Macr ic view of inability of dry forest in Androy region. A system dynamics
approach
Fanokoa Pascaux Smala, Economist, PhD
Environmental Management Consulting
6-8320 Durocher (QC) Montreal H3N2Z2 Canada
Abstract
The Tandroy communities do not cease to practice slash and bum agriculture to satisfy their subsistence needs. To
get rid of the spines, before feeding their zebu, peasants bum the cactus cladodes (omputia) and the mozotse
(euphorbia lada) ion. Despite these techniques, the performance of the agriculture and the breeding of
zebu are successful only for a brief period. Nevertheless, in long term, these practices are unsustainable vis-a-vis the
ecological pressure on the neighboring dry forest. These activities may lead to greater risk of socioeconomic
disasters on both local and global scales in the near future. In this paper, we report the concept of a methodological
framework for integrating the subjects of system of thinking and system dynamics and confront it with the Tandroy
macroeconomic view, accordingly. Thus, we analyze the effect of both interlinks and causal relations between
socioeconomic and environmental variables in Androy.
Keywords: Androy, Dry forest, Madagascar, Macroeconomic view, Natural stocks, Slush and burn agriculture,
System dynamics, Tandroy, Zebu.
1 Introduction
Throughout history, demand for timber, forest products and agricultural land have had a negative effect on the
world’s forest resources. Such forest loss is the result of many pressures, acting in various combinations in different
geographical locations (Geist and Lambin, 2002).
In this paper, we are interested in tropical dry forest and open woodlands in Androy Madagascar. According to
(FRA, 2005), only about seven percent of the Earth’s dry land, are covered by tropical dry forest and all of the
forests in the southem part of Madagascar belong to this zone. Dry forest in Madagascar is fragile because of its
high level of plant endemism, with 48% of the genera and 95% of the species endemic (Koechlin, 1972). Flora and
fauna in Madagascar is extremely popular as the island home for some of the most unique and rare species of the
world (WWF, 2011). The “spiny forest region” is also listed as one of the 200 most important eco-regions (Olson et
al., 2002). In 1970, ten years after gaining independence from French colonization, the Malagasy forests,
particularly in Androy were becoming increasingly depleted due to hatsake (slash and bum), ororaketa (cactus
buming for cattle herding), timber harvest and charcoal production (Fanokoa, 2007; Sussman et al., 1994; Sussman
et al., 2003).
The study zone is situated south of the tropic of Capricom between 24° and 26° South and 44° and 47° East. The
area is bordered by the Mandrare and Menarandra rivers figure 1. Climate is semi-arid, with average annual
precipitation varying from 35 centimeters on the N coast to 70 i toward the north. Irregular
rainfall makes the region subject to cyclic drought. Androy’s forest is characterized by xerophilous bush, dominated
by species of endemic plant families: the Didiereaceae and the Euphorbiaceae.
During recent decades, despite the recognition of the priority status of the forests little research was carried out on
the forest cover changes in the region. Official protected areas are also few' and the region itself is forgotten
(Elmqvist, 2004). Despite this lack of official protection, customary laws and taboos, which play an important role
in the local society, are institutional factors, which make a great contribution to protecting the forest patches in this
tegion.
In the Androy region, clan is the basis of traditional socio-political organization. Each clan has its size, area, wealth,
and ritual. The Tandroy has a social differentiation, which is based on the territory, ancestry and wealth. The zebu is
the central point of Tandroy culture and the animal plays a role in different practices and beliefs such as funerary
cults, maleficent (indigenous spirits), benign (foreigner spirits), sacred efficacy, taboo (unspoken words or what is
left unsaid), moral blame (largely determining prosperity and power). Zebus represent a tool of communication
between God and human being (Fanokoa, 2007). The cattle supply meat, milk and leather as well. Possessing
significant numbers of zebu determines status and wealth, which symbolizes a distinction of superiority within the
societies. Hence, everybody endeavors as much as possible to have an impressive number of livestock (Fanokoa,
2007).
The Tandroy populations are pastoralists, cultivators and gatherers. Over the last decade, the population has more
doubled in the last 30 years and the combined effect of an i pulation and of r to change their
traditional lifestyle and production system has led to great ecological pressure on the dry forest.
1 Angavo; Ambanisarika; Vohimena; Vohipary; Cap Sainte Marie...
BEKILY
MAHAFALY
REGION
District of BELOHA
Beloha
Marolinta
Trafiowaho CAPTIONS
"== Boundary of District
"== Boundary of REGION|
j— River
ANDROY REGION
Figure 1: Study zone - The region of Androy
As both human and cattle populations are increased, hatsake and ororaketa activities require increasing agricultural
land (Fanokoa, 2007; Andrés-Domenech, et al, 2011). The increase of conversion of the forest areas into pasture and
agricultural land is an evident problem in Androy. This happens because the property right on forest land is not well
defined i.e. the first who chops the trees is the owner of the patch of land. This insecure tenure system encourages
farmers to practice the hatsake activities in which they plant principally maize, manioc, sweet potatoes legumes,
groundnuts, paraky gasy (Malagasy tobacco) and cucurbits. Land from hatsake practice is cultivated for an average
of three to five years before the soil fertility is reduced to a point where it no longer becomes.
In this paper, our contribution is to identify core variables involved dynamically in the deforestation system and to
study the behavior of socio-economic and environmental system in the region by using system dynamics (SD)
approach. The main objective is to identify and to understand the impact of the Tandroy socio-economic activities
on environment.
The reminder of the paper is structured as follows: in section 2, we model the interaction between three natural
stocks (Zebu, dry forest and Tandroy population). The causal loop diagram (CLD) will be developed, then the stocks
and the flows model will be presented, illustrating the three steps of the model: the characterization of (1) zebu’s
stock, (2) stock of dry forest in area unit and (3) growth of Tandroy population. The results will be shown at the end
of each sub-model. Subsequently, section 3 concludes.
2 The model
2.1CLD
We use the VENSIM to write the entire model. Moreover, SD provides capabilities to follow and recognize cause-
and-effect mechanisms between the parts of the system over time. This approach improves the behavior
of stakeholders by ining the inten ionship between and flows, material information, through the
corporate structure. Basically the technique consists of the construction of a diagram indicating all the important
relevant relationships in the system.
Sterman (2000) argues that SD attempts to model the structure of a system, including its feedback loops and
dynamic relationships over time, in order to capture the behavior that it produces. What’s more CLDs characterize
major feedback mechanisms, which reinforce (positive feedback loop (R) or (+)) or counteract (negative feedback
loop (B) or (-)) a given change in a system variable (Sterman, 2000). CLD is an essential instrument to show the
feedback structure within the subsystems. The source hypothesis of dynamics can be identified. Besides, CLD
consists of variables connected by arrows denoting causal influence (named causal links) among variables and then
the formal definitions are summarized as follows.
Given a function Y dependent on x independent variables, the diagram:
a __
x1 Y
can be mathematically expressed as: = >0 orY= SoG +++-)ds + Y(to) in the case of accmulations.
On the contrary, the following relationship:
represents: = <0 orY= SiC —X, +++)ds + Y(t) in the case of accumulations.
1
In figure 2, arrows show the causal links or causal influence among variables.
Deforestation rate
Depreciation
Deforestation
Food demand *
* a+
+
Gap
Consumed food Ws
Zebu output ratio
Depreciation rate
B6 per capita Food production .
(Revenue) R1
+ Capital source
Mortality + Emigration i a Investment
ad Consumption eA
‘Saving +:
B3
Emigration rate
Mortality rate
Marginal
propensity to
consume
Natality rate
Figure-2: Causal loop diagram (CLD)
Description of the loops: Qualitative design of the model
This model incorporates the full range of issues, which is involved in sustainable development of Androy region.
The baseline descriptive model consists of three blocs of subsystems of natural stocks namely economic structure
(the accumulation of zebu as a capital), social di ion () lation, birth, death, emigration) and natural
(dry forest resource stock, its depletion and effect of agriculture production system). Figure 2 describes the whole
system, in which it has 3-state variables, 11-auxilliary variables, 11 constants (initial values) and 7 loops (2
reinforcing loops and 6 balancing loops). All variables influence each other.
(B1) is the deforestation loop. The increase of deforestation has a negative impact on stock of dry forest. Polarities
(negative and positive) result a negative feedback loop or balancing loop in figure 2.
Loops (R1), (B2) and (B3) influence directly between them in the economic pillar. The growth of food production is
desired which has a positive impact on the growth of zebus. In fact, macroeconomic model looks at the total output
of a nation and the way the nation allocates its limited resources of land, labor and capital in an attempt to maximize
production levels and promote trade and growth for future generations. In Androy, the economic output is equivalent
to total revenue, which is also equivalent to consumption plus savings or/and consumption plus investment. Loop
(B3) is the depreciation loop. Zebu is a tangible depreciable property of which her depreciation depends on the stock
of zebu itself. The sign of the loop is negative, i.e. balancing loop. The livestock depreciation begins when the
livestock reaches the age of maturity [in Androy Depreciated Age,.4, > 8 Years] (Fanokoa, 2007). It is possible
to determine an annual depreciation by the difference between the cost of the zebu and its sal vage value and divided
by the zebu useful life.
Loops (R2), (B4), (B5) and (B6) illustrate the system of population growth. The reinforcing loop (R2), population
itself grows, which is explained by birth growth. However, the loops (B4), (B5) and (B6) play a counterweight to
(R2) because emigration and mortality, decrease the stock of population. For the latest decades net migration has
been mainly negative i.e., emigration in Androy is greater than immigration (Fanokoa, 2007). By the loop (B4),
most of Tandroy has to migrate due to lack of food (Gap). In fact, the population growth by loop (R2), would need
more and more foods. CLD in figure 2 shows roughly that the Tandroy performs the hatsake activity for two
reasons: (1), to have more food production for solving problems of food security; and (2) to spare.
2.2. Stocks and flows
In the SD theory, stock and flow diagrams are essential. SD describes firstly all state variables of the system, and
then it generates information upon which both actions and decisions are founded. In figure 3, stock represents a
black box which can be viewed solely in terms of its input, output and transfer characteristics without any
knowledge of its intemal workings. Stocks produce delays by accumulating the difference between regulator inflow
to a process and its outflow. Information or materials are obtained from source and outflow towards the sink. Source
and sink are inexhaustible. The stock and flow diagram shows relationships among variables, which have the
potential to change over time. Several textbooks such as (Sterman, 2000), (Y amaguchi, 2014) and others give more
detail about building system dynamics blocks. In figure 4: The stock, the flow, the variable and the arow
information are interconnected as system dynamics bloc.
Valve Sink
Source :
Black box
Variable
\
a [stock | Fi
Inflow ow
Figure 3: Stock and Flow diagram (1) Figure 4: Langage of System Dynamics
Stock and flow are mathematically represented as follows:
Differential form: “2 = (inflow(t) — outflow(t)}
Integral form: Stock(t) = J {inflow(s) — outflow(s)}ds + [Stock(to)]
Characteristics of the stock
According to Sterman (2000), (i) Stock characterizes the state of the system in which many variables depend on the
current value of stocks. (ii) Stock guarantees memory and inertia in systems since it can accumulate past events. Its
content can change only through an inflow and outflow. (iii) Stock generates delay, which is defined as a process
whose output lags behind its input. The difference between input and output gives a stock. In case of modeling
perception delays as a stock, any material flow cannot be involved in it. (iv) Stock divides rate of flows and
generates disequilibrium dynamics. The behavior of inflow and outflow differs each other, because of the presence
of the stock (level) and the decision process that govems those both flows. The stock itself does not change in
equilibrium. The derivative of stock in SD is considered as exogenous variables and non-linear function.
State variables
Three principal state variables (natural stocks) are expressed in the model to explain the sustainability of
development poles in Androy: zebu capital K, Tandroy population L and forest resources F. The model will be
portrayed in 3 steps of dynamic sub-model with a discrete time. In each sub-model, the following matters will be
described: (i) equations of sub-model, (ii) flow and stock diagram, (iii) steady state equilibrium (SSE) and (iv) result
of simulation.
2.2.1. 1" step: Simple macroeconomic growth model
We adopt a simple mac ic growth model developed in the late 1940s. The model is applied in development
economics to explain the growth rate of economy in terms of the level of saving and the productivity of investment
i.e. the capital output ratio (Yamaguchi, 2001). In other words, the model underlines an economic prosperity and
growth that occurs through a reinforcing process where capital is accumulated. Assume that capital depreciation is
not considering in this first step. Consider five simple behavior relationships:
K,(t+ 1) = K,(t) + 1(0) (1)
where K,(t + 1) is the capital stock from the zebu, K,(t) is the initial capital stock, and I(t) is the investment of
zebu per year. Equation (1) shows a capital accumulation where stock of zebu is increased by the amount of
investment.
¥(t) == *K,() (2)
The production function in (2) is illustrated by the production or output Y (t) which is produced only by the stock of
zebu obtained from the production of food and from the immigrated Tandroy. In Androy, the surplus of food will be
immediately converted in zebu; and x the capital-output ratio d by number of zebu per unit of
food per year.
C(t) =c*Y(t) (3)
The equation (3) is very familiar in macroeconomic consumption function. Where C is consumption and c is
marginal propensity to consume (MPC)
S(t) =Y(t)- C(t) (4)
In (4) portion of disposable food (not J) is ace or invested directly in zebu.
I(t) = S(o) (5)
I(t) =9*S(t) (6)
In (5), the equilibrium can be achieved by equating investment / with saving S; otherwise output would not be
exhausted completely or in a state of shortage. For the unit conformity, saving S in equation (6) is multiplied by a
conversion factor y. This latter ensures a food unit of saving S to a zebu unit of capital investment. In other word,
the needed unit here is unit of zebu per food dimension.
SD modeling requires a precise specification of each variable as defined in the six equations above for allowing us
to build easily a model. Regarding the proportion of the number of five equations and the five unknown variables,
the economic growth model becomes consistent.
Steady state equilibrium (SSE) of zebu accumulation
With SD, determining steady state (SS) is also very essential because stocks are in standstill, and at the same time,
the net flows value tum into zero, i.e. there is no growth.
Stock and flow relation
Zebu output ratio
Food production
(Revenue)
Investment! ‘Saving <———_consumption
Conversion factor1 Marginal propensity
to consume (MPC)
Figure 5: Stock and Flow diagram (2)
ECONOMIC GROWTH
Proposition 1 SSE of the capital accumulation is reached in K,(t + 1) = K,(t) but SS is analytically reached,
assuming a single equation of capital accumulation which is given by:
K(t+ 1) = K(0 [-*] (0)
Proof. See Appendix.
Assume the whole revenue is consumed. This circumstance results that neither saving nor investment is available.
This can be numerically explained by S** = 1° = 0 and MPC is equal to 1. SS equilibrium is reached at K3* =
290000 and C** = 233611.
Simulation 1
4M xbu
4M kg/Year
4M kg/Year
2M abu
2M ke/Year
2M. kg/Year
0 xbu
0 kg/Year
0 kp/Year
2001 2021 2041 2060 2080 2100
(Year)
Zebus zebu
"Food production (reverme)" 222222222 kg/Year
C. a kg/Year
Figure 5: Simulation 1 —- Simple economic growth model
The growth path is shown in figure 5. Recall that the relative increase in personal spending (consumption) that
comes with an increase in disposable income is known as MPC. The latter indicates the portion of additional income
that is used for consumption expenditures. In simulation 1, the growth path is set by c = 0.87, means that 13% of
the revenue is saved for the investment in zebus. The infinity growth of the capital, revenue, consumption and
investment is at the rate of 2.4% for MPC equal to 0.87.
2.2.2. 2" step: Sustainable model
Let us develop the model by introducing capital depreciation and forest resources:
K,(t+ 1) = K,(t) + I(t) — D(t) (8)
D(t) =p * K,(t) (9)
where p is a depreciation rate of livestock per year and the inequality /(t) — D(t) = 0 should be satisfied.
In modem economy, depreciation has been widely known as machines, cars, homes, etc., but what about zebu? It
can obviously happen that livestock can be depreciated as long as they are used for breeding. By definition
depreciation is the depletion of capital assets in equation (8) where /(t) represents a gross investment and D(t) is
the depreciated zebu per year . However, we assume that breeding animal in Androy can be depreciated, no taking
into account raising cost such, for example, expense items (grass, plant, medicine...); these are negligible.
Proposition 2 As seen in precedent proposition, SS is analogically reached at K,(¢+ 1) =K,(t) or /(t) =
D(t), hence the equation of the model is reduced as:
K(¢4 1) = KO) + [Ps] (10)
A marginal propensity to consume becomes less than one, which implies that the portion of production Y(t) has to
be saved to replace the capital depreciation.
Deforestation rate
Depreciation rate
ov)
y Conversion factor2 Deforestation
Zebu output ratio
Depreciation
Food production
evenue]
AR
Investment [Hag Saving = Consumption
Marginal propensity
Investment rate Conversion factor ty consume (MPC)
Figure 6 : Stock and Flow diagram (3)
Economic sustainable model
Proof. See Appendix.
What if you catch a black swan?
Public policy design for climate change adaptation
Hugo Herrera
University of Palermo Bergen University
Department DEMS Geography Department
Via Ugo Antonio Amico 3, System Dynamics Group
90100 Palermo, Italy Fosswinckelsgate 6, N-5007
Bergen, Norway
EXTENDED ABSTRACT
What if you catch a black swan? So called black swans - unlikely but high impact unpredictable
events — are now of particular concern for public management as their effects impact widely
social and economic systems. As global climate change effects multiply, so does awareness of
the black swans (unseen droughts, floods, fires, etc.) the new climate condition might carry and
their consequences. Resilience thinking has been one of the main approaches used to frame
climate change dynamics by aiming to enhance the capability of social systems to adapt to these
new climate conditions. Thus, policymakers’ agenda now includes resilience-based strategies
oriented to protect preferred states of the system from unavoidable and unpredictable
disturbances.
However, there is still a sizable amount of work needed before to transform these resilience-
based strategies into policies. Particularly, there is a need for developing means to bridge the, so
far, mechanistic concepts of resilience with the real world and to overcome current contradictions
between resilience and the new public management approaches. Current paper addresses this
need by exploring how to use a Dynamic Performance Management approach to support
policymaking processes for climate change adaptation and to identify timely mechanisms to deal
with the unexpected.
Effects of climate change are now hard to deny. In the past years, climate change has manifested
in the rise of temperatures and changes in the rainfall seasonality around the glove. These effects
of climate change have shocked our social and economic systems exacerbating water scarcity,
hunger and even social conflicts in many parts of the world. Occurrence of unlikely events makes
us aware that while black swans (Taleb, 2010) have low probabilities to happen, they are still
possible. Moreover, the high impact of some of those unlikely events evidenced the dependence
of social and economic systems on their natural counterparts and arose interest in identifying
ways to reduce vulnerabilities and foster successfully manage adaptation.
Walker et al. (2004) define resilience as the capacity of a system to absorb disturbance while
remaining its essential function. However, even resilience is widely applied, a defining
characteristic of the resilience concept in SES literature is that “there is no single theoretical
framework under which all resilience-related research is subordinated” (Duit, 2015, p. 5). Instead
there is a diverse set of different definitions, concepts and descriptions of what resilience means
(Berkers, Colding, & Folke, 2002; Chapin Ill et al., 2009; Folke, Carpenter, Walker, Scheffer, &
Elmqvist, 2004; Walker, Gunderson, Knizig, Folke, & Carpenter, 2006; Walker, Holling,
If you want a copy of the full paper, please contact the author at:
hugojhdl|@gmail.com or hugo.leon@student.uib.no
1
Thus, from (10), SS can be expressed as follows:
1-—c* = Kp* (11)
Let us grow out the economy of the SS after introducing the forest resource; that is the growth of zebus as K,(t +
1>zt and the following condition has to be captured: (1) enhances the productivity: the zebus-output ratio ~ <
«SS; (2) improves the quality of livestock : < p** or (3) enhances the level of saving and investment or
diminishes the level of consumption such asc < c*S.
In previous economic growth model, zebus depreciate, and for maintaining the current level of production/output,
some portion of revenue has to be saved in order to replace D(t). If zebu’s depreciation rate is high, the portion of
revenue has to be saved at the same cost of consumption. Thus, Tandroy population overuses natural resources to
maintain the sustainability of their economy. However, the economy reproduction process creates an environmental
crisis’. The sustainable issue should be called to mind and this leads to the famous definition of the Brudtland
commission of sustainability. This definition is a kind of famous for devel that meets
the need of the present without the ability of future generations to meet their own needs (WCED, 1987). In this
sense, an envi pillar will be i in the next model.
Simulation 2.1
As illustrated in figure 7, the zebu keeps growing from the starting time of simulation until 2100. Numerically, we
consider the previous case (3) and we set p = 0.032. As shown in figure 7 Kz2001) = 290 000.
600,000
600,000
400,000
20,000
200,000
200,000
200,000
10.000
2001 2021 2041 2060 2080 2100
Tine (Year)
Zebu - zebu
Revenue 2— ke/Year
Consumption se i iver
Investment zebu/Year
Figure 7: Simulation 2.1 — Economic growth model
to Kz2199 = 313510. During the century the average growth of zebus has a rate forecast of 0.41% and for food
production increases from Y2991 = 268519t0 Yz199 = 412039. Nevertheless, we want to see whether such growth
can be sustainable?
Dry forest resources
2 At present time Tandroy population depends principally on the forest resources for reproduction (agriculture,
breeding, different economic activities...).
The condition in (8) presumes an availability of natural resources to be integrated in the model, which is represented
by the forest resources in the following equation:
F(t +1) = F(t)— AF(t) (12)
Equation (12) shows forest depletion dynamic due to hatsake and ororaketa for food production Y (t).F(t)
represents an initial forest area at time t, and AF(t) characterizes the deforested area which is needed for the input.
In other words, deforestation is considered in this context as raw material and consequently it will be described in
the following equation:
AF (t) = *Y(0) (13)
where, 7 denotes a rate of deforestation measured by the net stock of deforested area per unit of food.
SSE
To determine the SS of forest resource, we would equate F(t + 1) = F(t) whichimplies AF(t) = n*Y (t) = 0.
Both zebu capital and forest resources are integrated in the model as state variables. However, the SS of capital
accumulation is not influenced by the introduction of forest resources. Consequently, SSE of zebu capital is a
positive amount of production, which is contradictory to the SSE of forest resource. To avoid this confusion and to
make the model feasible, we skip the concept of forest SSE or we assume an availability of forest resource at any
time in the Androy economy system. Hence, this availability can be written as follow: D2 299: AF (t) < Yoo01-
Simulation 2.2
The dry forest resource is continuously depleted even at SSE of zebus’ accumulation. Deforestation attains its peak
att = 2026 before getting felt at the rest of simulation. This curve trend is supposed to be normal because the
depletion of dry forest is considerable from t= 2001 tot = 2100: the higher the depleted forest, the lower the
forest clearing, because there will not be enough forest to cut. Food production
600,000 Ha
8,000 Ha/Year =
300,000
4,000
°
2001 2021 2041 2060 2080 2100
‘Time (Year)
Dry forest 4 4 Ha
ti = = Ha/Year
Figure 8: Simulation 2.2 — Depletion of dry forest
and zebus grow weakly during the simulation which is contrary to the behavior of the forest loss curve. At F939 =
264355, half of the dry forest will remain. Long-term forest management is necessary; otherwise dry forest will be
practically cleared at Fro26.
1
2.2.3 3" step: Tandroy population model
Consider a Tandroy population growth model whose size L(t + 1) is given by the following simple dynamic:
Le +1) =(@-B- yl (14)
where, a, f and y are constant and denoting respectively birth, death and emigration rates and L(t) represents initial
population in time t. The agricultural population is defined as all persons depending for their livelihood on
agriculture, hunting, fishing or forestry (FAO, 2002). Despite poverty in any nation, assume that agricultural
population can provide at least a minimum amount of food in period of time for the reproduction of its population.
Accordingly, the consumption function (3) will be rewritten as follows:
C(t) = wht) (15)
where y denotes a minimum amount of consumed food per person. Hence, the integration of this minimum
requires an adj of all i which are involved with (15). Let revise a saving function S as
a non-negative saving, which is expressed as follows: S(t) = Max{Y(t) — C(t),0}. The net production can be
noted in (16):
Y(t) — D(t) — pL(t) = 0 (16)
The equilibrium in (5) is revised in (17):
I) = S®= YO-C§O) = YO-wO= DO (17)
The tandroy-agricultural population represents a number of workers which is denoted by W(t) and can be expressed
in the following:
W(t) =w* L(t) (18)
where, w = 0.85 is a participation ratio of Tandroy workers. (18) allows us to rewrite a production function in the
following expression:
Y(t) = Min€-K,(0),1W(} (19)
where, r = 1.1 is an output-Tandroy ratio.
Stock and flow diagram SSE of sustainable socio-economic model
Lastly, the model contains three stock variables K,(t + 1), F (t + 1) and L(t + 1). These stocks expand in nine
unknown variables and nine constants, which are structured in nine equations. Therefore, the consistency of the
model remains. Recall that non-existence of SSE of renewable resources is mentioned. Nevertheless, the SS of
population growth L(t+ 1) = L(t) is attained when aS = B** +y** = 0.01. As it is seen previously, SS of
zebus can be also attained for the value of constants (c**, «°°, p*) = (0.87, 1.08, 0.032). From equation (19), two
cases of SSE can be expressed:
a) “The food production” is constrained by zebus and from (2) Y(t) = : » K,(t); this can be re-written:
KO _
i@ 1_, °8
K
For L(t) = 548418, zebus have to be K,(t) = 290000 at SS. Thus, except the dry forest, the SSE is resumed in the
following table:
K | [| | | s =
290000 | 548418 | 252174 | 242339.22 | 9834.78 | 9834.78
Deforestation rate
Dry Forest
Moratality rate
Depreciation rate ss
QO Emigration rate
A
Zebu output ratio
Depreciation KIMortality
Food production Tandroy
(Revenue)
Gap Emigration
A
Consumed food
per capita
Investment Pgs aving DxINatality
Consumption
Food demand
Investment rate Marginal
propensity to Birth rate
consume
b) The “food production” is constrained by the labor and (18) W (t) = w * L(t); this can be expressed:
K,0)_ or-p
L(t) p
= 1.74
For L(t) = 548418, zebus has to be K,(t) = 290000 at SS. Thus, expect the that dry forest, a SSE is presented in
the following table:
K= i ys Cs = Ts
290000 | 548418 | 252174 | 484678.44 | 19669.56 | 19669.56
Simulation 3
13
400,000
oN
400,000
400,000
600,000
t)
0
i)
ok
0
2001 2021 2041 2060 2080 2100
Time (Year)
Zebus zebu
Tandroy e Person
(evenue)’ : + « kg /Year
consumption + + + 4 4 4 4 bg /Ver
Dry forest Ha
Figure 10: Simulation 3
Figure 10 illustrates the final result, which is gotten from the interrelation between the three pillars. The result
shows, firstly, that the dry forest in the Androy region is depleted fast and will practically disappear int = 2080.
This may happen because of the ororaketa and hatsake. Due to the reduction of fodder of zebus, which has a tight
link with the forest, zebus are reduced in number as well. However, population increases with 2.1% of rate per year.
In the same case, the lack of food appears because the food production cannot cover completely the gap. Then, the
consumption and the investment decline.
3 Conclusion
We identified the core variables that play an important role in the whole model. The model showed that the
economic and productive system in Androy is not sustainable. The Tandroy need to lower heir birth rate. The
growing of the population puts pressure on dry forest resource. As forest is open access resource, the deforestation
rate is harmful of the sustainability of forest resource.
The variable “food production” or revenue plays a principal role as decision variable upon which the future of the
three pillars (environment, economy and population) depends. Tandroy uses forest resource like an input (raw
material), which is too costly to control or to monitor, then it maybe necessary to strengthen afforestation by means
of public program to counterbalance the deforestation damage and to stabilize the forest surface area.
As the land cannot provide enough revenues for the current population and for feeding the cattle, then the
i cannot be A number of changes that may revert the situation, either on the demand
consumption side or on supply side. To ensure a sustainable development for the current population is to lower per
capita consumption in the region by roughly 30% with respect to the currents levels.
Clearance arises due to mix of lack of forest law and the poverty. Then, to spare the dry forest, it is necessary to
reduce the consumption rate but on contrary the deforestation issue may aggravate or population raises persist
overtime.
Three extensions would be worthwhile to highlight. First, other state variables would be integrated in the model such
as fertility of soil, agricultural livestock land etc. Second, it would be given as more reliable as social measurement
scales (gender, education, health, etc.) And lastly, other source of revenue would be deeply investigated (hunting,
fishing, selling, money transfer...).
4 Appendix
4.1 Proof of Proposition 1
Decomposing (1) with respect to K,(t), Y(t) and C(t), yields
K,(t + 1) = K,(t) + 1(t) = K,(t) + Y(t) — C(t)
Substituting in (20) leads to
KAt+1) =K,(t)* [1 +54
4.2 Proof of Proposition 2
K,(t +1) = K,(t) + 1(t) = K,(t) + Y(t) + C(t) — D(t)
Substituting in (22) leads to
K,(t+ 1) = K,(t)* [a ++£- |
At SS condition the following condition must be fulfilled:
ack
and 1—KSspss <1
eS
(20)
(21)
(24)
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Table 10: Presence of variables in feedback loops, MMDS6
Variables Loops
1 2° 3 4 5 6 789 10 11 12 13 14
production 111 1 1 1 11
profits 1121212222 141
categorization on the market 1122123122121
profitability al
differentiation 1
frauds 1
importance of volume in the majority business model 112122122212
price of grape 1 1
price of wine 11 11 11
production costs 1
quality 11 a 1 A, +t
territorial rootedness 1 1
The adjacency matrix of the loops of MMDS6 shown in
Table 11 suggests that there are two groups of loops: 1 — 9 and 10 — 14 are tightly interconnected amongst
one another, but with little connection between the groups. However, the distance matrix reveals that the
loops of these two groups are no further than 2 steps apart from one another. Just like in the case of MMDS4,
the second interviewee did recognize only a small minority of the loops inherent in the structure of the
variables and causal links he articulated during the interview.
Table 11: Adjacency and distance matrices for the loops in MMDS
Adjacency matrix of the loops in MMDS 6 Distance matrix of the loops in MMDS 6
Loop 1234567 89 10 11 12 13 14 Loop 1234567 89 10 11 12 13 14
1 TEnwhIYT 1 11 1 PRIS Pista 1 22 2 2
2 | Akbar . 11 2il FIidttidii i 22 2 2
3 11 oa1111 1 11 3 J11 2211111 22 2 2
4 111 111 11 4/111 111211 22 2 2
5 Litd i2 21 11 & jlLl11 Lidd 12:2 2 2
6 111i 1 os. & jTL1I£ 122 Be 2 B
7 LIighigl 4 I 1 BULLI TTL 2 2 2
8 aL 12h @ 1 BLLL2LLL PLkbh bh 2
9 Lit kh Ft LL 2 1 9 JITLITILI 22 2b 2 7
10 11 tadaiit 10 jITUbliiiidi bk b 2
11 111 111 1 6(2221222111 1, 1, 2
12 1111 11 22 (22222221111 Y tt
13; Jl1111111111da1i21 1 13) |(2:22:2222:21 1. 1 1 A,
46$[2i1ili1iiiiiliiil a 14, [2.225222 2511 1 1. 1. 2
4.3 The of not izing dark feedback loops
Each of the executives recognized that the variables belonging to the recognized loops are driven by these
loops, as virtuous cycles or as vicious cycles. Variables not belonging to any of the recognized loops could
then be influenced in a one-off manner. For instance, the first executive could decide to increase
mechanization to increase labor efficiency (this intermediate step is aggregated in the path shown in Figure
2 and Figure 4), thereby reducing the personnel costs to reduce the production costs and diminish costs.
There is a manifest difference between thinking to increase mechanization in order to reduce costs and
increase profitability, like displayed in Figure 4, and keeping in mind that a change to mechanization will
trigger all loops shown in Figure 2 and set off cyclical changes in all variables.
ersonnel costs
»?
) +
mechanization production costs nt production
+
R
costs lity “402
ae wality
price of wine
revenues <---
he
Figure 4: Causal diagram of a plan to increase profitability
Analogous reasoning could be made with costs, energy costs, marketing costs, mechanization, personnel
costs, production costs, sales (MMDS4) and categorization on the market, profitability, differentiation,
frauds, importance of volume in the majority business model, price of grape, price of wine, production
costs, quality, territorial rootedness (MMDS6). Considering that out of the dark loops, 3 and 11
respectively are reinforcing in nature, instability may be caused without the ability to recognized its
endogenous cause. Of course, without quantification and simulation, it is not possible to know how
important the combined effects of these dark loops will be in each case.
This limitation notwithstanding, any change to one of the variables in MMDS4 or MMDS6 will not only
have several side effects, but also come back to the initial variable in several ways. One single decision will
trigger sequences of behavior change, rather than one single event. Taking these variables as possible levers
for management decisions in an input-output way of reasoning will not be able to take this into account.
Mental models are the structure used to reason through different possible decisions (Johnson-Laird 2001),
but if the structure of the mental model is only partially recognized and understood, then many decisions
18
may be derived rather by repeating decisions from past experience than from systematically analyzing the
given possibilities.
Summing up, the interviewees behind MMDS4 and MMDS6 recognized only 20% and 13% of the inherent
loops in their MMDS, respectively. This made 57% and 77% of the variables mistakenly seem to be free
of the influence of feedback loops. The analysis of the two exemplary MMDSs makes a strong case for the
proposition that
Untrained decisi kers and pl need assi to recognize dark loops.
This is not diminished by the observation that the remaining MMDS have less dark loops — even that one
of the MMDS did not have any such loop at all. The fact remains that in almost all of the MMDSs, the
majority of the relevant variables was contained in dark loops.
4.4 Challenges for research
Therefore there is a need for tools helping executives to recognized what their mental models contain. It is
inherently helpful to use an external “boundary object” (Black 2013). The “cognitive mapping” thread has
contributed some tools (Eden 2004), but these are input-output oriented and do not help to recognize
feedback loops. System dynamics is based upon feedback loops (Forrester 1969; J. Sterman 2000), but its
tools are aimed at simulation modelling and demand too much training to be a tool for executives.
Qualitative modeling of feedback-rich situations is prone to misinterpreting behavioral consequences (M.
Schaffernicht 2010); however, not being able to determine plausible behaviors from a qualitative causal
loop diagram is preferable to not even recognizing the loops in the first place. Clearly, a tool able to
automatically detect feedback loops and classify their polarity while a executive or a management team
work through a problem — identifying variables and causal links — would give executives the opportunity
to more thoroughly consider possible strategies, decision policies or plans.
While the main software tools for system dynamics diagramming and modeling include a feature which
detects if a given variable belongs to loos (and which ones), this function has to be invoked by the modeler
each time, it refers only to the selected variable(s) and it is presented as pop-up information which becomes
invisible as soon as the modeler clicks on the diagraming canvas. This is not a trivial user interface problem
to solve because not only are there multiple loops, but on top of it most causal links participate in several
loops at the same time. One way to feed this information graphically back to the user/modeler can be to
define a separate color for each loop and draw each link one per loop, with its respective color. Additionally,
the ID of each loop can be displayed along the causal links. It may even become useful to create a new kind
of diagram, where the loops are represented as nodes in a network (or a directed graph), and arrows showing
the connections between them. Figure 5 shows how this might look in the case of the first 4 loops in MMDS
4, and how interconnected the network of loops of MMDS 4 is.
Carpenter, & Kinzig, 2004) and, hence, scholars usually refer to the research related to resilience
that resilience thinking rather than resilience theory (Walker and Salt, 2006).
Resilience thinking has gained recognition in the context of climate change as a possible
framework to analyse systems vulnerabilities and identify potential policies. Resilience has
become a common objective of climate change adaptation across a whole range of systems and
activities, and it is an overarching concept in many strategies (Heller & Zavaleta 2009; Mawdsley,
O'Malley & Ojima 2009).
In the public policy administration domain the idea of resilience is not new, already in the late
1980s Wildavsky (1988) described resilience as a mean to manage risk in the modern societies.
Nowadays, resiliance is a familiar concept in the crisis management literature (Aldrich, 2012;
Boin, Comfort, & Demchak, 2010). For instance, many scholars in organizational studies aim to
understand resilience and responsiveness of social structures (Crichton et al. 2009; Weick and
Sutcliffe 2011; Donahue and O'Leary 2012; Boin and van Eeten 2013) and colleagues in the
planning domain search for designs that help communities and societies to withstand
disturbances (Paton and Johnston 2006; Goldstein 2012). How to translate resilience concept
into effective policies, however, is still to a considerable extent unexplored in the public
administration domain.
Current research on resilience policymaking is mainly found in the SES domain (Biggs et al.,
2012; Chapin Ill et al., 2009). This literature focuses on the description of those social and natural
properties of the system that are hypothesised to foster resilience, like “redundancy”, “stakeholder
participation” and “understanding of the system”. The justification for these properties is found in
case study research showing how SES theories enhanced the resilience of a particular outcome
of the system to specific disturbances. Downsides in the current literature are: a) lack of
quantification of resilience and the impact of the policies to enhance the system resilience, b)
absence of a structured process to identify what are the properties of the system that need to be
enhanced in each particular case, and c) the political process and power relations embedded in
the development and management of public policies are underestimated.
Bianchi and Rivenbark (2012) describe a dynamic performance management (DPM) approach -
the combination of system dynamics and performance management systems - as an alternative
to output-based performance systems. The DPM approach supports policymaking process by
modelling organizational systems (in system dynamics model) and using simulation techniques to
understand the behaviour of the complex systems public policies deal with. The significant
contribution of DPM is to help policymakers to assess middle and long-term impacts of their
actions in the system outputs by placing the measure of performance in a broader context of the
system (Bianchi, Winch and Tomaselli, 2008). Alternatively to traditional policymaking
approaches, the main focus of DPM is the middle and long term implications of the potential
policies in different parts of the system structure and the responses that the observed system’s
behaviour is likely to give.
If you want a copy of the full paper, please contact the author at:
hugojhdl|@gmail.com or hugo.leon@student.uib.no
2
+ + P.
401 price of wine
404%, Ae)
sales
a) Causal diagram showing loops b) Network diagram of the loops in MMDS 4.
(part of MMDS 4). Dotted arrows Nodes represent loops. Arrows represent
are paths. Color indicates loop ID. connections because of shared variables.
Figure 5: Options for assisting decision makers and modelers
One challenge for the programs running beneath the user interface would be the automatic detection of
loops including the recalculation of the shortest independent loop-set. This may be rendered even more
difficult if the user/modeler wishes to rearrange the loop set because his business logic and his mental model
do not strictly comply to the rules and conditions of a shortest independent loop set.
This is certainly a challenge for software developers, but such a tool would doubtlessly be of substantial
help for planners, decision makers and consultants.
There is also a need for tools supporting researchers investigating the mental models of executives and
other decision makers. The need for taking feedback loops into account has been argued for (S. N. Groesser
and M. F. Schaffernicht 2012) and the so-called ‘distance ratio’ method (Markdczy and Goldberg 1995b)
has been adapted (M. F. Schaffernicht and S. N. Groesser 2011), but the current tools (M. F. Schaffernicht
and S. N. Groesser 2014) only take into account the feedback loops recognized by the interviewees. The
20
“loop distance ratio” (LDR) compares the elements (variables and causal links), the polarity and the delays
of those loops which the interviewees have recognized and the researchers deem to be equivalent. For
instance, neither of the two recognized loops in MMDS4 is equivalent to any of the recognized loops in
MMDS6, and therefore the LDR would be 100% (maximum distance, in other words: completely different
MMDS). However, amongst the unrecognized loops, there are equivalences, like displayed in Table 12:
Table 12: Equivalent loops
MMDS Loop Pol Del Elements
4 402 R 0 price of wine — revenues from wine sales — revenues — profitability >
production +
6 602 R 0 profits — profitability + production >
4 412 B 1 energy costs — production costs — energy efficiency +
6 603 B 0 profits — incentive to decrease costs — production volume — costs
A third challenge refers to MMDS elicitation. As opposed to intervention and consulting, research projects
usually take great care to avoid or minimize the influence of the researcher on the participating individuals.
This has lead to the interview — transcribe — code procedure applied in the current study. It also meant that
no visual feedback was given to the interviewee during the interview. However, this lead to the researcher
making multiple choices regarding causal links and can have some undesired consequences. The
interviewee may not mention a variable or a causal link or even a loop which is completely obvious to him,
leading to the danger that “not mentioned” is mistakenly interpreted as “not recognized”; it is then up to the
researcher to prompt for sufficient elaboration on behalf of the interviewee without priming or directing
him. The fact of constructing and displaying the causal loop diagram (like the ones shown in Figure 2 and
Figure 3) during the interview would allow the interviewee to articulate that which was obvious to him (but
maybe not to the researcher). As far as mental model research is carried out with experienced executives as
participants, the danger that the diagram might influence the interviewee’s mental model is minimal. A
diagramming tool like the one described above would be highly useful to assure that the interviewee
articulates every variable, link and loop he internally recognizes.
5 Conclusions
This paper had the purpose to show that in matters of mental model comparison, there is a significant
difference between those loops which individuals recognize when they talk about the subject and those
loops which are inherent in the structure they articulate but which remain dark. Out of nine executives
interviewed in the study reported here, only three recognized any feedback loops at all: 45 of the 50 loops
have remained dark and unrecognized, implying that the 47 most relevant variables in this set of MMDS
are held to be part of input-output models by the executives, but are really endogenously driven by manifold
feedback loops.
By consequence, an important share of each model’s variables had not been recognized as being under the
influence of loops. It has also been shown that by taking into account only recognized loops, current
methods and tools for mental model comparison may provide biased quantifications of how similar or
distant a pair of mental models is at the level of loops.
The mental model findings support the statement that without an extemal support, the mental models of
executives will be incomplete and the executives’ assessment of possible strategies and policies will not be
based on a thorough analysis of the likely unfolding of their management situations.
21
Based on this, a call is made to develop tools which help decision makers articulate variables and links and
which automatically detect and display loops, so that they be dark loop no longer. Such tools will also be
helpful for mental model researchers. There is also a need to adapt mental model comparison methods and
tools at the level of loops, helping to quantify the impact of the differences between the recognized and the
inherent loops.
Specifically for mental model research, the method and the tools for MMDS analysis and comparison (M.
Schaffernicht and S. Groesser 2014) will be enhanced by incorporating the possibility to detect and utilize
the SILS, make intra-model comparisons based on the different loop set and calculate two sets of ‘loop
distance ratios’ based on the recognized feedback loops and the SILS. This will allow to quantify the
distance between the mental model articulated by the decision maker and the mental model which an analyst
with experience in system dynamics hordes of the decision-makers mental model.
Of course, a study based on as few as nine mental models is limited by the small sample size. This limitation
notwithstanding, under the current conditions the effort to interview, code and analyze is huge and may be
prohibitive for many researchers. Therefore hope is that the availability of the methods and tools called for
would make mental model research less time consuming and more attractive.
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To achieve this, DPM operationalizes the analysis of policies on framework grouping three inter-
connected views of the system performance (Bianchi, 2012)
1. an “objective” view;
2. an “instrumental” view;
3. a “subjective” view.
The “objective” view opens the policy black-box and dissects the policy final outcomes into a
sequence of products or services offered to internal and external clients. This view focuses on the
actual activities and process that public bodies execute to implement the policy.
The “instrumental” view focuses on the dynamic structure and performance drivers producing the
observed end-results. This view supports identification and understanding of a) the end-results, b)
how strategic resources are built and depleted, c) relationships between strategic resources and
performance, and d) the importance of these relationships over time.
Finally, the “subjective” view links the previous two views in the context of the pursued objectives
by aligning actions and processes to strategic resources and drivers. This view comprehends the
targets and explicit ways to measure them.
The combination of these three views supported by simulation techniques represents an ideal
framework to operationalize resilience thinking into policymaking since it moves the discussion to
practical settings. By using DPM as a framework, policymakers are encouraged to a) define
resilience in terms of objective and measurable targets, b) describe the policies with regard to
intermediate products and services related to concrete activities and process and c) analyse the
system in terms of strategic resources and performance drivers.
Since DPM combines performance management framework with system dynamics methodology,
the approach proposed by Herrera & Kopainsky (2015) to conceptualize resilience into SD
models is used to measure and compare the policy results. Even though resilience is commonly
used as a general property of the system, in practice resilience often refers to a particular
outcome of the system that is able to withstand a particular disturbance the system is exposed to
(Barker, Ramirez-Marquez, & Rocco, 2013; Henry & Emmanuel Ramirez-Marquez, 2012). These
outcomes could be food, housing or safety, for example, and can be represented by a
quantifiable and time dependent outcome function F(x) (Barker, Ramirez-Marquez, & Rocco,
2013; Henry & Emmanuel Ramirez-Marquez, 2012). Resilience, then, is measured by the ability
of the system to maintain the normal behaviour of its outcome function, or bounce it back, after
been shocked by a disruptive event. The policy objectives, then, are defined as how to maintain
the normal behaviour of F(x) or, if it deviates from its normal behaviour, how to increase the
system chances to bounce back to it once the disturbance ceases.
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In order to measure resilience through the outcome function F(x), it is necessary to define a
dynamic measure of the disturbance affecting the system. This measure of the disturbance (o)
should account for the magnitude of the disruptive event and for the time the disruptive event
lasts (see Equation 1).
o=5* (tite) (1)
6: magnitude of the disruptive event
ta: time when the disruptive event ceases
te: time when the disruptive event starts
Since resilience is a dynamic and complex concept there is no one single generalized measure
for it but rather a set of measures used to conceptualize different aspects of resilience
(Frankenberger & Nelson, 2013). The five measures proposed by (Herrera & Kopainsky, 2015)
are used in this paper as key indicators for the performance targets. These measures, combine
concepts from engineering and ecological resilience paradigms in a system dynamics context.
Table 1 presents the proposed measures and their mathematical definition.
Table 1: Measures of resilience in system dynamics models
Paradigm Measure Description
The ability of the system to
withstand a disturbance o
without presenting change in the
Hardness om vertantancs of the outa ou = Ou X (ta ~ te) (2)
function F(x)
Average rapidity of the system's
Engineering Recover recover from a disturbance o 3
resilience Rapidity (Attoh-Okine et al. 2009) ta (3)
El]
The ability of the system to
withstand big disturbances o
without significant loss of g—=—~ (4)
performance (Attoh-Okine et al.
2009)
The ability of the system to
withstand a disturbance o
Elasticity 1 without changing to a different a, = 6, X (ta — te) (6)
Ecological steady state
resilience
Robustness
DI
Index of
The probability of keeping the
Resilience P(So Il a) (6)
current steady state or regime.
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The case study analysed in this paper shows how resilience can be operationalized to design and
evaluate climate change adaptation policies in the public sector. The case study shows that by
using DPM, building resilience is not an abstract concept but a well-defined and logical process
that helps policymakers to assess long-term perspective policies by shifting their focus from
outputs to outcomes driven.
Bridging the instrumental analysis with the public administration practices, the case study shows
how DPM can be used to combine the mechanistic approach of resilience thinking with public
sector management practices by connecting the instrumental view with subjective and objective
ones. The Figure 8 shows how DPM approach links the strategic resources and key performance
drivers, through feedback loop mechanisms, with goals, activities, processes and products. The
results of the structure analysis are smoothly moved to a performance control agenda. This
agenda allows policymakers to plan and control the policy implementation and performance.
Furthermore, the case study shows that DPM can help to evaluate and compare the policies
benefits and costs. Translation of the proposed policies into concrete activities and processes,
supported by computer simulations, allows to evaluate policies in terms of their costs and
benefits. The results of the case study show that resilience is not an absolute, but rather a relative
term. Systems can be resilient in different ways and to a different extent. Comparison and
selection of policies then requires clear measures to conceptualize their benefits in terms of
resilience and understanding of how much benefits each policy delivers against the cost of those
benefits. The NPV and value for money analysis are common and necessary in a public
administration that deals with scarce funds and needs to prioritize them wisely. Moreover,
identification and quantification of key drivers and strategic resources also support the
implementation and performance management processes by helping to set targets for
performance and clear deliverables.
The successful experience of applying the proposed framework raised the need for further steps
in the research to complement it and to overcome some of the framework’s current limitations.
First, to supplement the results of this study case, more case study research is needed. Different
contexts and problems should be assessed as well. Second, in order to draw conclusions about
how DPM supports resilience policymaking, it is required to follow up the implementation process
to see the policy results in the real system.
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