UVA
Páramo connectivity determined by the
change in temperature at the northern Andes
páramo ecosystems since the LGM
Bachelor Project Earth Science
Jan Timmerman
6/30/2014
Content
Abstract ................................................................................................................................................... 2
1. Introduction ......................................................................................................................................... 3
2. Methods .............................................................................................................................................. 4
2.1 Temperature change ................................................................................................................. 4
2.2 páramo area .............................................................................................................................. 5
2.3 páramo connectivity .................................................................................................................. 5
3. Results ................................................................................................................................................. 7
3.1Area ............................................................................................................................................ 7
3.2 Connectivity ............................................................................................................................. 10
4. Discussion .......................................................................................................................................... 13
5. Conclusion ......................................................................................................................................... 15
6. Acknowledgements ........................................................................................................................... 16
7. Literature ........................................................................................................................................... 16
Abstract
The past change in ecosystem connectivity is a key tool to explain differences in gene pools, wildlife
populations and the dispersal of species between comparable ecosystems. The objective of this
research is to model the distribution of the páramo ecosystem in the northern Andes since the Last
Glacial Maximum (LGM) and determine the change of the connectivity of the northern Andes páramo
ecosystem. This change is driven by variations in size of ecosystems and distances between
ecosystem patches. In the case of the páramo ecosystem in the Northern Andes both variations are
influenced by changes in temperature. The change in the distribution of the páramo ecosystem is
calculated by a model in open-source software R. The detailed change in size and connectivity of the
páramo ecosystem are derived by interpolation from the model results. In total the páramo area has
decreased from 100% at the LGM to just 22% in the current situation. This strong decrease in area
causes a great loss in connectivity. Less than 3% of the LGM páramo connectivity is left, even when a
very high dispersal distance is used. Differences in páramo connectivity between different dispersal
distances appeared to be minimal and are almost completely lost in the 24000 timespan of this
research.
2
1. Introduction
The páramo ecosystem is a unique ecosystem with a broad scale of ecosystem services. It is a rare
ecosystem as it can only occur in high mountain ranges (Anderson et al., 2011). To maintain this
system it is important to expand the available knowledge about ecosystem connectivity. A loss of
connectivity is a serious threat to the conservation of wildlife and biodiversity and it severely
decreases the ecological function of the páramo landscape (Pascual-Hortal and Saura, 2006).
The past change in ecosystem connectivity is a key tool to explain differences in gene pools, wildlife
populations and the dispersal of species between comparable ecosystems (Saura et al., 2011). In the
case of the páramo ecosystems in the Andes a lot of research has been done to quantify this
connectivity with different indices to aid landscape conservation planners (Pascual-Hortal and Saura,
2006). Some small páramo ecosystem patches may seem unimportant, but can have a large role in
connecting larger páramo patches. There are a lot of different studies available about quantifying
ecosystem connectivity (e.g. Tovar et al., 2012; Saura et al., 2011). Three corresponding points are
found in most of those studies (Saura and Rubio, 2010; Saura and Thorné, 2009). Firstly the distance
between ecosystem patches determines if a species is able to cross a barrier or not. In general a
larger distance reduces the chance species can hop on to another patch. Secondly the kind of barrier
between the patches, determines whether a species can cross it or not. Land animals can’t cross a
sea, most birds can’t cross a high mountain range. Thirdly, the size of the ecosystem patches is an
important factor in determining connectivity as some species can only occur in patches of a certain
size.
With these three criteria, although used in different ways, the current páramo connectivity can be
determined. However, the development of páramo patches, and therefore there current state, is
influenced by the past connectivity. Current gene pools and population numbers are the result of the
state of connectivity in the past. This information about past páramo connectivity is missing, and
needs to be researched.
Climate change, and in particular temperature change, has a great influence on the tree line, and
thereby the borderline from which the páramo ecosystem can start to develop. The border between
the páramo ecosystem and forested areas lies around 9.5 °C (Gonzalez et al., 2012). The way in which
the páramo ecosystem was distributed during temperature changes in the past is not clear. Changes
of connectivity in the past can explain a lot about the current situation and possible trends can be
exposed. Therefore it is highly relevant to fill up this knowledge gap and research the behaviour of
the páramo ecosystem since the LGM to contribute research about its current state.
The objective in this research is modelling the distribution of the páramo ecosystem in the northern
Andes since the Last Glacial Maximum (LGM) and determine the change of the connectivity of the
northern Andes páramo ecosystem. This is done by applying a model developed for calculating the
size of islands with a fluctuating sea-level on the páramo patches. To approach the páramo patches
as they are islands surrounded by a sea of trees, growing and declining in size as the treeline moves
makes this research innovative and original.
3
2. Methods
In order to model the past páramo connectivity, three processes needs to be researched. The
average temperature anomaly in the Colombian Andes for the last 24000 years. The decrease or
increase of the area covered with the páramo ecosystem in the research area. Finally it is essential to
quantity the way in which the connectivity between páramo patches reacts on a change in the size of
the patches. These three processes are described in this chapter.
The methodology of this research is based on different calculations in the research area. The
research area is shown in figure 1. The exact location of the area is: 0° till 2°N. and 77° till 79° W
(figure 1).
Figure 1. Research area: 0° - 2°N; 77° - 79° W.
2.1 Temperature change
The temperature change in the Colombian Andes has not been directly researched by a climate proxy
in the research area, so it has to be derived from proxies in other areas. For the calculations in this
research, the temperature change is assumed to be the same for the whole research area. This
means very specific temperature values are not realistic because the area consist of almost 50.000
km2 with a lot of variety in temperature. For the modelling in this research therefore a global
temperature anomaly is used based on the Vostok ice core (Shakun et al, 2012; Petit et al., 1999).
The Antarctic temperature change was about plus eight degrees Celsius for the last 24.000 years and
the temperature records inside this ice core contains very good quantitative data (figure 2).
Figure 2. Temperature data of the Vostok ice core (Shakun et al., 2012).
4
This detailed temperature change is compared with temperature information from pollen proxies in
the Southern Andes done by González-Carranza. It appeared the pollen proxy temperature range was
about four degrees Celsius. Even though their temperature research only dates back for 14.000 it
seems to confirm the theory that the tropical temperature change was half of the Antarctic
(González-Carranza et al., 2012).
Another climate proxy for the Andes near the research area is a combination of three glacial ice cores
dating 25.000 years BP. This data is not as clear as the Vostok ice core, but concerns tropical glaciers
and give therefore more information about the climatic conditions around the equator. The
conclusion drawn from the amount of δ 18O, pollen and dust in the three ice cores are not very
specific. They vary from a change in temperature of -2 till -8 degrees (Thompson et al., 2000).
Nevertheless the assumption made in this research from a total temperature change of about -4
degrees Celsius is enforced by these tropical ice cores.
2.2 páramo area
The change in total páramo covered surface in the research area is essential for calculating the
change in connectivity. Therefore the surface of each páramo patch in the research area must be
calculated. To be able to do this, a new program is developed by Sietze Norder. The pSIG (paleo Sky
Islands GIS) model can calculate the locations and sizes of páramo patches based on a current
worldwide 1 km2 temperature map (Worldgrids, 2014) and a table with the temperature change for
the research area. In the model the páramo is assigned to a grid cell when the temperature is below
9.5 degrees Celsius. For this research the model has calculated the páramo patches from 24.000
years ago until the present, so the effects of the increasing temperature since the last glacial
maximum on the páramo connectivity are seen in the outcomes.
The pSIG model created by Sietze Norder calculates the páramo polygons for five situations: dT = 0, 1, -2, -3 and -4. The different páramo states are then linked to the temperature so an interpolation
formula can be made. The páramo area since the LGM is then calculated by this formula. The area is
also calculated per polygon for each temperature situation. In the Results chapter only the total
páramo area per time step is shown. The individual area per patch can be found in the
supplementary information.
2.3 páramo connectivity
Calculations
The connectivity between páramo ecosystems depends on a lot different factors. For this research
the connectivity calculations are based on three characteristics. The size of a patch, the distance
between patches and the different dispersal distances of different species. To quantify the
connectivity, we will apply a formula published by Saura et al. (2011) (1).
𝑛
𝑛
1
𝑃𝐶 = 2 ∑ ∑ 𝑎𝑖 𝑎𝑗 𝑃𝑖𝑗∗
𝐴𝐿
[%] (1)
𝑖=1 𝑗=1
5
This formula gives the relative connectivity between all patches and is very useful for this research
(Saura et al., 2011). The area (ai and aj) for each of the páramo patches since 24.000 years BP have
already been calculated by pSIG. According to the formula two large páramo patches have more
chance to be connected than two small patches. The Pij value is the probability two patches are
connected, calculates as a function of the distance between these patches. It is a value between 1
and zero and lowers the connectivity if there is large distance between two patches. Pij Is calculated
from:
𝑃𝑖𝑗 = 1 ⁄ {1 + 𝑒𝑥𝑝((𝑑 − 𝐵)/𝜏})
[-] (2)
Where d is the distance between the patches, B is the dispersal distance, i.e. the distance at which
the probability is 0.5 and τ is a parameter that describes how fast the probability changes around the
dispersal distance.
Figure 3. The relation of Pij and the distance between two páramo patches when the dispersal
distance B = 6000 m and τ is 1000 m.
Pij requires the distances (d) between each patch and a 0.5 dispersal distance (B). To acquire the
distances a Matlab module is written to calculate the distance between each of the páramo polygons
provided by the pSIG model. This script calculated the distance between each point on the polygon
describing one patch to each of the points on the polygon of the other patch. The smallest distance
between two points on different polygons is the distance between the two patches.
The 0.5 dispersal distance value is an important parameter as it defines the distance where the
chance of connectivity is 50%. In figure 3 this B value is set at 6000 meters. This parameter for
calculating connectivity is different for each kind of species in the páramo ecosystem, some species
like birds may have a very large 0.5 dispersal distance, but a small flower can have a very small one.
For this research different B values have been used to determine the influence of a different
dispersal distance visible. The tau (𝜏) is always chosen to be half of B (table 1).
6
B (meters)
tau
2000
1000
5000
2500
10000
5000
20000
10000
50000
25000
Table 1. Used input for the Pij formula
In this study the A L2 is defined as the total result of ai*aj*Pij for all patches in the dT = -4 situation.
This creates PC values between 0 and 1 and implies the 24000 years BP situation as the time when
the total páramo connectivity was at its peak. The PC value is now calculated for each 0.5 dispersal
distance value for all five temperature situations.
Interpolations
The pSIG models the size and location of the páramo polygons for integer values of temperature
change. In our case this means calculations are made for 0, 1, 2, 3 and 4 degrees of temperature
change. Interpolations are made for both the páramo area and the páramo connectivity. A third
grade polynomial relationship for the five different páramo states is created and applied on the
original temperature input based on the Vostok ice core data. This interpolation method gives the
change in páramo area and connectivity determined by the temperature in our research area.
3. Results
This chapter describes the results of the calculations on the temperature driven dynamics of the
páramo ecosystem by graphs. First the original results are described followed by the interpolated
results. All tables, worksheets, Matlab scripts and interpolations results can be found in the
supplementary information.
3.1Area
3.1.1 Polygons
In figure 5 the five different stages of the páramo ecosystem in the research area are shown. The
páramo polygons were very abundant during the LGM 24000 BP. However, when the temperature
increases the páramo ecosystem is disappearing at most places. A lot of former páramo areas on the
mountain slopes now gets temperatures above the 9.5 degrees Celsius and are thereby favouring a
forest ecosystem. This can be seen in figure 5 as the polygons get smaller with every next stage.
Figure 5.f shows the difference between the 24000 BP situation and the current situation. A strong
decrease in páramo area can be seen, as well as a fragmentation initially large páramo patches. It
7
appears all of the current páramo was once part of one of the once large patches. None of the
current páramo lies outside of the 24000 BP páramo borders.
8
Figure 5 a-f (from top-left to bottom-right). All páramo polygons for the five different temperature
stages displayed in ArcGis. 5f is a combination of 5a and 5e.
3.1.2 Original data
The change in the area covered with the páramo ecosystem is visible in table below.
Temperature anomaly [°C]
Páramo surface [km2]
-4
8875
-3
6789
-2
4966
-1
3369
0
1950
Table 2. A decreasing páramo area with increasing temperatures
The change in páramo area in table 1 is shown km2. These numbers are the sum of the areas of all
polygons of each time step. The páramo area changes from 8875 km2 during the LGM, to 1950 km2 in
1950. This is a strong decrease, currently only 22% of the LGM páramo is left. The data shows very
clearly that temperature and the páramo area are negatively correlated for the last 24.000 years.
3.1.3 Interpolated data
The original data about change in páramo area gives limited information because only five stages are
calculated. Therefore the results are interpolated with a third grade polynomial. In the case of
páramo area this polynomial formula written below (3) and visualized in figure 6. A is the area in km2
and x stands for the temperature anomaly in Kelvin.
A = -7.083*dT^3 + 68.92*dT^2 – 1342.2*dT+ 1950
(3)
[km2]
Figure 6. A visualization of the interpolation formula (3)
9
This interpolation formula can be used to create detailed changes in páramo area from the adjusted
Vostok temperature data (figure 7).
Figure 7. Interpolated time series of a decreasing páramo and an increasing temperature
The interpolated results give a detailed image of the decreasing páramo since the LGM. Temperature
fluctuations can directly be seen in in the amount of páramo. The negative correlation is clearly
visible. The trend seen in both Figure 6 and 7 is high temperatures result in little páramo, low
temperatures result in more páramo.
3.2 Connectivity
3.2.1 Original data
The total probability of connectivity between al patches is calculated for five different dispersal
distances to investigate the influence of the maximal distance required for different species to
connect to other ecosystem patches. It appeared this parameter B (0.5 dispersal distance) has little
effect on the total change in connectivity over the past 24000 years. All results are summarized in
table 3.
x
B = 2000 [%]
B = 5000 [%]
B = 10000 [%]
B = 20000 [%]
B = 50000 [%]
dT = -4
100
100
100
100
100
dT = -3
44,1
44,1
44,7
46,5
46,2
dT = -2
14,8
14,9
16,3
20,3
22,9
dT = -1
6,6
6,7
7,3
10,1
11,4
dT = 0
0,8
0,8
1,1
1,8
2,5
Table 3. All the connectivity results for different 0.5 dispersal distances
10
The influence of the decreasing páramo area on the connectivity is clearly visible on the connectivity
results. Both are characterized by a strong decrease as temperatures are rising. The difference in PC
values between the different 0.5 dispersal distances seems remarkably low. It appears species in the
páramo ecosystem with either long or short dispersal distances all lost connection with many
neighbouring páramo patches as the temperature was increasing. Between the B=50 km and the B=2
km dispersal distances the difference in connectivity is a bit higher. In the next paragraph only these
two will be visualized by interpolation in graphs (graph 8, 9 and 10).
3.2.2 Interpolated data
Just as the area results, the results of the connectivity calculations are used for an interpolation. The
method is the same, a third grade polynomial is fit through the five date points to create a detailed
relation between temperature and páramo connectivity. The polynomial functions for the páramo
connectivity for B=2 km and B=50 km are written below (2 and 3), where x stands for the
temperature anomaly in Kelvin. Both formulas are visualized in figure 8 and 9.
B=2 km:
PC = -0.0203*dT^3 - 0.0351*dT^2 - 0.0639*dT + 0.0098
[%]
(4)
B=50 km:
PC = -0.0232*dT^3 - 0.0667*dT^2 - 0.1392*dT + 0.0241
[%]
(5)
Both the connectivity formulas for the 0.5 probability distances of 2 km and 50 km are applied on the
adjusted Vostok temperature data. The result is shown in figure 10. In the same figure the
temperature anomaly is visualized.
Figure 8. A visualization of the interpolation formula for B=2 km (4)
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Figure 9. A visualization of the interpolation formula for B=50 *dT km (5)
Figure 10. Interpolated time series of a decreasing páramo connectivity with an increasing
temperature.
The changes in páramo connectivity since the LGM are clearly visible in figure 10. Páramo
connectivity has decreased drastically at the end of the Pleistocene and remained low during the
Holocene. So if temperatures are rising, both páramo area and connectivity are dropping fast.
Another remarkable trend seen in figure 10 is that changes in temperature at the end of the
Pleistocene (24000-18000) have great influence in on the connectivity, as temperature changes
during the Holocene have only little influence. Even temperature fluctuations of about one degree
Celsius are difficult to connect with changes in connectivity. Only two high temperature peaks
around 8000 and 4000 BP can be easily linked to a temporary drop in páramo connectivity. The
difference between B= 2000 and B=5000 is barely visible in figure 10 because it has a timeline of
24000 years. The differences in páramo connectivity with different 0.5 dispersal distances can be
best seen in table 3.
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4. Discussion
Changes in páramo connectivity since the LGM are linked to temperature change. The method in this
research is a new way to approach ecosystem dynamics and the change of ecosystem characteristics
over time. The pSIG model can simulate paleo ecosystem dynamics and is therefore very useful for
research about past connectivity and current fragmentation.
The pSIG model has been used to calculate páramo polygons for five different temperature
anomalies. The polygons are based only on a temperature map, this means precipitation patterns in
the research area do not have any effect on the calculated polygon which means this is a simplistic
way of looking at the complex páramo ecosystem. However, the precipitation patterns in the
research area have not been quantified, therefore it is not yet possible to add its effect on the pSIG
model. On the other hand, modelling the páramo ecosystem without using precipitation also
excludes a lot of uncertainty in the outcomes. If the effects of precipitation on the páramo border
becomes clear, the results can afterwards be corrected to improve the simulation results.
Other climatic features influencing the appearance or disappearance of the páramo ecosystem are
the CO2 concentration and night frost during the end of the Pleistocene. During the end of the
Pleistocene CO2 levels where lower, favouring C4 plants over C3 plants (Boom et al. 2002). As most of
the páramo species are C3 plants, the páramo may have been a lot smaller than the simulations
show. Night frost may have occurred more often due to lower temperatures combined with the less
humid air during a glacial period (Kull et al., 2008). This creates a negative effect on forested areas,
therefore enhancing páramo conditions. Both effect counteract each other, although little is known
about the exact strength of both on the páramo ecosystem in the northern Andes. Therefore it
seems legit to use temperature as main cause for the páramo dynamics in the northern Andes.
The used temperature input for the pSIG model originates from the Vostok ice core. This record
contains information of the temperature fluctuations on Antarctica. The way the temperature
fluctuates in the proxy is probably more or less the same as the world wide average fluctuates
(Shakun et al, 2012; Petit et al., 1999). Adjusting the range between which the temperature
fluctuated in the research area since the LGM, based on pollen analyses and tropical glacial records,
provides a realistic paleo temperature course for the research area.
Although the temperature input for the pSIG model was detailed, the output only consisted of five
different stages. The model works with integer values, so the model outcomes represent the páramo
situation for zero, one, two, three and four degrees temperature change. These five data points are
though very suitable for creating interpolation formulas. When applied on the adjusted Vostok
temperature record, this interpolation creates a páramo connectivity reconstruction with a very good
time resolution. This method delivers high quality results while the computing time remains low. This
creates an opportunity to explore more trends in the páramo ecosystem dynamics by expanding the
research area and the total timespan of the model calculations.
The interpolation formulas (4 and 5) represent the way the páramo ecosystem reacts on
temperature change and are therefore actually a very interesting result. These formulas only need a
temperature record to calculate the connectivity change. Even though they are based on a relative
small area with only five data points to calibrate, they do reveal the trend of a strong decrease of the
páramo connectivity just before the beginning of the Holocene and the way the páramo reacts on
13
temperature change (figure 10). When the Holocene starts at 10000 BP, only 22% of the original
páramo area is left. The connectivity for species with a dispersal distance of 50 km has decreased
even further to just 3% of its PC value at 24000 BP. For páramo species with a dispersal distance of 2
km less than 1% of the 24000BP connectivity is left.
The relative páramo connectivity (RPC) is calculated as a value which describes the calculated
situation compared to the situation 24.000 year BP. A RPC of 100% represents the stage in which the
páramo ecosystem was at its peak (figure 5.1). In the original formula (Saura et al. 2011), the
connectivity compared the calculated situation to a situation in which the total research area was
covered with the páramo ecosystem. This has been adjusted in this research because it is unrealistic
for the area. There has probably never been a situation in which a region with so much height
differences was completely covered with páramo. The RPC value is based on the size of the páramo
patches and the distances between them. As can be seen in figure 5, the size of the páramo patches
have declined, and the distances between them has increased. These trends resulted in lower RPC
values (figure 10).
The effect of different dispersal distances of species is incorporated by calculating the RPC five times
for five different dispersal distances (B values). Surprisingly the effect of the dispersal distance on the
total trend appeared to be minimal. There exists almost no difference in connectivity between a Bvalue of 2 km and 20 km. Apparently because the total decrease in connectivity over 24000 years is
so big, the effect of different dispersal values is almost completely lost. The results of the PC
calculations in the results chapter have only been shown for B=2 km and B=50 km because only
between those values a small difference can be seen in the way they react on temperature change. It
has to be noted that those two B-values differ from each other by a factor of 25. With both B-values
the trend is the same: a strong loss of connectivity between 18000 BP and 10000 BP (figure 10). The
difference between the two B-values is only barely visible, and is best seen in table 3. The final PC
value of the B=50 km line is 3 times higher than the B=2 km line. The fact the difference in not seen it
the bigger picture is because both RPC values represent less than 3% of the original RPC value 24000
years ago.
The effects of different dispersal distances on the connectivity based on temperature change could
be researched more closely if the reference point (A2L) was set less far from the current situation, for
instance at 10000 BP. Because the time span is shorter, the dT could be lowered and the resolution
of the pSIG model be improved to create more data points so an even better interpolation can be
created. More data points and an lower reference point will probably result in larger differences in
connectivity between the dispersal distances.
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5. Conclusion
Many connectivity indices are available to express the current páramo connectivity. The changes in
connectivity since LGM and the way the páramo ecosystem reacted on temperature change are not
yet taken into account. In this research the dynamics of the páramo ecosystem have been modelled
and interpreted since the LGM to check whether there has been a trend in the change in
connectivity.
The temperature anomaly for the research area for 24000 years is reconstructed based on the
temperature record of the Vostok ice core on Antarctica and additional information from an analysis
of pollen and tropical glaciers nearby the research area. It appeared the average temperature in the
research area was about four degrees lower than the current situation.
The páramo surface and connectivity was calculated for each of the five different temperature
situations occurring between the LGM and the present day. 0, -1, -2, -3 and -4 degrees. A more
detailed relation between temperature and páramo connectivity was then constructed by an
interpolation between those values.
In total the páramo area has decreased from 8875 km2 at the LGM to just 1950 km2 in the current
situation, so only 22% of the LGM páramo is still present nowadays. This strong decrease in area
causes a great loss in connectivity. Less than 3% of the LGM páramo connectivity is left, even when a
very high dispersal distance is used (B=50km).
Comparing the RPC value of each time step with the 24000 BP situation gives a clear insight of the
way the páramo area and the páramo connectivity has decreased. Both values dropped very fast at
the end of the Pleistocene. The main conclusions of the research are that the páramo ecosystem was
a lot larger and better connected during the LGM than in the current (1950) situation. The large
decrease of the páramo happened just before the Holocene and since then little has changed. The
difference between dispersal distances of páramo species do influence the final connectivity, but
have little influence on the general trend. To look at this more closely, the reference point could be
placed closer to the current situation, for example at 10000 BP.
The method of modelling ecosystem dynamics based on one feature like temperature change has
proven to be very useful. The pSIG model creates good workable outcomes. The software tools
required for the calculations are freely available and use little computing time. The program is easy
to understand and needs little input information. The model is based on an island approach of
ecosystems, originally created to model the appearance and disappearance Mediterranean islands,
therefore creating a new way of looking at ecosystem dynamics.
.
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6. Acknowledgements
The pSIG model and the model results created by Sietze Norder have been essential for this research.
All calculations made in this paper are based on the output of the pSIG model. Also the comments of
both Kenneth Rijsdijk and John van Boxel strongly enhanced the quality of this paper.
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