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1 Papeles de Población ISSN: Universidad Autónoma del Estado de México México Azuz Adeath, Isaac; Rivera Arriaga, Evelia Estimación del crecimiento poblacional para los estados costeros de México Papeles de Población, vol. 13, núm. 51, enero-marzo, 2007, pp Universidad Autónoma del Estado de México Toluca, México Available in: How to cite Complete issue More information about this article Journal's homepage in redalyc.org Scientific Information System Network of Scientific Journals from Latin America, the Caribbean, Spain and Portugal Non-profit academic project, developed under the open access initiative

2 Population growth estimation for the coastal States of Mexico Isaac Azuz Adeath y Evelia Rivera Arriaga Centro de Enseñanza Técnica y Superior. Campus Ensenada/ Universidad Autónoma de Campeche Resumen El presente estudio muestra los resultados derivados de la aplicación de un modelo teórico de crecimiento poblacional (sigmoidal boltziano), construido a partir de la información censal disponible para cada estado costero de México (del año 1930 al 2000). El modelo fue validado y calibrado usando los resultados preliminares del II Conteo de Población y Vivienda del año Los pronósticos de crecimiento poblacional se realizaron de forma anual para el periodo comprendido entre el año 2006 y el Para el año 2030 se estima una población total de 58.8 millones de personas en los estados costeros de México. Se estima para este año una población total en los estados costeros de 64.2 millones de personas. Palabras clave: crecimiento poblacional, estimación del crecimiento poblacional, estado costero, México. Abstract Population growth estimation for the coastal states of Mexico This paper shows the results obtained with a theoretical population growth model (sigmoidal boltziano), developed using the census information for each Mexican coastal state (during the period ). The model was validated and calibrated using the population counting (2005). The annual population growth forecast comprises the period between 2006 and For year 2030, a total of 58.8 million people was predicted. With the population counting data of 2005 the sigmoidal model was corrected and a decadal forecast until 2050 was obtained. For the reference year (2050), the total population for the Mexican coastal zone will be 64.2 million people. Key words: population growth, population growth estimation, coastal state, Mexico. Introduction he seventeen Mexican coastal States constitute 56.3 percent of the country s continental surface and they had, in the year 2005, inhabitants (CONAPO, 2006), this corresponded to 45.8 percent of the Ttotal population. Demographic growth of the Coastal States in general, and in particular of the municipalities with littoral front, constitutes one of the most relevant socio demographic variables from the planning and coastal management points of view, since, among other factors, it allows an estimation of the basic

3 Papeles de POBLACIÓN No. 51 CIEAP/UAEM needs to be satisfied, the pressure this process exerts upon the environment and the modification to the risk and vulnerability patterns the population might be exposed to. The changes the total population experiences in a coastal State determine in time changes in vital necessities such as: housing, health and education services; employment, transport and roads; security, leisure and sport areas; supply, piping and availability of water; energy and residues handling. These demographic increment patterns, when take place in closed and defined territorial spaces (States limits), invariably put pressure on the environmental goods and services, modifications to the urban development patterns and their services networks (water, electric light, sewerage, telephone lines, drainage, water treatment plants, etc.), alterations in social structure and relationships, modifications in the consumption and production patterns, to eventually alter in a significant manner the quality of life of the local population. The changes experienced by the local population of the Mexican coastal States and municipalities are a phenomenon which requires special attention to the processes of territorial ordination, coastal integral handling, State and municipal plans of development, programs of regional and urban development, among other planning instruments. The correct interpretation and prediction of the demographic growth patterns allow conceiving, defining, and establishing long term policies, plans, and programs, with a clearer vision of the local needs that have to be satisfied, of the pressure exerted on the environment and of the increment in risks and vulnerability of the regions for which the forecast is made From the long term planning point of view it is equally important to know the number of inhabitants of a region (State or municipality), the rate of change of that number, as well as the population s age structure. This paper is focused on the projections of the growth of the total population of the coastal States of Mexico for the period between the years 2005 and 2030, as a first approach, and up to 2050 with the same model, though corrected, with data from the 2005 Counting of Population and Housing (Conteo de Población y Vivienda 2005). Table 1 shows the total population registered in the Mexican coastal States during the 1980, 1990, 2000 censuses, as well as the 1995 and 2005 population counting; in the case of the latter, with preliminary results (INEGI, 2006; CONAPO, 2006). 176

4 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera This table shows that Veracruz, in the east coast of the country, has had the highest levels of population in the last thirty years, followed by Jalisco in the west coast. Separately, Baja California Sur with the greatest coasts extension in Mexico, has had in the same period the smallest number of inhabitants and as a consequence of its territorial extension, the lesser population density. In the case of the east coast, Campeche has the smallest number of inhabitants of the slope of the Gulf of Mexico and the Caribbean Sea. TABLE 1 TOTAL POPULATION OF THE COASTAL STATES OF MEXICO Estado BC BCS SON SIN NAY JAL COL MICH GRO OAX CHIS TAM VER TAB CAM YUC QROO Total Source: INEGI, 2006 and CONAPO, January / March 2007

5 Papeles de POBLACIÓN No. 51 CIEAP/UAEM For the coastal States of Mexico, the number of registered population in the year 2000 is inversely related to the average annual demographic growth rate calculated for the period from 1990 to This means that the States with the most population, have in general, lower growth rates than those which have a smallest number of inhabitants. Graph 1 displays the diagram of dispersion and the parameters of linear regression calculated for the previously mentioned variables. It is assumed that the total population depends on the average annual growth rate. Graph 1 shows that States such as Veracruz and Jalisco, with the highest values of total population (above six million of inhabitants), have demographic growth rates below two, whereas States such as Baja California and Quintana Roo, with populations below three million, have higher average annual demographic growth rates (above four). When performing that very analysis in an independent manner for he States of the west coast (Pacific Littoral and Sea of Cortés) and those of the east coast (Gulf of Mexico and Caribbean Sea), the results show a similar behavior, it is, negative linear correlations with little significance between the demographic growth rate and the total population. This phenomenon has important consequences on the type of model to try using to forecast demographic growth, for it can be thought that the States with the most population have reached stages of demographic stability, whereas those with scarce population still experience accelerated growths of exponential character. Graphs 2 and 3 show the behavior of the west and east coasts States, respectively. Table 2 shows the average annual growth rate (percentage), for the different States of Mexico. With the exception of Colima, Chiapas and Oaxaca, all of the coastal States present a deceleration on the average annual growth rate between the periods and the total population of a country or a State depends on the phenomena s behavior such as birthrate, mortality and migration (López, 2002). The following graphs and tables show how these processes take place in coastal States. Table 3 shows the correlation matrix between total population in the year 2005, the gross birthrate in that year, the average annual growth rate between the years 1990 and 2000 and the percentage in respect to the average national total of the registered casualties, during the years 2001 to

6 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera GRAPH 1 RELATION BETWEEN AVERAGE POPULATION GROWTH RATE DURING THE PERIOD AND TOTAL POPULATION OF THE COASTAL STATES OF MEXICO IN 2000 Source: INEGI on line (2006). Author s model. The little significant correlation between the total population and the gross birthrate, as the inverse relation between total population and the average annual growth rate, could clearly state the importance of the migratory processes in the Mexican coastal States. In order to visualize this phenomenon, graph 5 displays, for every coastal state the net migratory rate (immigrants-emigrants) registered in the 2000 census (INEGI, 2001). In table 4 the correlation matrix, which results from incorporating the net migration measured during the year 2000, is presented. The rest of the variables have been previously defined. 179 January / March 2007

7 Papeles de POBLACIÓN No. 51 CIEAP/UAEM GRAPH 2 RELATION BETWEEN THE ANNUAL AVERAGE GROWTH RATE DURING THE PERIOD AND THE TOTAL POPULATION OF THE WEST COAST STATES OF MEXICO IN ,000,000 Relación entre la Población Total (2000) y la Tasa de Crecimiento Poblacional Media Anual ( ) COSTA OESTE (Fuente: INEGI en línea,2006) 6,000,000 JAL Población Total (2000) 5,000,000 4,000,000 3,000,000 2,000,000 R 2 = r= a 0 = 3,741,713 a 1 = -517,607 BC 1,000,000 0 NAY COL BCS Tasa Crecimiento Media Anual ( ) Source: INEGI on line (2006). Author s model. Table 2 shows that the average annual growth rate registered in the Mexican coastal States has an important positive correlation with the net migratory flow. Conversely, the total population registered in the year 2000 has a moderated negative correlation with the said migratory flow. This phenomenon is explained by the fact that not necessarily the States with the most (least) population are the ones with the greatest (lesser) gain of migratory inhabitants. The similarity between the Mexican coastal states behavior in terms of the variables involved in the correlation matrixes can be graphically described by means of a tree diagram, using in the grouping, as a measure of the resemblance among States, the Euclidian distance and the coefficient of linear correlation. 180

8 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera GRAPH 3 RELATION BETWEEN THE ANNUAL AVERAGE GROWTH RATE DURING THE PERIOD AND THE TOTAL POPULATION OF THE EAST COAST STATES OF MEXICO IN VER Relación entre la Población Total (2000) y la Tasa de Crecimiento Poblacional Media Anual ( ) COSTA ESTE (Fuente: INEGI en línea,2006) Población Total (2000) CAM R 2 = r= a 0 = 4,715,625 a 1 = -860,883 QROO Tasa Crecimiento Media Anual ( ) Source: INEGI on line (2006). Author s model. The differences observed between the two grouping methods are fundamentally due to the fact that while the Euclidian distance incorporates the difference among each analysis point (comparison among the studied demographic variables of the coastal States), the groups formed using the Pearsons coefficient of correlation are determined by the level of linear correlation existent among the set of selected variables. Finally, in respect to the demographic structure of the coastal States in terms of age, Guerrero, Chiapas, Oaxaca and Michoacán have the highest percentage of young people (0 to 14 years of age); Baja California Sur, Sonora and Tamaulipas, the highest percentage values of people between 15 and 64 years of age, whereas Yucatán, Nayarit and Jalisco have the highest percentage of people of 65 years of age and older. Graph 8 shows this behavior. 181 January / March 2007

9 Papeles de POBLACIÓN No. 51 CIEAP/UAEM TABLE 2 PERCENTAGE ANNUAL AVERAGE GROWTH RATE State Mexico Aguascalientes Baja California Baja California Sur Campeche Coahuila Colima Chiapas Chihuahua Distrito Federal Durango Guanajuato Guerrero Hidalgo Jalisco México Michoacán Morelos Nayarit Nuevo León Oaxaca Puebla Querétaro Quintana Roo San Luis Potosí Sinaloa Sonora Tabasco Tamaulipas Tlaxcala Veracruz Yucatán Zacatecas Source: INEGI, 1992, 1997,

10 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera TABLE 3 CORRELATION MATRIX AMONG DIFFERENT DEMOGRAPHIC VARIABLES FOR THE COASTAL STATES OF MEXICO Total population Birthrate Demographic growth Casualties (%) Total population Birthrate Demographic growth % of casualties With this general view of the demographic structure of the coastal States we will proceed, in the next part, to describe the methodology utilized to forecast the total population growth in the Mexican coastal States for the next twenty-five years, using a model of the Boltzian Sigmoidal type. Additionally and with the information of the II Counting of Population and Tenement of the year 2005, the model was calibrated and the forecast was extended up to the year Methodology Demographic growth has been modeled from the mathematical point of view out of deterministic models, such as the logistical equation (Pearl and Read, 1920; Zill, 2006: ), which is considered by different authors as a model that allows a wide range of applications and, in general, it has been accepted as a good first approximation to the phenomenon of growth of species with no competence (Maki and Thompson, 1973: , and Marchetti et al., 1996:1-30). In the present study data from the General Censuses of Population and Housing (Censos Generales de Población y Vivienda, INEGI, 2006) carried out every ten years, from 1930 to 2000 were used. The definitive results from the Counting of Population carried out in 1995 were included. 183 January / March 2007

11 Papeles de POBLACIÓN No. 51 CIEAP/UAEM GRAPH 4 GROSS BIRTHRATE (PERCENTAGE) FOR THE COASTAL STATES IN 2005 Source: data from CONAPO, Using these values for each coastal State and after performing different proofs it was proposed as the general model with the best adjustment that of Boltzian Sigmoidal type. The said model is tetraparametric and in it both the inflection point and the maximum mark of the demographic curve are included (Ledvij, 2003). It has been utilized in different spheres to model the growth of specific populations (Zullinger et al., 1984: ), their dynamics (Carrillo, 2003: ) and the growth of the world s population (Ausubel and Meyer, 1994:17-19) among others. 184

12 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera GRÁPH 5 NET MIGRATORY BALANCE (IMMIGRANTS-EMIGRANTS) REGISTERED IN 2000 FOR THE COASTAL STATES Source: INEGI, The equation of the Boltzian Sigmoidal model can be expressed as follows: y = A A x x + e 1 2 ( 0 )/ dx 1 + A 2 Being y the estimated population, A 1 and A 2 the inferior and superior marks of the curve or asymptotes, respectively; x 0 the abscissa of the inflection point and x the independent variable. Taking as elements of adjustment validation both the values of squared qui as the coefficient of determination (R 2 ), in general, all of the States had an excellent level of adjustment in respect to the proposed theoretical model (values above 0.99), being the highest value that of Baja California Sur (R 2 = ), and the lowest that of Chiapas (R 2 = ). 185 January / March 2007

13 Papeles de POBLACIÓN No. 51 CIEAP/UAEM TABLE 4 MATRIX OF CORRELATION AMONG DIFFERENT DEMOGRAPHIC VARIABLES FOR THE COASTAL STATES OF MEXICO Total population Birthrate Demographic growth Casualties (%) Migration Total population Birthrate Demographic growth Percentage of casualties Migration BC QROO BCS SON COL TAM CAM SIN NAY CHIS TAB VER YUC MICH GRO OAX JAL GRAPH 6 GROUP ANALYSIS USING THE COEFFICIENT OF CORRELATION OF PEARSONS (1-R) AS SIMILITUDE ELEMENT GROUP ANALYSIS COASTAL STATES OF MEXICO METHOD (1-Pearson r) LESSER SIMILITUDE LEVEL ---> 186

14 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera BC TAM SON SIN TAB YUC MICH CHIS GRO OAX BCS COL CAM NAY QROO JAL VER GRAPH 7 GROUP ANALYSIS USING EUCLIDEAN DISTANCE AS SIMILITUDE ELEMENT GROUP ANALYSIS COASTAL STATES OF MEXICO METHOD (Euclidean Distance) e6 1.5e6 2e6 2.5e e6 1.5e6 2e6 2.5e6 LESSER SIMILITUDE LEVEL ---> With the confidence of having a model that correctly adjusts the data, we proceeded to perform the forecast for the year 2005 (specifically for the middle of each year, with the aim to be congruent with CONAPO s estimations). Once the preliminary results from the II Counting of Population and Housing of the year 1995 were known, the results form the model were verified and contrasted to the predictions annually performed by the National Council of Population up to the year Graph 4 presents the percentage relative error produced in respect to the year 2005 measurement, for both CONAPO s (1999) and the proposed sigmoidal model s estimations. Once the error in the prediction for each State in relation to the average value for the year 2005 is known, there exists the option to adjust the model with the aim to perform estimations that can be potentially more accurate. It is observed in graph 9 that the average percentage relative error of the Boltzian Sigmoidal model is slightly inferior to that of the method utilized by CONAPO (1999). Table 5 shows the values of the coefficient of determination R 2 obtained from the adjustment process of the model hereby presented (Boltzian Sigmoidal). 187 January / March 2007

15 Papeles de POBLACIÓN No. 51 CIEAP/UAEM GRAPH 8 DEMOGRAPHIC STRUCTURE OF THE COASTAL STATES BY LARGE AGE GROUPS FOR THE YEAR 2000 Results Source: INEGI, The values obtained for the Mexican coastal States total population for the periods 2010, 2020, and 2030, using CONAPO estimations and the sigmoidal model are shown in table 6. In the aforementioned table it is observed that the total population expected in the States with littoral front in Mexico for the year 2030 will be close to 60 million people. Approximately 70 percent will live in the west coast and 30 percent in the Gulf of Mexico and Caribbean Sea s littoral. The current percentages (2005) are 67 and 33, respectively. 188

16 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera Jalisco, in the west coast, and Veracruz in the east will be the coastal States that will have a larger population in the next thirty years. On its own, Baja California Sur, Colima and Campeche will not reach one million inhabitants within the next thirty years. Graphs 10, 11 and 12 show the behavior of the demographic growth, measured and estimated, with the sigmoidal model for specific cases where the following is observed: 1. Stability in the growth levels (better adequacy to the sigmoidal method). 2. An abrupt diminution of the growth tendencies (greater model error). 3. A clear growth process with exponential character (possible adequacy of other methods). The estimation done with the sigmoidal model for the year 2005 in Sinaloa had a percentage relative error in respect to the value measured in the counting of population of 0.26 percent, being altogether with Yucatán, the States which presented values closer to reality. For Sinaloa it is observed that the stability value is found around inhabitants. The analysis of the demographic shows that, in general, there are three mechanisms that stabilize the curve of demographic growth, namely: diminution in birthrate, increment in mortality rate, and increment in immigration. For Sinaloa, during the year 2003, there was a gross birthrate of 18.3, being the national average 18.4 and that of the coastal States 19.7 (INEGI, 2006); in Sinaloa, the average annual growth rate suffered an important deceleration changing from 1.7 in the period to 1 during the period. For the year 2003, casualties registered in Sinaloa were , which corresponded to 2.34 of the national total, this was a similar value to that of Baja California, Sonora and Guerrero. For the year 2000, Sinaloa reported a negative net migration rate of around people, which implies a larger number of emigrants than of immigrants (INEGI, 2006). Graph 11 displays the behavior of the total population of Michoacán. This State had the greatest differences (both in the sigmoidal model and in CONAPO estimations) among the forecasted values and the ones measured in January / March 2007

17 Papeles de POBLACIÓN No. 51 CIEAP/UAEM GRAPH 9 PERCENTAGE RELATIVE ERROR AMONG THE VALUES MEASURED IN THE SECOND POPULATION COUNTING AND THE ESTIMATED BY CONAPO (1999) AND WITH THE BOLTZIAN-SIGMOIDAL MODEL Source: Second Counting of Population and Households (2005) and CONAPO (1999). For Michoacán, the gross birthrate was similar to the average of the coastal States for the year 2005 (1.8), nevertheless, the average annual growth rate decreased from 1.5 percent in to only 0.7 percent for the period. Additionally, Michoacán was the third coastal state from which the most people emigrated. Baja California had the largest net migratory flow of all the coastal States in Mexico. Its birthrate is exactly the same as the national average and slightly inferior to that of the coastal States. After Quintana Roo, it presented the greatest growth rate for the in the period from 1990 to 2000 in all of the States of Mexico. 190

18 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera TABLE 5 VALUES OF THE DETERMINATION COEFFICIENT OF THE BOLTZIAN-SIGMOIDAL MODEL FOR EACH COASTAL STATE Coast West Coast East State R2 State R2 BC TAM BCS VER SON TAB SIN CAM NAY YUC JAL QROO COL MICH GRO OAX CHIS In spite the percentage relative error registered for Baja California with the sigmoidal model is very close to the average value, and the difference shown against the calibration value (population in the year 2005) its magnitude is three percent, the growth pattern is still clearly exponential, as it is seen in graph 12, there can exist more simple and possibly more exact models to perform the forecast in this case. If the sigmoidal model is accepted as correct, and if the current tendencies continue, Baja California would be in the year 2050 the most densely populated in Mexico (with approximately 11 million people), surpassing Jalisco and Veracruz with about four million people. 191 January / March 2007

19 Papeles de POBLACIÓN No. 51 CIEAP/UAEM TABLE 6 ESTIMATED VALUES OF THE TOTAL POPULATION FOR THE COASTAL STETS OF MEXICO Author CONAPO BC BCS SON SIN NAY JAL COL MICH GRO OAX CHIS TAM VER TAB CAM YUC QROO Total Source: CONAPO (1999) and the sigmoidal model proposed by the author. Graph 13 shows the estimations up to the year 2050 for Baja California, Jalisco and Veracruz. It is clearly observed that as from the year 2040 Baja California would have a greater population than the two coastal States which currently take the first places in population (Jalisco and Veracruz). Table 7, presents the estimated values up to the year 2050 with the adjusted sigmoidal model, using as correction factor the values registered in the year 2005 during the II Counting of Population and Housing (CONAPO, 2006). 192

20 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera GRAPH 10 VALUES MEASURED BY MEANS OF THE SIGMOIDAL MODEL FOR THE STATE OF SINALOA ( ) Source: Measured data (INEGI, 2006) and author s model. Conclusions Demographic changes taking place in the coastal States of Mexico are only a small part of the variables that must be considered when performing long term planning studies tending to the sustainable development of the coastal zone. In terms of large figures, Mexico s total population experienced an increment of inhabitants between the years 2000 and percent of the said increment took place in the coastal States ( inhabitants). 193 January / March 2007

21 Papeles de POBLACIÓN No. 51 CIEAP/UAEM GRAPH 11 MEASURED AND ESTIMATED VALUES BY MEANS OF THE SIGMOIDAL MODEL FOR THE STATE OF MICHOACAN ( ) Source: measured data (INEGI, 2006) and author s model. The seven States with the most absolute growth in Mexico during that period contributed with 53.5 percent of the demographic increment registered. Baja California, Chiapas, Jalisco and Tamaulipas are coastal States that belong to this group. The coastal State that contributed the least to the country s growth was Michoacán, with a demographic growth of only inhabitants. This phenomenon is the result of the important immigration that takes place in the State. In terms of the projection of demographic growth, the Boltzian Sigmoidal used in this research presented for all the coastal States in general a good adjustment in respect to the value measured in the year

22 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera GRAPH 12 MASURED AND ESTIMATD VALUES BY MEANS OF THE SIGMOIDAL MODEL FOR THE SATE OF BAJA CALIFORNIA ( ) Source: measured data (INEGI, 2006) and author s model. A total population of 58.8 million people is estimated for the coastal States for the year 2030 (unadjusted method) and of 64.2 million for the year 2050 (adjusted model). If these estimations are confirmed, the Mexican coastal States population would increase seven times in the period between 1930 and This would mean that the pressure on the natural resources, goods and services needs would be increased, at least, in the same proportion. At a finer level of analysis, the study of the demographic dynamics must be taken both to the municipal level (as a second approach) and to the level of local communities. Unfortunately we only have censual information at municipal level and communities for the years 1990 and 2000 (data from 1980 were lost in the 1985 earthquake), this imposes severe restrictions from the point of view of the information statistical handling. 195 January / March 2007

23 Papeles de POBLACIÓN No. 51 CIEAP/UAEM GRAPH 13 DEMOGRAPHIC GROWTH FORECAST UNTIL THE YEAR 2050 FOR BAJA CALIFORNIA, JALISCO AND VERACRUZ USING THE BOLTZIAN-SIGMOIDAL MODEL Source: measured data (INEGI, 2006) and author s model. It is clear, from the performed analysis, that the national environmental policy for the sustainable development of seas and coasts, as well as the programs and plans of integral coastal management that come out of this policy, the marine and coastal organization processes performed or decreed, the environmental impact studies performed or evaluated, and the Mexican Official Regulations established, must take in consideration, in a special manner, the demographic changes experienced by the coastal States of Mexico. 196

24 Population growth estimulation for the coastal States of Mexico / I. Azuz and E.Rivera TABLE 7 ESTIMATED AND MEASURED VALUES ( ) FOR THE MEXICAN COASTAL STATES USING THE SIGMOIDAL MODEL ADJUSTED FROM THE COUNTING S DATA, 2005 Period West coast East coast Both coasts Source: measured data INEGI and CONAPO. Estimated data from the author s Sigmoidal model. 197 January / March 2007

25 Papeles de POBLACIÓN No. 51 CIEAP/UAEM Bibliography AUSUBEL, J.H. and P.S. Meyer, 1994, «Graphical representations of world population growth», Human Dimensions Quarterly, vol. 1, num. 2, Fall. CARRILLO, M., 2003, «Growth, life cycle and dynamic modelling», in Math and Comp, Modelling of Dynamic Systems, vol. 9, num. 2, June. CONAPO, 1999, Proyecciones de la población de los municipios, , Consejo Nacional de Población. CONAPO, 2005, Proyecciones de la población en México, , Consejo Nacional de Población, January 21 st, CONAPO, 2006, Resultados Preliminares del II Conteo de Población y Vivienda 2005, Com. núm. 024/06, February 13 th. INEGI, 1992, XI Censo General de Población y Vivienda, 1990, Instituto Nacional de Estadística, Geografía e Informática, Aguascalientes. INEGI, 1997, Conteo de Población y Vivienda, 1995, Instituto Nacional de Estadística, Geografía e Informática, Aguascalientes. INEGI, 2001, XII Censo General de Población y Vivienda, Tabulados Básicos, Instituto Nacional de Estadística, Geografía e Informática, Aguascalientes. INEGI, 2006, Población total según sexo , Instituto Nacional de Estadística, Geografía e Informática, Aguascalientes. LEDVIJ, M., 2003, Curve fitting made easy, The Industrial Physicist, April/May. MAKI, D. and M. Thompson, 1973, Mathematical models and applications, Prentice Hall. MARCHETTI, C., P.S. Meyer and J.H. Ausubell, 1996, «Human population dynamics revisited with the logistic model: How much can be modeled and predicted», Technological Forecasting and Social Change. PEARL, R. and L.J. Reed, 1920, Cited in Maki, D. and M. Thompson (1973), Mathematical models and applications, Prentice Hall. ZILL, D.G., 2006, Ecuaciones diferenciales con aplicaciones de modelado, Thomson. ZULLINGER, E., R. E. Ricklefs, K.H. Redford and G.M. Mace, 1984, «Fitting sigmoidal equations to mammalian growth curves», in Mammalogy, vol. 65, num. 4, November. 198

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