Ecological Modelling 174 (2004) 37–54
Investigations of indirect relationships in ecology and
environmental sciences: a review and the implications for
comparative theoretical ecosystem analysis
V. Krivtsov∗
Department of Civil Engineering and Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
Abstract
The understanding of complex interactions involving ecosystem components is indispensable for sustainable development
of humankind. To date, ecological research has mainly concentrated on investigations of direct relationships, whilst indirect
interactions (and in particular the less obvious, e.g. delayed ones) have often been overlooked. Investigation of mechanisms
underpinning complex indirect relationships in ecosystems is greatly aided by mathematical techniques, including correlation,
multiple regression and factor analysis, simulation modelling, path analysis and methods of network analysis, etc. This paper provides a brief review of the recent relevant studies. Mathematical modelling techniques may be especially useful if used in concert
on a range of ecosystems, thus integrating the information obtained in a comparative theoretical ecosystem analysis (CTEA). A
methodological framework for CTEA is given, limitations of the review are acknowledged and possible implications discussed.
© 2004 Elsevier B.V. All rights reserved.
Keywords: Indirect effects; Interaction chains; Interaction modifications; Higher order interactions; Environmental processes; Natural systems;
Integrative approach
1. Preamble
In this paper interrelations among ecosystem components and processes are subdivided into direct (i.e.
those which are restricted to the direct effect of one
component/process on another, and are attributable to
an explicit direct transaction of energy and/or matter between the components in question) and indirect
(i.e. those which do not comply with the above restriction; for further details on definitions, see Section
2). The direct relationships between ecosystem processes are easier to study. Some of them are fairly
straightforward and, therefore, fairly obvious (e.g. in∗ Tel.: +44-2380-593013; fax: +44-2380-677519.
E-mail addresses: [email protected], [email protected]
(V. Krivtsov).
crease in biological growth rate due to the spring increase in temperature, dependence of the population
density of a species upon available resources and predation, shading out of small plants by tall plants, etc.).
Many of indirect relationships (NB: in this paper no
distinction will be made between the terms ‘effect’,
‘relationship’, and ‘interaction’) are far less obvious,
and are often separated spatially and/or temporally.
For example, the dramatic increase in volcanic activity
(possibly caused by the impact of an asteroid) at the
end of the Mesozoic era is thought to have led to the
extinction of dinosaurs, which arguably stimulated the
eventual evolution of mammals (including humans).
The increased production and use of fertilisers in the
1950s led to the increased phosphate inputs, eutrophication and decrease in water quality in many lakes,
ponds and reservoirs during the subsequent decades.
0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved.
doi:10.1016/j.ecolmodel.2003.12.042
38
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
The increased consumption of fossil fuels in the 20th
century led to the increased emissions of carbon dioxide, which were eventually followed by global warming and an apparent increase in the frequency of natural disasters. This climate change was probably accelerated by the depletion of the planet’s ozone layer
due to the CFC (chlorofluorocarbon) containing deodorants and refrigerants.
It should be noted that indirect relationships are
not related just to the activities of humanity, but
have been important throughout the history of our
planet. For example, a gradual development of the
modern atmosphere was largely due to the activity of
cyanobacteria, which were among the first organisms
to produce oxygen as a byproduct of their metabolism
(see Schopf, 1983, and references therein). The indirect implications of the atmospheric oxygen enrichment were far reaching, and led not only to profound
global biological and geochemical changes, but also
ultimately enabled the development of Homo sapiens
and its current civilisation.
Hence, there are examples of indirect relationships
in natural systems, including the global one—the biosphere. The above examples are but just a few among
numerous other cases where indirect effects have led
to major environmental changes. Although a good deal
of these relationships have been successfully characterised (see Section 2), there is no doubt that the majority remain either overlooked or poorly understood.
Their modelling analysis is not straightforward, and
often requires a high level of submodel integration due
to the complexity of processes involved. This analysis, however, may be facilitated by a targeted use of
mathematical techniques. The present paper gives a
brief review of recent relevant studies, and a framework summary of the approaches and methods used.
A full account of the importance of indirect effects in
major environmental problems is intended for further
publications.
2. History and definitions
Arguably, the history of natural sciences is inseparable from the gradually increasing awareness and
understanding of indirect effects. By 19th century the
significance of indirect interactions was well realised,
and was (sometimes implicitly) accounted for in the
classic studies of Darwin, Dokuchaiev, Gumboldt, Engels, and many other scientists. In the 20th century
however, appreciation of indirect effects in nature received considerable acceleration.
There have been many definitions of direct and
indirect effects (see references in Fath and Patten,
1999). Information on indirect interactions is scattered in the literature, and may appear under various
terms. For example, among ecological phenomena
which may (depending on the exact definition) be
regarded as indirect effects are exploitative and apparent competition, facilitation, mutualism, cascading
effects, tri-trophic level interactions, higher order
interactions, interaction modification, non-additive
effects, etc. (Strauss, 1991; Wootton, 1993).
In community ecology, indirect effects are usually
defined in terms of influencing pairwise interactions
between species by some attributes of other species
present in the community (Strauss, 1991). Essentially,
in each particular case the problem is confined to the
question how species X alters the effect of species A
on species B.
A number of factors have been noted to modify
the strength of indirect interactions. For example, it
was argued (e.g. Holt, 1977; Holt and Lawton, 1994)
that the strength of the apparent competition between
prey species is largely determined by their specific
growth rate. Further factors important to the manifested strength of the density-mediated indirect interactions are density dependence of the transmitting
compartment, and the possibility of stochastic physical disruption (Abrams et al., 1996; Wootton, 1994a).
On the other hand, issues important in determining
the manifested strength of the behaviour-mediated indirect interactions involve ability of a focal species to
detect changes in factors which matter for energetic
costs and benefits of its behaviour, sensitivity of its
optimum behaviour to these costs and benefits, and
available behavioural options (Abrams, 1993).
For density-mediated effects, presence and strength
of indirect interactions can be determined by analysing
partial derivatives of the abundance of a species on
the abundances of other (not immediately connected)
species (Abrams et al., 1996). However, indirect interaction may involve ecologically important changes
other than changes in abundance, e.g. demographic
changes in the population structure, changes in the
genotypic composition, and changes in behaviour (e.g.
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
searching rates, antipredator behaviours), morphology,
biochemistry (e.g. nutrient content, toxin concentration) or physiology (see Strauss, 1991; Abrams et al.,
1996, and references therein).
2.1. Classifications of indirect effects
First of all, it is important to distinguish between
direct and indirect effects. Usually, the interactions
between two components not involving direct transfer of energy and/or matter are viewed as indirect,
while those which involve an explicit direct transaction are viewed as direct (see, e.g. Fath and Patten,
1998, 1999, and references therein). The literature is
inconsistent on the definitions of indirect effects, and
one way to clarify the problem is to stress the difference between a transaction and a relation. A simple
transaction between two ecosystem components is
always direct since it is the transfer of matter and/or
energy, whereas a relation is the qualitative type
of interaction. Relations include predation, mutualism, competition, commensalisms, ammensalism, etc.
Hence a direct relationship is the one which is based
on a direct (i.e. unmediated by another ecosystem
component) transaction only. For example, the classic
predation (NB not to be mistaken with, e.g. keystone
predation, indirect predation, etc.) is direct, and so
is the nutrient uptake by plants, algae and bacteria,
whereas mutualism and competition are always indirect, as they result from the combination of a number
of simple transactions. It is worth pointing out that the
observed patterns of interrelations between ecosystem
components (e.g. correlation between abundance indices) frequently result from a combination of direct
and indirect effects, as each component is involved
in a large number of pathways (Whipple, 1999).
Furthermore, if a direct relationship between two
ecosystem components (say A and B) is modified
by a third ecosystem component, attribute, or forcing function (the two latter notions will include, e.g.,
such modifiers as sunlight, temperature, pH, external
and internal concentrations of alternative nutrients)
then the indirect relationship between the modifying
agent and the first two components (i.e. A and B)
becomes superimposed upon the direct relationship
between the components A and B (Krivtsov, 2001;
Krivtsov et al., 2000c). Consequently, the observed
pattern of interrelation (e.g. correlation between the
39
abundance data) between A and B will in this case
result from the combination of direct and indirect
effects.
The definition of indirect effects given above is very
encompassing, and will include some of the effects
which may fall into the category of ‘direct’ under a
different definition. For example, it is useful to account for the distinction between those effects that
are directly and indirectly mediated (sensu Krivtsov,
2001), since the latter ones are particularly difficult to
observe, especially if the cause and effect are substantially separated in time (Krivtsov et al., 2000b,c).
The directly mediated effects have previously
(Krivtsov, 2001) been regarded as direct (i.e. as regards to the properties of their propagation). In this
paper, however, the directly mediated effects will be
treated as indirect, and the definition of indirect effects will, therefore, include such effects as trophic
cascades, top-down and bottom-up controls, etc. The
classification of indirect effects into directly and indirectly mediated is applicable to a wide range of
environmental processes (Krivtsov, 2001), and bears
certain similarities with the distinction between ‘interaction chains’ and ‘interaction modifications’ earlier recognised (Wootton, 1994a) for purely biotic
relationships.
Although detailed analysis of various possible classifications would be outside the scope of this overview,
it is worth mentioning, however, that indirect effects
can be characterised in a number of ways, related,
e.g. to the characteristics of exerting, receiving and
transmitting compartments (e.g. Abrams et al., 1996),
presence/absence of a lag phase before the manifestation of a response (Krivtsov et al., 2000c), strength
of the interaction (particularly in relation to the direct interactions—Ulanowicz and Puccia, 1990), dependence on a specific ecosystem context (Krivtsov
et al., 2001b,c), importance for the functioning of
the compartments involved (Ulanowicz and Puccia,
1990), importance for structural (e.g. successional or
evolutionary) changes in the populations involved and
the whole biological community, and significance for
overall ecosystem functioning (Fath and Patten, 1998).
In the author’s view, the different ways to characterise
indirect interactions are not contradictory, but rather
complementary, and may conveniently contribute to
the toolbox for comparative ecosystem analysis (see
Section 4).
40
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
2.2. Previous reviews related to indirect effects
As has already been noted, the information about
indirect effects may appear under a variety of terms,
and at least some relevant information may be found in
(or deduced from) a large proportion of environmental studies. This is perhaps not surprising, considering
how widespread indirect interactions are in nature.
However, there have been a number of reviews related
to indirect interactions specifically. Schoener (1983)
provided a review of 48 published studies, containing
the research conducted in a wide range of ecosystems.
The review addressed the importance, magnitude,
variability, and the relative time of appearance of
indirect effects compared to the direct ones and provided evidence that indirect effects, in general, tend
to be weaker and more variable than the direct ones
(this, however, contradicts the findings of Higashi and
Patten, 1986, who used a nekton model to show that
indirect effects are more significant then direct ones).
Menge (1995) examined both trophic and non-trophic interactions reported in 23 case studies conducted
in the marine rocky intertidal environment in either
tropical or temperate climate. Indirect effects were
shown to account for approximately 40% of the change
in community structure resulting from manipulations,
and this figure did not appear to depend upon the complexity of the web. Interaction types were classified on
the basis of similarity of direct and indirect effects. The
83 subtypes of the indirect effects were split into nine
types, including keystone predation, apparent competition, habitat facilitation, apparent predation, indirect
mutualism, trophic cascade, indirect defence, indirect
commensalism, and exploitation competition.
Strauss (1991) provided a concise elegant overview
addressing definition, importance, detection and probable future trends in studies of indirect effects in biological communities. Drawing heavily on previous
studies, she presented a classification of indirect effects based on how the relationship between focal
species A and species B may be affected by a third
species C. Four basic types of indirect effects were
recognised, including: (1) abundance, (2) behavioural,
morphological, chemical or physiological, (3) environmental, and (4) response. This review also contained
a brief mentioning of advantages and disadvantages
offered by application of two particular mathematical
techniques, ANOVA applied to the results of experi-
ments with a factorial design, and path analysis utilising a food web model.
Wootton (1994a) reviewed the mechanisms and
consequences of indirect effects in biological communities. An important distinction was made between
‘interaction chains’ and ‘interaction modifications’,
and five sample types of indirect effects (including
exploitative competition, trophic cascades, apparent competition, indirect mutualism, and interaction
modification) were reviewed in detail. A separate
section was devoted to possible consequences of
indirect effects for evolution of biological species,
and an overview of limitations and advantages of a
number of commonly used mathematical techniques
(including MANOVA, simulation modelling, network
analysis and path analysis) was given. In a more recent review published by the same author (Wootton,
2002a) there are also a number of references to applications of structural equation modelling, Markov
chain models, and the inverse Jacobian matrix. This
recent work contains a section on terminology (with a
particular attention to interaction chains and interaction modifications), and is focused (albeit somewhat
concisely) on future challenges for investigations of
indirect effects (e.g. as regards their detection, formal
mathematical description, prediction, and consideration of time-scale differences and environmental
variability). Importantly, the paper acknowledges the
importance of indirect effects arising due to the activity of ecosystem engineers (with plenty of useful
references related to aquatic environment), and suggests that a lot could be learnt from other disciplines
dealing with complex systems, including genetics,
economics, computer and social sciences.
Abrams et al. (1996) provided an in-depth review
of the role of indirect effects in the food webs. They
summarised the information available from a comprehensive range of studies, and gave a couple of examples related to the application of experimental and
theoretical approaches, respectively. Their second example was related to the interactions in a marine food
web. It was based on the network analysis of a dynamic model associating a number of energy-based
equations (Yodzis and Innes, 1992), and is, therefore,
particularly noteworthy for the purpose of this paper.
It was shown that the apparent net effect of seals on
the abundance of hake was extremely diffused, and
depended on the lengths of the pathways considered.
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
If only pathways of limited lengths were taken into
account, the effect appeared to be negative. However,
when indirect effects propagating via longer (containing not less than six components) pathways were accounted for, the observed net effect turned out to be
positive. The authors provided discussion related to
advantages and limitations of both (i.e. theoretical and
experimental) approaches recognised by the authors,
and advocated application of dynamic models and inverse matrix techniques (subject to the limitations discussed).
A recent monograph of Wardle (2002) examined
interrelations between above- and belowground components in terrestrial ecosystems. Although there is
no specific discussion related to application of specific mathematical techniques, the book not only provides a plethora of useful relevant references (including a number of modelling studies), but also gives a
comprehensive synthesis of information gathered over
decades by soil scientists and terrestrial ecologists.
Most interactions considered in this book are indirect,
and many of those are discussed in exhaustively comprehensive detail.
A recently published paper of Robinson and Frid
(2003) provides a review of 24 dynamic simulation models of coastal marine ecosystems as regards
their properties to reproduce complex combinations
of direct and indirect effects among the ecosystem
components and the potential to provide a realistic
expectation of the ecosystem effects of fishing. The
authors also give a nice succinct summary of direct
and indirect effects resulting from fishing activities.
Six of the best models reviewed were of the Ecopath
with Ecosim family of models. The Ecopath software
(Christensen and Pauly, 1992) implements the methods of network analysis, and allows description and
analysis of systems in terms of their development, flow
pattern, capacity to withstand external perturbations,
stability, and direct and indirect effects of a group of
species (or a single species) on the other compartments. Ecosim (developed by Walters et al., 1997) provides a dynamical extension to the Ecopath software.
It is worth pointing out, that although the role of
physical environment and abiotic ecosystem components is often acknowledged (e.g. Strauss, 1991;
Miller, 1994; Abrams et al., 1996) the ecological reviews (and introductory sections of most ecological
studies) written at the end of the last century have
41
mainly concentrated on investigations of indirect interactions between biological organisms. In some
cases (e.g. Wootton, 1994a) the account given was
deliberately restricted only to the interactions between
biological species. Such distancing of the ecological
insight from other areas of environmental sciences is a
bit unfortunate, considering the importance of abiotic
ecosystem components and energy sources (e.g. solar
energy and energy of inorganic chemical compounds)
for functioning of most natural biogeocenoses. However, the conclusions reached by studies of purely
biotic interactions may, with some adaptation, be applicable to a wider range of environmental processes.
2.3. Role of abiotic components
Although the importance of abiotic ecosystem components is commonly recognised, most of the ecological studies (including those addressing the indirect effects) tend to study in detail only relationships among
biota. The restriction of the integrative synthesis to
species interaction only cuts off a plethora of useful
environmental studies related, e.g., to issues of global
climate change. It should be noted, however, that the
science of ecosystem dynamics is highly interdisciplinary, and the information relevant to the present
discussion can, therefore, be found not only in ecology and biology, but also virtually in any section of
natural and environmental sciences, with geography,
palaeontology, geoecology and climatology comprising the most obvious candidates.
In ecology, it is widely recognised that species
interaction can be mediated by a non-living resource
(Strauss, 1991; Krivtsov et al., 2000b,c, 2001b), and
that a species can potentially exert a selective force
on another species through non-trophic interactions
(Wardle, 2002; Strauss, 1991). It should also be noted
that in nature many species are very well adapted to
modify their community and habitat (e.g. beavers by
changing the habitat’s hydrological regime, humans
by initiating dramatic changes in global climate and
geochemical fluxes, earth worms by increasing aeration and redistributing organic matter in soil, etc.).
Changes in physical characteristics of a habitat caused
by the activity of so-called ‘ecosystem engineers’
(see Wardle, 2002; Wootton, 2002a, and references
therein) may be regarded as an extreme case of such
non-trophic interactions. Often, however, even if abi-
42
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
otic components are considered in terms of detrital
pathways and/or nutrient cycling, the effects studied
in detail using methods of mathematical modelling
are mostly confined to trophic interactions only (e.g.
Ulanowicz and Puccia, 1990; Krivtsov et al., 2000b;
Patten, 1985). Furthermore, many indirect interactions
occur between different stages of ecosystem development and are therefore easily overlooked and understudied (Krivtsov, 2001). In ecological literature these
interactions are sometimes called ‘historical effects’,
‘priority effects’ (Strauss, 1991) or ‘indirect delayed
regulations’ (Krivtsov et al., 2000c). Consideration of
these effects is particularly important for the correct
understanding of an overall ecosystem functioning.
It should be noted that the boost of the growing
appreciation of indirect effects in 20th century was
partly initiated by Vernadsky’s fundamental theories
(see, e.g. Vernadsky, 1926) about the biosphere, the
noosphere, and interrelations between biota and geochemical cycling. Popularisation of these views half a
century later (e.g. by Lovelock’s Gaia theory) stimulated investigations of indirect effects even further.
The line of thought started by Vernadsky has eventually led to the creation of a new integrative branch
of natural sciences, sometimes referred to as ‘Global
Ecology’ (Budiko, 1977). Essentially, global ecology
encompasses methods and scope of virtually all other
environmental disciplines, and is predominantly concerned with the dynamics (including past and future)
of the global ecosystem—the biosphere. Methods of
mathematical modelling are central to global ecology, and have proved indispensable in elucidating
various aspects of interrelations between and within
global hydrological cycle, energy budget, biological
and geographical evolution, and the development of
mankind (see, e.g., Budiko, 1977, and references
therein).
As an example of the latter, it is worth mentioning
the now classic climatological research which led to
the creation of a half-empirical model of the thermal
regime of the atmosphere (Budiko, 1968), which was
subsequently used to simulate past and future dynamics of the atmosphere, and changes between glaciation and interglacial periods. Furthermore, the results
obtained aided interpretation of human evolution, and
led to further research aiming to counteract possible
global change, e.g. by injecting certain substances into
the stratosphere, and direct and indirect consequences
to which such manipulations may lead (e.g. Budiko,
1977, and references therein).
Hence, if one abstracts from the labels given to different branches of science, the importance of abiotic
ecosystem components and physical environment for
ecosystem dynamics and evolutionary development
becomes increasingly obvious. This is immediately
apparent in a number of recent modelling studies reviewed in Section 3.
2.4. ‘Indirect effects’—meaning in this paper
In these papers all the relations not restricted to
the effects of a direct transaction of matter and energy between the adjacent ecosystem components
will be treated as indirect. Hence, for the purpose of
the forgoing sections, all types of indirect interactions mentioned above will be considered as indirect
effects. However, the distinction between directly
and indirectly mediated effects will be made where
deemed appropriate. The terms ‘relationship’ and
‘interaction’ will be used interchangeably. Furthermore, although it is realised that for the purpose of
quantitative assessment the distinction between the
terms ‘effect’ and ‘interaction’ may be helpful (e.g.
Wootton, 1994a), no such distinction will be made in
this paper, as in many of the studies reviewed these
terms are used interchangeably.
2.5. Approaches used to detect and measure indirect
effects
Detection and measurements of indirect effects are
often far from straightforward, and are mostly based
on the intuition, common sense and prior knowledge of
any particular system. Abrams et al. (1996) described
two major approaches adopted in ecological studies,
namely theoretical and experimental.
Within the theoretical approach, observations (and/
or carefully considered experimental data) are used
together with theoretical considerations to construct
a model capable of investigating interactions among
the components incorporated in the model structure.
This model is subsequently used to examine indirect
effects between the components. There are a number
of drawbacks of this approach, e.g. difficulties related
to obtaining sufficient details about the components
represented in the models, unavoidable uncertainty
as regards fluxes, parameters, initial values, etc. This
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
uncertainty may mask the significance of the relationships studied, including indirect effects. Furthermore,
as it is impossible to reproduce all the complexity
of a real ecosystem, any model is a simplification of
reality. Therefore, some of the potentially important
interactions may be lost just by defining the model
structure, whilst the importance of the others may be
considerably altered.
Within the experimental approach, densities of individual species are manipulated (e.g. by total removal)
in microcosms or experimental plots, and statistical
analysis (e.g., ANOVA, ANCOVA) are subsequently
applied to estimate the magnitude of indirect effects
of manipulations on densities of other species. It has
been argued (Abrams et al., 1996) that this approach
is best applied using a factorial design, where the
densities of a number of components (e.g. species or
trophic groups) are changed both alone and in combination. If implemented properly, this approach leads to
a straightforward estimation of net effects. However,
there is always a danger that some of indirect interactions have not manifested owing to unavoidable time
constraints of any experiment. Also, partitioning of the
registered net effects may be subject to speculation.
Experiments are often costly and by definition are limited by their design and the hypotheses tested. The simplicity of the experimental design may mask the significance of the relationships studied for trait-mediated
effects, measurements of population abundances may
need to be supplemented by behavioural observations,
and/or biochemical, physiological, genetic, and other
analyses. Furthermore, there is always a big question
mark how applicable are the results obtained to the
processes happening in the real world.
It was noted (Abrams et al., 1996) that in practice,
the theoretical and empirical approaches referred to
above may be regarded as end points of a methodological continuum. On the basis of studies reviewed
in this paper, however, I shall argue that, in fact, this
methodological continuum is best represented by a triangle, with observational, experimental and theoretical nodes (see Section 4).
3. Recent studies of indirect relationships
The information about recent modelling research
involving analysis of indirect relationships in ecolog-
43
ical systems was obtained via an SCI search (conducted in early 2002) using the following keywords
combination: ‘ecological interactions’ and ‘indirect’
and ‘model’ or ‘ecosystem’ and ‘indirect’ and ‘model’.
The search returned 70 articles, but about half of them
were judged as irrelevant (e.g. a very common case
was related to those studies were either indirect estimates or indirect measurements were carried out, but
not modelling of indirect relationships; another typical
case comprised the studies were modelling was only
suggested). The majority of the remaining papers came
from Ecological Modelling, while the main topics appeared to be concerned with issues of climate change,
terrestrial ecology, and aquatic ecosystem dynamics.
A brief overview given below contains some examples
from the references found, together with some others
(restricted to the last decade till present), not returned
by the search, but deemed to be relevant by the author or the referees. The list of the studies reviewed in
Sections 3.1–3.3 is given in Table 1.
3.1. Ecological studies in terrestrial environment
Arguably, the awareness of natural scientists as
regards indirect effects in the terrestrial environment
can be traced back at least to the end of 19th century,
when the school of thought founded by Dokuchaiev
had developed a theory that soil was a product of
complex interactions between climate, and geological
and biological components of the terrestrial landscape (for later reprints of this original work see, e.g.
Dokuchaiev, 1948). To date, the importance of indirect interactions in the terrestrial environment is well
recognised (see Wardle, 2002, and references therein).
Indirect effects in terrestrial ecosystems relate, for
instance, to the dependence of plant nutrient supply
on mineralisation of nutrients by soil biota, and to the
propagation of these effects through the food chain.
Soil fauna may help to disperse micro-organisms crucial for plant functioning and biogeochemical cycling,
and physically modify the habitat, thus changing environmental conditions for all the biological community.
Plants, in turn, modify the habitat for other organisms,
e.g. by producing litter, providing shade, shelter, etc.
A number of studies recently conducted in the
terrestrial environment (this includes both field experiments and soil microcosms) adopted experimental
approach focusing on the density manipulation exper-
44
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
Table 1
List of main studies reviewed in Section 3 grouped by the type of study (i.e. aquatic, terrestrial, climate change, others)
Type of study
References
Terrestrial (Section 3.1)
Blagodatsky and Richter (1998), Blagodatsky et al. (1998), de Ruiter et al. (1993), Hunt et al.
(1991), Hunt and Wall (2002), Intachat et al. (2001), Krivtsov et al. (2002a, 2003b, 2003c), Leriche
et al. (2001), Miller (1994), Oglethorpe and Sanderson (1999), Rillig et al. (2002), Sinclair et al.
(2000) and Svendsen et al. (1995)
Bartell et al. (1999), Carrer and Opitz (1999), Daskalov (2002), Dippner (1998), Hanratty and Liber
(1996), Hulot et al. (2000), Krivtsov et al. (1998, 1999a, 2000a, 2000b, 2001b), Krivtsov (2001),
Loladze et al. (2000), Malaeb et al. (2000), McClanahan and Sala (1997), Naito et al. (2002),
Navarrete and Menge (1996), Ortiz and Wolff (2002a,b), Ulanowicz and Puccia (1990), Whipple
(1999) and Wootton (1994b, 2002b)
Dale et al. (1991), Loehle and LeBlanc (1996), McMurtrie and Comins (1996), Norberg and
DeAngelis (1997), Post and Pastor (1996), Rathgeber et al. (2000), Riedo et al. (1999), van Oene
et al. (1999), van Minnen et al. (1995) and Vukicevic et al. (2001)
Bockstael et al. (1995), Daufresne and Loreau (2001), Fath and Patten (1998), Loreau (1998) and
Patten (1992)
Aquatic (Section 3.2)
Climate change (Section 3.3)
Other (Section 3.4)
See text for further details.
iments followed by analysis of the results obtained using parametric (e.g. ANOVA, Tukey’s HSD) and nonparametric (e.g. Kruskal–Wallis and Mann–Whitney
U-tests) statistical tests (see a plethora of references
in Wardle, 2002). For instance, Miller (1994) used
exclusion experiments to elucidate direct and indirect
species interactions in a field plant community. Experimental results were analysed by parametric and
non-parametric techniques, which yielded interesting
information on the ecological characteristics of the
species involved. Particularly, it was established that
species with a large competitive ability due to direct
effects generally had almost as large indirect effects,
so that the two effects almost cancelled each other.
A number of indirect relationships in soil ecosystems was investigated by Hunt and coauthors (see e.g.
Hunt et al., 1991; Hunt and Wall, 2002, and references
therein). For example it was found that the increase
in net N mineralisation with precipitation was a consequence of not only the direct effect of moisture
supply on decomposition, but also an indirect effect of
changes in substrate supply and quality (Hunt et al.,
1991). In a recent comprehensive study Hunt and
Wall (2002) simulated deletion of ecological groups
within a soil ecosystem. A number of interesting results were obtained. For example, it was concluded
that although deleting all faunal compartments from a
soil ecosystem model’s structure affects the model’s
performance considerably (e.g. results in a shift from
fungal to bacterial dominance), omitting any specific
faunal compartment does not considerably affect the
performance of the model. The model of Hunt et al.
(1987) was also used by de Ruiter et al. (1993) in a
study of nitrogen mineralization conducted at a wheat
field. The impact of microfaunal functional groups
on N mineralisation was evaluated by calculating the
impact of group deletion. The results showed that
the effect of the removal of a group may exceed the
direct contribution of this group to N mineralisation
rather considerably, with amoebae and bacterivorous
nematodes having values of 18 and 28, and 5 and
12% for, respectively, direct contribution towards and
impact of deletion upon overall N mineralisation.
Rillig et al. (2002) used path analysis to distinguish direct and indirect effects of factors on soil aggregation. It was found that arbuscular mycorrhizal
fungi influence soil aggregation both directly, and indirectly, via properties of glomalin, a stable protein
which they produce in abundance. The effect of glomalin on water-stable aggregation was much stronger
than the direct effect of arbuscular mycorrhizal fungi
themselves.
Influence of the transitions of soil micro-organisms
between dormant and active stages was studied by
Blagodatsky and Richter (1998) and Blagodatsky et al.
(1998). Such transitions were shown to be important
for biogeochemical cycling and the rate of organic
matter decomposition.
Oglethorpe et al. (1995) coupled a farm-level linear programming model with the NELUP vegetationenvironment-management model to investigate direct
and indirect consequences of adopting environmental
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
sensitive area (ESA) grassland management prescriptions. It was shown that such coupling can be useful
both for working out economic logistics, and achieving desirable changes in the composition of the plant
community. Further similar investigations provided an
additional insight into economic farm-scale variables
and resultant ecological diversity, and highlighted the
importance of such integrated modelling systems for
environmental policy decision support (see Oglethorpe
and Sanderson, 1999, and references therein).
Svendsen et al. (1995) applied the model DAISY
(designed for agricultural ecosystems in Denmark) for
simulation of water and N balances, as well as crop
production in a couple of German agroecosystems.
The results showed that the distribution of nitrate in
the soil profile during a 2-year period depended on
the assumption whether the site was irrigated in the
first year. Although the authors did not actually use
the word ‘indirect’, their results suggest that the distribution of nitrate was affected by biota, which in turn
was influenced by irrigation.
Sinclair et al. (2000) analysed results of a comprehensive experiment conducted in a Canadian boreal
forest, where seven different perturbations either removed or supplemented original trophic levels. Subsequent changes in biomass of the other levels were
compared with the predictions of 27 simple models
testing linear interactions. The authors concluded that
observed indirect effects were weak, and rapidly attenuated along the food chain. It should be noted,
however, that, in fact, the study analysed only directly
mediated effects (sensu Krivtsov, 2001), and did not
attempt to account for indirectly mediated ones.
Leriche et al. (2001) applied the PEPSEE-grass
model to a West African humid grassland. They found
that the response of NPP to grazing intensity was
a complex result of both direct and indirect effects
of biomass removal on soil water availability, grass
nitrogen status and productivity, light absorption efficiency, and root/shoot allocation pattern.
Intachat et al. (2001) used stepwise regression analysis to model the effect of weather variables on the
phenology of Malaysian rain forest and the abundance
of geometroid moths. Due to coupled delayed meteorological effects, the abundance of certain moth
species appeared to precede trees flushing, flowering
and fruiting, which must be beneficial for emerging
larvae.
45
Huisman et al. (1999) analysed the steady state
outcome of a relatively simple simulation model, describing interactions between two plant species and a
herbivore along the productivity gradient. Some of the
interesting results of this study were in contradiction
with the established (i.e. in this case nutrient-based)
theories. For instance, for the situation when the
taller plant was assumed to be inedible, the total plant
biomass increased with productivity, whereas the herbivore was only present at low productivity. In other
words, the taller plant had an indirect effect on the
herbivore through outcompeting the lower plant (i.e.
the preferred herbivore’s food) at high productivity
levels (Huisman et al., 1999, p. 254). Hence, the decrease of the herbivore’s abundance at higher productivity was a consequence of a bottom-up effect. The
results of the study were in good agreement with the
patterns observed in a Dutch salt-marsh ecosystem.
A combination of statistical and simulation modelling has been applied to investigate ecological
patterns in the Heron Wood Reserve, located at the
Dawyck Botanic Garden in Scotland (Krivtsov et al.,
2001a, 2002a, 2003b,c,d, 2004a). The suite of statistical techniques included ANOVA, ANCOVA, correlation analysis, CCA, factor analysis, and stepwise
regression modelling. The study revealed a number of
indirect effects resulting from a complex multivariate
interplay among ecosystem components. For example, the results suggested that both direct negative
and indirect positive effects of the microarthropod
community on specific fungal groups appeared to
take place. The relatively high local abundances of
the dominant collembolan Folsomia candida might
have caused local declines in ectomycorrhizal fungi,
reflected, in turn, in the increase in pH. However, for
those samples where F. candida were less abundant,
overcompensatory fungal growth due to grazing by
mites and other collembola was implicated. Complex effects were also shown for bacteria, nematodes,
protozoa, plants, and soil properties.
3.2. Aquatic studies
Despite the claims (Wardle, 2002) that aquatic scientists have only recently recognised and started to
study indirect effects, awareness of indirect interactions in aquatic environment has rather a considerably
long history (e.g. Mortimer, 1941, 1942; Hutchinson,
46
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
1957; Reynolds, 1984). In particular, in an earlier
review it was even suggested that most studies specifically addressing behaviour-mediated indirect effects
tend to be conducted in freshwater ecosystems, while
many of the early demonstrations of density-mediated
indirect effects were done in community studies in marine habitats (see Abrams et al., 1996 and references
therein). Likewise, much of the knowledge related to
indirect ecological interactions has been contributed
through the development and applications of the methods of simulation modelling (e.g. Jorgensen, 1980,
1994) and network analysis (e.g. Ulanowicz and
Puccia, 1990; Patten, 1985; Patten et al., 1976, and
references therein) in relation to aquatic environment. Consequently, simulation models capable of
demonstrating indirect interactions in aquatic biogeocenoses (e.g. the Lake 2 model of J. Solomonsen, see
Jorgensen, 1994) are widely used for teaching in the
educational establishments across the world. Recent
studies of indirect effects in aquatic environment involved application of various statistical techniques,
methods of network analysis, simulation modelling
using ‘what–if’ scenarios, and sensitivity analysis.
Ulanowicz and Puccia (1990) used a modification
of network analysis to investigate complex ecological dynamics in Chesapeake Bay. They showed that
the trophic chains in pelagic environment contain
seemingly separated autocatalytic pairings (e.g. heterotrophic flagellates and dissolved organic carbon
separated by free living bacteria) which were functionally coupled via indirect interactions. It was also
demonstrated that ctenophores and coelenterates were
engaged in indirect mutualism with phytoplankton,
and in extended competition with most other heterotrophs. Consequently, these groups proved to be
extremely important for interpreting the dynamics
observed in the bay, which had not been appreciated
previously.
Carrer and Opitz (1999) investigated indirect interactions in the Lagoon of Venice using ‘Ecopath’,
a software implementing methods of network analysis. Among other interesting relationships, they found
that about half of the food of nectonic benthic feeders and nectonic necton feeders passed through detritus at least once, whilst there was no direct transfer
of such food according to the diet matrix. The paper contains a number of references to other studies
where network analysis was used to analyse indirect
relationships among ecosystem components (see also
Patten, 1992; Fath and Patten, 1998, 1999, and references therein), as well as a reference to the Ecopath
web site, which, in turn, gives a list of studies (mainly
aquatic) where this software was applied. A couple of
examples from this list are reviewed below.
Ortiz and Wolff (2002a,b) used Ecopath with
Ecosim software to study benthic communities in
Chile. They found that a simulated harvest of the clam
Mulinia generated a complex interplay involving direct and indirect effects, and drastically changed the
properties of the whole system.
Daskalov (2002) used Ecopath with Ecosim software to investigate effects of overfishing in the Black
Sea. He found that a reduction in the top predator
resulted in a ‘trophic casade’, leading to a increase in
the abundance of planktivorous fish, a decline in zooplankton biomass, and an increase in phytoplankton
crop.
In another network analysis study, Whipple (1999)
provided an analysis of the extended path and flow
structure for the well documented oyster reef model.
Few simple paths and large number of compound paths
were counted. The study provided structural evidence
for feedback control in ecosystems, and illustrated importance of non-living compartments (in this case detritus) for the ecosystem’s functioning. Even for the
model with a low cycling index (i.e. 11%) multiple
cyclic passage paths provided a considerable (22%)
flow contribution. Therefore, it was envisaged that for
ecosystems with higher cycling indexes the patterns
observed should be even more pronounced.
Modifications of the model CASM were used by
Bartell et al. (1999) and Naito et al. (2002) to study
direct and indirect effects in the aquatic ecosystems
of Canada (Quebec) and Japan (lake Suwa), respectively. Numerical sensitivity analysis was applied in
both cases (sensitivity of a state variable on changes in
a parameter was measured as the percent change from
the reference situation). For the Canadian case study it
was found that variability in the production of macrophyte population determines an indirect risk component of toxic Hg effects on phyto- and zooplankton,
periphyton and fish. In the Japanese case study it was
found that the annual production of piscivorous fish
was considerably influenced by the optimal consumption temperature of certain benthic insects. Another interesting finding was that the physiological parameters
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
of the diatom Melosira were the important sources of
the cyanobacterium Microcystis production variability.
Although the authors did not make a detailed interpretation of the latter relationship, their results suggest
that the underlying mechanism might be a common
inverse relationship between spring diatom and summer cyanobacterial blooms (see references related to
the Rostherne Mere case study below).
Hanratty and Liber (1996) studied indirect effects of
a pollutant diflubenzuron on growth of larval bluegill
sunfish in a littoral enclosure. At very high concentrations the model predictions were good, but at intermediate concentrations the accuracy was variable, with
some indirect responses being exaggerated due to cascading effects through the ecosystem trophic levels.
McClanahan and Sala (1997) used a simulation
model of the Mediterranean infralittoral rocky bottom
to study possible effects of various management options. Running a number of ‘what–if’ scenarios they
concluded that many of potential changes are likely to
be indirect effects caused by changes in trophic composition. For example, if invertivorous fish were removed as part of a management scenario, sea urchins
would reduce algal abundance and primary production, leading to competitive exclusion of herbivorous
fish. Although similar interactions were known from
tropical seas, these results were not anticipated by
previous field studies in the Mediterranean.
Loladze et al. (2000) investigated how the interactions between phytoplankton and zooplankton change
if the Lotka-Volterra model incorporates chemical heterogeneity for both trophic levels. It was found that
indirect competition between two populations for P
can shift the relationship from a usual (+, −) type to
an unusual (−, −) type, leading to a very complex
overall dynamics.
Hulot et al. (2000) compared the performance of linear food chain models and an intermediate complexity model, applied to data of a mesocosm experiment
simulating lake nutrient enrichment. The intermediate
complexity model (with separation of trophic levels
into functional groups according to size and diet) was
the only one which performed satisfactory, thus highlighting the importance of functional diversity and indirect interactions.
Malaeb et al. (2000) used structural equation modelling (a technique combining path, factor, and regression analyses) to estimate the contribution of indirect
47
effects of sediment contamination and natural variability on biodiversity and growth potential in a selection of North American estuaries. They found that a
positive indirect effect of natural variability (mediated
through biodiversity) on growth potential exceeded a
direct negative effect, resulting in the overall positive
relationship.
The simultaneous application of ANOVA and ANCOVA analysis allowed the investigator to elicit direct and indirect effects between the biota inhabiting
a North American intertidal rocky shore (Wootton,
2002b). The results indicated that consumers may
have a major influence on the dynamics of ecological
succession. In an earlier study published by the same
author, path analysis was helpful in predicting which
direct and indirect effects were important in a seabird
exclosure experiment (Wootton, 1994b). Statistical
techniques (including linear regressions and a number
of variation of ANOVA analysis) were also helpful in
another intertidal rocky shore study (Navarrete and
Menge, 1996).
Detailed attention to indirect effects was given in a
number of studies conducted at Rostherne Mere, one
of the best studied lakes in UK (see Krivtsov et al.,
1998, 1999a,b,c, 2000a, 2001b,c, 2002b, 2003a, and
references therein). Indirect effects were shown to
occur on (and across) various levels of organisation,
including intracellular, population and ecosystem
levels. Statistical analysis of the observed data sets
and sensitivity analysis (using mathematical model
‘Rostherne’) were used to elicit the hidden relationships between Si and P biogeochemical cycles
coupled through the dynamics of primary producers
(Krivtsov, 2001; Krivtsov et al., 2000b). It was shown
that there is an inverse relationship between spring
diatom and summer cyanobacterial blooms, which
could be utilised as a new method of eutrophication
control. Dynamic ecosystem modelling revealed a
complex interplay between direct and indirect effects in the ecosystem, including those related to the
influences of temperature, light, inflow/outflow characteristics, and interactions among nutrients, algae,
detritus, zooplankton and fish. These analyses have
led to the derivation of the ‘indirect regulation rule for
consecutive stages of ecological succession’, which
generalised the most notable interdependencies observed for other types of ecosystems (Krivtsov et al.,
2000c), and to a general classification of the eco-
48
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
system effects referred to in definitions (Krivtsov,
2001).
Indirect interrelations between Si and P availability
were also addressed by Dippner (1998). On the basis
of a simple numerical model it was concluded that indirect effect of the silicate reduction in coastal waters
causes an increased flagellate bloom, due to a high
availability of riverborne nutrient loads. These conclusions are highly in line with the results related to lakes
Suwa and Rostherne Mere quoted earlier.
3.3. Climate change studies
A number of studies considered were related to
investigation of global climate change. Norberg and
DeAngelis (1997) used a model of a closed phytoplankton–zooplankton ecosystem to investigate effects
of temperature, light and nutrients, while the majority of studies concentrated on the responses in the
terrestrial environment. Riedo et al. (1999) forced a
dynamic ecosystem model with weather scenarios derived using a general circulation model. The simulated
increase of shoot dry matter was attributed to the combination of direct effects of CO2 and increased T, and
indirect stimulation via increased N availability. The
results also highlighted the importance of site-specific
analysis.
McMurtrie and Comins (1996) used the forest
ecosystem model G’DAY to investigate possible responses to the elevated CO2 concentration. The analysis showed that responses on different time-scales are
determined by different ecosystem-level feedbacks,
thus the magnitude and even growth response to an
increase in atmospheric CO2 may be variable.
In another study van Minnen et al. (1995) used
the terrestrial carbon cycle submodel of the IMAGE
2 model to analyse the importance of feedback processes on global and regional scale. Simulations were
carried out using all combinations of CO2 fertilisation, temperature effect on plant growth, and climate
impact on soil decomposition. Consequently, strong
non-linearities between contributions of separate and
combined feedback factors were reported.
Vukicevic et al. (2001) developed a number of versions of a simplified spatially aggregated model, consisting of the following compartments: atmospheric
CO2 , vegetation, and two soil pools with different
turnover times. One of the versions also included N
cycle. The results indicated that the effects of temperature on ecosystems are manifested as a combination
of direct physiological and indirect lagged responses,
and the combined effect may therefore depend upon
specific conditions. For instance, warming and longer
growing seasons in high latitudes could either increase
or decrease NEP, depending whether indirect feedbacks of nutrients are larger or smaller than the direct
effects on NPP and respiration.
van Oene et al. (1999) modelled increased CO2
and N deposition effects on a natural vegetation succession on Dutch inland dunes. It was concluded that
indirect effects through changing competitive relations between species might be more important then
direct effects.
Dale et al. (1991) used a population model in the
site-specific ecological context to predict effects of
infestation of fir trees by the balsam woolly adelgid (BWA). The model suggested that temperature
may have an indirect influence on a spatial pattern
of living trees through effects on BWA survival and
development.
Rathgeber et al. (2000) used a biogeochemistry
model BIOME3 to study direct and indirect effects
of elevated CO2 on pine (Pinus cembra) productivity. It was concluded that in this case direct effects
will be prevalent. Post and Pastor (1996) showed,
using an individual-based forest ecosystem model
LINKAGES, that climate change results in a complex
combination of direct and indirect responses, and that
the exact outcome depends on the peculiarities of any
particular scenario. Modelling aspects and relative
importance of direct and indirect effects of climate
change on forests was also addressed in the review
by Loehle and LeBlanc (1996).
3.4. Other studies
Fath and Patten (1998) used methods of network
analysis to show that, in the ecosystem context, direct transactions between organisms produce integral
effects more positive than a simple sum of direct effects (see also Patten, 1992). This was in line with
the view that mutualism is an implicit consequence of
indirect interactions and ecosystem organisation, and
that the contribution of positive relationships should
increase along the course of evolution and ecological
succession.
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
Bockstael et al. (1995) published a progress report
on their ongoing attempt to integrate the Patuxent
landscape model (PLM) with a number of economic
submodels. The authors give a brief mentioning of
previous ‘attempts to grapple with interactions of
ecological functions and economic actions’, and imply that their study will be the first one to provide a
really good insight into indirect ecosystem effects of
current policy options over long time horizons. There
appears to have been substantial progress since then:
29 articles refer to this paper, and the readers may
wish to follow up the developments on the matter.
Among other studies it is worth mentioning the
papers of Daufresne and Loreau (2001), who examined the interactions between primary producers and
decomposers in a simple ecosystem using a stoichiometrically explicit model, and Loreau (1998), who
showed that certain changes in ecosystem properties
are indirect results of selection for different traits in
organisms.
3.5. Implications and limitations
The studies reviewed in Sections 3.1–3.3 cover a
wide range of habitats, organisms, and ecosystem processes involved and specific mathematical methods
used. However, they all have one notable feature in
common: each study enhanced the knowledge of the
investigated system by providing new information on
certain indirect interactions between its components.
Therefore the approaches used in these studies can
provide the basis for a methodological framework for
analysis of indirect relationships in ecosystems.
It should be noted that the selection of cited papers was limited by the keywords used, limitations of
the database (e.g. bias to English language journals,
restriction of the scope to titles, abstracts and keywords, etc.). Hence, quite a few relevant papers were
not found by the search. It is also worth pointing out
that the earliest reference found by the search was
published in 1991, although the database goes back
to 1981. This, of course, does not mean that the work
on modelling indirect interactions had not been carried out prior to that. Indeed, the origin of algorithms
capable of studying indirect interactions among biological organisms can be traced back to 18th century
(see references in Ulanowicz and Puccia, 1990), and
many papers quoted here extensively referred to earlier
49
Theoretical
Experimental
Observational
Fig. 1. Illustration of the methodological continuum spectrum for
analysis of indirect effects in ecology and environmental science.
The base of the spectrum represents two complimentary empirical
approaches (i.e. observational and experimental), while its top is
represented by the theoretical approach. Studies of indirect effects
may start from any point within the methodological continuum. In
practice, however, most studies appear to start at the observational
end.
work. However, it has clearly indicated that the investigations of indirect interrelations in ecological systems using mathematical modelling has greatly intensified during the last decade. I suggest that such investigations are now becoming sufficiently widespread to
warrant development of a methodological framework
for theoretical analysis of the patterns observed.
4. Comparative theoretical ecosystem analysis
The approaches used in the studies reviewed above
can be summarised in a methodological framework for
analysis of indirect relationships in ecosystems. This
will allow the scientific community to better understand and classify such relationships, and will greatly
facilitate further investigations, particularly related to
the assessment of subtle differences in the indirect effects due to peculiarities of particular ecosystems.
It was previously thought (Strauss, 1991; Abrams
et al., 1996) that approaches for studies of indirect
relationships are positioned between two extremes,
namely experimental and theoretical. In fact, however, the methodological continuum may be better
illustrated (Fig. 1) by a triangle with experimental,
observational, and theoretical nodes, and with most
studies starting on the observational end. It should
50
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
be noted here that the information obtained through
ecological monitoring is valuable in its own right, and
much of the knowledge of indirect effects in nature
has been obtained through comparative synthesis of
this information aided by careful interpretation of the
results of simple statistical analysis. In addition, many
(if not all) experimental and theoretical studies base
(at least partly) their own design on the information
available from observations and routine monitoring
programmes. For example, the Heron Wood research
discussed above started as a purely observational
study devoted to records of fungal fruiting, which
was later expanded into a comprehensive monitoring
programme of soil and forest floor biota, followed
by application of a suite of mathematical techniques
to the data collected (see Krivtsov et al., 2003b,c,d,
2004a, and references therein). Another example relates to investigations of indirect effects by Patten and
colleagues, who started with a combination of the
observational and experimental approaches (B. Fath,
personal communication). Basic radioactive tracer experiments were used to investigate internal ecosystem
flows (Patten and Witkamp, 1967). The observations
showed that the introduced tracer (Cs-137) was essentially everywhere in the ecosystem (although it
was only introduced into a selected area). The results, therefore, suggested that indirect pathways were
abundant in the ecosystem, and that the ecosystem
could be described as a network of interconnected
parts. These conclusions led to comprehensive modelling analysis and subsequently resulted in a number
of studies (some of which have been quoted throughout this paper) containing new theoretical findings
related to indirect effects. Hence, the recognition
of the importance of the observational part of the
methodological spectrum is indispensable.
Within the proposed framework, the CTEA may
comprise three stages outlined below. An important
prerequisite for CTEA is availability of data from
detailed monitoring studies. At stage 1, the data from
each ecosystem are analysed independently using a
suite of statistical techniques and methods of network analysis, and the interrelations observed are
then incorporated in the process-based simulation
models, constructed, e.g., using differential equations
or agent-based modelling. At stage 2, a complete
sensitivity analysis of the simulated dynamics of output variables on input values is carried out for each
model. The indirect relationships revealed by sensitivity analysis are then interpreted in terms of the existing ecological knowledge. If a variable is found to
be sensitive to changes in apparently unrelated input,
then either model definitions or the existing ecological theories are likely to require amendments (see,
e.g. Krivtsov et al., 2000b,c). Statistical techniques
might once again help interpretation of the peculiarities observed. At stage 3, the indirect delayed relationships found at previous stages could be classified
in relation to the underlying mechanisms and peculiarities of their manifestation. The latter could then
be used to assess the differences between different
types of ecosystems (e.g. aquatic versus terrestrial),
or differences related to small variation in ecosystem
structure (e.g. absence/presence and representation of
trophic levels, composition of a guild, parameters of
physical environment, etc.). The hypotheses about the
discovered relationships could now be tested using
structural equation modelling (see above the example
of Malaeb et al., 2000, and references therein), and
the whole process may need to be repeated from stage
1, particularly if additional data are available.
It should be noted that all the methods so far applied to investigations of indirect effects have both
advantages and limitations. Many of these have been
previously addressed (see, e.g., Wootton, 1994a, and
references therein) and no attempt to discuss the
benefits and disadvantages of the techniques used to
investigate indirect interactions has been done in this
paper. Neither it was intended to address any controversy and related discussion resulted from specific
applications (and/or implications of such applications) of any particular method (e.g. for arguments
regarding the conclusions reached using methods of
network analysis, see, e.g. Wootton, 1994a; Patten
et al., 1990, and references therein). Instead, it is
argued that the mathematical techniques should be
used in concert, thus allowing a detailed complementary insight into complex patterns of mechanisms
underpinning dynamics of natural ecosystems.
Although there as yet seems to be no research that
has rigorously followed all the sequence described
above, the components of the methodological framework presented here were variously applied in studies
reviewed in Section 3. For example, in the Rostherne
Mere case study, a comprehensive data set was analysed by means of statistical techniques, which facili-
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
tated the construction of a dynamic simulation model
(stage 1). This was then followed by an extensive
sensitivity analysis, which revealed a number of unexpected relationships (e.g. between winter concentration of dissolved Si and summer cyanobacterial
maximum). These results were then confirmed by new
statistical analysis, and ultimately resulted in changes
of the contemporary theory (stage 2). Then some of
the indirect relationships studied were classified in relation to the underlying mechanisms (i.e. in this case
directly and indirectly mediated), which facilitated
extrapolation of the conclusions for other types of
ecosystems (stage 3). A number of ‘what–if’ scenarios
examined provided information on the differences of
manifestation of the indirect effect of Si on cyanobacterial bloom in relation to, e.g., hydrological and
morphological parameters, thus assessing differences
between ecosystem types (e.g. deep versus shallow
lakes, lakes with high versus lakes with slow retention
time). It is intended that further work should involve
application of structural equation modelling, and the
comparison with the indirect relationships revealed for
a terrestrial ecosystem (Krivtsov et al., in preparation).
The methodological framework presented here is
aimed at bringing together separate lines of current
investigations, hence combining them in an integrative approach. However, further development and systematic application of CTEA is vital for improving
the accuracy of ecological forecasting, and has, therefore, potential societal benefits related to issues of
environmental impact assessment and sustainable development. In particular, I envisage that further developments should pay much attention to similarities
and differences of the indirect effects revealed in various types of ecosystems, or at different stages of
the ecosystem development, and that the characteristics (e.g. magnitude, sign, etc.) of indirect interactions
should be increasingly used for describing differences
in ecosystem state, structure and overall functioning.
For example, analysis of specific ecosystems may benefit from answering the following (to name but a few)
questions:
51
• Is the pattern of indirect effects relatively constant, or subject to (system specific) seasonal and
longer-term changes?
• How does the pattern of indirect interactions change
due to pollution, disturbance and various management practices?
• Do indirect interactions predominant in an ecosystem help to stabilise this ecosystem?
• What is the relative contribution of indirect interactions to resistance, resilience, and facilitation of
successional changes?
• How have the indirect effects changed during the
evolution of a particular ecosystem, and what was
their contribution towards the driving forces of this
evolution?
5. Summary
Indirect interrelations between ecosystem processes
are usually not obvious. Often they are realised after
a considerable time lag and/or separated spatially,
and, therefore, are easily overlooked. The understanding of these relationships, however, is indispensable
for sustainable development and ecomanagement.
Investigation of mechanisms underpinning complex
indirect delayed relationships is greatly aided by
mathematical methods, including statistical analysis
(e.g. parametric and non-parametric tests, path analysis, etc.), simulation modelling, network analysis,
etc., which have been useful in a wide range of the
recent studies reviewed. An emerging framework of
CTEA calls for these methods to be applied in concert, and in a wide range of environmental studies.
This will not only lead to a greater understanding of
the specific ecosystem processes, but will also allow
elucidation of the role of indirect effects in ecosystem succession, evolution, recovery after pollution,
disturbance, and alterations of prevalent patterns due
to changes in management practices.
Acknowledgements
• What types of indirect effects are important for the
overall functioning of an ecosystem under investigation?
• How does the importance of indirect effects compare with the importance of direct effects?
This study has benefited from comments of A.
Kartushinsky, R. Seppelt, and A. Voinov. Particular
thanks goes to B. Fath, who provided a very detailed (i.e. with many specific comments) review of
52
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
style and content, which helped to improve the final
version of the manuscript rather considerably. This
paper represents a considerably expanded version of
the preprint previously published (Krivtsov, 2002)
in the IEMSS conference proceedings (available
at http://www.iemss.org/iemss2002/proceedings/pdf/
volume%20uno/410 Krivtsov.pdf).
References
Abrams, P.A., 1993. Indirect effects arising from optimal foraging.
In: Kawanabe, H., Cohen, J.E., Iwasaki, K. (Eds.), Mutualism
and Community Organisation: Behavioral, Theoretical and
Food Web Approaches. Oxford University Press, Oxford,
pp. 255–279.
Abrams, P.A., Menge, B.A., Mittelbach, G.G., Spiller, D.A.,
Yodzis, P., 1996. The role of indirect effects in food webs.
In: Polis, G., Winemiller, K. (Eds.), Food Webs: Integration
of Patterns and Dynamics. Chapman & Hall, New York,
pp. 371–395.
Bartell, S.M., Lefebvre, G., Kaminski, G., Carreau, M., Campbell,
K.R., 1999. An ecosystem model for assessing ecological risks
in Quebec rivers, lakes, and reservoirs. Ecol. Modell. 124, 43–
67.
Blagodatsky, S.A., Richter, O., 1998. Microbial growth in soil and
nitrogen turnover: a theoretical model considering the activity
state of microorganisms. Soil Biol. Biochem. 30, 1743–1755.
Blagodatsky, S.A., Yevdokimov, I.V., Larionova, A.A., Richter, J.,
1998. Microbial growth in soil and nitrogen turnover: model
calibration with laboratory data. Soil Biol. Biochem. 30, 1757–
1764.
Bockstael, N., Costanza, R., Strand, I., Boynton, W., Bell, K.,
Wainger, L., 1995. Ecological economic modeling and valuation
of ecosystems. Ecol. Econ. 14, 143–159.
Budiko, M.I., 1968. O proishozsdenii lednikovih epoh (About the
origin of glacial epochs). Meteorologiya i Gidrologiya 11 (in
Russian).
Budiko, M.I., 1977. Global’naya Ekologiya (Global Ecology).
Misl’, Moscow (in Russian).
Carrer, S., Opitz, S., 1999. Trophic network model of a shallow
water area in the northern part of the Lagoon of Venice. Ecol.
Modell. 124, 193–219.
Christensen, V., Pauly, D., 1992. Ecopath-Ii—a software for
balancing steady-state ecosystem models and calculating
network characteristics. Ecol. Modell. 61, 169–185.
Dale, V.H., Gardner, R.H., Deangelis, D.L., Eagar, C.C., Webb,
J.W., 1991. Elevation-mediated effects of balsam woolly adelgid
on southern Appalachian spruce-fir forests. Can. J. For. Res.
(Rev. Can. Rec. For.) 21, 1639–1648.
Daskalov, G.M., 2002. Overfishing drives atrophic cascade in the
Black Sea. Mar. Ecol. Prog. Ser. 225, 53–63.
Daufresne, T., Loreau, M., 2001. Ecological stoichiometry, primary
producer–decomposer interactions, and ecosystem persistence.
Ecology 82, 3069–3082.
de Ruiter, P.C., Moore, J.C., Zwart, K.B., Bouwman, L.A., Hassink,
J., Bloem, J., Devos, J.A., Marinissen, J.C.Y., Didden, W.A.M.,
Lebbink, G., Brussaard, L., 1993. Simulation of nitrogen
mineralization in the belowground food webs of 2 winter-wheat
fields. J. Appl. Ecol. 30, 95–106.
Dippner, J.W., 1998. Competition between different groups of
phytoplankton for nutrients in the southern North Sea. J. Mar.
Syst. 14, 181–198.
Dokuchaiev, V.V., 1948. Uchenie o zonah prirodi (A treatise on
the zonation in nature). Moscow (in Russian).
Fath, B.D., Patten, B.C., 1998. Network synergism: emergence
of positive relations in ecological systems. Ecol. Modell. 107,
127–143.
Fath, B.D., Patten, B.C., 1999. Review of the foundations of
network environ analysis. Ecosystems 2, 167–179.
Hanratty, M.P., Liber, K., 1996. Evaluation of model predictions
of the persistence and ecological effects of diflubenzuron in a
littoral ecosystem. Ecol. Modell. 90, 79–95.
Higashi, M., Patten, B.C., 1986. Further aspects of the analysis of
indirect effects in ecosystems. Ecol. Modell. 31, 69–77.
Holt, R.D., 1977. Predation, apparent competition, and the structure
of prey communities. Theoret. Popul. Biol. 12, 197–229.
Holt, R.D., Lawton, J.H., 1994. The ecological consequences of
shared natural enemies. Annu. Rev. Ecol. Syst. 25, 495–520.
Huisman, J., Grover, J.P., van der Wal, R., van Andel, J., 1999.
In: Olff, H., Brown, V.K., Drent, R.H. (Eds.), Competition for
Light, Plant-species Replacement and Herbivore Abundance
Along Productivity Gradients. Blackwell Science, pp. 239–269.
Hulot, F.D., Lacroix, G., Lescher-Moutoue, F.O., Loreau, M., 2000.
Functional diversity governs ecosystem response to nutrient
enrichment. Nature 405, 340–344.
Hunt, H.W., Coleman, D.C., Ingham, E.R., Ingham, R.E., Elliott,
E.T., Moore, J.C., Rose, S.L., Reid, C.P.P., Morley, C.R., 1987.
The detrital food web in a shortgrass prairie. Biol. Fert. Soils
3, 57–68.
Hunt, H.W., Trlica, M.J., Redente, E.F., Moore, J.C., Detling, J.K.,
Kittel, T.G.F., Walter, D.E., Fowler, M.C., Klein, D.A., Elliott,
E.T., 1991. Simulation-model for the effects of climate change
on temperate grassland ecosystems. Ecol. Modell. 53, 205–246.
Hunt, H.W., Wall, D.H., 2002. Modelling the effects of loss of
soil biodiversity on ecosystem function. Glob. Change Biol. 8,
33–50.
Hutchinson, G.E., 1957. A Treatise on Limnology. Chapman &
Hall, London.
Intachat, J., Holloway, J.D., Staines, H., 2001. Effects of weather
and phenology on the abundance and diversity of geometroid
moths in a natural Malaysian tropical rain forest. J. Trop. Ecol.
17, 411–429.
Jorgensen, S.E., 1994. Fundamentals of Ecological Modelling, 2nd
ed. Elsevier, Amsterdam.
Jorgensen, S.E., 1980. Lake Management. Pergamon Press, Oxford.
Krivtsov, V., Bellinger, E., Sigee, D., Corliss, J., 1998. Application
of SEM XRMA data to lake ecosystem modelling. Ecol. Modell.
113, 95–123.
Krivtsov, V., Bellinger, E.G., Sigee, D.C., 1999a. Modelling of
elemental associations in Anabaena. Hydrobiologia 414, 77–83.
Krivtsov, V., Sigee, D., Corliss, J., Bellinger, E., 1999b.
Examination of the phytoplankton of Rostherne Mere using a
simulation mathematical model. Hydrobiologia 414, 71–76.
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
Krivtsov, V., Tien, C., Sigee, D., Bellinger, E., 1999c. X-ray
microanalytical study of the protozoan Ceratium hirundinella
from Rostherne Mere (Cheshire, UK): dynamics of intracellular
elemental concentrations, correlations and implications for
overall ecosystem functioning. Neth. J. Zool. 49, 263–274.
Krivtsov, V., Bellinger, E., Sigee, D., 2000a. Incorporation of
the intracellular elemental correlation pattern into simulation
models of phytoplankton uptake and population dynamics. J.
Appl. Phycol. 12, 453–459.
Krivtsov, V., Bellinger, E., Sigee, D., Corliss, J., 2000b.
Interrelations between Si and P biogeochemical cycles—a new
approach to the solution of the eutrophication problem. Hydrol.
Processes 14, 283–295.
Krivtsov, V., Corliss, J., Bellinger, E., Sigee, D., 2000c. Indirect
regulation rule for consecutive stages of ecological succession.
Ecol. Modell. 133, 73–82.
Krivtsov, V., 2001. Study of cause-and-effect relationships in
the formation of biocenoses: their use for the control of
eutrophication. Russ. J. Ecol. 32, 230–234.
Krivtsov, V., Garside, A., Thompson, J., Bezginova, T., Salmond,
R., Liddell, K., Griffiths, B., Staines, H., Watling, R.,
Palfreyman, J., 2001a. Interrelations between soil nematodes,
bacteria, fungi and protozoa in the ‘Dawyck cryptogamic
sanctuary’ in winter. Russ. J. Nematol. 9, 150–151.
Krivtsov, V., Goldspink, C., Sigee, D.C., Bellinger, E.G., 2001b.
Expansion of the model ‘Rostherne’ for fish and zooplankton:
role of top-down effects in modifying the prevailing pattern of
ecosystem functioning. Ecol. Modell. 138, 153–171.
Krivtsov, V., Sigee, D., Bellinger, E., 2001c. A one-year study
of the Rostherne Mere ecosystem: seasonal dynamics of water
chemistry, plankton, internal nutrient release, and implications
for long-term trophic status and overall functioning of the lake.
Hydrol. Processes 15, 1489–1506.
Krivtsov, V., 2002. Indirect effects in ecosystems: a review of
recent modelling studies and a methodological framework
for comparative theoretical analysis. In: Rizzoli, A.E.,
Jakeman, A.J. (Eds.), Integrated Assessment and Decision
Support. Proceedings of the First Biennial Meeting of
the International Environmental Modelling and Software
Society, Lugano, pp. 233–238. http://www.iemss.org/iemss
2002/proceedings/pdf/volume%20uno/410 Krivtsov.pdf.
Krivtsov, V., Liddell, K., Salmond, R., Garside, A., Thompson,
J., Bezginova, T., Griffiths, B., Staines, H.J., Watling, R.,
Palfreyman, J.W., 2002a. Analysis of microbial interactions
in forest soil. In: Shumny, V.K., Kolchanov, N.A., Fedotov,
A.M. (Eds.), Proceedings of the First Workshop on Information
Technologies Application to Problems of Biodiversity and
Dynamics of Ecosystems in North Eurasia (BDENE:WITA
2001). Selected Papers. IC&G, Novosibirsk, pp. 322–331.
Krivtsov, V., Sigee, D., Bellinger, E., 2002b. Elemental
concentrations and correlations in winter micropopulations of
Stephanodiscus rotula: an autecological study over a period of
cell size reduction and restoration. Eur. J. Phycol. 37, 27–35.
Krivtsov, V., Bellinger, E., Sigee, D., 2003a. Ecological study of
Stephanodiscus rotula during a spring diatom bloom: dynamics
of intracellular elemental concentrations and correlations in
relation to water chemistry, and implications for overall
53
geochemical cycling in a temperate lake. Acta Oecol. 24, 265–
274.
Krivtsov, V., Liddell, K., Bezginova, T., Salmond, R., Garside,
A., Thompson, J., Palfreyman, J.W., Staines, H.J., Watling, R.,
Brendler, A., Griffiths, B., 2003b. Ecological interactions of
heterotrophic flagellates, ciliates and naked amoebae in forest
litter of the Dawyck Cryptogamic Sanctuary (Scotland, UK).
Eur. J. Protistol. 39, 183–198.
Krivtsov, V., Illian, J.B., Liddell, K., Garside, A., Bezginova, T.,
Salmond, R., Thompson, J., Griffiths, B., Staines, H.J., Watling,
R., Brendler, A., Palfreyman, J.W., 2003c. Some aspects of
complex interactions involving soil mesofauna: analysis of the
results from a Scottish woodland. Ecol. Modell. 170 (2–3),
441–452.
Krivtsov, V., Walker, S.J.J., Watling, R., Knott, D., Palfreyman,
J.W., Staines, H.J., 2003d. Analysis of the fungal fruiting
patterns at the Dawyck Botanic Garden. Ecol. Modell. 170 (2–
3), 393–406.
Krivtsov, V., Walker, S.J.J., Staines, H.J., Watling, R., BurtSmith, G., Garside, A., 2004a. Integrative analysis of ecological
patterns in an untended temperate woodland utilising standard
and customised software. Environ. Modell. Softw. 19 (3), 325–
335.
Leriche, H., LeRoux, X., Gignoux, J., Tuzet, A., Fritz, H., Abbadie,
L., Loreau, M., 2001. Which functional processes control the
short-term effect of grazing on net primary production in
grasslands? Oecologia 129, 114–124.
Loehle, C., LeBlanc, D., 1996. Model-based assessments of climate
change effects on forests: a critical review. Ecol. Modell. 90,
1–31.
Loladze, I., Kuang, Y., Elser, J.J., 2000. Stoichiometry in producergrazer systems: linking energy flow with element cycling. Bull.
Math. Biol. 62, 1137–1162.
Loreau, M., 1998. Ecosystem development explained by
competition within and between material cycles. Proc. R. Soc.
London Ser. B 265, 33–38.
Malaeb, Z.A., Summers, J.K., Pugesek, B.H., 2000. Using
structural equation modeling to investigate relationships among
ecological variables. Environ. Ecol. Statist. 7, 93–111.
McClanahan, T.R., Sala, E., 1997. A Mediterranean rocky-bottom
ecosystem fisheries model. Ecol. Modell. 104, 145–164.
McMurtrie, R.E., Comins, H.N., 1996. The temporal response of
forest ecosystems to doubled atmospheric CO2 concentration.
Glob. Change Biol. 2, 49–57.
Menge, B.A., 1995. Indirect effects in marine rocky intertidal
interaction webs—patterns and importance. Ecol. Monogr. 65,
21–74.
Miller, T.E., 1994. Direct and indirect species interactions in an
early old-field plant community. Am. Nat. 143, 1007–1025.
Mortimer, C.H., 1941. The exchange of dissolved substances
between mud and water in lakes. J. Ecol. 29, 280–329.
Mortimer, C.H., 1942. The exchange of dissolved substances
between mud and water in lakes. J. Ecol. 30, 147–201.
Naito, W., Miyamoto, K., Nakanishi, J., Masunaga, S., Bartell,
S.M., 2002. Application of an ecosystem model for aquatic
ecological risk assessment of chemicals for a Japanese lake.
Water Res. 36, 1–14.
54
V. Krivtsov / Ecological Modelling 174 (2004) 37–54
Navarrete, S.A., Menge, B.A., 1996. Keystone predation and
interaction strength: interactive effects of predators on their
main prey. Ecol. Monogr. 66, 409–429.
Norberg, J., DeAngelis, D., 1997. Temperature effects on stocks
and stability of a phytoplankton–zooplankton model and the
dependence on light and nutrients. Ecol. Modell. 95, 75–86.
Oglethorpe, D.R., Sanderson, R.A., O’Callaghan., , 1995. The
economic and ecological impact at the farm level of adopting
Pennine Dales environmentally sensitive area (ESA) grassland
management prescriptions. J. Environ. Plan. Manage. 38, 125–
135.
Oglethorpe, D.R., Sanderson, R.A., 1999. An ecological–economic
model for agri-environmental policy analysis. Ecol. Econ. 28,
245–266.
Ortiz, M., Wolff, M., 2002a. Application of loop analysis to benthic
systems in northern Chile for the elaboration of sustainable
management strategies. Mar. Ecol. Prog. Ser. 242, 15–27.
Ortiz, M., Wolff, M., 2002b. Dynamical simulation of mass-balance
trophic models for benthic communities of north-central Chile:
assessment of resilience time under alternative management
scenarios. Ecol. Modell. 148, 277–291.
Patten, B.C., Witkamp, M., 1967. Systems analysis of Cs-137
kinetics in terrestrial microcosms. Ecology 48, 813–824.
Patten, B.C., Bosserman, R.W., Finn, J.T., Gale, W.G., 1976.
Propagation of cause in ecosystems. In: Patten, B.C. (Ed.),
Systems Analysis and Simulation in Ecology. Academic Press,
New York, pp. 457–579.
Patten, B.C., 1985. Energy cycling in the ecosystem. Ecol. Modell.
28, 1–71.
Patten, B.C., Higashi, M., Burns, T.P., 1990. Trophic dynamics in
ecosystem networks—significance of cycles and storage. Ecol.
Modell. 51, 1–28.
Patten, B.C., 1992. Energy, emergy and environs. Ecol. Modell.
62, 29–69.
Post, W.M., Pastor, J., 1996. Linkages—an individual-based forest
ecosystem model. Clim. Change 34, 253–261.
Rathgeber, C., Guiot, J., Edouard, J.L., 2000. Using a
biogeochemical model in dendroecology. Application to Pinus
cembra. C.R. Acad. Sci. Ser. Iii 323, 489–497.
Reynolds, C.S., 1984. The Ecology of Freshwater Phytoplankton.
Cambridge University Press, Cambridge.
Riedo, M., Gyalistras, D., Fischlin, A., Fuhrer, J., 1999. Using
an ecosystem model linked to GCM-derived local weather
scenarios to analyse effects of climate change and elevated CO2
on dry matter production and partitioning, and water use in
temperate managed grasslands. Glob. Change Biol. 5, 213–223.
Rillig, M.C., Wright, S.F., Eviner, V.T., 2002. The role of
arbuscular mycorrhizal fungi and glomalin in soil aggregation:
comparing effects of five plant species. Plant and Soil 238,
325–333.
Robinson, L.A., Frid, C.L.J., 2003. Dynamic ecosystem models
and the evaluation of ecosystem effects of fishing: can we
make meaningful predictions? Aquat. Conserv. Mar. Freshwater
Ecosyst. 13, 5–20.
Schoener, T.W., 1983. Field experiments on interspecific
competition. Am. Nat. 122, 240–285.
Schopf, J.W., 1983. Earth’s Earliest Biosphere. Princeton
University Press, Princeton.
Sinclair, A.R.E., Krebs, C.J., Fryxell, J.M., Turkington, R., Boutin,
S., Boonstra, R., Seccombe-Hett, P., Lundberg, P., Oksanen, L.,
2000. Testing hypotheses of trophic level interactions: a boreal
forest ecosystem. Oikos 89, 313–328.
Strauss, S.Y., 1991. Indirect effects in community ecology—their
definition, study and importance. Trends Ecol. Evol. 6, 206–
210.
Svendsen, H., Hansen, S., Jensen, H.E., 1995. Simulation of
crop production, water and nitrogen balances in 2 German
agroecosystems using the daisy model. Ecol. Modell. 81, 197–
212.
Ulanowicz, R.E., Puccia, C.J., 1990. Mixed trophic impacts in
ecosystems. Coenoses 5, 7–16.
van Minnen, J.G., Goldewijk, K.K., Leemans, R., 1995. The
importance of feedback processes and vegetation transition in
the terrestrial carbon cycle. J. Biogeogr. 22, 805–814.
van Oene, H., Berendse, F., de Kovel, C.G.F., 1999. Model analysis
of the effects of historic CO2 levels and nitrogen inputs on
vegetation succession. Ecol. Appl. 9, 920–935.
Vernadsky, V.I., 1926. Biosphera (Biosphere). Leningrad (in
Russian).
Vukicevic, T., Braswell, B.H., Schimel, D., 2001. A diagnostic
study of temperature controls on global terrestrial carbon
exchange. Tellus Ser. B 53, 150–170.
Walters, C., Christensen, V., Pauly, D., 1997. Structuring
dynamic models of exploited ecosystems from trophic
mass-balance assessments. Rev. Fish Biol. Fish. 7, 139–
172.
Wardle, D.A., 2002. Communities and Ecosystems. Linking
the Aboveground and Belowground Components. Princeton
University Press, Princeton.
Whipple, S.J., 1999. Analysis of ecosystem structure and function:
extended path and flow analysis of a steady-state oyster reef
model. Ecol. Modell. 114, 251–274.
Wootton, J.T., 1993. Indirect effects and habitat use in an intertidal
community—interaction chains and interaction modifications.
Am. Nat. 141, 71–89.
Wootton, J.T., 1994a. The nature and consequences of indirect
effects in ecological communities. Annu. Rev. Ecol. Syst. 25,
443–466.
Wootton, J.T., 1994b. Predicting direct and indirect effects—an
integrated approach using experiments and path-analysis.
Ecology 75, 151–165.
Wootton, J.T., 2002a. Indirect effects in complex ecosystems:
recent progress and future challenges. J. Sea Res. 48, 157–172.
Wootton, J.T., 2002b. Mechanisms of successional dynamics:
consumers and the rise and fall of species dominance. Ecol.
Res. 17, 249–260.
Yodzis, P., Innes, S., 1992. Body size and consumer-resource
dynamics. Am. Nat. 139, 1151–1175.