Cherry 1 1 6000. 1100. .567 .378

Choke cherry 1 2 10000. 1700. .567 .378

Balsam fir 3 3 3700. 700. .211 .245

Red Spruce 3 3 3800. 1300. .489 .245

White birch 2 3 4000. 700. .544 .378

Mtn.Ash 2 2 4000. 1800. .544 .290

Red Maple 2 3 12400. 2000. .322 .450

Scarlet oak 1 3 8000. 3900. .933 .450

Hornbeam 1 2 10300. 2750. .933 .450

Green alder 2 3 3000. 540. .322 .130

Speck. alder 2 3 5299. 2174. .211 .050

Chestnut 2 3 8499. 3686. .933 .450

Black ash 2 1 5300. 1700. .322 .130

Butternut 1 2 6500. 3200. .933 .450

White spruce 2 1 3750. 600. .544 .245

Black spruce 2 3 3800. 600. .156 .130

JackPine 1 3 4000. 1150. 1.250 .530

Red Pine 1 3 4100. 2000. 1.250 .500

White pine 2 3 6000. 2100. 1.000 .450

Tremb. aspen 1 2 5600. 600. .700 .450

White oak 2 2 10204. 2966. .933 .450

Red oak 2 2 9600. 2400. .933 .450

White cedar 2 1 3700. 1500. .100 .050

Hemlock 3 3 6559. 2416. .489 .245

Silver maple 2 1 9000. 2200. .400 .187

Tamarack 1 2 3800. 600. .156 .050

Pitch pine 1 3 5800. 3800. 1.250 .530

Gray birch 1 3 4800. 2800. 1.000 .450

Amer. elm 2 1 12000. 1900. .400 .245

Basswood 3 1 6000. 2300. .567 .290

Bigt. aspen 1 2 6000. 2100. .400 .187

Balsam popl. 1 1 4300. 1000. .400 .378

Black cherry 2 2 10945. 3899. .567 .378

Red Cedar 1 3 10204. 2966. .700 .450

Key to Parameter Table

The parameters in (A) refer to the intrinsic (inherited) properties. B₂ and B₃ are parameters in equations [2.3] and [2.4], which occur also in equation [2.6]. C is the parameter in equation [2] relating leaf weight to tree diameter. G, which is a constant times C, is a parameter in the fundamental growth equation that determines when the inflection point in the curve will occur (how rapidly a tree growing under optimum conditions reaches one-half of its maximum size). Maximum diameter (cm) and maximum height (cm) are used in equation [2.6]. Maximum age is used in equation [3.10] to determine the first probability of mortality.

The parameters in (B) refer to functional response equations (the effect of the specific environment at a site on tree growth and reproduction). ITYPE is the shade tolerance class: 1 is intolerant, 2 intermediate and 3 tolerant. Similarly, NTYPE is the soil nitrogen tolerance type (1 is intolerant, meaning that good soil nitrogen supplies are required, 2 is intermediate and 3 is tolerant). DEGDMAX and DEGDMIN are the maximum and minimum degree days under which individuals of the species can grow; DTMIN is the depth to the water table parameter (m); WLMAX is the maximum wilt tolerable by species i.

The effect of soil nitrogen on site quality is shown in Table 3.5 for the Hubbard Brook site of Table 3.2. Soil texture is a sandy-loam intermediate in moisture-holding capacity (150 mm/m), but the nitrogen content in Table 3.5 is 35 kg/ha, less than half the value of the site in Table 3.2 (79 kg/ha). The model is sensitive to changes in soil nitrogen content and is comparatively much less sensitive to changes in soil-moisture holding capacity. When the soil nitrogen is 35 kg/ha (Table 3.5), nitrogen-intolerant species such as white ash can neither grow nor regenerate, in contrast to growth calculated for this species when the soil nitrogen is 79 kg/ha. Even nitrogen tolerant species, such as white birch, undergo a large decline in nitrogen response when nitrogen drops from 79 to 35 kg/ha.. Low soil nitrogen results in a site quality of less than 0.3 for all species. In contrast, under the high nitrogen level of Table 3.2 and the high nitrogen and high soil texture of Table 3.1, site quality ranges up to 0.47. None of these sites is of high quality for any of the species. White birch, a cold-climate, early- succession species tolerant of coarse soils and low nitrogen, maintains the highest site quality under all conditions shown in Tables 3.1, 3.2, and 3.5. Under high nitrogen content, the soil quality for sugar maple and beech approaches that for white birch, and these species can be expected to dominate the old-age forests. In the low nitrogen case, it is not clear from inspection of the table whether any late-succession species will persist.

These examples show the relative sensitivity of the model to site conditions, and they emphasize the greater sensitivity of the model to soil nitrogen than to soil texture which in part determines soil water holding capacity.

As I discussed in Chapter 1, the calculation of site quality creates a static model of forests somewhat analogous to the biogeographical models implied by the Holdridge Life-zone (Holdridge, 1947), the methods used by Lieth and Whittaker (1975) to project worldwide biomass and production of vegetation, and Box's biogeographical models (Box, 1981). In examination of site quality factors gives insight into the relative dominance of species to be expected, but the dynamic quality of the forest is not represented, and the actual dominance of species can only be discovered by running the model. A map drawn of past, present, and future distributions of vegetation based on the correlations between past distribution of fossil pollen and climate is a model of this kind (Davis and Botkin, 1985); I will refer to this as a static response surface model. Analogously, site quality calculations of JABOWA might be used for certain applications, such as development of large-scale regional maps of steady-state distribution of vegetation, calculated from environmental conditions. That is, the JABOWA site conditions calculations could be used as a static model for certain biogeographic applications, such as the drawing of global maps of vegetation distribution in relation to environment, an application for which JABOWA has not yet been used.

Effect of Low Soil Nitrogen Content on Site Quality(SQ)^a

^aVariables at site:

ELEVATION: 500.00 m; ADJUSTED_ROOT_DEPTH: 0.50 m;

K: 2.70 mm/day ^oC; WATER_TABLE: 1.75 m;

SNOW_TEMP: -3.40 ^oC; W_FC: 23.49 mm;

DEGREE-DAYS: 1756.79; W_K: 16.45 mm.

SOIL NITROGEN: 35 kg/ha;

(mm) (mm) (mm)

1 -8.98 101.95 70.48 232.36 0.00 0.00 30.25 0.98

2 -7.01 97.21 70.48 329.57 0.00 0.00 30.25 0.98

3 -2.11 110.20 70.48 331.53 108.23 40.09 30.25 0.98 4 4.14 102.60 70.48 0.00 331.53 226.22 30.25 0.98 5 11.26 123.61 62.30 0.00 0.00 454.56 30.25 0.98

6 16.01 125.28 44.83 0.00 0.00 582.33 30.25 0.98

7 18.71 110.63 35.87 0.00 0.00 685.46 30.25 0.98

8 17.69 119.58 40.64 0.00 0.00 653.65 30.25 0.98

9 13.12 116.60 50.92 0.00 0.00 495.58 30.25 0.98

10 7.17 110.48 68.22 0.00 0.00 327.78 30.25 0.98

11 0.89 125.21 70.48 0.00 0.00 128.81 30.25 0.98

12 -5.83 130.41 70.48 130.41 0.00 0.00 30.25 0.98

TOTALS 1373.75 439.77

MONTH DELTA_W RAIN UP_CAP_TR (E0) EVAP RUNOFF RUNOFF+ DW+ (mm) (mm) (mm) (mm) (mm) (mm)

1 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 2 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 3 12.46 108.23 0.00 0.00 0.00 95.77 12.46 0.00 4 17.18 434.13 0.00 24.53 24.53 392.43 17.18 0.00 5 -8.18 123.61 0.00 74.06 74.06 57.73 0.00 -8.18 6 -17.47 125.28 0.00 105.47 102.94 39.80 0.00 -17.47 7 -8.96 110.63 0.00 124.84 96.98 22.61 0.00 -8.96 8 4.77 119.58 0.00 109.22 86.95 27.86 0.00 4.77 9 10.29 116.60 0.00 70.35 67.19 39.12 0.00 10.29 10 17.29 110.48 0.00 35.28 35.28 57.90 0.00 17.29 11 14.81 125.21 0.00 3.85 3.85 106.54 12.55 2.26 12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

42.19 1373.75 0.00 547.60 491.79 839.77 42.19 0.00

TABLE 3.6 (Continued)

1 0.060 0.835 1.000 0.789 0.090

2 0.060 0.835 1.000 0.793 0.090

3 0.055 0.664 1.000 0.913 0.090

4 0.000 0.664 1.000 0.320 0.000

5 0.056 0.731 1.000 0.844 0.090

6 0.052 0.731 1.000 0.789 0.090

7 0.000 0.859 1.000 0.975 0.000

8 0.045 0.859 1.000 0.581 0.090

9 0.163 0.664 1.000 0.589 0.417

10 0.211 0.664 1.000 0.760 0.417

11 0.272 0.859 1.000 0.758 0.417

12 0.065 0.760 1.000 0.943 0.090

13 0.149 0.900 1.000 0.397 0.417

One other qualitative factor is added to the growth equation (2.6), the factor s(BAR). s(BAR) is the proportion unoccupied of the maximum potential stem area on the site, SOILQ.

s(BAR) = 1 - BAR/SOILQ (3.13)

= 1 - (BAR/SOILQ)

where BAR is the total basal area on the plot and SOILQ is the maximum allowed basal area. This was added to the model originally so that the model would include the forester's notion of site quality, or "site index" (Smith, 1986) that is as an upper limit to the number of trees that could be supported on a site. But the value of SOILQ is set to a very large number and functions only to prevent those rare cases where the abundance of trees would increase uncontrollably. The default setting of SOILQ is 20,000 for 100 m² (200 cm²/m²). In actual operation, the basal area does not approach values anywhere near the default level, and this comparatively arbitrary factor has little effect in practice on the dynamics of the model. Users of the model can vary this factor and test its effect. With these factors calculated, the growth, reproduction, and death of each species of tree can then be determined.

A summary of parameters appears in Table 3.6.

a Table 3.6 (A) is the same as Table 2.1; it is repeated here for the reader's convenience

AGE (n) DIAMETER(cm) HEIGHT(cm)

Sugar maple 400. 170. 3350. 37.8 0.111 118.7 1.570

Beech 366. 160. 3660. 44.0 0.137 87.7 2.200

Yellow birch 300. 100. 3050. 58.3 0.291 143.6 0.486

White ash 150. 150. 2440. 30.7 0.102 147.5 1.750

Mountain maple 25. 14. 500. 53.8 2.000 72.6 1.130

Strip.maple 30. 23. 1000. 76.7 1.700 109.8 1.750

Pin cherry 30. 28. 1126. 70.6 1.260 227.2 2.450

Choke cherry 20. 10. 500. 72.6 3.630 233.3 2.450

Balsam fir 200. 86. 2290. 50.1 0.291 102.7 2.500

Red spruce 400. 60. 2290. 71.8 0.598 50.7 2.500

White birch 140. 76. 3050. 76.6 0.504 190.1 0.486

Mountain ash 30. 10. 500. 72.6 3.630 155.6 1.750

Red maple 150. 150. 3660. 47.0 0.156 213.8 1.570

Scarlet oak 200. 30. 3050. 194.2 3.230 128.7 1.750

Hornbeam 150. 30. 1520. 92.2 1.530 144.4 0.486

Green alder 30. 5. 300. 65.2 6.520 143.3 2.000

Speckled alder 30. 8. 400. 65.8 4.100 196.9 2.000

Chestnut 200. 122. 2740. 42.7 0.175 195.2 1.750

Black ash 70. 60. 2130. 66.4 0.554 96.2 1.750

Butternut 90. 91. 3050. 64.0 0.352 192.2 1.750

White spruce 200. 53. 3350. 121.2 1.140 91.8 2.500

Black spruce 250. 46. 2740. 113.9 1.240 32.0 2.500

Jack pine 185. 50. 3050. 116.5 1.160 142.0 2.000

Red pine 275. 91. 3050. 64.0 0.352 156.4 2.000

White pine 450. 101. 4570. 87.8 0.435 141.2 2.000

Trembling aspen 100. 100. 3050. 58.3 0.291 173.7 0.486

White oak 600. 122. 3050. 47.8 0.198 72.0 1.750

Red oak 400. 100. 3050. 58.3 0.291 107.7 1.750

White cedar 400. 100. 2440. 46.0 0.230 35.7 2.500

Hemlock 600. 150. 3660. 47.0 0.156 86.0 2.000

Silver maple 125. 122. 3960. 62.7 0.257 164.8 1.570

Tamarack 200. 85. 3050. 68.5 0.403 86.3 2.000

Pitch pine 200. 91. 3050. 64.0 0.352 86.5 2.000

Gray birch 50. 38. 910. 40.7 0.535 119.5 0.486

American elm 300. 152. 3840. 48.7 0.160 180.0 1.600

Basswood 140. 137. 4270. 60.3 0.220 169.8 1.600

Bigtooth aspen 70. 60. 2130. 66.4 0.554 176.7 0.486

Balsam poplar 150. 100. 2440. 46.0 0.230 232.5 0.486

Black cherry 258. 91. 3050. 64.0 0.352 166.7 2.450

Red cedar 250. 60. 1520. 46.1 0.384 88.7 2.000

Sugar maple 3 2 6300 2000 0.567 0.350

Beech 3 2 6000 2100 0.489 0.350

Yellow birch 2 2 5300 2000 0.600 0.245

White ash 2 1 10947 2414 0.400 0.245

Mountain maple 3 2 6300 1800 0.489 0.274

Strip.maple 3 2 6300 2000 0.567 0.274

Pin cherry 1 1 6000 1100 0.567 0.378

Choke cherry 1 2 10000 1700 0.567 0.378

Balsam fir 3 3 3700 700 0.211 0.245

Red spruce 3 3 3800 1300 0.489 0.245

White birch 2 3 4000 700 0.544 0.378

Mountain ash 2 2 4000 1800 0.544 0.290

Red maple 2 3 12400 2000 0.322 0.450

Scarlet oak 1 3 8000 3900 0.933 0.450

Hornbeam 1 2 10300 2750 0.933 0.450

Green alder 2 3 3000 540 0.322 0.130

Speckled alder 2 3 5299 2174 0.211 0.050

Chestnut 2 3 8499 3686 0.933 0.450

Black ash 2 1 5300 1700 0.322 0.130

Butternut 1 2 6500 3200 0.933 0.450

White spruce 2 1 3750 600 0.544 0.245

Black spruce 2 3 3800 600 0.156 0.130

Jack pine 1 3 4000 1150 1.250 0.530

Red pine 1 3 4100 2000 1.250 0.500

White pine 2 3 6000 2100 1.000 0.450

Trembling aspen 1 2 5600 600 0.700 0.450

White oak 2 2 10204 2966 0.933 0.450

Red oak 2 2 9600 2400 0.933 0.450

White cedar 2 1 3700 1500 0.100 0.050

Hemlock 3 3 6559 2416 0.489 0.245

Silver maple 2 1 9000 2200 0.400 0.187

Tamarack 1 2 3800 600 0.156 0.050

Pitch pine 1 3 5800 3800 1.250 0.530

Gray birch 1 3 4800 2800 1.000 0.450

American elm 2 1 12000 1900 0.400 0.245

Basswood 3 1 6000 2300 0.567 0.290

Bigtooth aspen 1 2 6000 2100 0.400 0.187

Balsam poplar 1 1 4300 1000 0.400 0.378

Black cherry 2 2 10945 3899 0.567 0.378

Red cedar 1 3 10204 2966 0.700 0.450

COMMON NAME SCIENTIFIC NAME L N S_i

Sugar Maple Acer saccharum 3 2 3

Beech Fagus grandifolia 3 2 3

Yellow Birch Betula alleghanensis 2 2 15

White Ash Fraxinus americana 2 1 10

Mountain Maple Acer spicatum 3 2 2

Striped Maple Acer pensylvanicum 3 2 2

Pin Cherry Prunus pensylvanica 1 1 60

Choke Cherry Prunus virginiana 1 2 60

Balsam Fir Abies balsamea 3 3 2

Red Spruce Picea rubens 3 3 2

White Birch Betula papyrifera 1 3 10

Mountain Ash Sorbus americana 2 2 2

Red Maple Acer rubrum 2 3 3

Scarlet Oak Quercus coccinea 1 3 3

Hornbeams Ostrya & Carpinus 1 2 3

Green Alder Alnus crispa 2 3 10

Speckled Alder Alnus rugosa 2 3 10

Chestnut Castanea dentata 2 3 0

Black Ash Fraxinus nigra 2 1 3

Butternut Juglans cinerea 1 1 3

White Spruce Picea glauca 3 1 2

Black Spruce Picea mariana 2 3 2

Jack Pine Pinus banksiana 1 3 50

Red Pine Pinus resinosa 1 3 3

White Pine Pinus strobus 2 3 4

Trembling Aspen Populus tremuloides 1 2 10

White Oak Quercus alba 2 2 10

Northern Red Oak Quercus rubra 2 2 10

White Cedar Thuja occidentalis 2 1 2

Eastern Hemlock Tsuga canadensis 3 3 3

Silver Maple Acer saccharinum 2 1 2

Eastern Larch Larix laricina 1 2 10

Pitch Pine Pinus rigida 1 3 2

Gray Birch Betula populifolia 1 3 10

American Elm Ulmus americana 2 1 3

Basswood Tilia americana 3 1 3

Bigtooth Aspen Populus grandidentata 1 2 3

Balsam Poplar Populus balsamifera 1 1 3

Black Cherry Prunus serotina 2 2 10

East. Red Cedar Juniperus virginiana 1 3 3

L is the light tolerance type; N is the nitrogen tolerance type; and S_i is the maximum number of saplings that can be added in any single year. For Both tolerance types, 1 = intolerant, 2 = intermediate, and 3 = tolerant. Note that S_i is large for type

L =1.

This chapter describes the influence of the environment on tree growth, mortality, and species reproduction, as these are expressed in the model. Mathematically, the response of a tree to each environmental factor can be expressed as a function that has values from 0 to 1 (or in some cases more than 1), which affects the fundamental growth equation (2.1) and (2.6). Each of these relationships is called a response function. A tree responds to the totality of environmental conditions, and a fundamental question is how this response integrates all the individual effects of separate environmental factors. Models can use additive or multiplicative interactions of environmental factors. JABOWA uses multiplicative interactions of light, temperature, drought, soil-water saturation, and soil nitrogen content. Each involves specific assumptions about the relationship between environmental conditions and tree growth and species regeneration. The assumptions, rationales, and mathematical forms of each response function were described. Other assumptions are inferred by the model. These include: (1) only four environment factors are required to explain the dynamics of trees in a forest: light, temperature, soil nitrogen, and soil moisture; (2) spatial position of a tree within a plot does not matter, as long as the plot is small enough so that a tall tree can shade all of its neighbors within the plot during a year; (3) seeds are available from an unlimited pool; reproduction and regeneration are limited by germination and growth conditions, not by the availability of seeds; (4) impact of herbivores can be ignored (or assumed to occur at a constant, time-invariant rate); (5) soil decomposition can be ignored (feedbacks between soil decomposition rates and the availability of nutrients does not affect the dynamics); and (6) growth is deterministic - regeneration and mortality are stochastic functions.

With the material provided in Chapters 2 and 3, it is now possible to use the model and explore its implications for the dynamics of forest ecosystems. This is the topic of the next chapter.

This is a graph of E_i for several species, including pin cherry, white and yellow birch, sugar maple and beech.