Modeling population growth and the implications of urban expansion in Belize, Central America







Central America lies between the tropical latitudes 5º to 30º N and has a global reputation for sparkling blue waters and sunny beaches. These warm paradises also contain a large percentage of the World’s biodiversity. Tropical rain forests and coral reefs cover a relatively small area of the globe, yet are home to thousands of rare species not found anywhere else. Because these unique ecosystems require very particular sets of physical conditions, they are often very sensitive to changes in the environment. Increasing human populations and the development that accompanies them often threaten these areas of biodiversity and run the risk of driving rare species to extinction.



Belize is of particular interest because it is the most sparsely populated country in Central America, leaving much of the land relatively undeveloped. This country contains many ecosystems with high biodiversity; mangrove forests line the coast, the second largest barrier reef in the world lies less than a kilometer off-shore, and over 90% of land is under tropical forest cover (Figure 1).

Figure 1: Extent of forest cover in Belize, Central America, represented by the colours green and brown. Image provided by the Biological Diversity of Belize Mapping Service (Jan Meerman).


The government of Belize has recognized these sensitive ecosystems by establishing protected areas in approximately 42% of available land (Protected Area Conservation Trust). These designated areas include terrestrial, marine, and even archeologically significant regions (Figure 2).


Figure 2: The Protected Areas of Belize, Central America, including the status the Government of Belize has designated these areas and the political boundaries of all six districts. (Dataset provided by Jan Meerman).


The wide variety of environments represented in these protected areas hope to maintain the integrity of biodiversity and rare species within the country. Conserving the natural environment in Belize while it is still relatively pristine allows for the opportunity to employ a more preventative approach to conservation, rather than a reactionary one.



Although the government of Belize has taken the initiative to recognize these diverse ecosystems at the early stages of the country’s growth, changes in population will affect protected areas drastically in the following decades. The current growth rate of Belize (2.39%) is more than two times the rate of global population growth (1.1%), so that if this trend continues, Belize will double in approximately 30 years (Government of Belize; for population doubling time see Appendix I). Encroachment by a growing population and the increase of agricultural, industrial and commercial activities necessary to sustain this expansion will threaten the surrounding environment (Joshi and Suthar, 2002). In addition, tourism contributes over 20% GDP to the economy and the government has made developing tourism a “national priority” (Belize Tourism Board).This economic reliance on the tourism industry means more people are arriving in Belize each year. The number of visitors has already increased since 1998 so that in recent years, the tourists almost outnumber the residents (Immigration Department).





My intent for this term project was to use ArcGIS (version 9) to address development in Belize by constructing predictive models, displaying biological data in a spatial context, and relating the results to physical features. In particular, I wanted to:


1. Predict the increase of Belize’s population over time by using current census data to model growth estimates for the next 30 years (predicted doubling time).


2. Show the distribution of an estimated population increase for each district.


3. Demonstrate how predicted population growth would compromise designated Protected Areas.





            Finding geographical datasets for international countries can be more challenging than using regional data sources such as USGS. Information is not always up to date and it can be saved in files that are not compatible with ArcGIS. The best source for my basemap data was downloaded from the Digital Chart of the World website in the form of a zip file that contained relevant features saved in interchange format (extension .e00). I created a new geodatabase in Arc Catalogue called ‘Belize’ and using the ArcToolbox function Import features from Interchange file, I added each feature class to a feature dataset ‘BelizeUTM’ so that each layer would have the same UTM projection (Figure 3).



Figure 3: Using the Import to Interchange File tool in ArcToolbox.


I originally had a lot of difficulties opening this data as the import function kept rejecting my output files. This was reportedly caused by operating ArcGIS on a vast network and I was able to successfully import the data by saving the converted files in a temporary folder on the local hard drive. I also obtained a polygon feature class from Jan Meerman (Biological Diversity in Belize) which delineated the six districts of Belize as a shapefile and another polygon feature class which showed the Protected Areas in Belize (See Figure 2). I imported both the ‘District’ and ‘ProtectedAreas’ feature classes to the BelizeUTM dataset in Arc Catalogue.


            I hoped to find Digital Elevation Model and satellite imagery land use datasets, however the region I focused on was extensive (22 ,966 km2), making DEMs from sources such as SRTM too large and there was no adequate land-use data available.



Population data and current growth rate was acquired from the Government of Belize. I used 2000 and 2004 census data (Central Statistical Office) as archive and current populations, respectively. The population in each of the six districts of Belize and the division between urban and rural areas were also based upon CSO data. I added a new field to the attribute table of the political polygon of Belize and entered total population numbers for 2000 and 2004. I exported this feature class as ‘TotalPopulation’ into the BelizeUTM dataset. I added new fields to the attribute table of the district feature class and entered district population and urban and rural populations.  I also calculated a new field for the proportion of total population represented in each district (Figure 4). I exported this feature class as ‘DistrictPopulation’.


Figure 4: Attribute tables for TotalPopulation and DistrictPopulation feature classes.






Population Growth


Population growth can be estimated using exponential or logistical equations. These formulas take the initial population N0 and calculate increases or decreases over t amount of time. Each equation uses different parameters to incorporate variables that affect population growth. A basic exponential equation uses only time and growth rate, whereas a logistical equation also requires estimates of population carrying capacity, which defines the limit of a population to expand due to resources or space. Calculating the carrying capacity of human populations is virtually impossible, so for the scope of this project, I chose to use an exponential equation.


Nt = N0*ert


or put more simply


Population at time t = Initial population * e(growth rate r * time t)


NOTE: The exponential growth equation does not take into account immigration, emigration, or limits to resources and space.


In order to examine population growth in Belize, I first made a new toolbox in Arc Catalogue called ‘Belize’. I constructed a model in this toolbox called ‘TotalPopulation’ and used the exponential growth equation in Model Builder to calculate population estimates over 30 years (projected doubling time for the population). The model adds a new field to the attribute table of the TotalPopulation feature class and names it according to year. The model then multiplies the initial population (year 2004) by the growth rate and time. I found that model builder does not enable complex mathematical functions such as exponents so I calculated this figure by hand and added it to a new field in the attribute table called ‘GrowthRate’ using the Editor toolbar. I estimated the population of Belize for years 2005 - 2035 in 5 year intervals by running the model 7 times (Figure 5).


Figure 5: TotalPopulation model in ArcToolbox used to calculate the estimated population of Belize between 2005-2035 in 5 year intervals.



Each step of the model calculates the predicted population of a year based upon the preceding year’s estimate. This way I could use the same GrowthRate figure as t remained constant. After running the model, I displayed the population estimates using Chart - Bar Graph under Symbology (Figure 6).


Figure 6: Estimated population growth of Belize for the next 30 years.




Population Distribution


            The six districts of Belize each contain unique topographical and environmental features. In addition, current data shows that the population is not evenly distributed between districts (Figure 7). In order to display the variation in population between each individual district, I could not apply the exponential equation used in my TotalPopulation model. This formula requires district growth rates, which involve calculations of factors and data unavailable to me. Instead, I used proportional distribution because between the years 2000 and 2004, each district contained a relatively similar percentage of people even though the total population increased 17%.


Figure 7: Population within each district of Belize for the year 2004.


Figure 8: Population within each district of Belize for the years 2000 and 2004 projected on an ArcMap. The Excel chart indicates the district proportion of the total population does not change.

I estimated district population growth by building another model in my Belize toolbox called ‘DistrictPopulation’, and used the predicted total population numbers generated in my TotalPopulation model to derive the proportional distribution of people in each district between 2005 - 2035 in 5 year intervals. The model adds a new field named by year to the District attribute table and multiplies the total population estimate to each district proportion (Figure 9).


Figure 9: DistrictPopulation model in ArcToolbox used to calculate the proportion of the population in each district between 2005-2035 in 5 year intervals. (NOTE: The model is longer than displayed).



I entered the population estimate for each year because Model Builder could not join these numbers from one feature class to the other. I could have created redundant fields in the District attribute table of total population, however entering a single number into the model saved me time as this dataset was relatively small. If I was to apply this model to a larger group of districts, I would use redundant fields to remodel population estimates and calculate district proportion from the single table. I felt comfortable operating under the assumption that growth would occur at a constant proportion because this model did not generate any new data, but merely showed the possible distribution of total population estimates within the country.


Figure 10: Estimated population growth of each district of Belize for the next 30 years.



Population Expansion


            To determine the effect that population growth would have on sensitive ecosystems, I looked at how the expansion of city limits would encroach upon neighboring Protected Areas. The feature class ‘Towns’(from the Digital Chart of the World dataset) represent single points of populated areas in Belize without distinguishing between rural villages or urban cities. In order to examine population expansion, I first had to ensure that urban and rural areas would not grow at different rates. The tendency of cities to expand more rapidly than rural areas is known as urbanization. If urbanization is significant in each district, population increases would be concentrated in a few cities and the proportion of the population residing in rural areas would decrease over time. Again, using data from 2000 and 2004 I found that growth occurred evenly between urban and rural areas, maintaining the ratio of city dwellers to remote villagers (Figure 11).


Figure 11: Towns feature class projected on an ArcMap. The Excel chart indicates the distribution between rural and urban populations for the years 2000 and 2004.



            I measured population expansion using the Euclidean Distance function in ArcToolbox. By calculating the distance from each Town to another, I projected growth of these populated areas in increments of kilometers (Figure 12).

Figure 12: Euclidean Distance function measuring the distance (in meters) between Towns.


I set the increments to 1000 meters in Symbology and designated radial increases of less than 5 km as red, orange and yellow (moving away from Town centers).These regions pose the most immediate threat to endangered ecosystems, as even small settlements can easily reach diameters of 10 km. Values represented in green are still in danger of encroaching upon Protected Areas, however, this growth depends entirely upon the magnitude and direction of urban sprawl. Due to the large percentage of land designated as parks or reserves, more than half of the Towns currently lie within 5 km of a Protected Area and all Towns lie within 20 km (Figure 13). Therefore, if each Town feature expanded up to 20 km, the surrounding ecosystems would be drastically reduced.


Figure 13: The vicinity of Protected Areas to populated areas in Belize.


            I also used the Euclidean Distance function to project the expansion of roads. These thoroughfares connect populated areas and are associated with construction, pollution, and often become the first areas to be developed. Population growth would increase the demand for wider existing roads and the formation of new ones (Figure 14).    


Figure 14: The expansion of existing roads and the Protected Areas that they intersect.





            I was able to determine population growth in Belize using Model Builder to predict population estimates, ArcMap to display these results in their spatial context, and ArcToolbox functions to observe population expansion within the vicinity of protected ecosystems.  ArcGIS software allowed me to approach the future development of Belize by examining both numerical representations of biological results and relate the implications of growth in physical space. Being able to use a variety of data types such as values, points, and areas in a particular problem strengthens the ability of the analysis to address more than one question. In this case, population estimates could have been calculated and displayed in tabular format which would neglect the spatial context to which it applies. Looking at these estimates in GIS form serves as a reminder of how an increase in numbers is related to a geographical area and encourages the further examination of what these changes imply.  For my project, I would have liked to continue to study the effects of population growth by calculating flow in the streams of Belize and estimating the expansion of land-use from areas instead of points. Provided with a high resolution DEM and hydrography data, I could delineate watersheds where the effect of increased runoff or stream blockage might change drainage areas providing valuable water sources to the population (using ****). Using satellite images to build a polygon feature class of all human related land-use would allow me to incorporate agricultural and industrial areas instead of unrepresentative points of populated places. In addition, water quality data from marine monitoring points would enable me to analyze the potential effects on Marine Protected Areas from increases in pollutants, discharge, and boat use with tools such as Tracking Analyst.



            The capabilities of ArcGIS are adept at analyzing a multitude of information, however there are some limitations. To perform any kind of ecological modeling, users must be able to calculate a variety of functions. Unfortunately, in the Calculate Field tool complex functions such as exponents and logs are not possible.  A looping function in Model Builder would also improve efficiency so that data does not have to be entered repeatedly.                                        






            This exercise in ArcGIS gave me the opportunity to approach estimating the population growth in Belize using a variety of analyses. Without being limited by unavailable data, more of the functions in this software may have been utilized to address my project. The wide range of possible solutions to a single question makes this tool very useful for fields such as Conservation. By illustrating areas of interest like Protected Areas, the effects of biological and physical changes can be examined. The use of multifaceted programs such as ArcGIS has the potential to improve the accuracy of conservation planning which can hope to prevent the degradation of biodiverse ecosystems in the future. 






This project was completed with helpful advice from correspondence with Jan Meerman (Biological Diversity in Belize) and Dr. Jay Raney (Bureau of Economic Geology, University of Texas at Austin) in addition to modeling guidance and suggestions from Dr. David Maidment (University of Texas at Austin).


*     ArcGIS version 9x. ESRI 2003.


*     Belize Tourism Board (Ministry of Tourism)


*     Central Statistical Office (Ministry of Finance)


*     Digital Chart of the World


*     Government of Belize


*     Jan Meerman (Biological Diversity in Belize)


*     Joshi, K.N. and Suthar, C.R. 2002. Changing urban land use and its impact on the environment (a case study of Jaipur city).


*     Protected Area Conservation Trust






APPENDIX I: Population Doubling Time


In order to estimate the amount of time it will take for a population to double, a simple calculation can be used.


Growth Rate of Belize = 2.39% (Government of Belize)


When a population doubles,                                N = 2N0

Using the exponential growth equation,                N0*ert = 2 N0

Canceling the N0 on each side leaves                   ert = 2

Growth rate r is known, therefore solving for t        rt = ln 2

Results in                                                          0.69/r

Therefore, doubling time is                                  0.69/0.0239 = 28.9 years