Article Information







	



Authors:




Robert J. Scholes1



Judith M. Kruger2





Affiliations:




1Natural Resources and Environment, CSIR, Pretoria, South Africa
2South African National Parks, Skukuza, South Africa



Correspondence to:




Judith Kruger





Email:






Judith.kruger@sanparks.org






Postal address:




Private Bag X402, Skukuza 1350, South Africa



Dates:

Received: 20 Jan. 2010

Accepted: 19 May 2010 

Published: 13 May 2011



How to cite this article:

Scholes, R.J. & Kruger, J.M., 2011, ‘A framework for deriving and triggering thresholds
for management intervention in uncertain, varying and time-lagged systems’, Koedoe 53
(2), Art. #987, 8 pages.
doi:10.4102/koedoe.v53i2.987





Copyright Notice:

© 2011. The Authors. Licensee: OpenJournals Publishing. This work is licensed under the Creative Commons Attribution License.


ISSN: 0075-6458 (print)

ISSN: 2071-0791  (online)














	
	






A framework for deriving and triggering thresholds for management intervention in uncertain, varying and time-lagged systems






	
	







In This Essay...


	 Open Access









• Abstract

• Introduction

• A general approach to the problem

   • Define a sensitive, relevant and measurable indicator of the issue at hand

   • Set a limit of acceptable change in the indicator 

   • Add a safety margin based on societal risk tolerance and technical certainty

   • Project the indicator into the future using a model, including an uncertainty range

   • Note the time at which the relevant uncertainty limit intercepts the safety margin

   • Subtract the system response time

   • Subtract the management response time

   • Subtract the monitoring interval

      • Is an action triggered?

• Example: Elephants and big trees in the Kruger National Park

   • Choosing the indicator

   • Setting a safety-buffered limit

   • Projecting the dynamics forward

   • When is the limit likely to be transgressed?

   • Subtracting the response times 

   • Is an action triggered?

• Discussion and conclusion

• Acknowledgements

• References









	



	



Abstract



	 (Back to top)











Ecosystems are characterised by complexity: high connectivity, the presence of positive and negative feedback loops,
non-linear, abrupt and sometimes irreversible changes, delays between cause and effects, and uncertainties in observations,
understanding and prediction. ‘Adaptive management’ is the preferred approach for the rational management of
such systems. Where the management objective is to allow natural feedbacks and adaptive processes to operate as much as
possible – as it is in many areas set aside for biodiversity conservation – a key issue is defining the thresholds
that will trigger management intervention. This paper outlines and illustrates a logical process for doing so, taking into
account the characteristics of complex, continuously changing ecosystems and the reality of information that is partial and
understanding that is always provisional. After identifying a key ecological process that is believed to have an element of
irreversibility beyond a certain point, the process has several steps, (1) define an indicator of the system state, (2) set
a limit of acceptable change and add a safety margin, (3) project the indicator forward using a model, including uncertainty,
(4) note the time when the indicator might transgress the safety-buffered limit and (5) subtract ecosystem and management
response times. If the resultant time is at hand, an action is indicated – if not, the action is to continue to monitor
the situation and refine the observations and models.
Conservation implications: Ecosystems are characterized by abrupt and sometimes irreversible changes. The challenge
that face conservationists and managers are to identify which of these changes are likely to be irreversible and at what
levels this will occur. This paper describes a logical process that enable mangers to determine which ecological processes
have levels of irreversibility and monitor their status at all times. Once these processes are nearing the levels that are
undesirable management actions can be invoked to prevent this from happening.











	

 



Introduction




	 (Back to top)










The formal and informal management philosophy that has guided ecosystem management in state-owned, protected areas in South
Africa has evolved through various phases over the past century (Carruthers 1995). The approach adapted in the early years
(up to the mid-1950s) has been characterised as ‘command and control’. The first conservation officers were military
men – decisive, action-orientated and used to being in charge. They assumed that the desired state was known, unchanging
and achievable using the tools at hand. The desired state usually amounted to ‘preservation’: a perpetuation of the
status quo or a return to some pre-existing, Eden-like ideal. The underlying world view was the notion that nature is
intrinsically in balance, but perturbed by human activities. Therefore, self-regulation can be achieved by simply eliminating
the human impacts, or, where this is impossible, by intervening to restore the balance. 
This first generation of conservators was replaced by a generation of technocrats, many trained as biological scientists,
and backed up by a powerful, but not very consultative state apparatus (mid-1950s to about 1990). They were increasingly able
to implement ‘grand schemes’ such as fencing, water provision, game translocation, culling and fire control.
Nevertheless, the ecological outcomes were often not what was anticipated or desired. These experiences, which were not unique
to South Africa, eventually taught a degree of humility regarding both our state of relative ignorance towards ecosystem
functioning and in relation to how ineffective our interventions can be (Holling & Meffe 1996). 
The past three decades have seen a fundamental shift, worldwide, in the scientific perspective regarding ecosystem dynamics
(a key paper in the African savanna context is Ellis and Swift 1988). It is now generally accepted that ‘natural’
ecosystems may be intrinsically variable due to their internal dynamics and as a result of the variability of external drivers,
such as climate. Thus, although the ecosystem may have a theoretical point of balance or equilibrium, it is seldom actually at
that point, and it is neither desirable nor possible in the long term to suppress the variability. It is now thought to be
necessary for ecosystems to vary in time and space in order to maintain their diversity and resilience in light of
future challenges (Folke et al. 2004). Furthermore, many ecosystems may exhibit more than one equilibrium state, with
transitions between them that may be somewhat abrupt and irreversible, and that very often are unanticipated. Since both human
and ecological systems are self-organising, the position of the threshold itself may change over time. Finally, the distinction
between ‘human’ and ‘natural’ disturbances is often spurious. For instance, people have been important
shapers of ecosystem structure and function in Africa for millennia and are internal to the system, rather than external forces
impinging on it. These considerations, and a realisation of how expensive (and often unintentionally injurious) ongoing
interventions on multiple fronts can be, have led to a much greater reluctance on the part of conservation managers to intervene
in ecosystems. 
Furthermore, the conservation authorities themselves, and interested parties outside the agencies, began to ask questions
regarding what the desired state is, and who decides it. This trend started in the 1980s, and in South Africa, accelerated
after 1994 as a broader and more participatory style of governance took root in many facets of South African society.  
In this paper, we start from a position that there is probably no universally ‘right’ style of ecosystem management
(although it is likely that there are some that are clearly ‘wrong’ in a given situation). There are circumstances
in which one style is more likely to achieve the desired ends, at lower financial and ecological cost, than others. Command and
control is a reasonable approach when the level of understanding and the capacity to effect change are both high. Where the
 understanding of how the system works is essentially no better than blind guesswork and the capacity to take directed action
 is very low, a non-interventionist stance (sometimes called a ‘laissez faire’ approach) is both theoretically
 defensible and practically unavoidable. In the case where understanding is high but the capacity or desire to intervene is
 low, ‘watchful tolerance’ might be a sensible philosophy.
South African National Parks (SANParks) are generally neither completely powerless nor completely ignorant. Furthermore, there
is a societal and legislated expectation that the conservation authorities act to meet various explicit and implicit objectives,
including the avoiding of ecosystem degradation and the prevention of species extinction. The park managers have demonstrated a
capacity to influence certain ecosystem outcomes, even on a large scale, and are relatively well resourced to do so. After more
than half a century of research, some things are relatively well understood, and at least reasonable hypotheses as to what might
be going on can be posed on most topics. Under these circumstances, we argue that the most reasonable management philosophy is
‘adaptive management’ (Biggs & Rogers 2003). In this style of management, objectives are stated provisionally
but explicitly – in other words, they are equivalent to ‘hypotheses’ in experimental research. Management
actions are treated as experiments from which learning can take place, even if the outcome is not the expected one. This requires
that the interventions are designed and implemented with enough scientific rigour for the outcomes to be attributed to causes.
The interventions are undertaken on a scale and with an intensity that permits the consequences to be distinguished against the
background noise of inherent variation. The actions are documented and the outcomes are monitored. It is an axiom of this style
of management that the actions and, if necessary, the objectives are subject to change on the basis of evidence provided by the
experiment itself, or because changing societal expectations require it.
Gregory, Ohlson and Arvai (2006) highlight four criteria that must be met for adaptive management to be valid; (1) it must be
able to cope with the spatial and temporal scale of the issue, (2) it must deal explicitly with the uncertainty associated with
observing and making predictions, (3) it must evaluate costs, benefits and risks and (4) it must have stakeholder support.
This is the context in which SANParks, starting in the Kruger National Park, began to define their management plan, based on
the ‘thresholds of potential concern’ (TPC) (Biggs & Rogers 2003). The approach is summarised briefly as follows:
a set of high-level goals is defined and then translated into more specific objectives. A threshold or thresholds are then set
in relation to selected indicators of each objective. The thresholds are often expressed in the form of a traffic light analogy:
an ‘amber light’ warns of an impending problem, and a ‘red light’ triggers an intervention. Initially the
TPCs were determined by expert judgement, following a debate among specialists and a review of the evidence that was available.
The TPCs have subsequently been refined and reviewed in several iterations. Problems have surfaced as the system has been implemented.
For instance, the number of TPCs and indicators has proliferated, which makes the system burdensome and open to internal
contradictions. Secondly, in the cases where TPCs have been transgressed, the reaction has most often been to simply redefine
the acceptable level of change, rather than to embark on an expensive and far-reaching intervention. This underscores the
often arbitrary nature of the ‘thresholds’ that have been set.
This paper suggests a conceptual framework for setting trigger points for management action, such as the SANParks TPCs,
in time-varying ecosystems, taking into account uncertainty and the time lags inherent in both ecosystem processes and
intervention actions.







	

 



A general approach to the problem





	 (Back to top)







The approach outlined below is analogous to a control-theory problem (Brogan 1985), such as guiding a missile to a moving
target or steering a vehicle down a twisty road. The control system consists of a sensor, which provides information
(including a degree of error) about the position and motion of the object relative to the current location. This information
is used to activate course adjustments, taking into account the time lag in the response of the system. 
In this paper, we assume that the highest-level objective has been set, that is, there is clear guidance regarding what the
area is managed for. In the missile analogy, the target has been selected. In our view, the top-level goal is not principally
 a technical decision, but a societal one. A ‘political’ process – in other words, a legitimate, values-
 driven consensus-based process – must be followed to decide on the desired state, taking into account the various
 tradeoffs, perceptions and power relations between the stakeholders. Once the overarching purpose has been agreed upon
 (accepting that this social consensus process is non-trivial and will always be provisional and dynamic), the following,
  more ‘technical’ (i.e. expert-based) analysis can follow. The way in which the approach is developed is
  illustrated in Figure 1 (panels [a] to [c]).








	
	
	

FIGURE 1: Steps in establishing a management action trigger.




























  
 

Define a sensitive, relevant and measurable indicator of the issue at hand






Although it typically is a system that is being managed, with many component parts, we need to settle on a single measure
of system performance for tracking purposes, otherwise potentially contradictory signals will result. ‘Indicator’
is a term that also embraces proxy measures, but the preferred indicators are the ones most closely linked to the actual factor
of concern. For instance, if soil loss is the issue, a direct measure of soil export in tonnes per hectare is unambiguous; an
indirect observation such as the area of bare ground is less preferred, while an index such as a calculation based on the Universal
Soil Loss Equation (USLE, see Risse et al. 1993) is only indirectly based on observations. If complex indices are chosen,
then those with physical units and a clear and established underlying logic (such as USLE) are by far preferable to arbitrary
combinations of indicators, such as averages of a number of variables that are thought to be related to the state of the system in some way.











  
 

Set a limit of acceptable change in the indicator






In this paper, we avoid calling the limit of acceptable change a ‘threshold’ in order to prevent it from becoming
confused with the notion of a system threshold separating one state from another; in other words, a boundary in
system state-space at which negative feedbacks are overwhelmed by positive feedbacks, and thus, when crossed, causes the system
to accelerate into a new domain of attraction under its own dynamics. Many of the limits that are typically set for ecosystem
management do not have this property of discontinuous change, but are simply agreed levels along a continuum, beyond
which you do not wish to proceed, for whatever reason. Nonetheless, it is very helpful to the identification of limits if they
are true system thresholds, since this introduces a much stronger element of causality and non-arbitrariness into the
definition, which usually cuts out a lot of unproductive debate. Furthermore, we argue that these ‘true’ thresholds
of relative irreversibility (very few things are truly irreversible, if you have enough time and money to fix them) are the ones
that the managers of protected areas really need to worry about. Therefore, selecting system thresholds as the limits, even if
they are relatively rare, has the advantageous effect of reducing the number of criteria that have to be monitored. (See
Martin et al. [2009] for a discussion of the differences between ecological thresholds, utility thresholds and decision
thresholds.) Here we are concerned with decision thresholds, but it is helpful if they are founded on ecological thresholds.
Note that ecological thresholds are themselves dynamic, so the process of defining the limit needs to be revisited periodically.












  
 

Add a safety margin based on societal risk tolerance and technical certainty





It is very rare that ecologists know the position of a threshold or limit exactly. Neither is the present state of the system
known with absolute precision. Faced with a situation of risk, most people prefer to stay well away from the edge –
especially if they are not too sure where the edge lies. Our willingness to stay near to the limit depends on what is at stake.
For instance, if a population were allowed to drop below some minimum viable level, would the result be a global extinction, or
just a local extirpation? The level of risk taken also depends on the appetite for risk among the stakeholders. For example,
people struggling to meet basic human needs are thought to be willing to take greater local environmental risks in meeting
those needs than populations that are more comfortably off (Goklany 2001). The central point is that the magnitude of the
safety margin is not simply a technical or statistical issue, but a decision that is taken within a particular ecological
and social context. Figure 1(a) illustrates the steps so far.













  
 

Project the indicator into the future using a model, including an uncertainty range






Knowing that you have crossed a limit after the fact is not very helpful. It is much more useful to be able to predict
well ahead of time that you are likely to cross the line, so that corrective action can be taken. Therefore, decisions should
generally be made on the basis of some sort of predictive ‘model’. Models can range in sophistication from a simple
extension of a trend line to a complex, multi-variable, non-linear systems model. Expert judgement and experience are also
‘models’, but not very transparent ones. Any model, regardless of its sophistication, has uncertainty associated
with it. For instance, the 95% confidence interval can be calculated for a linear trend, as is suggested in Figure 1(b).
In the case of a complex systems model with many variables, each of which has some uncertainty, the joint uncertainty distribution
is quite complex. This uncertainty is often approximated by running an ensemble of different models incorporating different
assumptions, or else by running the same model but varying the key parameters in a statistically realistic way within their
likely ranges (‘Monte Carlo simulation’, Vose 1996).













  
 

Note the time at which the relevant uncertainty limit intercepts the safety margin






The approach we describe aims to be conservative. Therefore the key point is not where the mean of the forward
projections breaches the safety-buffered limit that you have set, but the earliest moment when there is a reasonable
probability of such a limit being exceeded. Note that for ‘upper limits’ being approached from below,
it is the higher uncertainty range that matters, whereas for ‘lower limits’ being approached from above
it is the lower uncertainty range. What is ‘reasonable’ must be considered against the risk tolerance of
the stakeholders, and it should be consistent with the implied risk tolerance used when setting the safety buffer,
described above. In many cases, the default is the widely accepted scientific norm of the 95% confidence limit –
in other words, there is a less than one in 20 chance that the safety margin will be breached earlier than the time projected.








  
 

Subtract the system response time






From the time when the limit is crossed by the lower 95th percentile confidence limit, we subtract a period that reflects the inertia
in the ecosystem – in other words, the response time following an intervention. In our car analogy, think of it as how responsive
the vehicle is to a touch on the steering wheel. If the car is fast and heavy, the turning circle will be large and the response
sluggish, but if the car is light and agile, last-minute course corrections are possible. Ecosystem inertia can have many causes.
One of the most common sources of ecosystem inertia is the longevity of the organisms involved. For example, if you try to alter
the population dynamics of an elephant herd through contraception, you need to start a decade ahead of time, since that is more or
less the period between birth and sexual maturity. If you are similarly intervening in an impala population, 2 years would be
sufficient. Sources of ecosystem inertia that are short-lived (weeks) are probably virtually irrelevant in this context, as are
exceedingly slow processes – for instance, land-forming processes that take millennia. The most critical issues for
management lie inbetween – processes where you need to act years to decades before the threshold of non-return is reached
if you wish to materially affect the outcome. Multiple runs of the projection model, starting at progressively earlier times and simulating the appropriate corrective action
in the model until a starting moment is reached, that does not result in the safety limit being transgressed, is a way of
assessing the inertial delay. Bear in mind that the models are invariably imperfect – so an informed judgement based on
a consideration of the key lags in the ecosystem may be nearly as good.











  
 

Subtract the management response time






It is not only the natural world that has delays built into it – the human side of the system does as well.
For instance, you may need to wait until the next management meeting, or the next budgetary cycle, to commence an
action. Or you may need to initiate a protracted stakeholder engagement process. While it is tempting to think that
we have a bit more control over human delays than we have over the time lags in the ecosystem, experience teaches
us that big decisions take time to implement. The uncertainties in the magnitude of the management response time
underscore the futility of trying to be too precise in estimating the ecosystem response time, since the two numbers
are added together.








  
 

Subtract the monitoring interval






A further time lag must be subtracted to allow for the fact that observations of the system take place only
occasionally. Sometimes the period is very short – for instance, satellite-derived images of fire extent
are obtained weekly. In other cases, the interval may be long: for example, full census data for large mammals
in the Kruger National Park are only obtained once every 3 to 5 years because of the effort and expense of doing
so. On average, you are only half a monitoring interval away from the next estimate, but in order to be conservative,
this lag should be set as equal to the monitoring interval.







 
Is an action triggered?


Since the point at which we identified when the conservative limit of projected trend intercepts the safety-buffered
threshold of concern we have been working in time units, backwards from that moment. The final steps in the procedure
are illustrated in Figure 1(c). We first subtracted the ecosystem response time, then the management response time,
then the monitoring interval. If the result is a date that is at or before the current date, then an intervention is
triggered. If the result is after the current date, then, in theory, you can safely wait until the next monitoring
date, assuming that reanalysis will occur at that time on the basis of the updated data. If the indicated trigger
date is between the current date and the next monitoring date, it is appropriate to indicate an ‘amber’
(caution) light, which would set off various actions aimed at increasing your confidence or proactively decreasing
the various delays in the system. For instance, you could shorten the monitoring period or intensify the monitoring
effort for the key variable involved; you could commission research to improve the confidence in the projection model;
you could take actions to reduce the delays in the decision cycle; or you could take actions to reduce the ecological
lag – for instance, you could proactively administer immuno-contraception primers to reduce population response
delays to contraception. Often you would undertake some combination of these actions. 
The practical application of these steps is illustrated in a worked example below.






	

 



Example: Elephants and big trees in the Kruger National Park





	 (Back to top)







The elephant population in what is now the Kruger National Park and surrounding private and state-owned wildlife areas had
been reduced to close to zero at the beginning of the 20th century. Small groups of elephant began to wander into the region
from Mozambique after the first reserves were established. By 1967, the elephant population had reached an estimated 6600
through a combination of in-migration and natural increase. At this time, on the basis of expert consideration of the elephant
densities in a range of protected areas in Africa, it was decided to limit the number of elephants in Kruger Park to a total
of 7000 (which corresponded to ‘one per square mile’, the threshold above which several experienced persons at the
time considered unacceptable damage to the vegetation to occur). The Kruger Park elephant population was kept near this level
through annual culling until 1994, when a moratorium on culling was imposed in response to pressure from animal rights advocates.
Since then, the population has grown at a rate of approximately 6% per annum, and an intense debate is underway about what action
to take (if any) in the future, and what the trigger points might be (Carruthers et al. 2008, and other chapters in
Scholes & Mennell 2008). 
We have chosen this example because it nicely illustrates several points made in the preceding section. Our analysis of the
topic is solely for the purposes of illustrating the procedure we propose for setting action thresholds. It does not represent
the policy of the South African government, SANParks or the authorities in the Kruger National Park. While the worked example
is broadly grounded in observed data, in some respects it involves our informed judgement (as will be the case in almost any
real-life situation). If a management trigger were to be set in practice for the elephant-tree system using an approach based
on the one we describe, it would need to be based on a process somewhat more inclusive than the opinion of these two authors alone.










  
 

Choosing the indicator






The first thing that can be learned from the elephant-and-tree example is that taking an overly simple and purely technocratic
view is likely to lead to implementation problems sooner or later. The culling moratorium was motivated partly by the arbitrariness
of the ‘one elephant per square mile’ rule, the origin and validity of which was never properly researched or documented.
As the Scientific Assessment of Elephant Management in South Africa (Scholes & Mennell 2008) points out, elephant population
density per se is not the problem. Elephants are part of a system, which involves, at a minimum, elephants and the plants
that they consume or damage. An even wider view would also consider indirect ecosystem effects (for instance, other species that
are in competition with elephants for food, or are affected by the habitat changes elephants bring about). A yet wider view
contextualises elephants within human society and the choices this society collectively makes regarding the desired appearance
of landscapes and the relative importance of different species.Therefore, the indicator variable on which the intervention trigger is set in this case should not be the size of the elephant
population, but some variable that reflects our underlying concern for the effects the elephants have on the ecosystem. The
issue that usually surfaces in consultation with a range of stakeholders in the context of the Kruger Park ecosystem is damage
to trees (and, specifically, large and old trees) caused by elephants. This often has an aesthetic component – visitors
have grown accustomed to seeing the Kruger Park landscape in a certain way, with scattered large trees and dense riparian forests,
and do not wish to see a landscape consisting of bushy coppice and downed trees, regardless of whether the latter situation
supports the same productivity or biodiversity. This is a legitimate stance, but raises difficult questions in terms of setting
an operational limit – whose opinion counts in the poorly defined trade-off between the appearance of a landscape and the
 desire not to interfere with the lives of elephants? How much landscape transformation is acceptable, and to whom?











  
 

Setting a safety-buffered limit






Further unpacking of the ‘large tree issue’ reveals that a whole guild of species – the large
raptors – are almost totally dependent on large trees for nesting opportunities. Since there is well-established
literature on the importance of maintaining top predators and scavengers in functional ecosystems (e.g. Terborgh
et al. 1999), conserving large raptors by providing nesting opportunities provides a somewhat more robust
ecological basis for setting a limit. Large raptors and vultures occur relatively sparsely and, in some cases, are
rare outside large protected areas such as the greater Kruger National Park. Some are arguably dependent for
their regional population viability on having a core breeding population in the Kruger Park. The lower limit for
a minimum viable population could therefore conceivably be reached if the breeding habitat was restricted.
Population viability analysis (Shaffer 1990) could be applied to determining what the safe lower limit of breeding
pairs might be. Since the birds nest in the crown of live trees, typically at a height of 12 m or more above
the ground, this minimum population level can be translated into a number of nesting sites, and, in turn, into
a minimum density of large trees. We do not intend to do this full analysis here, but simply assume that it
works out at about one tree per square kilometre, including a generous safety margin. (In practice, because
the decline in large trees accelerates as they become rarer, the exact value of the threshold hardly matters
in setting the trigger. This is a very desirable property in an indicator.) This can be considered a ‘
threshold of irreversibility’, since the regional or global extinction of some species could result if
the large tree population falls below this threshold.







  
 

Projecting the dynamics forward






Reasonably reliable data exist to build simple models of both elephant population dynamics and tree demography. The two models
can then be coupled to create a model of the elephant-tree system (for example, Duffy et al. 1999; Owen-Smith 2002). A
 simple implementation of such a model is applied here, again for illustrative purposes only. Because important time lags are
 introduced by both elephant maturation and the growth of large trees, the minimal model needs to include an age structure.
 Our discrete-timestep elephant model has annual cohorts of female elephants (the number of bulls is simply assumed to equal
 the number of females) that reach sexual maturity at age 12, and thereafter produce one calf every 2.5 years until death at
 age 60. The basic rate of mortality is 3% per year for all size classes, and increases as food becomes scarce. The values are
 chosen to reproduce the observed 6% per annum growth rate in the elephant population, as well as the extensive research on
 elephant population dynamics in the Kruger Park system (Van Aarde et al. 2008). No direct effect on population growth
 rate resulting from food shortage or other density-dependent phenomena has been observed at the densities experienced to date
 in the Kruger Park ecosystem, but there are data from elsewhere in southern Africa to suggest that the inter-calf interval
 extends when forage becomes scarce (Van Aarde et al. 2008) and, at some degree of forage inadequacy, mortality must
 occur. These effects should be included in the model if it is to be realistic when projected forward sufficiently to take
 into account the inertia of tree and elephant populations. Forage is produced by both trees and grasses, in an inverse
 relationship, and a portion of it (set nominally at half) is consumed by other species of herbivores. The tree model is based on discrete size classes of stem diameter, in 5 cm increments up to a maximum diameter of 80 cm.
All species are combined. There is a rough relationship between stem diameter (d, cm) and height (H, in m): 
H = -0.011 d2 + 0.2162 d+1.336
derived from a database of several thousand stems measured in the Kruger National Park (Scholes, unpublished data).
Trees taller than 12 m have a diameter at breast height of 80 cm or more on average. The same database was used to
calculate the size-based mortality rates for trees. On average, the number of trees in each size class is 32.3% fewer
than the number in the next smallest diameter class, for all classes with a diameter greater than 5 cm.
In order to allow the size-structured tree model to run on a common basis with the age-structured elephant model, it
is necessary to know the stem diameter growth rate. Based on multi-year repeated measurements on savanna trees throughout
South Africa (Shackleton 1998), the percentage annual growth rate in stem cross-sectional area (DA) is a function of
both the diameter of the stem and the degree of competition to which it is exposed:  
DA = (1.0 + 19.0 e-0.2d )*(1-B/Bmax)
where B is the basal area of woody plants (m2/ha) and Bmax is the maximum basal area that can be attained
given the rainfall (converted from the data used by Sankaran et al. 2005 into basal area terms, Bmax= 0.03
[MAP-100]), which in this example is about 12 m2/ha for the average Kruger Park rainfall of 500 mm/year. Seed
production was made proportional to stem cross-section, and began when the trees reached a third of their maximum height.
A combined germination and survival rate for seedlings up to the 5-cm diameter class was estimated on the basis of the
assumption that the tree population was initially in a steady state.
Coupling of the two models was achieved by assuming that elephants have two main impacts on trees. For trees larger than
15 cm in diameter but smaller than 40 cm, the stem is snapped or uprooted as a result of being pushed over by elephants
in order to browse on the canopy foliage. For trees smaller than 15 cm in diameter, the canopy is entirely within reach
and, although browsed, the main stem (if one exists) is not broken. Trees larger than the upper limit are harder to
break or uproot, but are subject to debarking. The resulting mortality is complex, depending on the fraction of bark
circumference lost and the presence of other agents, such as wood-boring insects and pathogens. We assumed that tree
death occurred when the equivalent of a full circumference was debarked. In the absence of data, we assumed that
each elephant strips 1 m of bark circumference per day, distributed over the size classes in proportion to their
circumference. The fraction of a size class that dies per year (Fi) through this mechanism is thus:
Fmortality = [ni pdi /S(ni pdi )] [365 E /nipdi ]
where ni is the number of trees in size class i (km-1), pdi is the
midpoint circumference
of size class i, Snipdi is the sum over all size classes of
the stem circumferences, and
E is the number of elephants (km-1).
Pushed-over trees do not die, but revert to the smallest size class as coppice resprouts. Female elephants push over an average
of one tree a day and bulls, four times as many.









  
 

When is the limit likely to be transgressed?






Starting this model with the observed tree size distribution and the observed elephant age distribution for the Kruger
Park shows the trajectories illustrated in Figure 2. Note that our model projects a slow decline in the number of large
trees even in the absence of elephants, suggesting that the observed tree size distributions are not in a steady state.
The ensemble results presented in the same figure are the year in which the threshold is crossed in a hundred independent
model runs, when both a key ‘tree’ parameter (the mortality due to elephant damage) and a key elephant
parameters (mortality and its dependence on density) were systematically and independently varied according to a normal
distribution using the mean and standard deviation reported in the literature. More of the assumptions in the model could
be tested in this way, but this scheme is sufficient to demonstrate the principle of creating an uncertainty range.





	
	
	

FIGURE 2:  An example of a model for a hypothetical elephant-tree system, based on data from the Kruger National Park.














The lower 95th percentile of the predicted number of trees taller than 12 m intersects the chosen threshold of one tall
tree per km2 at a time 60 years from the simulation start (which nominally represents year 2009). This is the
starting date from which we begin the intervention calculation.








  
 

Subtracting the response times






In this example, we have assumed that the chosen management intervention is to reduce the fertility of elephant
cows using immuno-suppressant contraception. A 75% success rate is assumed (Bertshinger et al. 2008).
Running the model using just the ‘best estimate’ values for the parameters but reducing the fertility
of the cows by this fraction results in the response trajectories illustrated in Figure 3, depending on when the
intervention begins. By plotting the years of pre-emptive management against the extra years of non-transgression
of the threshold thereby gained, we can deduce that the ‘inertia’ of the elephant-tree system as defined
above is in the order of 30 years.





	
	
	

FIGURE 3:  The effect of the year of commencement of elephant contraception on the decline of large trees.


















We further estimate that it would take about 3 years to launch a contraception programme of this magnitude,
including making the decision, getting approval in terms of an elephant management plan approved by the minister
concerned, consulting with stakeholders, manufacturing the vaccines, and conducting field operations to vaccinate
all sexually mature elephant cows. Finally, we added a monitoring interval for the key elements in the system
(trees taller than 12 m, and elephant population) of one year.













  
 

Is an action triggered?






The indicated time to trigger a decision regarding elephant contraception in order to prevent the limit of one tall tree per
km2 being exceeded, thus, is the year in which more than 5% of the model runs indicate the limit being breeched
(2069), minus the sum of the system response time (30 years), the management delay (3 years) and the monitoring interval
(1 year). This suggests that a decision would need to have been made, at the latest, by 2035. We stress once again that this
is a theoretical example only.









	

 



Discussion and conclusion





	 (Back to top)







This paper has outlined a logical procedure for triggering management interventions in systems that are dynamic and prone
to measurement error and theoretical uncertainty. The steps seem complicated, but we would argue that they are necessary
and that the level of detail aimed for in any one of them needs to be matched to the uncertainty inherent in the full
logical chain, which is determined by the data that are available or readily accessible. The effort involved should be
guided by the consequences of getting the signal wrong, either as a result of initiating an action where no action was
needed, or by failing to do so when intervention was necessary. The process we have described reveals where the key
uncertainties lie and what can be done to address them. Finally, it is clear that several of the steps (selecting the
overall objective, setting the level of risk aversion) are not purely technocratic, but require input from stakeholders
in a legitimate fashion. On the other hand, there are elements (particularly the forward projection of system trajectories)
that do require specialised technical input, and the quality of those technical inputs can be increased through
investment in monitoring and research.







	

 



Acknowledgements





	 (Back to top)







Two anonymous reviewers made useful comments that improved the paper.








	

 



References





	 (Back to top)







Bertshinger, H., Delsink, A., Van Altena, J.J., Kirkpatrick, J., Killian, H., Ganswindt, A., et al., 2008, ‘Reproductive
control of elephant’, in R.J. Scholes & K.G. Mennell (eds.), Elephant management: a scientific assessment for South Africa
, pp. 257−327, Witwatersrand University Press, Johannesburg.
Biggs, H.C. & Rogers, K.H., 2003, ‘An adaptive system to link science, monitoring and management in practice’, in
J.T. du Toit, K.H. Rogers & H.C. Biggs (eds.), The Kruger experience, pp. 59−80, Island Press, Washington DC.
Brogan, W.L., 1985, Modern control theory, Prentice-Hall, New York.
Carruthers, J., 1995, The Kruger National Park: A social and political history, University of Natal Press, Pietermaritzburg.
Carruthers, J., Boshoff, A., Slotow, R., Biggs, H.C., Avery, G. & Matthews, W., 2008, ‘The elephant in South Africa:
history and distribution’, in R.J. Scholes & K.G. Mennell (eds.), Elephant management: a scientific assessment for
South Africa, pp. 23−83, Witwatersrand University Press, Johannesburg.
Duffy, K.A., Page, B.R., Swart, J.H. & Baji, V., 1999, ‘Realistic parameter assessment for a well known elephant–tree
ecosystem model reveals that limit cycles are unlikely’, Ecological Modelling 121, 115−125.
doi:10.1016/S0304-3800(99)00091-5
Ellis, J.E. & Swift, D.M., 1988, ‘Stability of African pastoral ecosystems: alternate paradigms and implications for
development’, Journal of Range Management 41, 450−459.
doi:10.2307/3899515
Folke, C., Carpenter, S., Walker, B., Scheffer, M., Elmqvist, T., Gunderson, L., et al., 2004, ‘Regime shifts,
resilience and biodiversity in ecosystem management’, Annual Review of Ecology and Systematics 35, 557−581.
doi:10.1146/annurev.ecolsys.35.021103.105711
Goklany, I.M., 2001, The Precautionary Principle: a critical appraisal of environmental risk, Cato Institute, Washington DC.
Gregory, R., Ohlson, D. & Arvai, J., 2006, ‘Deconstructing adaptive management: criteria for application to environmental
management’, Ecological Applications 16, 2411−2425.
doi:10.1890/1051-0761(2006)016[2411:DAMCFA]2.0.CO;2
Holling, C.S. & Meffe, G.K., 1996, ‘Command and control and the pathology of natural resource management’,
Conservation Biology 10, 328−337.
doi:10.1046/j.1523-1739.1996.10020328.x
Martin, J., Runge, M.C., Nichols, J.D., Lubow, B.C. & Kendall, W.L., 2009, ‘Structured decision making as a
conceptual framework to identify thresholds for conservation and management’, Ecological Applications 19(5), 1079–1090.
doi:10.1890/08-0255.1,
PMid:19688917

Owen-Smith, N., 2002, ‘Credible models for herbivore-vegetation systems: towards an ecology of equations’,
South African Journal of Science 98, 445−449.
Risse, L.M., Nearing, M.A., Laflen, J.M. & Nicks, A.D., 1993, ‘Error estimation in the Universal Soil Loss Equation’,
Soil Science Society of America Journal 57, 825−833.
doi:10.2136/sssaj1993.03615995005700030032x
Sankaran, M., Hanan, N.P., Scholes, R.J., Ratnam, D.J., Augustine, B.S. Cade, J., et al., 2005, ‘Determinants
of woody cover in African savannas’, Nature 438(7069), 846−849.
doi:10.1038/nature04070,
PMid:16341012

Shackleton, C.M., 1998, ‘Annual production of harvestable deadwood in semi-arid savannas, South Africa’,
Forest Ecology and Management 112, 139−144.
doi:10.1016/S0378-1127(98)00321-1
Shaffer, M.L., 1990, ‘Population viability analysis’, Conservation Biology 4, 39−40.
doi:10.1111/j.1523-1739.1990.tb00265.x
Scholes, R.J. & Mennell, K.G. (eds.), 2008, Elephant management: A scientific assessment for South Africa,
Witwatersrand University Press, Johannesburg.
Terborgh, J., Estes, J., Paquet, P., Ralls, K., Boyd-Heger, D., Miller, B., et al., 1999, ‘The role of top
carnivores in regulating terrestrial ecosystems’, Wild Earth 9, 42−56.
Van Aarde, R., Ferreira, S.M., Jackson, T.P., Page, B., De Beer, Y., Junker, J., et al., 2008, ‘Population
biology and ecology’, in R.J Scholes & K.G. Mennell (eds.), Elephant Management: A scientific assessment for
South Africa, pp. 84−l45, Wits University Press, Johannesburg.
Vose, D., 1996, Quantitative risk analysis: a guide to Monte Carlo simulation modelling, John Wiley & Sons, New York.