SCOPE 21 -The Major Biogeochemical Cycles and Their Interactions 

ABSTRACT

A model is proposed to interrelate carbon, nitrogen, phosphorus, and sulphur in individual organisms and simple ecosystems. The objective is to relate differences in nutrient cycling patterns among C, N, S, and P to their fundamental chemical properties, to information from microbial physiology and trophic ecology, and to current theories about the formation and decomposition of soil organic matter.

The model distinguishes fungi from bacteria and includes a trophic structure with amoebae feeding on bacteria and nematodes feeding on fungi. The biomass of organisms is divided into three functional categoriesthe structural component, synthetic machinery, and stored material. Variation in these functional categories is related to expected patterns of variation of C:N, C:S, and C:P ratios. The amount of structural material also is used to predict the digestibility of prey and the kinds of substrates generated when organisms die.

Humic materials are divided into chemically protected, aggregate protected, and resistant fractions. The aggregate protected fraction is formed through the adsorption of soluble organic material excreted by living organisms or released when organisms die. Chemically protected humic material is formed by a reaction between soluble organic matter and the aromatic cores released during the decomposition of the structural component of plants. Partial decomposition of the chemically and aggregate protected fractions leaves the resistant fraction as residue.

Five classes of chemical bonds, C-C, C-N, C-S, C-O-S, and C-O-P, are distinguished in each of the organic substrate pools. The use by microbes of soluble organic material in the five bond classes is assumed to be regulated by demand as reflected in microbial element ratios. The two ester linkages, C-O-S and C-O-P, are distinguished from the other bond classes by their susceptibility to the action of esterases.

The model yields predictions about the relative turn-over times of C, N, S, and P, and about the constraints on variation in element ratios of living organisms.

10.1 INTRODUCTION

Element cycling can be viewed from a variety of perspectives, ranging from global cycles with exchanges among land, oceans, and atmosphere, through the movement of substances within a single ecosystem, and to a consideration of the constraints on the elemental composition of single organisms. Studies at all these levels of resolution are legitimate, although the objectives necessarily differ. In this paper we direct our attention to interactions among C, N, S, and P at the level of individual organisms and simple ecosystems. An understanding of element cycling at this level should facilitate the study of biogeochemical cycling on a global scale.

Simulation modeling has been a useful tool for understanding grassland ecosystems. This paper describes the first step in the construction of a simulation modeldefining the general structure (state variables) of the system and describing the processes transferring material within the system. Eventually the model will be converted to an operational simulation model and its performance compared to data on C, N, S, and P transformations in soil. The model is based largely on information from native and managed grassland ecosystems and agricultural systems replacing them, although it may have wider applicability.

The principal objective of the model is to integrate the concept of chemical bond classes (McGill and Cole, 1981) with our current understanding in two general areas of study. The first area is the variability in element ratios of organisms and the possible importance of trophic interactions in soil (Coleman et al., 1978). The second area is the chemical composition of soil organic matter and the processes of its formation and decomposition. The recognition of bond classes may advance understanding in both of these areas and help in relating them to each other.

10.1.1 Modelling Approaches to Element Interactions

Methods of modelling several elements simultaneously have changed considerably over the past few years. In ELM, a total system model for C, N and P in grasslands (Cole, 1976; Innis, 1978), the elements were treated in separate submodels. The C, N, and P submodels interacted with each other only to a limited extent. For example, the P model, but not the N model, distinguished microbes from dead plant material, while the C model not only separated microbes from their substrate but included separate state variables for active microbes and resting stages. Such disparities in model structure do not lead to a mechanistic treatment of interactions among elements.

McBrayer et al. (1974) constructed a model of forest litter decomposition that was basically for energy or biomass flow. Nutrients (N, P, etc.) were included but were assumed to passively follow biomass. Several aquatic modelsone for transfer of C, N, and P through a phytoplanktonzooplankton food web (Canale et al. 1976), and the other through a decomposer food web (Clesceri et al., 1977)also assume fixed element ratios. In this approach, element ratios of a consumer may differ from those of its food, but must be brought into line through the release of organic or inorganic waste products.

A few models allow organism element ratios to vary. Hunt et al. (1977) modelled C, N, and P of bacteria in continuous culture. They assumed fixed, but different, element ratios for the cell wall and for synthetic machinery (enzymes and RNA). Small molecules in the cytoplasm had variable element ratios. Whole cell composition depended on the ratio of walls to synthetic machinery, as well as on the amounts of NH₄⁺ , PO₄^3-, and stored glycogen and polyphosphate in the cytoplasm. This model handled element interactions implicitly, but required too much detailed information about cell physiology to be practical for use in a total system model. In a less mechanistic approach, element ratios of whole organisms were used to regulate consumption of resources and production of wastes (McGill et al., 1981; Cole et al., 1983). Such a feedback mechanism allows the ratios to vary within reasonable limits.

This paper outlines a scheme for modelling C, N, S, and P transfers in ecosystems. The approch is similar to some of the models described above in that biomass is divided into functional categories (walls, storage products, etc. ) and element ratios vary within limits. Many features of the model are taken with little or no modification from models of C and N cycling in grasslands (McGill et al., 1981), C, N, and P content of bacteria in liquid culture (Hunt et al., 1977), and C, N, and P transfers in simple food webs in soil (Cole et al., 1983). The most important addition to the concepts in the above models is the distinction among elemental bond classes. The relevance of these bond classes to grassland ecosystems is elaborated by Stewart et al. (Chapter 8, this volume) and by McGill and Christie (Chapter 9, this volume).

10.2 BACKGROUND AND REVIEW 

10.2.1 Bond Classes

Carbon, nitrogen, sulphur, and phosphorus are involved in both biochemical and geochemical reactions. Halstead and McKercher (1975) related the predominance of hydrogen, oxygen, nitrogen, and carbon in living tissues to their status as the smallest elements of the periodic system that achieve stable electron configuration by addition of 1, 2, 3, and 4 electrons respectively. They also form relatively stable covalent bonds and C, N, and O participate in multiple bonding.

Phosphorus and sulphur, in contrast to oxygen and nitrogen, are essential as agents for the transfer of chemical groups and energy during biosynthesis. The ability of phosphorus and sulphur to act as transfer agents may be explained on the basis of their bonding energy. Both phosphorus and sulphur, but not nitrogen, may expand covalent linkages beyond 4 through their 3d orbitals. Thus they can form multiple bonds, a characteristic seeming to require small atoms that can exist in proximity to others. This characteristic is responsible for the large number of resonance structures available to phosphorus and, in turn, for the high free energy changes associated with phosphorus group transfer reactions.

Orthophosphate ions (H₂PO₄^-, HPO₄^2-, PO₄^3-) are the principal forms of P found in an oxidizing environment. Phosphonates (C-P) have been found in moist top-soils in New Zealand (Newman and Tate, 1980), and polyphosphate (P-O-P) (Anderson and Russell, 1969; Pepper et al., 1976) and other non-orthophosphate phosphorus (Beever and Burns, 1976) occur in soil and microbes. Presumably, other P-C, P-N and P-S linkages exist, but phosphate esters (C-O-P) must be considered the predominant form of organic phosphorus in soils. Phosphate esters, such as inositol phosphates (up to 60% of the total organic phosphorus), nucleic acid phosphorus (5 to 10%) and phospholipid phosphorus (<1%), are bonded to soil organic and inorganic components by mechanisms such as adsorption and are generally less a part of soil humic materials than organic nitrogen or sulphur (Scott and Anderson, 1976).

Sulphur exists in multiple oxidation states ranging from +VI in SO₄^2-and its derivatives to II in H₂S and its derivatives. Intermediate oxidation states include 0, +II, and +IV. Reduced forms of S exist in sulphoamino acids, co-enzymes and in major cellular metabolites such as glutathione. Oxidized sulphur, mainly in the form of sulphate esters, also is prevalent in many organisms. In soils most of the S occurs in organic rather than an inorganic state (Biederbeck, 1978; Kowalenko, 1978). Soil organic S is generally divided into two major fractions, namely carbon bonded sulphur and ester bonded sulphur (C-S and C-O-S) (reviewed by McGill and Christie Chapter 9, this volume and by Stewart et al. Chapter 8, this volume).

McGill and Cole (1981), in a comparison of organic C, N, S, and P cycling through soil organic matter during pedogenesis, proposed that element cycling can best be interpreted within the framework of a dichotomous system. In this system, elements considered to be stabilized as a result of covalent bonding with C (C-N and C-S) are mineralized during C oxidation to provide energy, whereas those elements existing as esters (C-O-S and C-O-P) are stabilized through reaction of the ester with soil components and may be considered to be mobilized by the need for the element. McGill and Cole also reviewed published information on soil organic matter composition and its changes with time, across environmental gradients and with cultivation. Their conceptual model appears to provide a feasible, rational framework within which the interrelations of C, N, S, and P may be interpreted on both geological and biological time scales. Data from a wide range of soils appear to be consistent with their model. We will further apply this concept by examining the variability in the composition of decomposers, whose activity and turn-over affect the soil organic matter content and composition.

10.2.2 Element Ratio and Variability within Organisms

Biological approaches have been used to measure dynamics of nutrient transformations in soils (Stewart and McKercher, 1981). The techniques require an understanding of microbial biomass, its activity and its varying elemental composition. A method to estimate microbial biomass C has been developed in which the live biomass is made susceptible to mineralization by chloroform fumigation and the subsequent flush of CO₂ gives a measure of soil biomass (Jenkinson and Powlson, 1976). Anderson and Domsch (1978a, b) examined this chloroform fumigation technique using 15 soil fungus species, 12 soil bacteria species and 4 different types of soils. Using the above CHCl₃ techniques, Paul and Voroney (1980) and Voroney et al. (1981) suggested a method for the determination of biomass N in soils. Hedley and Stewart (1982) proposed a method to measure the biomass P in calcareous soils by using a chloroform treatment to lyse the microbial cells and measuring the P released to 0.5 m NaHCO₃ extracts. Saggar et al. (1981a) recently developed a technique to estimate the amount of sulphur held by the microbial population in soil. This method involves lysing the microbial cells with cloroform and measuring the S released to 10 mM CaCl extracts. Therefore it is possible to examine the composition of the microbial biomass in soils to supplement information derived from growth of microbial populations in pure cultures.

From these studies it becomes clear that bacteria and fungi differ in the forms of N, S, and P immobilized and this alters subsequent redistribution of organic N, P, and S. Perhaps the clearest distinction is with sulphur. Both bacteria and fungi accumulate sulphate, and at lower concentrations most of the sulphate is converted to amino acids (C-S bonds). At higher soil solution concentrations bacteria do not accumulate excess sulphate whereas fungi have the ability to store sulphate as organic sulphate compounds (C-O-S bonds).

10.2.3 Soil Organic Matter

Of the numerous approaches to the study of soil organic matter, our ideas have been most influenced by information on changes across environmental gradients and changes associated with cultivation.

Changes in soil organic matter content and quality are thought to be affected by temperature and moisture and accelerated by cultivation. Sites selected across moisture and thermal gradients differ in soil organic matter composition. Various approaches to fractionation and characterization of soil organic C, N, P, and S have been tested. One approach follows ideas on the processes of humus formation and transformation in soils of the North American Great Plains and the methodology developed by Anderson, Paul, and co-workers for the Northern Great Plains (Anderson et al., 1974; McGill and Paul, 1976; McGill et al., 1975; Paul and McGill, 1977; Paul and Van Veen, 1978; Anderson, 1979; Paul and Voroney, 1980). This approach involves extraction and characterization of humus from paired virgin and cultivated soils selected along environmental gradients. Humus is extracted in a NaOHNa₄P₂O₇ solution in combination with sonication treatments to isolate material described as clay-associated humic and fulvic organic matter, in addition to conventional humic, fulvic, and humin fractions. This methodology has been useful in explaining changes in the quantity and quality of organic matter with particular reference to C, N, and S content (Bettany et al., 1974, 1979, 1980; Anderson et al., 1981). The successful use of this technique has been through linkage of methods of assessing biological availability with specific soil fractionation techniques (Oades and Ladd, 1977).

A second approach attempts to separate soil organic matter on a physical size basis without using any strong chemicals and with only enough ultrasonic energy to aid in separation but not enough to cause a major disruption in chemical bonding (Genrich and Bremner, 1974; Turchenek and Oades, 1979; Cameron and Posner, 1979; Young and Spycher, 1979). Use of physical size separation in combination with chemical fractionation has revealed differences in composition and turn-over time of C associated with physical size fractions. These results have implications for N and S availability (Anderson et al., 1981) .

Both of the above approaches fall short of defining soil organic matter fractions that are mechanistically related to the processes of organic matter formation and decomposition. Thus, nutrient cycling models tend to treat soil organic matter empirically. A variety of models have been used to represent long term changes in soil organic matter composition. Initial models assumed the decomposition of organic matter to be constant and did not allow for changes in decomposition rate resulting from changes in the composition of soil organic matter. Campbell et al. (1976) improved upon this model by dividing soil organic matter into stable organic matter and relatively labile organic matter with turn-over times of 1429 years and 53 years respectively. Paul and Van Veen (1978) further improved the model by dividing the plant residue into recalcitrant and decomposable fractions and by introducing the concept of physically protected and non-physically protected soil organic matter. Critical assumptions in their model are that physically protected organic matter has a much lower decomposition rate than non-physically protected organic matter and that the percentage of physically protected soil organic matter is greatly decreased by cultivating the soil. Jenkinson and Rayner (1977) developed a model in which soil organic matter was represented by five compartments: decomposable plant material, resistant plant material, soil biomass, physically stabilized organic matter, and chemically stable organic matter.

10.3 MODEL STRUCTURE

10.3.1 Overview

Figures 10.1 and 10.2 present most of the state variables and transfers for a model of microbes and their consumers growing in soil in the absence of a plant. Each figure simplifies different aspects of the model for the sake of clarity. All the boxes except for inorganic compounds and aromatic cores actually represent a series of state variables. For substrates this series consists of the five chemical bond classes C-C, C-N, C-S, C-O-S, and C-O-P. For live organisms the series consists of the elements C, N, S, and P. It seems impractical to describe mechanistically the dynamic biochemical reactions and interconversions of material among bond classes within living organisms.

Figure 10.1 Soil biota and their relationships to organic and inorganic substrates. The four organism compartments each include state variables for C, N, S and P. For a complete presentation of organic substrates see Figure 10.2

Figure 10.2 Soil organic matter fractions and their transformations. Each substrate compartment includes state variables for the five chemical bond classes. See Figure 10.1 for a disaggregation of decomposers

Amoebae are assumed to be the most important consumers of bacteria, and nematodes the main consumers of fungi (Figure 10.1). Bacteriovorus nematodes may feed on amoebae (Coleman et al., 1978), but fungivorus nematodes have a stylet, in common with plant feeders (Lee and Atkinson, 1977), and would not be expected to eat amoebae. This particular trophic structure is feasible for axenic microcosms but is probably an oversimplification for natural grasslands.

The model assumes spatial homogeneity and predicts only biomass, not numbers or age structure of populations. The assumptions of the model are described in greater detial in the following sections.

10.3.2 Cell Composition and Element Ratios

Cell walls are distinguished from synthetic machinery because these two components have different element ratios, and because the ratio of walls to machinery probably varies with cell size, which depends on growth rate (Hunt et al., 1977). Walls and synthetic machinery are described as `constitutive' because we assume that their chemical compositions are constrained within fairly narrow limits compatible with their function.

Table 10.1 shows the kinds of chemical compounds characteristic of the chemical structural classes. The levels of inorganic N, P, and S in cell walls are assumed to be insignificant. Phosphorus is assumed never to be stored in an organic compound. S-containing amino acids should not be stored if growth is limited by either C, N, or S, and limitation by P should not eliminate the incorporation of protein into walls and synthetic machinery. Thus we assume there is no material in the C-S fraction of `storage'.

Table 10.1 Substances typical of bond classes in different parts of a cell

The C:N:P ratios of bacterial walls and synthetic machinery are about 15:3.6:1 and 17:7.8:1, respectively (Hunt et al., 1977). Coughenour et al. (1980) reported a C:S ratio of 210 for bacterial walls and 3575 for a `metabolic' component, which includes both storage and synthetic machinery. If C: S in the high end of the range reported by Coughenour et al. represents a metabolic component lacking stored S, then the C:S ratio of synthetic machinery may be taken as 75. This yields an N:S ratio of 30, which is in the range of 1446 for bacterial soluble proteins (from data in Laskin and Lechevalier, 1973). If the chemical composition, and thus the element ratios, are invariable for walls and for synthetic machinery, then variation in whole cell element ratios will result partly from changes in the ratio of walls to machinery, but more importantly from variation in the amounts of stored materials, since there are few functional constraints on the element ratios of stored material.

Table 10.2 shows the 15 possible combinations of growth limiting elements and the kinds of storage materials expected in each case. The table examines only extreme cases, not recognizing degrees of limitation. Assuming that variation in whole-cell element ratios is largely attributable to storage materials, we have included in Table 10.2 the predicted element ratios for each case. For these predictions, we assume that extreme element ratios (high or low) can exist only when stored materials are unbalanced. For example, when both N and S are much more limiting than either C or P, the organism will accumulate both C-C and PO₄^3-. Thus the C:P ratio will be intermediate. Since there are no N or S reserves, C:N and C:S ratios will have high values. Similar reasoning was used to predict element ratios for each combination of limiting elements.

Only 15 of the 27 (3³) possible combinations of high, intermediate and low ratios of C to N, S, and P are represented in Table 10.2. For example, if C:N is high, stored C-C must be present and neither C: S or C: P can be low. However, the three ratios all can be high, or all low, at the same time. Thus the region in 3-dimensional space circumscribing possible element ratios is asymmetrical (Figure 10.3). In the model the region is approximated by an ellipsoid of the form

K =	((nn1)2 + (ssl)2 + (pp1)2)1/2
	+ ((nn2)2+ (ss2 )2 + (pp2 )2)1/2	(1)

where (n, s, p) are points on the surface of the ellipsoid, the points (n₁, s₁, p_l) and (n₂, s₂, p₂) are foci, and K determines eccentricity.

When organisms die or release wastes, the substrate generated must be allocated among inorganics and the bond classes of particulates and soluble organic matter, and the allocation is calculated from the C:N:S:P ratio of the dying organism. This prediction is made by assuming that cells do not store materials that could be converted into the constitutive fraction, and that the ratio of walls to synthetic machinery is a linear decreasing function of growth rate, which depends on the level of the limiting element. From these two assumptions and the fixed element ratios of walls and synthetic machinery, the C, N, S, and P of the organism can be allocated into the constitutive fraction in such a way that the most limiting element is exhausted. The storage component will then receive the excess of non-limiting elements, but none of the limiting element. The material assigned to walls and to synthetic machinery is distributed among the chemical classes (Table 10.1) in fixed proportions. Material assigned to storage is distributed among storage compounds (Table 10.2) in variable proportions chosen to accommodate all the material.

Table 10.2 Relationship between limiting elements and storage materials (+ indicates storage; no storage)

	Storage compound						Whole Cell Element ratio*
Limiting	Glycogen,	Amino	Choline SO42-	NO3-	PO43-	SO42-	C:N	C:S	C:P
element(s)	starch	acids	CN and	and
	CC	CN and	COS	NH4+
		CS
C				+	+	+	lo	lo	lo
N	+				+	+	hi	me	me
P	+	+	+	+		+	me	me	hi
S	+			+	+		me	hi	me
CN					+	+	me	lo	lo
CP				+		+	lo	lo	me
CS				+	+		lo	me	lo
NP	+					+	hi	me	hi
NS	+				+		hi	hi	me
PS	+			+			me	hi	hi
CNP						+	me	lo	me
CNS					+		me	me	lo
CPS				+			lo	me	me
NPS	+						hi	hi	hi
CNPS							me	me	me
*lo = low, hi = high, me = intermediate.

Figure 10.3 Ellipsoid containing the possible values of CN, C/S and C/P. The foci are the two points on the line within the figure

More information is needed on the chemical composition of the structural component of plants and microbes, and on the kinds and amounts of storage materials they can accumulate. The above approach provides a framework for relating such information to growth in soil.

10.3.3 Respiration

Respiration is modelled by assuming a fixed maximum yield (Y = 0.6) with respect to carbon. Thus a fraction (1 Y = 0.4) of carbon taken up, plus a maintenance component proportional to biomass, is lost as CO₂ (Hunt, 1977). 

10.3.4 Soil Organic Matter Fractions

Figure 10.2 includes three kinds of stabilized soil organic matterchemically protected, aggregate protected, and resistant (Paul and Van Veen, 1978; Anderson, 1979). Chemically protected organic matter results from reactions between the aromatic breakdown products of lignin and soluble organic material, especially proteins. Aromatic cores are released from the C-C fraction of particules during decomposition. The rate of supply of these cores will vary with the degree of lignification of particulates, which depends on plant species and phenological stage. Aggregate protected organic matter results from the strong adsorption of some soluble organic matter compounds. The extent of this adsorption varies among soils depending on the extent and reactivity of colloidal surfaces. Resistant organic matter, the refractory residue left behind after enzymatic attack of aggregate- and chemically-protected organic matter, corresponds to the HA-A fraction in the scheme of Anderson (1979).

Our treatment of soil organic matter fractions follows that of McGill et al. (1981), except that we have represented bond classes and that McGill et al. combined the aggregate- and chemically-protected fractions into a single compartment.

10.3.5 Decomposition and Uptake

Use of a substrate by microbes is governed by the substrate's physical state and chemical composition, and by the microbes' demand for that substrate and innate ability to use it. We assumed that fungi are better able to break down particulates and bacteria better able to take up soluble organic matter. The effects of demand are realized through inducible exo-enzymes and carrier proteins. Consumption will be regulated in order to maintain microbial element ratios within limits. Figure 10.4 shows the effects of element ratios on the `demand factors' (Dcn, Dcs, etc.) used to regulate uptake, and Table 10.3 shows how these demand factors are combined together in their effects on uptake. For example, the C-S component should be taken up if the biomass is limited either by C (low ratios of C: N, C: S and C: P) or by S (high C: S ratio).

A. Particulates

The use of a MichaelisMenten equation (see below) for breakdown of particulates is inappropriate, because particulates are not in solution, and because they are both substrate and habitat to microbes (McGill et al., 1981). If we assume that most bacteria and fungi are intimately associated with substrate particles, then none of them are in any sense limited by the concentration of substrate. Decomposition rate will be determined by the quality of substrate and by the quantity of biomass, unless some environmental factor not included explicitly in our model, such as pH or O₂ concentration, is altered. For these reasons we adopt the decomposition equation of McGill et al. (1981) for rate of decomposition U_s(µg C(g soil)^-1 hr^-1).

Figure 10.4 The effects of bacterial element ratios on demand factors. See Table 10.3 for the relationship between demand factors and demand D used in the uptake equations

  where M (µg C(g soil)^-1) is biomass, X is level of particulates (µg C(g soil)^-1), K is the maximal rate (hr^-1) depending on substrate quality, D is demand, and K₁ and K₂ are parameters. The form of equation (2) is empirical, and was chosen to represent our best understanding of particulate decomposition (McGill et al. 1981).

The various bond classes of particulates are assumed to decompose (i.e. to be reduced by exo-enzymes to small molecular weight soluble organic compounds) at the same rate because of their intimate physical association (however, see the action of esterases, below). A residual fraction (1%) of the particulate C-C decomposed becomes aromatic cores (Figure 10.2) which lead to the formation of chemically protected organic matter.

Breakdown products of decomposing substrates might be taken up immediately by the microbes responsible for the hydrolysis. Soil factors determining rate of diffusion will affect the rate of dispersal of these products to a common pool shared by other microbes. A variable fraction of decomposing material is allowed to enter the soluble pool, with the rest taken up directly (Figure 10.2). Sensitivity analysis of the model will be used to study the effects of varying the fraction entering the soluble pool.

B. Soluble Organic Matter

The material most readily available to microbes is soluble organic matter released when organisms die and their cells lyse. This material is mostly adsorbed onto clays and soil organic matter, but is readily desorbed to establish a new equilibrium when material is taken up from solution by microbes. The dissolved and adsorbed phases are not modelled separately, but solution concentration is predicted from a Freundlich isotherm, following McGill et al. (1981). Part of the C-O-P fraction of soluble organic (inositol phosphates) is adsorbed particularly strongly, and its adsorption is treated separately from the other fractions, which are assumed to be adsorbed to an equal extent and to compete for the same adsorption sites in the soil.

Uptake of each of the bond classes is governed by a separate Michaelis-Menten equation with different parameters. Rate of uptake, U (µg(g dry soil)^-1 hr^-1) is

where D is demand (Table 10.3), V_m (µg element (µg (biomass C)^-1 hr^-1)is the maximal uptake rate, X (µg ml^-1)isthesubstrate solution concentrations, K_s (µg ml^-1) is the half-saturation constant for uptake, and M is biomass (µg C(g dry soil)^-1).

Uptake of inorganic N, P, and S is also governed by equation (3). Solution concentrations of PO₄^3- and NH₄⁺ are predicted from Langmuir isotherms, while NO₃^- and SO₄^2- are assumed to be entirely in solution.

C. Protected and Resistant Fractions

We assume that the breakdown of these relatively unavailable soil organic matter fractions is a side effect of the activity of enzymes released in the decomposition of particulates. Thus their decomposition rate will correlate with the rate of breakdown of particulates. In the model the rate is assumed to be proportional to U_S (equation 2).

Chemically- and aggregate-protected organic matter, when attacked by enzymes, yield small molecular weight substances released to the soluble organic pool and a resistant residue, which is transferred to the `resistant' state variable (Figure 10.2). The aliphatic peripheral portions of chemically-and aggregate-protected materials apparently are attacked enzymatically more readily than are the more aromatic interior portions (Anderson, 1979). In the model, when chemically- and aggregate-protected organic matter decomposes, part of the material goes to the soluble pool and part to resistant soil organic matter (Figure 10.2). A relatively higher fraction of the C-C bond class than the other bond classes is sent to the soluble pool. Thus the C:N, C:S and C:P ratios of resistant material will tend to be lower than that of chemically- and aggregate-protected organic matter.

The effect of cultivation on soil organic matter levels has been represented as an effect on the availability of the chemically- and aggregate-protected fractions (Paul and Van Veen, 1978), although Parton et al. (1981) suggested that changes in soil temperature, soil water, and rate of primary production are sufficient to account for observed changes.

D. Action of Estereases

Probably the most significant qualitative difference among the element cycles is the importance of exo-enzymes in mineralizing organic P and the C-O-S fraction of organic S. Although exo-enzymes may decompose macromolecular C-C and C-N, mineralization of C and N are essentially intracellular processes. Externally released esterases are produced facultatively when microbes or plants experience P or S limitations. Not enough is known about the quantities (in units of mass, as well as activity) of esterases released in soil, or their stability, to include phosphatases and sulphatases explicitly as state variables in the model. Thus the model treats esterases as though they were released instantly when needed, at no cost to the organism, and with zero residence time.

The reactions are represented as: 

C-O-PC-C + PO₄^3-

C-O-SC-C + SO₄^2-

Thus when P is transfered from the C-O-P state variable to PO₄^3-, a corresponding amount of C is transferred from C-O-P to C-C.

The reactivity of esters is assumed to depend on the form of the substrate, being most available in the soluble organic pool, followed by particulates, aggregate-protected, chemically-protected, and resistant soil organic matter, in that order.

The rate of transfer of S in C-O-S to S in SO₄^2- (R, (µg S(g soil)^-1 hr^-1) is

where K is a constant depending on the substrate, E is the concentration of ester SO₄ (µg S(g soil)^-1), M is microbial biomass (µg C(g soil)^-1), and D_s is microbial demand for S (Table 10.3). Transfer of C-O-P to PO₄^3- is handled similarly.

10.3.6 Release of Wastes

When microbes are limited by one element, they should take up all compounds containing that element at the maximal rate, whether or not these compounds contain non-limiting elements in excess of the organisms' needs. In this situation, the excess material will be released into the soil solution as metabolic wastes. The section `Cell Composition and Element Ratios', above, describes how microbes' content of storage materials can be predicted from their element ratios. This provides a natural way to predict the rate of production of wastes. When the fraction of an organism's S (C, N, P) in storage materials exceeds a fraction f_S (f_C, f_N, f_P), the excess is excreted. If both organic and inorganic storage compounds are present in excess, both forms are excreted in the ratio they exist in the organism.

Bacteria in solution culture are known to release considerable organic wastes (Cooney et al., 1976), and the general scheme described above has proved to be useful for predicting waste production (Hunt et al., 1977). The approach is distinctive because it places mineralization in the context of waste production. 

10.3.7 Consumption by Amoebae and Nematodes

In modelling the consumption of bacteria by amoebae and by nematodes (Cole et al., in preparation), we have assumed that a number of bacteria are protected within small, water-filled soil pores (Elliott et al., 1980) and that at extremely high levels of bacteria, the predator becomes `saturated.' These characteristics are exhibited by a Michaelis-Menten equation, with the substrate level taken as bacterial biomass in excess of the protected level. The particulars of these equations are not critical to the present discussion.

The proposed breakdown of microbial cells into functional and chemical classes (Table 10.1) provides an opportunity to relate the digestibility and nutritive value of microbial prey with their elemental composition. In particular, we assume that the synthetic machinery and storage components are entirely digestible, but that cell walls are only slightly digestible. Inorganic N and S, although perfectly digestible, are of no use to amoebae or nematodes, and will be rapidly excreted. Orthophosphate will be assimilated and retained as needed. The digestible parts of C-C, C-N, C-S, and the carbon skeletons of C-O-S and C-O-P will be assimilated. Since bacteria and fungi have relatively low C:N, C:S and C:P ratios, their consumers will probably always be C or energy limited, and excess N, S and P will be mineralized.

The release of metabolic wastes by amoebae and nematodes can be predicted in a manner analogous to that used for microbes. It is only required to divide animal biomass into walls, synthetic machinery, and storage as in Tables 10.1 and 10.2. Obviously some modifications will be required to apply the approach: amoebae lack walls; nematodes exoskeletons are chemically very different from microbial cell walls, but like microbial cell walls, offer a greater resistance to decomposition; the kinds of substances stored by amoebae and nematodes (C-C) will be less diverse than for microbis. Nevertheless, the same approach should be capable of predicting waste production of a variety of organisms, with only quantitative changes to model parameters.

10.4 TESTS OF THE MODEL 

We plan to test the model by adapting it to laboratory data on C, N, P, and S transfers in phosphate, sulphate and cellulose amended soils (Saggar et al., 1981b; Chauhan et al., 1981). Eventually the model will be coupled to a primary producer model (Detling et al., 1979), and heat and water flow models (Parton, 1978) in order to predict dynamics of C, N, S, and P in the field. Although the model cannot yet generate quantitative predictions, careful examination of its structure can yield predictions about its qualitative behavior. For example, McGill and Cole (1981) and McGill and Christie (Chapter 9, this volume) deduced many consequences of the chemical bond class concept for soil organic matter compositionits changes during soil development and its response to cultivation. The concept was generally successful in accounting for observed trends.

Several additional behaviours of the model can be deduced. These predictions, if they should prove realistic, will lend credence to the validity of the model.

The first prediction, already developed in a previous section, is that element ratios are constrained in such a way that high values of one element ratio never coincide with low values of another. Element ratios are determined mainly by an organism's content of storage materials, but are also affected by the ratio of the more carbon-rich structural component to the less carbon-rich synthetic machinery. The structural component of terrestrial plants generally has much higher C:S, C:N and C:P ratios than that of bacteria. Thus, plants will have higher and more variable element ratios than bacteria, assuming there is no great difference in the degree to which plants and bacteria can accumulate storage products. Fungi are probably intermediate between plants and bacteria.

Amoebae and nematodes, in general, will store only an energy source (C-C), and not N, S, or P. For animals such as amoebae, lacking a significant structural component, the N:S and N:P ratios will show minimal variation. Ratios of C:N, C: S, and C: P will therefore tend to vary together, depending on how `fat' the amoeba is, and the ellipsoid in Figure 10.3 would tend to collapse to a line.

Nematode cuticles consist largely of protein with C:N:S of 43:16:1 (from data of Fujimoto and Kanaya, 1973), so the C:N and C:S ratios should differ little from internal tissues. Presumably cuticles are low in P. If so, C:N and C:S will vary together, as in amoebae, but C:P will vary with the ratio of cuticle to weight (size) of the animal as well as fat stores. Thus, the region of possible element ratios for nematodes will approach a plane perpendicular to the C: N C: S plane (Figure 10.3).

The second prediction concerns the turn-over time of elements in the various substrate pools (Figure 10.2). The model assumes that, due to the physical intimacy of the various compounds in particulates, and due to the aggregate nature of the three less available soil organic matter fractions, the five bond classes decompose at rates proportional to their relative abundance. However, P and a fraction of the S can be mobilized to some degree from these pools by an additional process, the action of esterases. Thus, the turn-over times for elements will decrease in the order CN > S > P, within a substrate pool. Of course, the turn-over times for all elements in the resistant pool are greater than in particulates. This ordering of turn-over times will not necessarily hold within the soluble organic pool, since uptake from each of the various bond classes is regulated independently.

In a system long limited by S, the C-O-S fraction should be greatly reduced in all pools, and sulphatases cannot speed S transfer. In this case the turn-over time of S will be similar to that of N and C. In a system only occasionally limited by S, S limitation will lead to the production of sulphatases which will act on the C-O-S pool, and the turn-over time of S will be less than that of C or N. In a system never limited by S, there will be no occasion for the induction of sulphatases. The turn-over time of C-S will equal that of C and N, and that of C-O-S will exceed that of C and N. Thus the turn-over time of S will exceed that of C and N.

The qualitative predictions deduced in this section will be compared to quantitative predictions generated by simulation in a future paper. In the meantime, we invite communication from workers who have data to test the predictions.

We thank W. B. McGill for several insightful comments on the model. 

10.5 REFERENCES

Anderson, D. W., Saggar, S., Bettany, J. R., and Stewart, J. W. B. (1981) Particle size fractions and their use in studies of soil organic matter. I. Nature and distribution of forms of carbon, nitrogen, and sulfur, Soil Sci. Soc. Amer. J., 45, 767-772.

Anderson, G., and Russell, J. D. (1969) Identification of inorganic polyphosphates in alkaline extracts of soils, J. Sci. Fd. Agric., 20, 78-81.

Anderson, J. P. E., and Domsch, K. H. (1978b) A physiological method for the quantitative measurement of microbial biomass in soils, Soil Biol. Biochem., 10, 215-221

Bettany, J. R., Saggar, S., and Stewart, J. W. B. (1980) Comparison of the amounts and forms of sulfur in soil organic matter fractions after 65 years of cultivation, Soil Sci. Soc. Amer. J., 44, 70-75.

Bettany, J. R., Stewart, J. W. B., and Saggar, S. (1979) The nature and forms of sulfur in organic matter fractions of soils selected along an environmental gradient, Soil Sci. Soc. Amer. J., 43, 981-985.

Cameron, R. S., and Posner, A. M. (1979) Mineralizable organic nitrogen in soil fractionated according to particle size, J. Soil Sci., 30, 565-577.

Canale, R. P., DePalma, L. M., and Vogel, A. H. (1976) A plankton-based food web model for Lake Michigan, in Canale, R. P. (ed.) Modeling Biochemical Processes in Aquatic Ecosystems, 33-77, Ann Arbor Science.

Clesceri, L. S., Park, R. A., and Bloomfield, J. A. (1977) General model of microbial growth and decomposition in aquatic ecosystems, Appl. Environ. Microbial., 33, 1047-1058.

Cole, G. W. (ed.) (1976) ELM: Version 2.0. Range Science Dept. Sci. Ser. No. 20. Colorado State Univ., Fort Collins.

Cooney, C. L., Wang, D. I. C., and Mateles, R. I. (1976) Growth of Enterobacter aerogenes in a chemostat with double nutrient limitations, Appl. Environ. Microbial., 31 ,91-98.

Detling, J. K., Parton, W. J., and Hunt, H. W. (1979). A simulation model of Bouteloua gracilis biomass dynamics of the North American short-grass prairie, Oecologia, 38, 167-191.

Fujimoto, D., and Kanaya, S. (1973) Cuticulin; A noncollagen structural protein from Ascaris cuticle, Arch. Biochem. Biophys., 157, 1-6.

Halstead, R. L., and McKercher, R. B. (1975) Biochemistry and cycling of phosphorus, in Paul, E. A., and McLaren, A. D. (eds) Soil Biochemistry, Vol. 4, New York, Dekker, 31-63.

Hunt, H. W. (1977) A simulation model for decomposition in grasslands, Ecology, 58, 469-484.

Innis, G. S. (ed.) (1978) Grassland simulation model. Ecological Studies 26, New York, Springer-Verlag.

Jenkinson, D. S., and Rayner, J. H. (1977) The turnover of soil organic matter in some of the Rothamsted classical experiments, Soil Sci., 123, 298-305.

Laskin, A. I., and Lechevalier, H. A. (eds) (1973) Handbook of Microbiology, Vol. II, Microbial Composition. Cleveland, Ohio, CRC Press.

McBrayer, J. F., Reichle, D. E., and Witkamp, M. (1974) Energy flow and nutrient cycling in a cryptozoan food-web, Publ. No. 575, Environ. Sci. Div., Oak Ridge National Lab.

McGill, W. B., and Cole, C. V. (1981) Comparative aspects of organic C, N, S, and P cycling through organic matter during pedogenesis, Geoderma (in press).

McGill, W. B., and Paul, E. A. (1976) Fractionation of soil and ¹⁵N nitrogen to depart the organic and clay interactions of immobilized N, Can. J. Soil Sci., 56, 203-212. 

McGill, W. B., Shields, J. A., and Paul, E. A. (1975) Relation between carbon and nitrogen turnover in soil organic fractions of microbial origin, Soil Biol. Biochem., 7, 57-63.

Oades, J. M., and Ladd, J. N. (1977) Biochemical properties: Carbon and nitrogen metabolism, in Russell, J. S., and Greacen, E. L. (eds) Soil Factors in Crop Production in a Semi-arid Environment, St. Lucia, Australia, University of Queensland Press, 136-138.

Parton, W. J., Anderson, D. W., Cole, C. V., and Stewart, J. W. B. (1981) Soil organic matter formation model, in Todd, R. L. (ed.) Agricultural Ecosystems, Athens, Georgia, Sept. 1980. Ann Arbor, Michigan, Ann Arbor Sci. Publ. (in press).

Paul, E. A., and Van Veen, J. (1978) The use of tracers to determine the dynamic nature of organic matter, Trans. 11th Int. Congr. Soil Sci., 3, 61-102.

Pepper, I. L. Miller, R. H., and Ghoniskar, C. P. (1976) Microbial inorganic polyphosphates: Factors influencing their accumulation in soil, Soil Sci. Soc. Amer. Proc., 40, 872-875.

Saggar, S., Bettany, J. R., and Stewart, J. W. B. (1981b) Sulfur transfers in relation to carbon and nitrogen in incubated soils, Soil Biol. Biochem. 13, 499-511.

Stewart, J. W. B., Cole, C. V., and Maynard D. G. Interactions of biogeochemical cycles in grassland ecosystems, Chapter 8, this volume.

Turchenek, L. W., and Oades, J. M. (1979) Fractionation of organo-mineral complexes by sedimentation and density techniques, Geoderma, 21, 311-343.

Young, T. L., and Spycher, G. (1979) Water-dispersible soil organic-mineral particles: I. Carbon and nitrogen distribution, Soil Sci. Soc. Amer. J., 43, 324-328.