openLandscapes - Ecosystem Theories - Gradient theory

University of Kiel, Ecology Centre, Msc Environmental Science, a seminar paper
Status: completed (2009)

Ecosystem Theories: Gradient Theory - An Overview

Jessica Mottl and Cornelius van der Westhuizen
Stu87272@mail.uni-kiel.de and corne@daad-alumni.de

Abstract

The gradient concept originated from the thermodynamic non-equilibrium principle. According to the latter gradients are the build-up of potentials to carry out work in the mechanical form, chemical reactions and biological interactions. It is difficult to measure interactions, energy flow and energy storage in ecosystems. Therefore, gradient theory can be used as a theoretical tool to measure and analyse holistic ecosystem functions. Gradients in the ecosystem could thus theoretically be used as an integrating tool for the aspects of thermodynamics, self-organization and hierarchy theory (Müller, 1998). These gradients can be divided into structural and functional gradients.

Key words: ecosystem theory; thermodynamics; self-organization; ecological hierarchies; structural gradients; temporal gradients; functional gradients

Content

2.1 Non-equilibrium principle (Schneider & Kay, 1984)
2.2 Exergy optimization principle (Joergensen, 2000)
2.3 Gradients develop from and are caused by self-organization (Müller, 1998)

4.1 Structural gradients
4.2 Functional gradients

Gradients in ecosystem analysis

5.1 Gradients in ecological hierarchy theory
5.2 Gradients as orientors

1. Gradient theory background

In the past, ecosystems were researched either by their structural characteristics or their functional characteristics. The problem with this approach was that it did not represent the holistic characteristics of the system. In recent times there have been attempts to unify the two strategies. It was mostly attempted by energetic values (Jörgensen, 1992), thermodynamic concepts (Brooks and Wiley, 1986; Jörgensen, 1992; Schneider and Kay, 1994), network theories (Patten and Jörgensen, 1996) and deduced or systems analytical strategies (Pahl-Wostl, 1996) to explain the interactions between structural and functional ecosystem components. These integrative methods often proved to lack the holistic view of the system and to be based on immeasurable variables.

Hence there was a need for a measurable indicator that could be used to test theoretical hypothesises with empirical data. From the thermodynamics ideas of Schneider and Kay (1994) and Jörgensen (1992) on the one hand and the potentials of practical ecosystem research on the other (Breckling and Müller, 1996) Müller (1998) proposed a simple integrative concept. This concept has the point-of view that structures as well as functions are systems of interacting gradients. These gradients are the result of different states of ecological variables. Hence, it is possible to observe biocoenotic, energetic or materialistic disequilibria (structures) as patterns of gradients (Müller, 1998).

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2. Theoretical concepts

When analysing ecosystem development with regards to ecological heterogeneities, ecosystem boundaries, ecotones or patch dynamics there are three main concepts to be considered. These three theoretical concepts are:

2.1. Non-equilibrium principle (Schneider & Kay, 1994)

According to this principle ecosystem development can be measured by the flow and storage of exergy in the system. Ecosystem development is thus a measure of the capacity of the system to perform useful work (see also Jörgensen 1992, 2000). Thus it is the capacity of the system to degrade due to the available amount of stored exergy available for degradation.

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2.2. Exergy optimization principle (Joergensen, 2000)

Self organising systems will utilize through-flowing exergy to move away from thermodynamic equilibrium. The pathway most likely to be taken to accomplish this will be the one yielding the most stored exergy. Thus the pathway leading to the most ordered structure or the state furthest away from equilibrium will have a propensity to be selected.

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2.3. Gradients develop from and are caused by self-organization (Müller, 1998)

According to this principle in ecosystem development gradients emerge as fundamental features of self-organization processes. It can be deducted that self-organization or ecosystem development can be measured by using gradients as an indicator.

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3. Gradient properties

Gradients are the results of the interaction between creative and destructive ecological processes. They are consequences of accumulating processes on the one hand (gradient creation) and fundamentals for eroding processes on the other (gradient degradation) (Müller et al., 2008)
Gradients operate on distinct ecological scales. Between these scales, certain mechanisms of self-regulation determine ecosystem development (Müller et al., 2008)
Gradients are ecological orientors. Their size, extent, diversity and eco-physiological linkages between each other are optimized throughout undisturbed ecosystem dynamics. Therefore, gradients can be used as fundamentals for the indication of developmental ecological states. (Müller et al., 2008)
Gradients are causes for and results of ecological self-organization. Thus they can be designated as emergent properties of ecosystems (Nielsen and Müller, 2000)

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4. Gradient types

4.1. Structural gradients

Structural gradients depict the spatio-temporal distribution of structural components of an ecosystem (Golley, 2000). These structural components refer to the appearance of all types of abiotic (soil conditions, climatic factors) and biotic (species communities) elements. The existence and distribution of all of these elements can be measured by their abundance and arrangements for ecosystem research.

As illustrated in figure 1 the result of such a gradient measurement could be visualised as a gradient triangle. The x-axis will be representative of the spatial or temporal extent of the gradient. The y-axis will represent the strength of the gradient (quantity of storage or concentration).

Figure 1. Illustration of the components of a structural gradient and the development of its strength. (Teaching material F. Müller, CAU Kiel)

The result is a description of a potential flow between the high and the low value (erosion) and hence, a change to a state of equilibrium. The state of equilibrium will never be reached in nature since ecosystem self-organization processes continuously produce new gradients. These processes will be explained later in relation with the development of ecological hierarchies.

This triangle is used to describe the distribution of ecological variables as metric vectors and determine their potentials and the potential changes or the temporal differences of potential changes at a certain place. The vector is characterized by its direction and steepness, resulting from the quantitative difference between the high and the low value and their distance to each other (length of the x- axis).

In general the abiotic gradients (e.g. solar radiation) determine the developments of biotic gradients (plant communities) which later influence again the abiotic gradients (e.g. nutrient availability). So the higher the heterogeneity of the constraining abiotic gradients, the higher is the diversity of potential ecological niches which can be occupied by again a higher number of species (Müller et al. 2008). It is a well known fact that gradients are not constants. They are involved in continuous creation and degradation processes due to the physiological activities and dynamics within the ecosystem. Their development adds a third dimension to the gradient triangle as illustrated in figure 2.

Figure 2. Illustration of the change in gradient strength (concentration or storage) with distance from the reference point with an added 3rd dimension for dynamics over time.

The variation of concentrations or abundances in time in a certain place along the gradient extension is the temporal gradient. It describes the temporal characteristics of the reactions of system elements which can easily be graphed in frequencies and amplitude substituting the spatial axis of the gradient triangle by a temporal axis. An example for such a temporal gradient is the fluctuation of a water table as illustrated in figure 3. If these gradients, which coincide with many well-known statistical measures from time-series analysis, are small, the system will be highly buffered (Müller 1998).

Figure 3. Illustration of the fluctuations of groundwater in the Alder Break Ecotone at different depths during the year of 1992. (Teaching material F. Müller, CAU Kiel)

The structural features of an ecosystem form ensembles of environmental constraints in different spatial and temporal scales, forming patterns of structural gradients which determine the potential for ecological interactions. That means that the existence, composition and characteristics of different structural gradients in a certain place enable their interaction. An example is the composition of spatial gradients of soil organic matter, oxygen content and microorganism abundance in a sampled soil. Its characteristics facilitate exchanging processes which in this case would be degrading processes, causing functional gradients.

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4.2. Functional Gradients

Functions are defined as selected relations between ecosystem components (Müller & Windhorst, 2000). They are connecting distinct structural elements (biotic and abiotic) which are defined by their gradient and changing their qualities and quantities through exchange processes (Müller et al., 2008).

The developing flows, storages and regulations between the ecosystem compartments are defined as functional gradients. They describe the concentration differences of the elements accumulated in the different pools the observed flow passes on its way from source to sink.

The reference axis for functional gradients is the dominating flow direction between imports from the environment and exports to neighbouring systems. Figure 4 shows this reference axis in the example of a simplified carbon cycle. It connects the elements input with the consecutive storage pools and the output point, determining the transfers between the pools and considering the losses through divergence to adjacent systems.

Figure 4. Schematic illustration of a simplified unfolded ecosystem carbon cycle showing the accumulation pools and the flows induced by the gradients between them. (Müller, 1998)

The gradient triangles in the picture shall help to understand the gradient concept of a flow. While structural gradients consider the concentration differences of one single structural component in space and time, but always within the same pool, functional gradients show the concentration differences and efficiencies of an element passing from one storage pool to another, being these pools independent from strict spatial and temporal constraints.

Unfolding the scheme from above the actual gradient values appear like illustrated in figure 5.

Figure 5. Illustration of the different carbon pools and the flows through them due to concentration differences (functional gradients) in the Alder Forest (Teaching material F. Müller, CAU Kiel)

The concentration profiles derived by the measurement of functional gradients are important fundamentals for the investigation and understanding of ecological processes. Structural gradients build up and evolve from structural patterns, facilitating the development of functional gradients forming patterns of ecosystem processes which again influence the quality and quantity of the structural gradients. The flows passing through ecosystems can be divided into three general groups as there are energy, water and matter following gradients between ecosystems and its environment as well as within the ecosystem.

Energetic Gradients - The energetic gradients are based on the ecological energy balance of energy uptake, consumption and export processes in a broad variety of scales. As the energy storage of the individual ecosystem components is difficult to measure it is usually measured and described by the carbon cycle.
Hydrological Gradients - All driving forces of water movements are results of gradients, for example the vertical temperature and humidity profiles in the atmosphere causing water to be evaporated or transpired. Thus the hydrological gradients are sequences of gradients in water contents and water potentials of the water cycle. Their development is strongly influenced by the energetic processes.
Chemical Gradient - Chemical gradients describe the fluxes of nutrients and other chemical compounds as they exist for example along the nutrient cycles. Their flows are strongly influenced by the hydrological as well as energetic processes within the ecosystem.

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5. Gradients in ecosystem analysis

5.1. Gradients in ecological hierarchy theory

Ecological hierarchy can be comprehended as a partly ordered set of gradients which are interrelated by interactions (Müller et al., 2008), because gradients are basic structural characteristics of holons (Allen and Starr, 1982). They represent functionally autonomous entities which are built up by inferior gradients, as well as subsystems of superior organizational units. Figure 6 represents a general scheme of gradient hierarchies. The functional gradients are symbolized by the arrows, indicating the input of the three gradient types (energy, water, chemicals) their flow through pools on all kinds of scales and their corresponding outputs. The triangles are symbolizing the sets of structural gradients which are limited to their hierarchical level and where the inferior hierarchical levels are constraint and coordinated by the superior ones.

Figure 6. Schematic illustration of flows of energy, water, and chemicals through pools, organized on different hierarchical levels, each of them representing functional gradients on different scales. (Teaching material F. Müller, CAU Kiel)

This hierarchy is developing and maintained by the fact that living systems are degrading and utilizing externally applied gradients by the self-organized formation of a hierarchy of nested, internal gradients (Müller et al.,2008). Only this hierarchy enables the system to cope with the external gradients, because without this exergy degradation staircase the applied exergy could not be utilized at all, as the gradient would be too strong to be operated (Müller, 1996).

Figure 7. Illustration of the possible pathways that can be followed for exergy degradation with an exergy degradation staircase being one. (Teaching material F. Müller, CAU Kiel)

The y- axis of the graph in figure 7 represents the amount of exergy received and stored by the system. If the development and degradation of a tree is taken as an example for this system, the yellow arrow would describe the growing amount of exergy stored in the tree. As the storage grows the exergy gradient between the tree and its surrounding (the energy load of the input materials) is increasing. This gradient is too high to be naturally degraded and utilized in one step. Only burning the tree could release all the stored exergy in one step, but will only produce entropy and this would have no benefit for the ecosystem. Thus degradation has to take place somehow to keep the system working. If a system is moved away from thermodynamic equilibrium, by the application of a flow of exergy, it will utilize all avenues available, that is, build up as much dissipative structure as possible, to reduce the effects of the applied exergy gradient (Schneider & Kay, 1994). Therefore, nature creates the degradation staircase through its self-organizing processes. A high number of small gradients which are actively interacting in an interdependently adapted degradation network are produced (Müller, 1998). In the case of the tree, that would mean a stepwise degradation, e.g. through an animal eating from the tree and being eaten by another animal which later dies and is degraded by microorganisms or just parts of the tree falling on the earth and being decomposed.

Within this hierarchy, those gradients with large spatial extents coordinate/ constrain the small-scaled gradients of the inferior hierarchical levels (soil, climatic and landscapes conditions) define development of species / trees. Such spatial characteristics are interrelated with the temporal features of the holons, slowly changing structures with broad extents on high levels constrain structures and gradients with high temporal dynamics that are assigned to small spatial extensions (Müller 1998).

The non-equilibrium principle states that the number of structural subsystems that take part in the exergy degradation pathway will increase with the amount and duration of the energy imported.

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5.2. Gradients as orientors

The development of gradients is a general feature of successional dynamics, enhances the exergy storage in biomass as well as in structure and information (Jörgensen and Mejer, 1979, 1981; Jörgensen 1992). This means that throughout an undisturbed development the biomass and the complexity of the ecosystems increases up to the state of maturity, increasing thereby the size, extent, diversity, and number of interrelations between ecological gradients (Odum, 1969). Thus the potentials for transfer grow, increasing the exergy flows in the system (Schneider and Kay, 1994). The flow diversity will increase as well as the total system’s throughput.

As the flow densities are increasing, the system is also producing and exporting a growing amount of entropy (Brooks and Wiley, 1986), due to a higher energetic demand for the maintenance of the achieved gradient system (respiration), as well as unavoidable losses at the interfaces between the single transfer steps, although the specific entropy production, which is produced by the single transfer steps, will decrease (Müller, 1998). As a consequence of the growing structurization (amount of gradients), exergy storage is rising at the same time.

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6. Conclusions

The basic hypothesis is that all living systems transform gradients and thereby build up an interior hierarchy of nested gradients (Müller et al., 2008). The existence of gradients provides the possibility for degradation and they are prerequisites for all flows and transfer in ecosystems. Thus gradients are to be found in the structural, functional as well as the organizational characteristics of ecosystems. Hence, gradients can be used as measurable indicators to analyse ecosystems in a holistic sense.

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References

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Brooks DR and Wiley EO (1986) Evolution as Entropy: toward a unified theory of biology. The University of Chicago Press. Golley F (2000): Ecosystem structure. In: Joergensen SE and Müller F (eds): Handbook of ecosystem theories and management. Bocca Raton, pp 21-32
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