Ecological Complexity 28 (2016) 36–46

Contents lists available at ScienceDirect

Ecological Complexity
journal homepage: www.elsevier.com/locate/ecocom

Original Research Article

Vegetation, herbivores and fires in savanna ecosystems: A network

perspective
Antonio Bodinia,* , Nicola Clericib
a
Department of Life Sciences, University of Parma, Viale Usberti 11/A, Parma, Italy
b
Biology Program, Faculty of Natural Sciences and Mathematics, Universidad del Rosario, Kr 26 No 63B-48, Bogotá, Colombia

A R T I C L E I N F O A B S T R A C T

Article history:
Received 14 June 2016 The dynamics of savanna ecosystems depends on the interplay between multiple factors such as grazing,
Received in revised form 8 October 2016 browsing, fires, rainfall regime and interactions between grass and woody vegetation. In most modelling
Accepted 9 October 2016 applications this interplay may not be fully understood because some of these drivers enter the models as
Available online 28 October 2016 dynamically independent factors. In this paper we consider such factors as dynamic variables. To analyze
their interplay we focus on the structure of the interactive network of variables and exploit the properties
Keywords: of signed digraphs using the algorithm of Loop Analysis. Qualitative signed digraphs for the savanna
Savanna ecosystems ecosystem are developed and their predictions used to interpret patterns of abundance observed in case
Cause and effect mechanisms
studies selected from the literature. The outcomes of this exercise unveil that: 1) the structure of the
Complex systems
interactions is appropriate locus for the explanation of patterns observed in savannas; 2) signed digraph
Fires
Loop analysis can help disentangling causative mechanisms by linking correlation patterns, source of change and
Positive feedback network structure. This study highlights that central to the understanding of savanna dynamics is our
ability to diagram the important relationships and understand how they interrelate with sources of
variations to cause ecosystem change.
ã 2016 Elsevier B.V. All rights reserved.

1. Introduction The mechanisms that govern the evolution and allow the
maintenance of savannas have long been the target of investigation
Savannas are defined as seasonal ecosystems characterized by (Dublin et al., 1990; Sankaran et al., 2004; Staver et al., 2011). It has
the co-dominance of a continuous herbaceous stratum, dominated been generally accepted that characteristic, across site (Archer,
by C4 grasses, and a discontinuous layer of fire-tolerant shrubs and 1989; Adamoli et al., 1990; Savage and Swetnam, 1990; Kaufmann
trees (Walker and Noy-Meir 1982; Ratnam et al., 2011). Further et al., 1994) patterns of co-occurrence for woody and grass
identification of savannas exists on the basis of their structure and vegetation depend on a complex interplay between grazing,
on the environmental conditions (Cole, 1986). Savannas are browsing, rainfall and fire intensity (Scholes and Archer, 1997;
geographically widespread and cover approximately a fifth of Higgins et al., 2000; Sankaran et al., 2008). Disentangling this
the world’s land surface (Sankaran et al., 2004); they also represent interplay has become a major focus of investigation (McNaughton,
a key carbon sink with respect to global biogeochemical cycles 1992; van Langevelde et al., 2003; Holdo et al., 2009; Holdo,
(Thiessen et al., 1998). Savannas are socio-economically important Sinclair et al., 2009) and observed patterns were analyzed using
ecosystems because they support a large and fast growing both statistical (correlation, linear and multiple regression
proportion of the world’s population and the bigger part of their analysis, Roques et al., 2001; regression tree analysis, Sankaran
livestock (Scholes and Archer, 1997). Also, tropical and sub-tropical et al., 2008; Bayesian state space models, Holdo et al., 2009; Holdo,
savannas host a large number of species under extinction risk; Sinclair et al., 2009) and mathematical models (stability analysis of
because of this they are considered key ecosystems for biodiversity equilibria, Higgins et al., 2010; De Michele et al., 2011; Holdo et al.,
conservation (Gill, 2015). 2012).
Modelling applications greatly contributed to our knowledge
about conditions for co-existence, bi-stability, limit cycles and
feedback mechanisms in savanna ecosystems. Most of these
* Corresponding author.
models, however, considered only grass and trees as dynamic
E-mail addresses: antonio.bodini@unipr.it (A. Bodini), variables whereas other key factors such as herbivores, browsers,
nicola.clerici@urosario.edu.co (N. Clerici). fires and rainfall were treated as positive or negative contributions

http://dx.doi.org/10.1016/j.ecocom.2016.10.001
1476-945X/ã 2016 Elsevier B.V. All rights reserved.
 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46 37

to the rate of change of the variables via parameter estimation (van one variable on the growth rate of another: arrow and circle-head
Langevelde et al., 2003; Higgins et al., 2010; Staver et al., 2011; links originate from the signs of the coefficients of the Jacobian
Bekage et al., 2011; De Michele et al., 2011; but see Holdo et al., matrix for a system of differential equations (Puccia and Levins,
2012). By these models only the dynamics of grasses and trees in 1986, see Appendix A in the Supplemental on line material, SM
respect to each other and under the effect of external drivers that henceforth).
were set up at different levels (i.e. levels of browsing, grazing, or Using qualitative mathematics to analyze pathways and system
fire intensity) could be investigated. This approach treats the feedbacks, allows the making of predictions about a variable’s
drivers as independent factors that are not influenced by the response to perturbations. Any perturbation emanates from the
dynamic variables, and do not affect each other. affected variable and it is transmitted along direct and indirect
Nevertheless browsers and grazers as well as fires may be pathways to other variables. Such pathways determine the
dynamically affected by the vegetation variables and through them qualitative direction of change (i.e., whether a variable increases,
may also indirectly interact with each other (McNaughton, 1992; decreases or remains the same) as modulated by the feedbacks
Holdo et al., 2009; Holdo, Sinclair et al., 2009). Including these formed by all the variables in the system. For relatively small
factors as variables in a model can better portray the complex systems (i.e., <5 variables), this can easily be accomplished
dynamics of savanna ecosystems and possibly enlarge our through direct analysis of the signed digraph (Puccia and Levins,
comprehension of how these ecosystems function. This paper 1986, SM, Appendix A). Fig. 1 shows a simple predator-prey model
focuses on savannas as multi component systems, in which factors as a signed digraph.
that are commonly assumed as dynamically independent enter as The interaction between a predator and its prey gives rise to a
dynamic variables. negative feedback. A feedback is always associated to a loop. In
When the number of interacting variables augments, multiple Fig. 1 this loop can be easily visualized by following the direction of
linkages are established. One obvious consequence is that the links: from X (Y) to Y (X) and back. This loop produces a
complexity increases: for example system feedbacks may become negative feedback, according to the product of the links that make
intricate and their effects difficult to disentangle (Lane, 1998). The the circuit. Now suppose something happens that makes the rate of
effects of such complex interactions must reflect on dynamical change of X increase (i.e. its fecundity augments). Some of this
patterns; therefore to examine the structure of the interactions impact would be passed along to Y (the more prey the more
may contribute to unveil how patterns are produced. According to predators). The final outcome will be a change in Y proportional to
this, we focus here on the linkage structure that is established the magnitude of the intervention on X multiplied by the strength
when woody plants, grass, browsers, grazers and fires dynamically of the link from X to Y (effect pathway) divided by the “gain” or
interact. In particular we analyze how the structure of the “feedback” of the whole system. This latter factor measures the
interactions mediates the response of the variables to external resistance of the whole system to change. If there are no other
press perturbations that change the parameters that govern the variables in the system then our naïve expectation about this
growth rate of the variables (Bender et al., 1984, Puccia and Levins change would be easily met, depending on the relative magnitude
1986). of the links and feedbacks. A detailed explanation of how these
The objective of this exercise is twofold: a) we want to explore concepts refer to a graphical algorithm to make predictions is given
to what extent the structure of the interactions may explain in the Appendix A of the SM.
observed patterns in savanna ecosystems; b) we examine how the In larger and more complex systems, there can be a very high
analysis of the linkage structure can help interpret those patterns number of pathways (both direct and indirect) between input and
in terms of cause and effect. Thus, finding some new mechanism response variables; this can make graphical feedback analysis
responsible for patterns in savanna ecosystems is not among the difficult. In such circumstances, one can calculate response
objectives of this work; rather by this study we attempt to frame predictions from mathematical operations on the community
known mechanisms in the perspective offered by the analysis of matrix (matrix A in Fig. 1). Hence, the net effect (the sum of the
the network of the interactions. direct effects plus all the individual indirect effects) on variable i
To accomplish this exercise we exploited the qualitative resulting from a perturbation on variable j is given by the j  ith
properties of signed digraphs by means of the algorithm of Loop
element of the inverse community matrix ½A1 . The signs of the
Analysis (Levins 1974; Puccia and Levins, 1986). This technique
coefficients of the inverse of the community matrix give the
precludes any quantitative statement but it offers the opportunity
directions of change expected for the variables following parame-
to connect in a causal perspective the structure of the linkages
ter changes in the equations of the variables themselves (Montoya
between the variables and their patterns of variation (Dambacher
et al., 2009).
and Ramos-Jiliberto, 2007).
To obtain robust predictions we used a routine that randomly
Central in this effort was our ability to diagram the important
assigns numerical values to the coefficients of the community
causal relationship and understand how they interrelate. Signed
matrix (i.e. the coefficients of the links in the signed digraph).
digraphs were assembled on the base of commonly accepted
interactions between the variables. Alternative models were
developed and selected according to their ability to capture and
describe observed patterns that were reported in selected case
studies that we extracted from the literature.

2. Methods

2.1. Qualitative modelling

Qualitative models are used here sensu Puccia and Levins

(1986). A qualitative model graphically represents interactions Fig. 1. Graph of a predator-prey system, its community matrix (A) and the matrix of
between variables in a system using only two types of connections: predictions (A1). Predictions can be read as follows: for a press perturbation that
arrow (!) for positive effect and circle-head link ( ) for increases the rate of change of X (positive input) no variation ðaXX Þ1 ¼ 0 is
negative effect. Effects are dynamical as they refer to the action of expected for X itself and an increase ðaYX Þ1 ¼ þ is predicted for Y.
38 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46

Numerical values are extracted from a uniform distribution. This emphasize on realism and generality (Puccia and Levins 1986;
procedure was executed, for each model, N  N  100 times, where Knapp et al., 2004) and necessarily leave out details in favor of a
N is the dimension of the matrix A. Of these matrices, only those more general representation, the typical approach that qualitative
that satisfied the asymptotic Lyapunov criteria (Logofet, 1993) analysis privileges.
were accepted and inverted. On this set of inverse matrices the According to the bulk of the literature, core variables for
routine calculated predictions. Each prediction becomes a proba- savanna ecosystem models are the biomass of grass and woody
bility of sign determined on the base of the percentage of positive vegetation (Scholes and Archer, 1997). Trees and grasses are said to
signs, negative signs and zeroes that characterize the response of a compete for water in the upper soil profile, and grass is a superior
given variable over the entire set of the matrices. To compile the competitors for this resource (Le Roux et al., 1995). Trees however
final table of predictions a set of rules has been defined to translate have exclusive access to deeper water (Schenk and Jackson, 2002;
the percentage of cases obtained from simulation into signs. van Langevelde et al., 2003). Percolation of water from the upper to
According to these rules a variable is expected to increase if the the lower soil profile is a recognized mechanism through which
sign + appears in 75% or more of the matrices (this means that 25% deep water reserves are fed by rainfall (Le Roux et al., 1995).
or less of the matrices yield a negative sign). If this percentage is Grasses and trees negatively affect each other. The negative
between 60% and 75% we considered a likely tendency to increase effect of trees on grass may result from rainfall interception, litter
(it is signaled by the “?+” in the table of predictions). If the accumulation, shading, root competition or a combination of these
percentage of + is between 40% and 60% the routine considered factors (Scholes and Archer, 1997). Direct effect of grass on woody
that variable as remaining the same (“0*”, pathways carrying vegetation is described as reducing emergence, growth and
positive and those responsible for negative effect compensate each survival of woody seedlings, but these effects rarely cause high
other). These rules hold also for the negative signs. All routines mortality (Scholes and Archer, 1997). So the assumption that tree–
were written in R language. The code used for the simulations is in grass competition is asymmetrical seems plausible (Holdo et al.,
the SM (Appendix A) 2009; Holdo, Sinclair et al., 2009).
By predicting directions of change for the variables in response Four variables were then used to build up an initial core model
to parameter variations entering as input in a system, qualitative for the system: in addition to grasses (G, in the model) and woody
models can also predict correlation patterns between variables. If vegetation (W), we included water that resides in the upper soil
two variables change in the same direction in response to a profile (w1) and water in the deeper layer (w2). Grass biomass
particular input, then they will show positive correlation over a consists of both grasses and herbs; woody biomass consists of
range of that parameter. If they change in opposite directions they wood, twigs, small trees and shrubs. With the support of a large
will show a negative correlation. If one or both show a null body of literature (see e.g. Scholes and Archer, 1997 and references
response, this input would result in no correlation between the there in) we delineated 8 possible alternative structures for this
variables. Predictions can thus be used to analyze observed core model. Alternative graphs present different hypothesis about
correlation patterns (Puccia and Levins 1986; Bodini, 2000). interactions. In the literature G and W have been described as
The qualitative approach that is used in this exercise (i.e. loop interacting each other either through reciprocal inhibition, one
analysis) exploits the properties of signed digraphs. These latter way inhibition, in general from woody vegetation to grass, or no
have a long history in ecological applications: because of their interaction at all. This may depend on the different magnitude of
versatility they have been used in different contexts and with the effects. For example, Scholes and Archer (1997) posited that the
different goals. In the early 1970s they supported scholars in their competitive effect of grass on woody plants may not be as intense
effort to unveil stability properties of ecosystems (Jeffries, 1974; as to heavily affect the growth of this latter component. In this case
Levins, 1974). As a convenient way to represent who eats whom in the one way inhibition from W to G seems a reliable representation
the ecosystem they have been used to understand keystone species for their interaction. In some cases, trees may also benefit on
(Liu et al., 2010) and energy delivery in ecosystems (Allesina et al., grasses, because they can mitigate harsh environmental con-
2005; Bellingeri and Bodini, 2016). Because they pictorially ditions, modify substrate characteristics or increase resource
describe multiple interactions between dynamic variables they availability (Belsky and Canham, 1993; Callaway, 1995). Given this
have become ideal tools to represent the structural complexity of multiplicity of effects the way one can represent the way W affects
ecosystems and the possibility they offer to analyze paths and the growth rate of G must necessarily be is the net effect of the
feedbacks have been exploited to understand ecosystem response positive and the negative actions.
to change. In this framework they have greatly contributed to the The two water reserves are not independent from one another.
development of the ecosystem based management approach Water in fact percolates down to the subsoil. Water percolation
(Dambacher et al., 2007; Carey et al., 2013). depends on a number of factors, among which the soil type plays a
key role. So it may be that this supply may become null in certain
2.2. Savanna qualitative models combinations of soil type and rainfall regime (Ludwig et al., 2004;
van Langevelde et al., 2003). Water percolation is depicted as a
2.2.1. The core model positive effect from w1 to w2. W and G are self-damped variables.
Several models for the persistence of tree-grass mixtures in This reflects the regulation that is set up both by internal
savannas have been advanced thus far. These models can be competition and the regulative effect of other variables that are
divided in two groups: one set considers these systems as not explicitly considered in the model (Levins, 1974; Bodini, 2000),
governed by competition based mechanisms; the other group such as inorganic nutrients. Finally, the self-damping on water
concentrates on demographic mechanisms where disturbance resources (w1 and w2) depends on the continuous supply of water
factors such as fires, herbivores and rainfall play a decisive role. In from rainfall and underground fluxes. If these fluxes depended
this paper we do not give prominence to one view over the other; completely on percolation then w2 resulted not to be self-damped.
rather, we focus on how each variable interacts with the others so Qualitative analysis requires that a set of models are developed for
that a whole linkage structure is reproduced. No single model can any given system. This is a necessary step so that various
account for the variety of phenomena at all savanna locations, and assumptions about the structure of the interactions can be tested.
the range of behaviors exhibited at one location in different As many as 8 alternative graphs for the core model were developed.
seasons or stages of succession is quite diverse (Scholes and Archer, They are presented in the SM (Appendix B).
1997). The models we present here have been conceived to
 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46 39

Fig. 2. Woody-grass core model for the savanna ecosystem: signed digraph and
table of predictions. Keys are: W woody plants; G grasses, w1 superficial water
table; w2 deep water table. The table shows predictions assuming positive input on
the row variables. Effects of negative inputs are obtained by simply reversing the
signs.

The model in Fig. 2 seems the most reliable reconstruction of

relevant interactions between the variables for the core model. It
corresponds to graphs “g” among the 8 alternative schemes
presented in the SM (Appendix B). It was after the comparison of
model predictions with evidences reported in the literature (see
Results) that we selected this graphs as the most reliable
description of the structure of the interactions for this system.

2.2.2. Herbivores action

Direct and indirect effects of large herbivores are also believed
to be very important regulators of variations of woody and grass
biomass in space and time (van der Waal et al., 2011; Goheen et al., Fig. 3. Graph representing the enlarged savanna model and its table of predictions.
2010; Roques et al., 2001; Dublin et al., 1990). Large herbivores Grazers (HG) and browsers (HB) feed on grass (G) and woody plants (W)
respectively. Early fires (not intense, EF) consume grass vegetation, whereas late
modify plant recruitment and establishment by eating, trampling,
fires (intense, LF) interact with both grass and woody plants.
urinating and trashing, which kill or damage plant individuals
(McNaughton et al., 1988). Depending on feeding habits and
example, fires and vegetation coexisted at least since the
physiology, it is common to distinguish between two main groups
quaternary period (Kershaw et al., 1997). Currently, a very small
of large herbivores: those that feed mainly on woody species, or
proportion of fires in savanna comes from lightning, whereas the
browsers, and those feeding on herbaceous vegetation, or grazers.
bulk of fire events have anthropogenic origin.
Browsers (i.e. elephants, Loxodonta africana Blumenbach), heavily
Many parameters can describe fire activity in a given
affect trees abundance and woody vegetation dynamics (Asner and
ecosystem, like fire intensity, frequency and burning season
Levick, 2012; Jeltsch et al., 2000). Their activity is expected to curb
(Gregoire, 1996; Clerici et al., 2004). Fire intensity is generally
tree growth (Staver et al., 2009; Sharam et al., 2006). Experimental
considered the most important factor affecting the dynamics of
studies showed that tree growth, recruitment and survival
savannas (Liedloff et al., 2001). It is controlled by several
increased following a reduced browsing pressure (Daskin et al.,
parameters: amount of grass biomass (main fire fuel), grass
2016; Staver et al., 2009; Asner and Levick, 2012).
moisture content, wind speed and air temperature (Sawadogo
Grazing is also a key regulative process because it influences
et al., 2005).
grass competitive ability and fire frequency (Staver and Bond,
Fires that occur during the early dry season are generally of low
2014). Its role was extensively treated in the literature due to its
intensity, due to the high moisture content of the grass vegetation;
importance for the associated socio-economic impacts (see Ellis
low intensity fires have little or no effects on the survival of the
and Swift, 1988 for a synthesis on grazing systems and develop-
woody vegetation (Liedloff et al., 2001). Late-dry-season fires, on
ment; Scholes and Archer, 1997 and references there in; Roques
the contrary, are more intense due to the very low moisture
et al., 2001). Intensive grazing reduces the grass standing crop,
content in the grass fuel. Intense fires thus can heavily damage
which is the main fuel for fires in savannas (Trollope, 1996); as a
woody plants and increase their mortality (Brookman-Amissah
consequence, both fire intensity and frequency are reduced. This in
et al., 1980; Hochberg et al., 1994). A number of studies reported
turn can increase the competitive advantage of the woody species
that in African savanna woodlands repeated intense, late dry-
(Adamoli et al., 1990; Kaufmann et al., 1994; Trollope, 1996). In
season fires reduced woody biomass. Hot fires damage adult plants
some cases prolonged and intensive livestock or wildebeest
and kill individuals in the smaller size classes: individuals of
grazing associated with low fire frequency or intensity results in
woody species with a height less than 2 m can be killed or have a
shrub encroachment (Goetze and Hörsch, 2006; Briggs et al.,
retarded growth (Trollope, 1987; Hochberg et al., 1994; van
2002).
Langevelde et al., 2003).
Feeding mechanisms can thus be represented as two distinct
Grasslands and savannas herbaceous plants are hardly killed by
resource-herbivore interactions (Fig. 3): browsers (HB) consume
fire (van Langevelde et al., 2003). Oliveras et al. (2013) found that
woody and shrub vegetation (W); grazers (HG) feed on grass (G).
total aboveground biomass of herbaceous vegetation in a neo-
tropical savanna was not affected by a variety of fire treatments of
2.2.3. Fire disturbance
varying intensity. In South African savannas fires distributed in a
Fires are considered fundamental regulative elements of the
gradient of intensity (from 925 to 3326 kJ/s/m) were examined for
savanna’s vegetation structure, and a driving force that played a
their effects on vegetation and evidences were that intensity had
key role in the formation of savanna ecosystems. In Africa, for
no significant influence in the recovery process of grass sward in
40 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46

the two growing seasons after the burns (Trollope and Tainton, pathways one would expect G to decrease (2 to 1 in favor of a
1986). On the other hand, Trollope (1982) found that repeated diminishing effect).
burnings in arid savannas could negatively influence grass The percentage of simulated cases (see SM, Appendix B, model
production when in combination with water stress. According to g) in which the positive effect prevails is greater than that in which
these evidences we decided to include two fire variables in our the negative effect predominates (56% and 44% respectively), but it
models (Fig. 3). They are early (EF) and late fires (LF), which can be remains within the range (40%–60%, see Methods and SM
also classified as non-intense and intense fires, respectively. We Appendix A) for which negative and positive effects compensate
assumed that only intense fires (LF) have a direct control on woody for each other and the prediction is considered null.
vegetation. Grass biomass, on the other hand, is the main fuel for Two reasons can explain this outcome. First is the balance
fires (Trollope, 1987), so it is depicted as positively affecting both between positive and negative feedbacks. The direct pathway
intense and not intense fires. ðw1 ! GÞ contributes a negative feedback at level F 2 (SM
Starting from the core model depicted in Fig. 1 we developed Appendix C), whereas the paths ðw1 ! W  oGÞ and
five graph models in which herbivores, browsers and fires ðw1 ! w2 ! W  oGÞ produce positive feedbacks at level three
variously interacted. All the graphs include interactions that could and four (SM Appendix C). It might thus happen that the whole
be deduced from literature, so they are plausible ecologically. matrix becomes unstable when these positive feedback become
Alternative structural hypothesis however have been considered stronger for certain combinations of links value. In this case an
due to uncertainty about certain links that emerged from the excess quota of positive feedback enters the model causing the
literature analysis. These five graphs and their analysis are matrix to be unstable. Because only stable matrices are accepted to
presented in the SM (Appendix D). Here, the graph in Fig. 3 calculate predictions, it follows that cases in which the two
represents the most reliable representation of the system given the pathways that carry a negative effect prevail over the direct link
correspondence between predictions and evidences presented in ðw1 ! GÞ may not take part in the calculation of the predicted
various pieces of the literature. change (for stability reasons). The stability analysis for this model
is given in detail in the SM (Appendix C).
3. Results: predicting observed patterns The other reason is that the contribution of pathways becomes
of minor importance as their length increases. Link strength in fact
The model in Fig. 2 has been selected among a set of 8 is within the interval 0–1 and the intensity of each path is the
alternative graphs (SM, Appendix B). Its predictions design product of the magnitude of the links that compose it. Accordingly,
qualitative trajectories of change for the variables that may the longer the pathways the lower its magnitude can be.
explain, better than the other models do, the patterns observed or In areas where sandy soils dominate, water infiltration rate
predicted in previous studies. Walker and Noy-Meir (1982) increases, with beneficial effects on woody biomass, at the
indicated rainfall as a key driver for the transition from grassland expenses of grass (van Langevelde et al., 2003). Still, this situation
to savanna to woodland. In their stability analysis van Langevelde reflects in a positive input to w2, as the rate of change of this
et al. (2003) reiterated that increasing water availability may variable depends on the link (w1 ! w2) which describes water
induce that transition. In northern hemisphere African savannas, percolation rate. For positive input to w2 we expect woody biomass
scholars observed an increase in mean precipitation towards the W to increase whereas grass will be declining. When the amount of
Equator, with an associated increasing latitudinal gradient in tree infiltrated water decreases, trees may find harsher environmental
dominance (Mayaux et al., 2004). conditions and woodland may become savanna. This corresponds
To simulate the effect of increased rainfall in the model of Fig. 2, to a negative input to w2, which yields a diminution for W and an
we assumed positive parameter changes on both w1 and w2. increase for G.
Precipitations in fact increment the rate at which water becomes The presence of fires and herbivory shapes the model according
available in the grass root zone (positive input to w1). If rainfall to the graph illustrated in Fig. 3. In this model the responses of
increases so that the soil moisture content is exceeded, water starts grass and woody vegetation to external impacts entering w1, w2, G
to percolate in the woody plant root area and the rate of change of and W coincide with those of the core model.
w2 increases as well. The model predicts that a positive input to w1 Roques et al. (2001) conducted a detailed long term (50 years,
(first row of the table in Fig. 1) leaves G unaffected while increasing from 1947 to 1997) experimental study to investigate the dynamics
W. The positive input to w2 (second row of the table) decreases G of shrub encroachment in respect to fires, grazing activity and
and increases W. Overall the model shows that an increasing rainfall in the Lowveld savanna of Swaziland, South Africa. They
rainfall regime and water availability tends to reduce G in favor of found a strong negative correlation between grazing pressure and
W, in agreement with the transition from grass to woody fires, which was accompanied by a positive relationship between
vegetation that the above cited authors observed or predicted. shrub encroachment and grazing pressure. In addition, shrub
The intensity at which this phenomenon occurs determines the encroachment showed a negative relationship with fire frequency.
final state of the system, but the model correctly grasps the Finally they found that low rainfall resulted in a decline of shrub
qualitative trajectory of the effect. cover, whereas high rainfall favored shrub encroachment.
The model suggests that increasing percolation in the deeper Over the whole period of study a general increase in shrub cover
layer is necessary to speed up the transition from grassland to characterized the area. According to the correlation patterns above
woodland. A unique, positive input to w1 (simply increasing the described this would be accompanied by a reduced frequency of
rainfall regime) in fact would leave the level of grass vegetation fires and by an increased grazing pressure. These authors analyzed
unchanged. This outcome would not be immediately predictable trends of grazing pressure, probability of fires, and shrub cover
from the analysis of the pathways. Any impact affecting w1 in fact (Roques et al., 2001, Figs. 2 and 3) and concluded that high grazing
spreads to G along three different pathways of interaction: the pressure in the area promoted shrub encroachment indirectly
direct link ðw1 ! GÞ, the path through W (w1 ! W  oG) and the through fires.
pathway (w1 ! w2 ! W  oG). These indirect pathways both The table of predictions associated to the model in Fig. 3 shows
carry a negative effect to G (the effect is product of the sign of the variations expected in the level of the model’s variables (number of
links that make the pathway, see SM Appendix A). The direct link individuals or biomass). Each variable’s response to the different
has, instead, a positive effect. Thus according to the sole number of inputs that affect any row variables can be read along its column.
According to the correlation patterns observed by Roques and
 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46 41

coauthors a variation in the level of grazers (HG)1 should be carry negative effects. But these negative pathways are longer
accompanied by a change in woody plants (W) of the same type, and include links that form positive feedbacks at level 3, 4 and 5
whereas fires should change in the opposite direction. If we scroll (and higher, see SM, Appendix E for a description of these positive
down the columns of W and HG, positive covariations between feedbacks). So stability reasons and of pathways strength, that
these two components occur only in two cases: input to HG and becomes weaker as the path elongates, as discussed for the core
input to LF (variation in the rate of change of late, intense fires). But model above, apply here. They may explain the incongruity
for the model to correctly predict the correlation pattern between the number of pathways with opposite effects and the
documented by Roques et al. (2001) fires should change in result of the simulation.
opposite direction in respect to HG and W. In particular, the table of The increased level of fires that is predicted for positive input to
predictions in Fig. 3 shows that this pattern of correlation occurs w1 is associated to pathways that include same links that enter in
only in the case of a positive input to grazers (a positive input to the composition of positive feedback loops. However, positive
HG). pathways outnumber negative pathways by 3 to 1 and links that
These authors did not provide any evidence for this potential enter in the positive feedback are present in the positive pathways
positive input. Shrub cover increased sharply around 1967 (Roques but also in the negative one (see SM Appendix D, model d).
et al., 2001, Fig. 3) and continued along that trend during the As said before the rainfall regime must have affected the other
following years. In 1967 the area was divided into sites of different two sites (Communal and Hlane) as well. Accordingly, in these
land use and this might have created the conditions for change areas two factors must be considered as causes of variations: the
according to the observed correlation pattern. We hypothesize that improved conditions for grazers and the increased water
better conditions for grazers must have occurred so that a positive availability due to rainfall. By combining the predicted effects of
parameter change for HG can be assumed. Not all sites however the two sources of variation (first and fifth row of the table of
manifested same dynamics with respect to the overall correlation predictions) one obtains the overall direction of change for the
pattern described above. In the first two sites, Communal land and variables. Grazing pressure (level of HG) augments: the positive
Hlane Wildlife Sanctuary respectively (see Roques et al., 2001, input on HG increases its own level and the positive input to w1
Fig. 2) increased shrub cover, lower fire frequency and increased leaves this variable unchanged. The abundance of woody plants
grazing pressure started more or less immediately after 1967 augments because both inputs produce positive variations on this
(Figs. 2 and 3, Roques et al., 2001). variable. Fire frequency becomes higher: again both inputs
Interestingly enough two other sites, namely Malahleni and produce positive changes on this component. Likely both inputs
Ranch site, did not show the same trends. Shrub cover increased, contributed to set up conditions that determined the observed
fire frequency increased as well but the grazing pressure remained patterns of abundance (and correlation).
unchanged. These evidences are in contrast with the mechanism A prolonged drought during 1991–93 caused widespread
proposed on the base of the observed correlation patterns herbivore mortality (herbivores declined by more than 50% in
according to which grazing pressure would reduce fires to the the study area). This increased mortality enters the model as a
benefit of shrubs. Field data and model predictions help explain negative input on HG. Predicted consequences (fifth row of the
this apparent contradiction. The period 1967–1975 was one in table in Fig. 3, reverse the signs) are that the level of grazers and of
which rainfall increased (Roques et al., 2001, Fig. 1). In our model woody vegetation would be declining; fires (both early and late)
increasing rainfall determines a positive input to w1, because it instead would be increasing. Different sites in the study area
increases the incoming flow of water from outside the system.2 If showed different patterns in respect to the effects of drought. In
we consider this positive input (first row of the table in Fig. 3) the Hlane site less grazing pressure, more fires and less woody plants
model predicts exactly the changes that were observed in the two followed the drought event (Roques et al., 2001, Figs. 2 and 3).
sites. Grazers would not change and both intense fires (LF) and Model predictions for the sole negative impact on HG would
shrubs (W) would be increasing. So in Malahleni and Ranch sites explain the observed pattern. However, as said earlier, if abundant
improved conditions for grazers likely did not occur and the rainfall increases water availability, causing a positive input to w1, a
observed pattern can be attributed to the increased rainfall only. negative input to w1 must be considered now to take into account
But the augmented rainfall might have affected also the other sites the reduced water availability caused by drought. The expected
of the study area. We will return on this later. effects of this negative input (first row of the table, reverse the
Here we focus a bit on the null change in the abundance of signs) are that the abundance of grazers would not change; woody
grazers associated to the input to w1. It is not a real inertia of this vegetation would be decreasing whereas the level of fires would be
component in respect to parameter change in the dynamics of w1 increasing. Now the effects of the increased mortality of herbivores
but rather a compensation between opposite effects associates to and of the reduced water availability must be combined. Both
the multiple pathways that connect w1 to HG. The simulation (see inputs are predicted to reduce woody vegetation; the abundance of
SM Appendix D, model d) shows that the percentage of matrices in grazers would be decreasing but only because of their increased
which the positive input to w1 augments HG is 50.35% whereas a mortality (input to w1 does not change the level of HG) whereas the
negative effect appears in the 49.65% of cases. These percentages two inputs have opposite actions on fires. In the absence of any
signal that there is no prevalence of effects when link strength is quantitative assessment the net effect on the level of fires cannot
assigned; accordingly we can assume that compensation between be ascertained. However field observations suggest that fires
the two effects is likely to occur. However, compensation does not increased; likely the effect on fires of the augmented mortality of
immediately come from counting the pathways. In fact only one herbivores dominated over that of the lower availability of water.
path carries a positive effect: it is ðw1 ! G ! HGÞ. The other During the same period in the Malahleni buffer zone the
pathways, ðw1 ! w2 ! W  oG ! HGÞ, frequency of fires dropped sharply and the shrub cover dimin-
ðw1 ! w2 ! W ! LF  oG ! HGÞ, and ðw1 ! W  oG ! HGÞ ished; from the data presented in the study it is impossible to
ascertain about the reduced level of grazing pressure because of
the lack of annual data in 1991–1993, although it seems that such
1
as decrease did not take place (Roques et al., 2001, Fig. 3 diagram e).
Roques and coauthors used the number of individuals (i.e. population
abundance) as a measure of grazing pressure.
If so, we could assume that only the negative input to w1 might
2
This inflow is included in the self-loop on variable w1, see Puccia and Levins, have affected this area. This input is predicted to lower both the
1986.
42 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46

frequency of fires (level of LF) and shrub cover (level of W) while Holdo et al. (2009) and Holdo, Sinclair et al. (2009) posited that
HG remains unchanged, which correspond to the observations. grazing and intra-annual rainfall variation contributed to the
The recovery from reinderpest in the Serengeti ecosystem is observed global patterns of fire occurrence in the Serengeti. So the
perhaps the most influential case study on the role of grazing on variation in the rainfall regime must be considered as a further
encroachment in savannas (McNaughton, 1992; Holdo et al., 2009; driver that, beside inoculation, was at work in that ecosystem from
Holdo, Sinclair et al., 2009). Rinderpest removed 95% of cattle, the beginning of the investigation period up to mid-1970s. The
buffalo, wildebeest, gazelle, and zebra. In the 1950s a cattle temporal trend for rainfall is reported in Fig. 4D (as wet:dry data,
vaccination campaign surrounding Serengeti resulted in the virus Holdo et al., 2009; Holdo, Sinclair et al., 2009). This chart indicates
disappearing from the wildlife. Right after cattle were inoculated a tendency to decline for this feature in the considered period.
wildebeest populations began to increase in abundance. The Clearer is the reduction in the spatial extent of burning (Fig. 4E).
sequence of events that followed cattle inoculation is described in Because McNaughton (1992) showed that during the period of
the charts of Fig. 4. In these charts we show the abundance trends ecosystem recovery there was a positive correlation between the
for the main variables. We reproduced them using the original data spatial extent of burning in the dry season and the rainfall level
set (Holdo et al., 2009; Holdo, Sinclair et al., 2009, Dataset S1 Time- during the wet season Fig. 4D and E lead to conclude that from
series data for model variables used in the analysis, http://dx.doi. 1960 to mid-1970s the rainfall regime declined.
org/10.1371/journal.pbio.1000210.s001). As already said a lower availability of water becomes a negative
The period 1960–1980 show very clear trends: concomitant input to w1. Consequences of this reduced availability can be
with the steep increase of the grazers (i.e wildebeest, Fig. 4A), the obtained by reversing the signs in the first row of the table of
browsers (i.e. elephants, Fig. 4B) augmented their abundance (up predictions that accompanies the model in Fig. 3. A diminution is
to mid-seventies), fires (Fig. 4E) dropped and tree cover (Fig. 4C) expected for woody vegetation. If combined with the expected
remained at low levels. To assess whether inoculation could have increase due to the positive input on grazers a compensation of
produced the observed trends, the model in Fig. 3 can be applied by effects takes place. This might explain the lack of variation in the
assuming a positive input that enters the system via HG (the level of this component, as shown by its trend in Fig. 4C. This
positive effect of the inoculation on the growth rate of the grazers). conjecture would however require a quantitative assessment to be
The table in Fig. 3 yields the following predictions: the grazers confirmed.
would be increasing (HG +); so the browsers would (HB +); fires Following the negative input to w1 the level of grazers (HG) is
would be declining (LF ) and woody biomass would be increasing expected not to change, while browsers should be declining. Fig. 4
(W +). With the exception of the woody cover a qualitative shows that browsers markedly increased in the period 1960–1980.
correspondence between model predictions and the observed This requires that the effect of the reduced mortality of grazers
trends after inoculation emerges. (positive input to HG) on the abundance of the browsers must be

Fig. 4. Charts that show time series for 5 variables as provided by Holdo et al., 2009, Dataset S1, http://dx.doi.org/10.1371/journal.pbio.1000210.s001: A, Grazers (wildebeest
population size, thousands of individuals); B Browsers (elephant population size, n. of individuals); C Trees (tree density, ind ha 1); D rainfall (dry-season rainfall, mm y1);
E, Fires (proportion of burned area).
 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46 43

more than enough to compensate for the decline that would be table (Fig. 3) in fact tells us that an increase in the growth rate of G
imposed by the reduced availability of water. Still, a conclusion yields more grass, less woody plants and induce a higher level of
presented with circumspection because a quantitative assessment fires (both early and late). But the model clearly indicates that an
would be necessary and we could not make it here. increased standing stock for grass is not always coupled with an
The Serengeti elephant population declined because of poach- increased level of fires. For input to w2 (negative), W (negative),
ing in the 1970s and 1980s, and subsequently recovered following and HB (positive) the level of G increases but that of intense fires
the ivory ban in 1989 (Holdo et al., 2009; Holdo, Sinclair et al., (LF) does not, although for all these inputs the level of woody
2009). Poaching must have affected the dynamics of the entire plants is predicted to decrease.
system. Increased mortality from poaching is a negative input on Often the search for causative mechanisms in ecosystems is
HB. Reversing the signs in the corresponding row of the table of based on the correlation between abundance levels between
predictions in Fig. 3 yields that browsers would be diminishing, variables; that is the search for shifts in the abundance of a
woody biomass as well as fires would be increasing and grazers population that accompanies the change in the abundance of
would be in decline. The trend showing the area burned in time another. In this paper we show that the reification of observed
(Fig. 4) does not allow for any comparison with model prediction patterns of change into interactive mechanisms can be successful if
due to the lack of data after 1980. The abundance of the browsers we may be able to link correlation patterns, sources of change (i.e.
(Fig. 4B) lowered from 1980 to 1990. Woody vegetation shows a the inputs) and community structure. Qualitative models can be
neat increase in the same period (Fig. 4C). Grazers present a useful in this respect because in mapping out interactions between
steadily level around their carrying capacity (Fig. 4A). Some of the relevant variables they help understanding how the links of
effects of the increased mortality due to poaching are captured by recognized direct effects also determine indirect effects. In
the model if a negative input to HB is assumed, with the exception addition, signed digraphs may become diagnostic tools in that
given by the discrepancy between observed and predicted trend they allow using correlation patterns to identify source of changes,
for grazers. Also a more complete data set about the areas burned the variables through which press perturbations enter the system
during time would allow for a more precise assessment. (Puccia and Levins, 1986; Levins and Puccia, 1988).
McNaughton (1992) indicated that the analysis of the recovery
4. Discussion pattern (i.e. changes in the abundance of critical variables) from
rinderpest in the Serengeti ecosystem allowed a plausible
The presence of multiple interacting variables increases the reconstruction of the network of interconnected chains of cause
structural complexity of the ecosystems: more pathways are and effect induced by the rinderpest. Holdo, Sinclair et al. (2009)
generated for indirect effects and the system feedbacks, which made McNaughton’s assertion explicit by identifying a linear chain
modulate the effects of pathways, become more intricate. This of causality that operated in that environment. They reconstructed
increased structural complexity affects the way variables respond a sort of “rinderpest trophic cascade hypothesis” that would give
to stimuli, perturbations and management interventions. One rise to the following events ordered in a causative succession:
feature of this complexity is that patterns of ecosystem response decreased pathogen, increased specialist consumer (wildebeest),
become difficult to disentangle in causal terms. Roques et al. decreased producer (grass), decreased generalist “consumer” (fire)
(2001) found that a significant negative correlation between and increased producer (trees). These authors generalized their
grazing pressure and fires had a major impact on shrub cover. They finding by positing that dominant factors controlling tree density
interpreted this evidence according to the following chain of in the Serengeti would be essentially top down (Holdo et al., 2009;
events ordered in a causative succession: sustained heavy grazing Holdo, Sinclair et al., 2009).
of grasses would remove combustible herbage which would However, rainfall regime and poaching contributed to the long
reduce the probability of ignition and restrict the spread of fires, term dynamics of the Serengeti ecosystem as well, acting as inputs
thus favoring bush encroachment. This chain of events implies to variables different than grazers (water availability, large
high abundance of grazers (heavy grazing pressure), less grassy browsers). According to this the overall dynamics must have been
herbs, lower frequency of fires to end with a high shrub cover. The the net outcome of the effects of different inputs produced by
table of prediction in Fig. 3 reveals that such concomitant different sources of change (i.e. the reduced mortality for
variations are possible (thus the chain of causal events is wildebeest due to cattle inoculation, the increased mortality of
plausible), but only when a positive input on grazers (HG) occurs. browsers due to poaching, and the increment of water availability
It is not the sole augmented abundance of grazers that produces due to rainfall). These effects percolated throughout the ecosystem
these effects. In fact a higher level of grazers can be obtained in using multiple pathways and combined with one another to yield
several ways (i.e. negative input to w2;negative input on W) but in the observed patterns. The picture that emerges from our analysis
these other cases the higher abundance of grazers is accompanied suggests that there is no unique control mechanism (i.e top down)
by changes in the level of the other variables that do not match but that the locus of control is diffuse. Controlling factors are inputs
with the hypothesized chain of events. For example, when a to parameters that govern the rate of change and the structure of
negative input affects W (its rate of change diminishes) the level of the network of the system (Levins and Puccia, 1988; Levins and
grazers increases, but so does also that of the grass vegetation G Schultz, 1996).
(fourth row of the table in Fig. 3, invert signs), a contrasting Discussion in ecology is often hampered by the posing of
outcome if compared with the above described pattern. dichotomous choices: are populations regulated by density
The same approach in which correlation patterns are translated dependent or density independent factors? Do physical or biotic
into hypothesis of dominant controlling factors is taken by Higgins factors predominate? This holds also for savannas. In fact,
et al. (2000). They hypothesized that increasing grass production3 proposed explanations for the persistence of both trees and
would negatively affect tree density by increasing fire intensity. grasses in these ecosystems fall into two categories: those that
But if the increased production of grass comes about because its emphasize the fundamental role of competitive interactions in
growth rate augments (positive input), then Higgins and fostering coexistence (competition-based mechanisms), and those
colleagues’ conclusion holds. The third row of the table prediction that focus on the limiting roles of demographic bottlenecks to tree
establishment and persistence and that are influenced by external
factors such as herbivory, browsing and fires (Sankaran et al.,
3
Those authors estimated grass productions as the standing stock (Kg ha1). 2004). The structure of the interactions configured in the model of
44 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46

Fig. 3 shows that the effect of grazing on the level of woody plants The qualitative analysis has certainly many limitations, among
depends on pathways involving fires ðHG  oG ! LF  oW Þ as well which the impossibility to make any quantitative statements is the
as pathways that encompass soil moisture, such as most relevant. This precludes digging in details the dynamics of the
ðHG  oG  ow1 ! w2 ! W Þ and ðHG  oG  ow1 ! W Þ. It might savannas: for example several works showed that quantitative
be that these paths have different importance in determining the levels of rainfall define thresholds for different behaviors (i.e. bi-
effect on W in different conditions (van Wilgen, 2009) but this can stability, Sankaran et al., 2005; Higgins et al., 2010). Also the need
be ascertained only on a quantitative basis. We think that the to explore quantitative details that may affectsystem behavior has
interesting question is not what relative weights to assign the stimulated innovative approaches to parameter quantification
different factors but, rather, to elucidate how they interpenetrate (Higgins et al., 2010; Holdo et al., 2012).
and how this interplay determines the overall result. By recognizing these limitations of the qualitative analysis we
We already pointed out that the qualitative analysis is relatively posit that these methods are not alternatives to quantitative
uninterested in precision so that exact predictions are not its models; rather we see the potential for integration wherever
primary goal (Levins, 1974). Models for accurate quantitative parameter estimation is impossible or difficult to obtain. The
predictions in savanna ecosystems must include, among others, management of savanna ecosystems will become more complex in
spatial heterogeneity, temporal variability and thresholds as the near future under the effects of global change. Impacts that can
critical factors (van Wilgen et al., 2004; Holdo et al., 2009; Holdo, be hypothesized are many and will be due to altered CO2 balances,
Sinclair et al., 2009; Staver and Levin, 2012). Nevertheless the increasing temperatures, invasion of alien plant species and the
qualitative approach, by predicting directions of change, can be growing human population pressed by urgent needs (van Wilgen,
helpful when we are interested in pushing on the system in a 2009). Making predictions in that context will become more
particular direction. In the Kruger National Park fire management difficult because of the uncertainty associated with new, unknown
approaches changed several times from 1948 to 2001. van Wilgen events, changing dynamics and lack of quantitative data. An
et al. (2004) documented the outcomes of changing fire- adaptive management approach that allows for continually
management policies. Because they were unable to quantitatively assessing new evidence and changing approaches as understand-
assess whether fire intensity was influenced by the different ing increases has been called for. There is no recipe for modelling
management approaches they suggested that managers could development but great effort must be devoted to assimilation of
reduce fire intensity by preempting late dry-season fires (intense) facts, observation and hypotheses. We believe that in the new
by igniting fires early in the dry season. This was intended as a scenario that is approaching qualitative models can be helpful.
measure to curb the effect of fires on tree size. To assess the They have the necessary adaptability to be used in changing
potential of this management option we must enter a positive contexts: when in doubt about critical linkages and dynamic
input to variable EF as its rate of change is forced to increase by features, alternative models can be developed to find out which
management. As a consequence (last but one row of the table in difference matters and to reach robust conclusions. They are also
Fig. 3) late, intense fires would be reduced, and the model confirms flexible: they allow including and discarding variables easily and
that favoring early fires push the system in the direction of having above all they permit working with variables and links that are not
less intense fires. But this measure should be carefully evaluated readily measurable, but their effects are crucial.
for its effects on other variables: grassy plants and grazer’s
population in fact are expected to diminish. Acknowledgements
van Wilgen et al. (2004) found that the elements of the fire
regime they considered, such as the extent of area burned or The present study was supported in its initial phase by a grant
variability of inter-fire intervals, appear to be strongly influenced from the Italian Ministry for Scientific Research and University
by rainfall regime. This may also be true for fire intensity. (MURST). Dr Jean-Marie Grégoire (European Commission Joint
Increasing rainfall (positive input to w1) is expected to increase the Research Centre) is acknowledged for the insightful discussions on
level of intense fires. On the other hand preempting intense fires, as fire ecological effects in savannas. Many thanks are due to Stefania
said before, is expected to reduce the intensity of fires. However, if Favilla (Department of Biomedical, Metabolical and Neurosciences,
we look at the results of our simulations (see Supplementary University of Modena and Reggio Emilia) for writing the R code
material Appendix D, model d) we can observe that the positive used here for simulations.
input on w1 generates an increment in the level of LF in 95% of the AB wishes to dedicate this paper to the memory of Richard
simulated matrices; the positive input to EF on the other hand Levins, who has been a continuous source of inspiration
yields a reduced level of LF in 77% of the matrices, whereas in some
22% of the matrices the positive input to EF tend to increase LF. This Appendix A. Supplementary data
means that there is a counteracting effect that mitigates the
magnitude of the negative variation predicted for LF. Our model Supplementary data associated with this article can be found, in
thus confirms that high rainfall regime may obscure the effect of the online version, at http://dx.doi.org/10.1016/j.
the management action, at least in respect to fire intensity (van ecocom.2016.10.001.
Wilgen, 2009; van Wilgen et al., 2004).
Stability analysis is the framework in which most of the savanna References
modeling applications are discussed (van Langevelde et al., 2003;
Higgins et al., 2010; De Michele et al., 2011; Holdo et al., 2012). In Adamoli, J., Sennhauser, E., Acero, J.M., Rescia, A., 1990. Stress and disturbance:
vegetation dynamics in the dry Chaco region of Argentina. J. Biogeogr. 17, 491–
this paper we do not focus on stability properties of equilibria but 500.
on the evolution of equilibrium conditions that is driven by Allesina, S., Bodini, A., Bondavalli, C., 2005. Ecological subsystems via graph theory:
changes in the parameter values (input). The fact that our model the role of strongly connected components. Oikos 110, 164–176.
Archer, S., 1989. Have southern Texas savannas been converted to woodlands in
can interpret observed patterns indicates that the moving recent history? Am. Nat. 134, 545–561.
equilibrium approach is another way to look at the effect of the Asner, G.P., Levick, S.R., 2012. Landscape-scale effects of herbivores on treefall in
variable environment. This in turn suggests that variability is African savannas. Ecol. Lett. 15, 1211–1217.
Bekage, B., Gross, L.J., Platt, W.J., 2011. Grass feedbacks on fire stabilize savannas.
matter of changing parameters (press perturbation, Bender et al.,
Ecol. Modell. 222, 2227–2233.
1984) and not solely of variable fluctuations (Levins, 1974). Bellingeri, M., Bodini, A., 2016. Food web’s backbones and energy delivery in
ecosystems. Oikos 125, 586–594. doi:http://dx.doi.org/10.1111/oik.02244.
 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46 45

Belsky, A.J., Canham, C.D., 1993. Forest gaps and isolated savanna trees: an Lane, P., 1998. Assessing cumulative health effects in ecosystems. In: Rapport, D.,
application of patch dynamics in two ecosystems. Bioscience 44, 77–84. Costanza, R., Epstein, P.R., Gaudet, C., Levins, R. (Eds.), Ecosystem Health:
Bender, E.A., Case, T.J., Gilpin, M.E., 1984. Perturbation experiments in community Principles and Practices. Blackwell Science, Malden, MA, pp. 129–153.
ecology: theory and practice. Ecology 65, 1–13. Le Roux, X., Bariac, T., Mariotti, A., 1995. Spatial partitioning of the soil water
Bodini, A., 2000. Reconstructing trophic interactions as a tool for understanding and resource between grass and shrub components in a West African humid
managing ecosystems: application to a shallow eutrophic lake. Can. J. Fish. savanna. Oecologia 104, 147–155.
Aquat. Sci. 57 (10), 1999–2009. Levins, R., 1974. The qualitative analysis of partially specified systems. Ann. N. Y.
Briggs, J.M., Knapp, A.K., Brock, B.L., 2002. Expansion of woody plants in tallgrass Acad. Sci. 231, 123–138.
prairie: a 15 year study of fire and fire-grazing interactions. Am. Midl. Nat. 147, Levins, R., Puccia, C.J., 1988. The controlling factor in biological communities.
287–294. Coenoses (now Community Ecology) 3, 149–154.
Brookman-Amissah, J., Hall, J.B., Swaine, M.D., Attakorah, J.Y., 1980. A reassessmenof Levins, R., Schultz, B.B., 1996. Effect of density dependence, feedback and
fire protection experiment in north-eastern Ghana savanna. J. Appl. Ecol. 17, 85– environmental sensitivity on correlation among predators, prey and plant
89. resources: models and practical implications. J. Anim. Ecol. 65, 802–812.
Callaway, R.M., 1995. Positive interactions among plants. Bot. Rev. 61, 306–349. Liedloff, A.C., Coughenour, M.B., Ludwig, J.A., Dyer, D., 2001. Modelling the trade-off
Carey, M.P., Levin, P.S., Townsend, H., Minello, T.J., Sutton, G.R., Francis, T., Harvey, C. between fire and grazing in a tropical savanna landscape, Northern Australia.
J., Toft, J.E., Arkema, K.K., Burke, J.L., Kim, C.K., Guerry, A., Plummer, M., Environ. Int. 27 (173), 800.
Spiridonov, G., Ruckelshaus, M., 2013. Characterizing coastal foodwebs with Liu, W., Chen, H.-W., Jordan, F., Lin, W., Wai-Jen, Chester, 2010. Quantifying the
qualitative links to bridge the gap between the theory and the practice of interaction structure and the topological importance of species in food webs: a
ecosystem-based management. ICES J. Mar. Sci. 71 (3), 713–724. signed digraph approach. J. Theor. Biol. 267, 355–362.
Clerici, N., Boschetti, L., Eva, H., Grégoire, J.-M., 2004. Assessing vegetation fires Logofet, D.O., 1993. Matrices and Graphs. Stability Problems in Mathematical
activity and its drivers in west-Central africa using MODIS and TRMM data. IEEE Ecology. CRC Press Boca Raton, FL, USA, pp. 308.
International Geosciences and Remote Sensing Symposium 2004. Conference Ludwig, F., Dawson, T.E., Prins, H.H.T., Berendse, F., de Kroon, H., 2004. Below-ground
Proceedings vol. III, 2087–2090. competition between trees and grasses may overwhelm the facilitative effects
Cole, M.M., 1986. The Savannas: Biogeography and Geo-botany. FL. Academic, of hydraulic lift. Ecol. Lett. 7, 623–631.
Orlando. Mayaux, P., Bartholomé, E., Fritz, S., Belward, A., 2004. A new land-cover map of
Dambacher, J.M., Ramos-Jiliberto, R., 2007. Understanding and predicting effects of Africa for the year 2000. J. Biogeogr. 31 (6), 861–877.
modified interactions through a qualitative analysis of community structure. Q. McNaughton, S.J., 1992. The propagation of disturbance in savannas through food
Rev. Biol. 82, 227–250. webs. J. Veg. Sci. 3, 301–314.
Dambacher, J.M., Brewer, D.T., Dennis, D.M., Macintyre, M., Foale, S., 2007. McNaughton, S.J., Ruess, R.W., Seagle, S.W., 1988. Large mammals and process
Qualitative modelling of gold mine impacts on Lihir Island’s socioeconomic dynamics in African ecosystems. Bioscience 38, 794–800.
system and reef-edge fish community. Environ. Sci. Technol. 41, 555–562. Montoya, J.M., Woodward, G., Emmerson, M.C., Sole, R.C., 2009. Indirect effects
Daskin, J.H., Stalmans, M., Pringle, R.M., 2016. Ecological legacies of civil war: 35- propagate disturbances in real food webs. Ecology 90, 2426–2433.
year increase in savanna tree cover following wholesale large-mammal Oliveras, I., Meirelles, S.T., Hirakuri, V.L., Freitas, C.R., Miranda, H.S., Pivello, V.R.,
declines. J. Ecol. 104, 79–89. doi:http://dx.doi.org/10.1111/1365-2745.12483. 2013. Effects of fire regimes on herbaceous biomass and nutrient dynamics in
De Michele, C., Accatino, F., Vezzoli, R., Scholes, R.J., 2011. Savanna domain in the the Brazilian savanna. Int. J. Wildland Fire 22, 368–380.
herbivores-fire parameter space exploitinga tree–grass–soil water dynamic Puccia, C.J., Levins, R., 1986. Qualitative modelling of complex systems. An
model. J. Theor. Biol. 289, 74–82. Introduction to Loop Analysis and Time Averaging. Harvard University Press,
Dublin, H.T., Sinclair, A.R.E., McGlade, J., 1990. Elephants and fire as causes of Cambridge.
multiple stable states in the Serengeti-Mara woodlands. J. Anim. Ecol. 59, 1147– Ratnam, J., Bond, W.J., Fensham, R.J., Hoffmann, W.A., Archibald, S., Lehmann, C.E.R.,
1164. Anderson, M.T., Higgins, S.I., Sankaran, M., 2011. When is a ‘forest’ a savanna, and
Ellis, J., Swift, D., 1988. Stability of African pastoral ecosystems: alternate paradigms why does it matter? Global Ecol. Biogeogr. 20, 653–660.
and implications for development. J. Range Manage. 41 (6), 450–458. Roques, K.G., O’Connor, T.G., Watkinson, A.R., 2001. Dynamics of shrub
Gill, J.L., 2015. Learning from africa's herbivores. Science 350 (6264), 1036–1037. encroachment in an African savanna: relative influences of fire, herbivory,
Goetze, D., Hörsch, B., 2006. Dynamics of forest-savanna mosaics in north-eastern rainfall and density dependence. J. Appl. Ecol. 38, 268–280.
Ivory Coast from 1954 to 2002. J. Biogeogr. 33, 653–664. doi:http://dx.doi.org/ Sankaran, M., Ratnam, J., Hanan, N.P., 2004. Tree grass coexistence in savannas
10.1111/j.1365-2699.2005.01312.x. revisited: insights from an examination of assumptions and mechanisms
Goheen, J.R., Palmer, T.M., Keesing, F., Riginos, C., Young, T.P., 2010. Large herbivores invoked in existing models. Ecol. Lett. 7, 480–490.
facilitate savanna tree establishment via diverse and indirect pathways. J. Anim. Sankaran, M., Hanan, N.P., Scholes, R.J., Ratnam, J., Augustine, D.J., Cade, B.S.,
Ecol. 79, 372–382. Gignoux, J., Higgins, S.I., Le Roux, X., Ludwig, F., Ardo, J., Banyikwa, F., Bronn, A.,
Gregoire, J.-M., et al., 1996. Use of AVHRR data for the study of vegetation fires in Bucini, G., Caylor, K.K., Coughenour, M.B., Diouf, A., Ekaya, W., Feral, C.J.,
Africa: fire management perspectives. In: D’souza, G. (Ed.), Advances in the Use February, E.C., Frost, P.G.H., Hiernaux, P., Hrabar, H., Metzger, K.L., Prins, H.H.T.,
of NOAA AVHRR Data for Land Applications. ECSC, EEC, EAEC, Brussels and Ringrose, S., Sea, W., Tews, J., Worden, J., Zambatis, N., 2005. Determinants of
Luxembourg, pp. 311–335 Printed in Netherlands. woody cover in African savannas. Nature 438 (7069), 846–849.
Higgins, S.I., Bond, W.J., Trollope, W.S.W., 2000. Fire, resprouting and variability: a Sankaran, M., Ratnam, J., Hanan, N., 2008. Woody cover in African savannas: the role
recipe for tree-grass coexistence in savanna. J. Ecol. 88, 213–229. of resources: fire and herbivory. Global Ecol. Biogeogr. 17, 236–245.
Higgins, S.I., Scheiter, S., Sankaran, M., 2010. The stability of African savannas: Sawadogo, L., Tiveau, D., Nygård, R., 2005. Influence of selective tree cutting
insights from the indirect estimation of the parameters of a dynamic model. livestock and prescribed fire on herbaceous biomass in the savanna woodlands
Ecology 91, 1682–1692. of Burkina Faso, West Africa. Agric. Ecosyst. Environ. 105 (1-2), 335–345.
Hochberg, M.E., Menaut, J.C., Gignoux, J., 1994. The influence of tree biology and fire Schenk, H.J., Jackson, R.B., 2002. The global biogeography of roots. Ecol. Monogr. 72,
in the spatial structure of the West African savanna. J. Ecol. 82, 217–226. 311–328.
Holdo, R.M., Holt, R.D., Fryxell, J.M., 2009. Grazers, browsers, and fire influence the Scholes, R.J., Archer, S., 1997. Tree-grass interactions in savannas. Annu. Rev. Ecol.
extent and spatial pattern of tree cover in the Serengeti. Ecol. Appl. 19, 95–109. Syst. 28, 517–544.
Holdo, R.M., Holt, R.D., Fryxell, J.M., 2012. Herbivore-vegetation feedbacks can Sharam, G., Sinclair, A.R.E., Turkington, R., 2006. Establishment of broadleaved
expand the range of savanna persistence: insights from a simple theoretical thickets in Serengeti, Tanzania: the influence of fire, browsers, grass
model. Oikos 122, 441–453. competition, and elephants. Biotropica 38, 599–605.
Holdo, R.M., Sinclair, A.R.E., Dobson, A.P., Metzger, K.L., Bolker, B.M., et al., 2009. A Staver, A.C., Bond, W.J., 2014. Is there a ‘browse trap’? Dynamics of herbivore
disease-Mediated trophic cascade in the serengeti and its implications for impacts on trees and grasses in an African savanna. J. Ecol. 102, 595–602. doi:
ecosystem C. PLoS Biol. 7 (9), e1000210. doi:http://dx.doi.org/10.1371/journal. http://dx.doi.org/10.1111/1365-2745.12230.
pbio.1000210. Staver, A.C., Levin, S.A., 2012. Integrating theoretical climate and fire effects on
Jeffries, C., 1974. Qualitative stability and digraphs in model ecosystems. Ecology 55, savanna and forest systems. Am. Nat. 180, 211–224.
1415–1419. Staver, A.C., Bond, W.J., Stock, W.D., van Rensburg, S.J., Waldram, M.S., 2009.
Jeltsch, F., Weber, G.E., Grimm, V., 2000. Ecological buffering mechanisms in Browsing and fire interact to suppress tree density in an African savanna. Ecol.
savannas: a unifying theory of long-term tree–grass coexistence. Plant Ecol. 161, Appl. 19, 1909–1919.
161–171. Staver, A.C., Archibald, S., Levin, S.A., 2011. Tree cover in sub-Saharan Africa: rainfall
Kaufmann, J.B., Cummings, D.L., Ward, D.E., 1994. Relationships of fire, biomass and and fire constrain forest and savanna as alternative stable states. Ecology 92,
nutrient dynamics along a vegetation gradient in the Brazilian cerrado. J. Ecol. 1063–1072.
82, 519–531. Thiessen, H., Feller, C., Sampaio, E., Garin, P., 1998. Carbon sequestration and
Kershaw, A.P., Bush, M.B., Hope, G.S., Weiss, K.-F., Goldammer, J.G., Sanford, R., 1997. turnover in semi-arid savannas and dry forest. Clim. Change 40, 105–117.
The contribution of humans to past biomass burning in the tropics. In: Clark, J.S., Trollope, W.S.W., Tainton, N.M., 1986. Effect of fire intensity on the grass and bush
Cachier, H., Goldammer, J.G., Stocks, B. (Eds.), Sediment Records of Biomass components of the Eastern Cape Thornveld. J. Grassl. Soc. South. Afr. 2, 27–42.
Burning and Global Change. NATO ASI Series 51. Springer, Berlin, pp. 413–442. Trollope, W.S.W., 1982. Ecological effects of fire in South African savannas. In:
Knapp, A.K., Smith, M.D., Collins, S.L., Zambatis, N., Peel, M., Emery, S., Wojdak, J., Huntley, B.J., Walker, B.H. (Eds.), Ecology of Tropical Savannas. Springer-Verlag,
Horner-Devine, M.C., Biggs, H., Kruger, J., Andelman, S.J., 2004. Generality in Berlin, Germany, pp. 292–306.
ecology: testing North American grassland rules in South African savannas. Trollope, W.S.W., 1987. Effect of season of burning on grass recovery in the false
Front. Ecol. Environ. 9, 483–491. thornveld of the eastern cape. J. Grassl. Soc. South. Afr. 4 (2), 1987.
46 A. Bodini, N. Clerici / Ecological Complexity 28 (2016) 36–46

Trollope, W.S.W., 1996. Biomass burning in the savannas of southern Africa with van Wilgen, B.W., 2009. The evolution of fire management practices in savanna
particular reference to the Kruger National Park in South Africa. In: Levine, J.S. protected areas in South Africa. S. Afr. J. Sci. 105, 343–349.
(Ed.), Biomass Burning and Global Change. MIT Press, Cambridge, Mass, pp. van Wilgen, B.W., Govender, N., Biggs, H.C., Ntsala, D., Funda, X.N., 2004. Responses
260–269. of savanna fire regimes to changing fire-management policies in a large African
Walker, B.H., Noy-Meir, I., 1982. Aspects of the stability and resilience of savanna national park. Conserv. Biol. 18, 1533–1540.
ecosystems. In: Huntley, B.J., Walker, B.H. (Eds.), Ecological Studies, Vol 42: van der Waal, C., Kool, A., Meijer, S., Kohi, E., Heitkonig, I., de Boer, W., van
Ecology of Tropical Savannas. Springer-Verlag, Berlin. Langevelde, F., Grant, R., Peel, M., Slotow, R., de Knegt, H., Prins, H., de Kroon, H.,
van Langevelde, F., van de Vijver, C.A.D.M., Kumar, L., van de Koppel, J., de Ridder, N., 2011. Large herbivores may alter vegetation structure of semi-arid savannas
van Andel, J., Skidmore, A.K., Hearne, J.W., Stroosnijder, L., Bond, W.J., Prins, H.H. through soil nutrient mediation. Oecologia 165, 1095–1107.
T., Rietkerk, M., 2003. Effects of fire and herbivory on the stability of savanna
ecosystems. Ecology 84, 337–350.