Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
A modelling approach for evaluate the pre-industrial natu-
ral carrying capacity of human population in Iceland
Hérdur V. Haraldsson' and Rannveig Olafsdottir 2
‘Chemical Engineering,
Lund Institute of Technology,
Lund University, Box 124 Lund, Sweden
Email: hordur.haraldsson@chemeng.Ith.se
2 Hornafjordur University Centre
University of Iceland
Nyheimar, Litlabru 2, 780 Hofn, Iceland
Email: ranny @hi.is
Abstract
A simple approach was used to evaluate the potential human population that the
pre-industrial Icelandic environment could sustain. A model was constructed that
simulated the population size according to potential biological production available
for livestock. Biological production was determined by the extent of the total poten-
tial vegetation cover based on the Degree-day concept. Fluctuations in the mean an-
nual temperature cause changes in the potential vegetation cover and as a conse-
quence change the biological production sustaining livestock and ultimately human
population. The simulation's results indicate that the potential population that the
environment could sustain during the pre-industrial period fluctuated around 40-80
thousand. The results further indicate that the severe land degradation experienced
after the settlement period had a marginal impact on the population size. The pre-
historical population did however overshoot the natural sustainability on few occa-
sions.
Key words: Systemic, vegetation cover, sustainable population, carrying capacity,
pre-industrial, climate change, Iceland
1 Introduction
To increase our understanding of the factors affecting natural sustainability, understanding the
past is critical. Iceland is currently facing severe land degradation. It is generally believed that
the Icelandic ecosystems have lost half of its vegetation cover and nearly all of its forest cover
since the recorded Viking settlement in AD 874 (Bérarinsson, 1961; Einarsson, 1963; Por-
steinsson, 1972; Bergbdrsson, 1996). Many factors are likely to have contributed to these
changes, such as harsh climate, natural catastrophes, fragile ecosystems and human settle-
ment. Changes in mean temperature are believed to be the largest factor attributed to long
term changes in the vegetation cover (Bergbérsson, 1985; Bergpdrsson et al., 1987; Bergbérs-
son, 1996).
' Corresponding author
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
2 Objectives and aims
This study attempts to assess the carrying capacity (CC) of the Icelandic ecosystem to sustain
a population in a pre-industrial environment (the period before AD 1850) by using simple
approach through a System Dynamic (SD) modelling procedure. The SD modelling procedure
is a top-down analysis where variables are sorted to understanding cause and effect and out-
lined in a Causal Loop Diagram (CLD) (Roberts et al., 1983). By understanding processes on
an aggregated level, it is possible to gain an overview of the basic system properties
(Richardson and Pugh III, 1981; Ford, 1999; Maani and Cavana, 2000).
The Icelandic environment is treated as a single system that exists on multiple hierarchal lev-
els, i.e. the ecosystem productions and the abiotic environmental factors. The observation
takes the ‘eagle’ perspective and focuses on feedbacks that are responsible for sustaining CC.
The main approach is simplicity over details and the purpose is to obtain an approximate
overview. The study aims to:
e To use earlier model effort to develop a new model that includes livestock population,
human population and erosion
e Estimate the potential biological production available for livestock
e Evaluate the potential human population in the pre-industrial Icelandic environments
e Investigate the impact of land degradation on a) the total potential biological produc-
tion, and on b) the potential human population size
The key questions the study seeks to answer are:
e How large pre-industrial population could the Icelandic ecosystem sustain during and
after the settlement period (AD 900)?
e What is the impact of land degradation on maximum sustainable population after the
declination of the forests and vegetation cover?
3 Carrying capacity
The concept of CC, in it most generic form, determines the maximum livestock or wildlife
population that a habitat or ecosystem can support on a sustainable basis (Kessler, 1994).
Kessler (1994) and Monte-Luna et al. (2004) define CC as the maximum population size that
i tained on multiple hierarchal levels of biological integration and environmental proc-
esses on a given area, with finite resources, that is confined both spatially and temporally.
Regarding land-use, the human CC is depended on maximum exploitation of resources in a
given area (spatially and temporally) that are used sustainable and cause no irreversible land
degradation. Monte-Luna et al. (Monte-Luna et al., 2004) points out that the CC is dynamic
and can vary according to the interplay between different biotic and abiotic feedback proc-
esses. In sub-arctic and arctic environments, this interplay is very sensitive toward climatic
fluctuations. Climatic changes may sprout a new development to the ecosystems, in which the
ecosystems have to adapt towards the changes (Woodward, 1987; 1992). However, numerous
definitions on the CC exist and the concept has been largely debated and criticized. Dijkman
(1999) gives a detailed review of the different definitions and discusses if the concept still is a
useful management tool. He concludes the concept to be an important issue in the present
natural resource management. Hence, along with the increasing recognition on sustainable
development, CC may advocate management of land use within sustainable limits.
Haraldsson and Olafsdsottir (2003) generated a model for simulating long term potential
vegetation and forest cover in Iceland during the Holocene. Their model give a rise to exam-
ine the ecosystems CC. Hence, how large human population could the vegetation and forest
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
cover sustain during the pre-industrial period? The pre-industrial period in Iceland is regarded
as the time from the recorded Viking settlement in AD 874 until mid 19" century. Further, is
the human settlement the triggering factor of the ecosystems decline?
4 Theoretical background
4.1 Previous modelling effort
In the Haraldsson and Olafsdéttir (2003) study, a CLD was developed to map out the impor-
tant factors and feedback loops responsible for vegetation development and land degradation
during the Holocene (Fig. 3).
cover cover
™
I
'
|
'
4 Z
a — +N % Wind
/ P Land aa
|
'
'
|
'
'
'
|
degradation
us
X
Frost/thaw
ven nens
| Temperature Sp
u 4
Natural
catastrophes
Precipitation
Fig. 3: A CLD representing an overview of the processes of vegetation and land degradation
in Iceland during Holocene (excluding human interference). The dotted line represents the
first stage (Stage I) of the model (VFC) as published by Haraldsson and Olafsdéttir (2003).
Of influencing variables, temperature drives both of the loops (B1 and R1) and is through
vegetation cover responsible for increased soil formation. Land degradation is influenced by
wind, precipitation and frost/thaw processes. These variables constantly drive land degrada-
tion and the only way to suppress it is through increased vegetation cover that increases the
soil formation (or reclaims the degraded land). In that sense, there exists a tug of war between
the processes that serve to increase the vegetation/forest cover and the degrading forces that
are constantly at work. The first modelling effort (stage I) focussed on developing vegetation
and forest cover model (VFC) dependant on temperature (Fig. 3) (Haraldsson and Olafsdéttir,
2003).
4.2 Present model development
Before the Viking settlement no herbivorous mammals are known to have existed in the Ice-
landic ecosystems. Hence, it has been suggested that the loss of forest cover due to grazing
pressures in combination with a colder climate, resulted in an accelerated land degradation
and consequently lower CC of the environment to sustain its population (Porarinsson, 1961;
Arnalds et al., 1997). If anthropogenic factors are added to the above CLD analysis (Fig. 4), it
is clear that increased population and livestock reduces the forest and vegetation cover and
may result in accelerated land degradation (Loop R1). Still, the climatic fluctuations, through
temperature, either increase the forest and vegetation cover sufficiently to counter the utilisa-
tion of the livestock and population or enhance the destruction of the cover.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
po------- (LP and HP) ,
i Human i
! population
| (*Re areata 1
I + po--------- 4 Ice-CC 1
1 | ERR TET =
| Livestock |
\ population | |
Loar a |
i \+
{ 1 |
1
1 |
wai Ts \ {
+ 1 \ i
Forest Bt! Vegetation | RI i
4 cover cover a (a 4 (WE) 4
= |
/ " Wind |
/ Land Ae
! degradation :
| rn ar —- ee 4
Natural — Frost/thaw
catastrophes oon
| Temperature _7
ce aoe 4
Precipitation
Fig. 4: An overview of the integrated natural and anthropogenic factors influencing potential
biological production in Iceland. The dotted line shows the stage I model simplified with sub-
models; livestock and Population model (LP and HP) and wind erosion model (WE), added in
stage II for building the combined Ice-CC model used for simulating the natural carrying
capacity for human population in Iceland. The shaded links and loops show feedbacks that
are not used in the Ice-CC model setup.
The stage II model development builds upon the VFC modelling effort which has been modi-
fied to simulate vegetation cover (VC) only. As in the VFC model, temperature drives the VC
model. The VC model divides the vegetation cover up to six different modules that represent
vegetation cover at different elevation levels (c.f. Fig, 10). The VC model is used to simulate
biological production (c.f. parameterisation in chapter 6) which sets the limits for the maxi-
mum number of livestock (LP) and the LP in turn sets the limits for maximum human popula-
tion (HP). In the model setup, the LP and the HP model have no feedback to the VC model
(c.f. CLD shaded links in Fig. 4). As a result the VC model simulates biological production as
a natural sustainable production and the LP and HP use that as basis. A wind erosion model
(WE) is attached to the VC model to recreate erosion history. The WE model is independent
from VC model (i.e. there is no feedback, c.f. Fig. 4). The WE model, only intents to recreate
the erosion history and starts right after the settlement. The combination of the VC, WE, LP
and HP make up the Ice-CC model that is used tosimulate the CC for the human population in
Iceland.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
5 The principles of the VC, LP, HP and WE models
5.1 The VC, LP and HP models
The basic approach in the models structure is simplicity. The purpose is to give an overview
of approximate numbers in the simulations and at the same highlighting the assumptions and
the limitations. The basic function in the VC model calculates the area of vegetation as follow
(dA/dt):
Masala) (a)
Where k, is coefficient of growth establishment rate and k, is the coefficient of decay rate, A is
the actual area cover in km? according to the function k, - A and the favorable area A, is de-
pended on the calculated number of Degree-Days (Haraldsson and Olafsdéttir, 2003). The Ap
is the maximum vegetation cover that can be s ined according to the conditions given by
the Degree-Days. The basic principles are shown as a CLD and a System Dynamic Tool Dia-
gram (SDTD), (Fig 5). The basic structure of the VC was used as a template for simulating
the LP and the HP model.
Populatic
a ~ Pkyoun POPUIAHON Pky,
Pkyown R PB PKeecay Population
C REL IR ‘
Pkgrown B PK sccay
P
Acs
LP ratio
7
LKyown Ro LB LKgecay Lavestocs
CR RLS
Uk oth B Usecay
Avs
Abiatio
* Vegetation
al a. Akgoun cover / AKygcay
Kom BAK secay Vegetation
a ae ai Model
Ak grown A Akon c ae,
o
Re DD Q
Fig. 5: The VC, LP and HP models. The CLD was translated into a SDTD which is used for
the numerical simulation. The VC model is arrayed to represent the effect of elevation. The
model is the basis for the LP and the HP model.
The L, and P, variables are limiting factors for the size of LP and HP populations. The mod-
els, VC, LP and HP are combined through ratios that have the dependence functions AL atic
and LPyario. The size of the vegetation cover A is translated, using the ratio AL,«o, into the
potential biological production for sustaining a livestock population. The number of livestock
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
Lis translated, using the LP,ario, into the maximum sustained human population. For the pur-
poses of this paper the variables A,, L, and P, are defined as the carrying capacity for each
module. The L, is the sum of the biological production available for livestock, the P, is the
sum of livestock available for human population. The simulated sustainable population is ul-
timately dependent on the variable A, and the temperature fluctuations.
5.2 The WE model
Wind erosion is considered to be the largest erosion mechanism in the Icelandic environments
(e.g. Arnalds et al. (1997)). The effect of wind erosion on vegetation cover in Iceland has
been categorised into six stages (Aradéttir et al., 1992). The first stage represents fully vege-
tated area and the sixth stage represents total lack of vegetation (Fig. 6). The third and fourth
stages show the critical thresholds triggering changes in stable stages. The loss of vegetation
over time is conceptually perceived through non-linear behaviour.
Vegetation cover
0%
>
Time
Fig 6: A conceptual model of the effect of erosion on vegetation cover (Aradottir et al., 1992).
A CLD describing the principles of erosion is presented in Fig. 7. Vegetated area (highland
and lowland) is reduced by erosion, which in turn is determined by the erosion rate. The CLD
for the erosion is translated into a SDTD for running numerical simulation of WE model
forvegetation cover. The WE model was divided into five sections according to the five given
erosion grades, and attached to each elevation interval (Fig. 7).
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
f° S Higland Erosion
fe area km? highland
Highland B Erosion
area km? highland
B
ee:
R R
Erosion EiGéIon
rate, rate 4,
+ Midland Erosion
Midland Erosion area km? midland
+
KO area km? midland
q
- Total area
Total area R NY H+M km2
H+M km?
Sees Erosion Erosion
rate, rate yy
sO Lowland Erosion
Lowland Erosion area km? lowland
+
area km? lowland
KO .
Total area R NY
2
Heel kny Total area
. H#M#L km?
-, Erosion i
Erosion
rate, rate L
Fig. 7: Basic layout of erosion setup used in the erosion model (WE), represented in CLD and
SDTD.
Erosion rate for each interval is given the start value (c.f Fig. 10), where grade one is given to
the lowest elevation interval (0-100m) and the grade five is given to the highest elevation in-
terval (400-600m). The erosion rate of the lower elevations is affected twofold, by the area
km? under its elevation interval and the sum of area of the vegetation cover above its interval
range, i.e. sum area between 200-300m plus the sum of all area above 300m. The assumption
is made that erosion on lower elevations is affected by the erosion on higher grounds through
wind borne materials that is transported to onto the lowlands. At higher elevation larger ero-
sion rate is assumed since the vegetation cover is more vulnerable towards the climatic
changes than the vegetation cover in lowlands.
5.3 The Ice-CC model
The Ice-CC model is an integration of the VC, WE, LP and HP models. Ice-CC evaluates the
CC. Figure 8 illustrates the simplified CLD and how it is translated into a SDTD.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
Livestock and
DD st Livestock and population
population
Np
i ae
Erosion B 3 “
rate op Erosion J) Erosion
rate
ey Erosion
Fig. 8: The Ice-CC is an integrated model from the VC, LP, HP and the erosion model (WE).
6 Model parameterisation
6.1 Parameterisation for human population and livestock population
Historical records are used to estimate the human population size in the early settlement pe-
riod and to create the ratio of livestock per person and furthermore the potential biological
production per hectare land. The beginning of the human settlement in Iceland is set to AD
874 and the following 100 years are assumed to be the settlement period. According to his-
torical records (Julfusson, 1990) the human population size is believed to have fluctuated
around 50,000 inhabitants until the 18" century where it progressively increased to the present
level of 290,000 (Statistic Iceland 2004). The following assumption and limitation strategy is
used in the Ice-CC model:
e The forest cover is assumed to be part of the vegetation cover. The model, therefore,
only simulates vegetation cover.
Only livestock is affected by vegetation cover and not vice versa
Erosion only recreates historical behaviour and is not affected by vegetation cover.
The model uses livestock (sheep, cattle and horses) to influence human population.
The human population renewal and decline is an arbitrary number of 2%.
Studies have shown that biomass availability for livestock in moderate grazing condi-
tions range between 35-45% (Holechek et al., 1999). This study uses 35%.
e Lowland is considered all the area below 300 meters a.s.l., and highland all the area
above 300 meters a.s.1.
e Biological production from lowlands and highlands is converted into ‘winter feed’
units for livestock.
e Estimates of farmable land area in Iceland range between 10-15,000 km?
(Johannesson, 1960). Currently the land utilised for farming is c.a. 1,200 km?. Before
AD 1900 the farming land was approximate 170 km? (Porsteinsson, 1972). Kristinsson
(1998) uses 6,000 km? as easily farmable area after subtracting wetlands areas, that
number is used in this simulation.
e The biological production in lowlands is a triangular function. The highest productions
are at sea level and close to zero at the transitional zone at the upper limits of the vege-
tation cover. The biological production is a function of annual temperature (9.5x10° *
(Degree Days)-2.04) which is derived and modified from Porsteinsson (1972).
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
e Individual minimum requirements of livestock (LPyatio) for human population was es-
timated from Julfusson (1998) and (Olafsdottir and Juilfusson, 2000) as: 1 cow, 5.5
sheep, 0.5 per individual for horses.
e = The annual renewal of livestock (Lk) in favourable conditions is based on individuals
requirements for livestock (i.e. | cow/person, 0.5 horse/person and 5.5 sheep/person).
The decline is a function of biological production availability per livestock. Ten per-
cent of the livestock is removed if requirements are not met.
e Annual produced biomass per hectare is converted into units for winter feed (ALyatio).
Biomass requirements per animal are based on daily dry matter intake (DMI) of their
live weight (LW). Table 1 shows required winter feed per livestock according to LW.
Table 1. Annual winter feed requirements for livestock.
Daily requirement | Annual winter feed
Livestock} LW kg |_% DMI of LW DMI in Tonnes
Horse | 350 gt 1.5
Cattle | 400 3° 4.02
Sheep | 70 2.5° 0.37
‘Planck, 2001), “OMAF, 2004), “(NRS, 1985)
¢ 20% is subtracted from the total biological production due to loss of nutrition in the
storing process of the winter feed.
e Fishery activities are excluded as a part of diet for the population
¢ Catastrophic events (such as volcanic activity) and plagues are excluded from the
model
6.2 Erosion model parameterisation
To model an annual loss of vegetation cover in Icelandic ecosystems this study uses the ero-
sion calculations by (Arnalds er al., 1997). They use five erosion grades to describe the condi-
tion of the vegetation cover from fully vegetated to barren landscape, where the most de-
graded land is graded 5. This information is used to plot the rate of erosion according to pro-
portion of vegetation cover in all the erosion grades (Fig 9). The different erosion grades used
by Arnalds et al. (1997) are consistent with the conceptual diagram developed by Aradottir et
al. (1992). Hence, it is assumed that the rate of erosion for each grade in Fig. 9 could be com-
bined with the different stages in Fig. 6. This information is used for calculating the erosion
rate in the WE.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
25 T T T T
Grade 5
ae ° 4
<
ao)
7
2 15} 4
oO
c=
8 Grade 4
a L 4
o 1 °
05 + 4
Grade 3
. Grade2 Grade 1
°
0 L L L L ¢
0 20 40 60 80 100
Percent vegetation cover
Fig. 9: The rate of erosion in relation to proportion of vegetation cover (modified from
(Arnalds et al., 1997).
7 Integrated model utilisation
The input parameters for the Ice-CC model are the same as for the stage J VFC model with
additional coefficients for the human and the livestock population as well as coefficients for
erosion. The whole model utilisation process for the modelling procedure is shown in Fig. 10.
I The Model Utilisation -------------------------+
Limitation Purpose
| Theoretical model
Ice-CC
GRIP raw
DEM
data ve >| LM & POP
Parameterisation
| Coefficients
Temperature
calibration pi : i
model Elevation 3-400 m | we
Elevation 2-300 mj} Ls: oamsut
.. Input data preparation ----!
Interpretation <—
LL, Results
A Model Utilisation chart of the Ice-CC model and sub-models as well as its support-
ing modules for producing simulated outputs.
The Model Utilisation includes the complete process form developing the core principles for
the model theory to using different tools for input data preparation and parameterisation of the
coefficient for the numerical model.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
8 Results
8.1 Simulated Carrying Capacity
The simulated results are based on 30 year running mean with standard deviation (shaded area
when shown) from 100 Montecarlo runs. Sensitivity was ssed by varying the input pa-
rameters by 10%. This was done for vegetation cover as well as for erosion. Simulated poten-
tial biological production for both lowlands and highlands is shown in Fig. 11. The simulation
present sustainable production, i.e. the amount of biomass removed that does not affect the
natural development of vegetation cover. Fluctuated trend in biomass over the whole period is
observed, with apparent higher impacts for the vegetation in the highlands.
210°
1,5 10° | 4
Lowland
Production Tonnes
S
——
weer ~
cae
nl
—_
nas
' | i}
510° } A \
Af
i
|
2000
Year AD
Fig. 11: Simulated potential biological production in lowlands (<300m) and highlands
(>300m) respectively.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
8.2 Pre-industrial
1 carrying capacity
The simulations suggest that if all cultivatable land area is used sustainable as well as
yieldable biological productions from the highlands, then the environment could support a
human population between 40-80,000 during the pre-industrial period in Iceland (Fig. 12).
The pre-industrial population in Iceland fluctuated from 50,000 to 60,000, which is within the
simulated result of sustainable human population from the Ice-CC, assuming no erosion ef-
fects (Fig. 13).
210° 310°
Yields
\ \ | 2,5 10°
|
15 10° i \ | |
i \ A
ij N\ MH at08
e (Swi AA
= | al | \ | i\ x
E \f\ | LE AP Yd ae 8
B 110° + V vay I | | 1510° &
2 i Vo | &
= ‘ 4 3
S \
2 y
110°
510° +
4 510°
| Population
0 L a L 0
0 500 1000 1500 2000
Year AD
Fig 12: The Ice-CC results on pre-industrial carrying capacity. (shaded area is
viation).
1,210°
110°
810°
6 10*
Population
410*
210°
T T T
Measured population —»
Pre-industrial popt
fluctuation
| Sustainable population
7
'
'
ulation
Industrialisation
_
1000 1200 1400
Year AD
1600 1800 2000
Fig. 13: The simulated pre-industrial human population in Iceland.
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standard de-
Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
8.3 The relationship between land degradation and carrying capacity
The WE model attempts to recreate historical erosion behaviour. The impact of erosion on
biological production is shown in Fig, 14. The impact of erosion on the human population
carrying capacity is shown in Fig, 15.
210° -
1,510° + 4
A fi \ Lowland
110° \
Production Tonnes
510° H\ | \ Highland +
0 500 1000 1500 2000
Year AD
Fig. 14: Biological production from cultivatable area from lowlands and usable area in the
highlands with the impact of erosion.
710° + 310°
= Vegetation cover
‘ erosion
S10 2,5 10°
510°
Se 210°
2
oy a
$40 gs
2 se
© 1510) &
S . , 2
3S 310° L Population no-erosion g
©
Po po Population erosion
> + 110°
210° F
riot lL 5 10°
0 1 L L 0
400 800 1200 1600 2000
Year AD
Fig. 15: The impact of simulated erosion on sustainable human population is small compared
to the declined vegetation cover. Human population in erosion scenario is imposed on popu-
lation simulated with no erosion.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
9 Discussions and conclusions
9.1 Historical implications
The simulated biological production from cultivatable lands fluctuated considerably during
the last 1000 years. The biological production from lowlands, obtained from the maximum
possible land area suitable for winter feed, is 600,000 hectares, is probably not an underesti-
mate since the area used today for winter feed production is 150,000 hectares. This suggests
that the human population in the pre-industrial era maximised the total potential area for pro-
duction. All winter feed needed during wintertime for livestock could only come from these
sources unless winter grazing was practiced. This implies the sustainable threshold, i.e. the
amount available for grazing without hampering vegetation development and triggering even-
tual degradation. The simulated results further suggest that the long-term effects of tempera-
ture fluctuations may have reduced the biological production up to 40% during the coldest
periods of the LIA. This is somewhat more than estimated by Dyrmundsson and Jonmundsson
(1987) which showed that fluctuations in the annual mean temperature could result in a 10-
20% decrease in the biological production from the rangelands.
If the assumption is given that all of the easily accessible land (600,000 hectares) for biologi-
cal production is utilized and the highlands are used for sustainable grazing, the maximum
sustainable human population ranges between 40,000 and 80,000 according to the assump-
tions in section 6.1 (c.f. Fig. 12). This coincides with Jiliusson (1990) revealing the human
population to fluctuate between 50,000 to 60,000 inhabitants in the pre-industrial era. That
amount would have resulted in an occasional overstepping the natural carrying capacity. Sub-
arctic environments are fragile and possibly less resilient toward grazing pressure than many
other environments. In colder periods the vegetation cover is likely to have been under much
stress, especially when livestock was winter grazed. The simulated sustainable population is
frequently above the actual pre-industrial population (c.f. Fig. 13). Only in a few periods, the
simulated sustainable population matched the actual population. Around AD 1400 there is a
sharp decrease in the annual mean temperature which lasted few decades . It reflects a steep
decline in the simulated population. Such a scenario would probably be devastating to the
potential vegetation cover and perhaps be a trigger for the land degradation processes that
characterised the LIA.
Land degradation shows a reduction in the total biological production (c.f. Fig, 14), resulting
in reduced carrying capacity for the human population (c.f. Fig. 15). Livestock is dependant
on the winter feed from the lowlands and since the most reduction in the vegetation cover
takes place in the marginal areas in the highlands, there is not much reduction in the long-term
CC of the human population. Thus, the potential vegetation cover may reduce in the highland
and still show no significant changes on biological production from the lowlands and subse-
quently the CC of the human population (c.f. Fig. 15). That may explain why the land degra-
dation continued without severe consequence for the population throughout the centuries into
the mid 19" century. The general notion (Hallsd6ttir, 1987; 1995) is that loss of habitat for
grazers kept the human population around the 50,000-60,000 limits . The simulated results in
this study show much wider fluctuations and furthermore that loss of habitat was not the limit-
ing factor but the biological production from the cultivatable areas in the lowlands.
Addressing the question initially stated in the paper, the following can be said; 1) The simu-
lated human population (in the pre-industrial era) in Iceland fluctuated considerately the last
1100 years and thus the population CC was dynamic ranging between 40-80 thousands during
the period. 2) The impact of land degradation on the population CC is marginal given the as-
sumptions used in the model.
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Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
9.2 Model limitations and sensitivity
The limitation of the model is twofold; 1) the omission of feedback from livestock population
to vegetation cover, and 2) the feedback from vegetation cover to erosion being omitted (see,
CLD in Fig. 4). This is purposely done, since the model can actually answer the basic ques-
tions stated in the beginning without including these mechanisms. Therefore the performance
of the model rests on the questions the model is designed around. If more detailed questions
are required, e.g. how does livestock contribute to reduction of vegetation cover? Or how is
the interplay between vegetation and land degradation?, the model will not be sufficient to
answer that. A modification or a complete new model is required that is designed for address-
ing questions on these levels of details. For answering the basic questions in this study, the
Ice-CC model performance ands its accuracy was adequate.
In order to address the initial question on land degradation with the sufficient performance, it
was required to divide the vegetation cover into 6 segments. This was done in order to recre-
ate the scenario as given by Aradéttir, et al. (1992) in Fig. 6.
The sensitivity setup in the model was identical to the one used in the Haraldsson and
Olafsdéttir (2003) study, ie. 10% variation of the variables. Sensitivity analysis on erosion
the rate, at the different erosion cla: showed not significant variation in loss of vegetation
cover. Sensitivity on the biological production and livestock parameters were not performed
but observed during the model construction. From these observation the Porsteinsson (1972)
function on biological production was a key sensitivity variable. It is a linear function for bio-
logical production and since that is such a key variable for the model, exchanging that one for,
e.g. a non-linear one will produce different results.
Although the results are estimates with some complex assumptions, there are obvious advan-
tages of using this simplistic approach. It serves to test initial ideas and give approximation on
the historical population fluctuation after the colonisation period in Iceland.
Refernces
Aradéttir AL, Arnalds O and Archer S. 1992. Hnignun grddurs og jardvegs. In Arnalds A.
Gredum IslandReykjavik. V: 73-82.
Arnalds O, borarinsdéttir EF, Mettisalemsson S, Jénsson A, Grétarsson E and Arnason A.
1997. Jardvegsrof 4 Islandi [Soil Erosion in Iceland]. Jn. The Icelandic State Soil Conserva-
tion Service & Icelandic Agricultural Recearch Institute: Reykjavik: 157.
Bergpérsson P. 1985. Sensitivity of Icelandic Agriculture to Climatic Variations. Climatic
Change 7(1): 111-127.
Bergpérsson P. 1996. Hitafar og grédur [Temperature and vegetation]. Bivisindi [Icelandic
Agricultural Sciences] 10: 141-164.
Bergporsson P, Bjérnsson H, Dyrmundsson O, Gudmundsson B, Helgadéttir A and Jén-
mundsson JB. 1987. The effects on Climatic Variations on Agriculture in Iceland. In Parry M,
Carter TR and Konijn NT. The Impact of Climatic Variation on Agriculture, assessment in
Cool Temperate And Cool Regions. TASA and UNEP: Dordrecht. I: 387-444.
The 2005 International Conference of the System Dynamics Society, July 17-21 Boston
15
Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
Dijkman J. 1999. Carrying capacity: oudated concept or useful livestock management tool?
Grassland Group of the Crop and Grassland Service
(AGPC) of FAO for the FAO/AGAP electronic conference on “Livestock - Coping with
Drought”, http://www.odi.org.uk/pdn/drought/index.html, FAO.
Dyrmundsson © and Jénmundsson J. 1987. The effect of climatic variations on the carrying
capacity of rangeland pastures. In Parry M, Carter TR and Konijn NT. The impact of Climatic
Variation on Agriculture. IASA and UNEP: Dordrecht. I: Assessment in Cool Temperate
and Cool Regions: 384-444.
Einarsson. 1963. Pollen-analytical studies on the vegetation and climate history in Late Post-
glacial time. In Love A and Léve D. North Atlantic Biota and their History. Pergamon Press:
Oxford: 355-365.
Ford DN. 1999. A behavioral approach to feedback loop dominance analysis. System Dynam-
ics Review 15(1): 3-36.
Hallsd6ttir M 1987. Pollen analytical studies of human influence on vegetation in relation to
the landnam tephra layer in Southwest Iceland. Department of Quaternary Geology. Lund,
Lund University: 45.
Hallsdéttir M. 1995. On the pre-settlement history of Icelandic vegetation. Agricultural Sci-
ence 9: 17-29.
Haraldsson HV and Olafsdéttir R. 2003. Simulating the dynamics in vegetation cover with
regards to long-term climatic variations in sub-arctic landscapes. Global and Planetary
Change 38: 313-325.
Holechek JL, Gomez H, Francisco M and Galt D. 1999. Grazing Studies: What we have
learned. Rangelands 21(2): 12-16.
Johannesson B. 1960. fslenskur Jardvegur [Icelandic Soils]. Békarétgéfa Meningarsj6ds:
Reykjavik
Jtiliusson AD. 1990. Ahrif folksfjéldaprounar 4 atvinnuhetti gamla samfélagsins [ in Ice-
landic]. Saga 18: 149-156.
Juliusson AD. 1998. Valkostir sé6gunnar- Um landbiinad fyrir 1700 og pjddfélagsproun 4 14.-
16. dld [in Icelandic]. Saga 36: 77-111.
Kessler JJ. 1994. Usefulness of the human carrying capacitynext term concept in assessing
ecological sustainability of land-use in semi-arid regions. Agriculture, Ecosystems & Envi-
ronment 48(3): 273-284.
Kristinsson A. 1998. Productivity and population in pre-industrial Iceland. International
Congress on the History of the Arctic and Sub-arctic Region 18-21 June, 1998, Reykjavik
Iceland.
Maani KE and Cavana RY. 2000. System Thinking and Modelling, Understanding Change
and Complexity. Prentice Hall: Auckland
The 2005 International Conference of the System Dynamics Society, July 17-21 Boston
16
Haraldsson and Olafsdéttir- A modelling approach for evaluating the pre-industrial natural carrying capacity...
Monte-Luna P, Brook BW, Zetina-Rején MJ and Cruz-Escalona VH. 2004. The carrying ca-
pacity of ecosystems. Global Ecology and Biogeography 13: 485-495.
NRS. 1985. Nutrient Requirements of Sheep, Sixth Revised Edition. National Academy of
Sciences:
Olafsdéttir R and Juiliusson AD. 2000. Farmers perception of Land-cover changes in NE Ice-
land. Land Degradation and Development 11: 439-458.
OMAF 2004. Pasture Production. Publication 19. Guelph, Ministry of Acgriculture and Food,
Government of Ontario, Canada.
http://www.gov.on.ca/OMAFRA/english/crops/pub19/pub19toc.htm.
Planck C. 2001. Hiisten : niringsbehov och fodermedel. In. Rapport/Sveriges
lantbruksuniversitet - SLU. Swedish University of Agricultural Sciences, Department of
Equine Studies: Uppsala: 36.
Richardson PG and Pugh III A. 1981. Introduction to system dynamics modeling. Productivity
Press: Portland
Roberts N, Anderssen DF, Deal RM, Garet MS and Shaffer WA. 1983. Introduction to Com-
puter Simulation. Productivity Press: Portland
Porarinsson S. 1961. Uppblastur 4 fslandi ( lj6si Oskulagarannsokna [Soil erosion in Iceland,
a tephrocronological study]. Skégrektarfélags Islands: Reykjavik
Porsteinsson I. 1972. Grédurvernd: byggd 4 héflegri nytingu og rektun lands [Carrying ca-
pacity of Icelandic rangelands]. Rit Landverndar 2: 128.
Woodward FI. 1987. Climate and plant distribution. Cambridge University Press: Cambridge
Woodward FI. 1992. A review of the effects of climate on vegetation: ranges, competition and
composition. In Robert L, Lovejoy P and Lovejoy TE. Global warming and biological diver-
sity. Yale University Press: New Have: 105-123.
The 2005 International Conference of the System Dynamics Society, July 17-21 Boston
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