Fuzzy Modeling of Migration from the State of Oaxaca, Mexico
Anais Vermonden and Carlos Gay
Programa de Investigación en Cambio Climático, Universidad Nacional Autónoma de México, CU, Mexico
Keywords: Fuzzy Logic, Migration, Oaxaca, Mexico, ANFIS.
Abstract: This study shows an important innovation with the use of fuzzy logic to develop models on the migration
factors occurring in the state of Oaxaca, México, since fuzzy logic has not been applied in this field.
Migration is a complex system as individuals make their own decision to migrate. The major factors causing
migration are: higher employment in the primary sector, high grades of unemployment, high
marginalization index, small communities, soil degradation, violence and remittance received. Another
tendency shown in these models is that municipalities in Oaxaca with greater levels of education are having
higher migration levels due to the lack of opportunities to continue studies or well-paid jobs. Climate
change may impose greater movement of people as it can worsen the already precarious soil situation. Even
if the models present some error in the calculation of the migration index, it made clear what other variables
should be included to show the impacts of climate change on migration.
1 INTRODUCTION
Oaxaca is located in southwest Mexico; it is divided
into 570 municipalities. Oaxaca is one of the poorest
states with 61.9% of the population living under the
poverty line and, has one of the highest rates of rural
migration. During the last three decades, the rate of
migration has increased considerably. There has
been a substantial movement of people from rural
areas to urban areas and the United States (USA).
Most of the migrants come from remote and
marginalized villages and have a low level of
education. Since 2005, it is estimated that over
80,000 people from Oaxaca live somewhere else in
Mexico (Juarez 2008). Those who migrated to the
United States (USA) concentrate in the states of
California and Illinois. In 2007, it was estimated that
the number of Oaxacans, residing in Los Angeles,
could be up to 250,000 (Kresge 2007).
Part of the economy of Oaxaca is based on
agriculture, mostly practiced communally in
“ejidos” (communal land used for agriculture, on
which community members possess and farm a
specific parcel) or similar arrangements. 30% of the
population is employed in agriculture, about 49% in
commerce and services and 21% in industry. The
commercial sector dominates the gross domestic
product with 65.4%, followed by industry/mining
with 18.9% and agriculture with 15.7% (INEGI
2013).
There are a number of causes for the migration
from Oaxaca, and some of the most significant are
lack of economic development, need for
diversification of income (remittance), ecological
deterioration, lack of educational opportunities,
marginalization and growing violence.
The lack of economic development is the main
cause for poverty and, migration is the best response
farmers have found to benefit their household and
communities by seeking better-paid and more secure
employment. In the early 90’s, when the North
American Free Trade Agreement (NAFTA)
initiated, the flood of cheap, subsidized American
corn caused the price of the crop to fall 70% in
Mexico (Wise 2010). The price of other crops such
as beans and coffee also fell. As the prices fell,
poverty rose causing the vanishing of subsistence
farming. Many left to work in the industry sector,
which became a complementary income in the
family economy, but salaries in this sector have also
fallen and the growing unemployment worsens the
already fragile family economy (Contreras 2004).
The decreasing demand for local crops and the
increasing large-scale agriculture had a detrimental
effect on the traditional agricultural practices and
land productivity. Environmental factors such as
changing rain patterns, droughts, floods, use of
chemicals, change of land use, add pressure on good
845
Vermonden A. and Gay C..
Fuzzy Modeling of Migration from the State of Oaxaca, Mexico.
DOI: 10.5220/0005135308450851
In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (MSCCEC-2014), pages
845-851
ISBN: 978-989-758-038-3
Copyright
c
2014 SCITEPRESS (Science and Technology Publications, Lda.)
farmland. People have historically left places with
harsh or deteriorating conditions.
Violence is a growing factor, especially in the
Mixteca region where political and agrarian conflicts
have surfaced. Also, community self-defenses are
getting organized in region of el Itsmo de
Tehuantepec to protect the communities from the
construction of wind parks and organized crime.
Migration is a complex system; many factors
take place in the personal decision to migrate. Fuzzy
logic is a powerful tool to better understand the
relationships between those many factors. It allows
the use of large qualitative and quantitative data sets
resulting in migration patterns and variations in
order to predict outcomes for the region and develop
decision-making tools. This is the first attempt of
using fuzzy logic to build a Migration Index.
2 METHOD
Fuzzy logic is a form of multi-valued logic;
approximate reasoning can be modelled, as fuzzy
variables may have a partial truth-value ranging
from 0 to 1 (Perfilieva et al. 1999). Furthermore,
linguistic variables may be used; these degrees can
be managed by specific functions. For this study
nine variables were used to describe migration.
These variables are: percentage of the economically
active population occupied (EAP), percentage of the
EAP working in the primary sector (SIM 2014),
educational index (CONEVAL 2012),
marginalization index, percentage of the population
living in localities with less then 5000 people,
percentage of the indigenous population (CONAPO
2014), average of the soil degradation (INEGI
2002), the rate of homicides (INEGI 2014), and the
percentage of households receiving remittances
(CONAPO 2014), all at municipality level. The
average of land degradation was calculated using the
map of land use, extracting agricultural practices and
grazing and averaging the degree of land
degradation in the areas within the municipality. The
migration intensity was calculated using the
information form the Instituto Nacional de
Estadística y Geografía (INEGI) (National Statistics
and Geography Institute), of total population
numbers of 2000 and 2010.
Due to the quantity of variables fuzzy clustering
will be used to determine the strength of the
association between the elements and the clusters.
For this study both the fuzzy c-means (FCM) and
subclustering will be used. The FCM is a clustering
technique wherein each data point belongs to a
cluster to some degree that is specified by a grade of
membership (Bezdec 1981). The subtractive method
is a fast one pass algorithm to estimate the number
of clusters and the cluster centres in a dataset (Chiu
1994). The subclustering best approximation to
reduce both errors to a minimum was ten clusters,
with a radii of 0.62 which is a vector that specifies a
cluster center's range of influence in each of the data
dimensions, assuming the data falls within a unit
hyperbox. The FCM method showed no reduction in
the calculated errors with the increase in clusters,
from 2 to 100, the results were the same. Five
clusters were used to generate the model to allow a
greater improvement with the use of ANFIS. From
three to five clusters there was an improvement
using ANFIS, five being the best number of clusters,
over six there were no notable improvements.
To be able to check the models, 75% of the data
was used to construct the models using GENFIS3
and GENFIS2 from MATLAB (MATLAB 2009),
which respectively used the FCM and Subclustering
method to generate the FIS’s. The resting 25% of the
data was used to check the models. Both models will
be improved using Adaptive Neuro Fuzzy Inference
System, or simply ANFIS, which is a neural network
based on Takagi-Sugeno fuzzy inference system. By
integrating both neural networks and fuzzy logic
principles, it has the potential to capture the benefits
of both in a single framework. It has the ability to
construct sets of fuzzy if-then rules to approximate
nonlinear functions. ANFIS also can appropriate
membership functions to generate the stipulated
input-output pairs (Jang 1993) to be used in the
model. The Neuro-adaptive learning techniques
provide a method to build a fuzzy model from the
information contained in a dataset. The fuzzy system
enables flexibility in the variables and the
representation of incomplete data, as membership to
a fuzzy set is denoted by the degree of membership
to the set. Since the ANFIS can deduce relationships
between the inputs/outputs. ANFIS forms an input
output mapping based both on human knowledge
(based on fuzzy if-then rules) and generated
input/output data pairs by using a hybrid algorithm
that is the combination of the gradient descent and
least square estimates (Jang 1993). The main
characteristic of the Sugeno inference system is that
the consequent, or output of the fuzzy rules, is a
function as shown in equation 1.
R1: If A is A1 and B is B1 the
(1)
f1=p1*a+q1*b+r1
R2: If A is A2 and B is B2 the
f2=p2*a+q2*b+r2
SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand
Applications
846
Figure 1: Diagram of a Sugeno model (Evaluation of two
fuzzy rules with two input variables, i.e. A and B).
(Raveendranathan 2011).
The first step combines a given input tuple
(Figure 1), x and y, through antecedent rules by
determining the degree to which each input belongs
to the corresponding fuzzy set. The min operator is
used to obtain the weight of each rule, which is later
used in the final output computation, f. Sugeno has
two differentiated set of parameters, the first set
corresponds to the input variable and the second to
the output function of each rule, i.e. pi, qi and ri.
ANFIS uses two optimisation algorithms to
automatically adjust the two sets of parameters.
Back-propagation (gradient descendent) to learn the
parameters of the antecedents (membership
functions) and least square estimation is used to
determine the coefficients of the linear combinations
in the rules’ consequents.
3 DATA
The data chosen for this study were: percentage of
the economically active population occupied (EAP),
percentage of the EAP working in the primary
sector, (SIM 2014), educational index (CONEVAL
2012), marginalization index, percentage of the
population living in localities with less then 5000
people, percentage of the indigenous population
(CONAPO 2014), average of the degradation of
soils (INEGI 2002), the rate of homicides (INEGI
2014), and the percentage of household receiving
remittances (CONAPO 2014), all at municipality
level.
These variables were chosen over the studies
directed over the years in different municipalities of
Oaxaca, like “Transnational Migration in Rural
Oaxaca, Mexico: Dependency, Development and
Household” (Jeffrey 2001), Contreras focused on the
Indigenous region of the Cuicateca (Contreras 2004)
only focuses on the Zapotec region, Bautista focused
on the region of the Central Valleys (Bautista 2011).
The study produced by Ana Margarita Alvardo
Juárez, Migration and poverty in Oaxaca sets four
important conditions for migration to happen: 1. The
existence of high rates of marginalization and
poverty; 2. The deterioration of rural activities
where more than half of the population is
economically active; 3. The lack of jobs well paid,
and low educational levels; and 4. Social and family
networks can promote the movement of people.
These are conditions repeated in the previous works
in the different regions. Therefore, from these
articles were selected the variables of percentage of
the EPA, percentage of the EAP working in the
primary sector, educational index, and the
percentage of household receiving remittances.
Another important migration happening everywhere
in Mexico (and the world) is the movement of
people from rural areas to urban areas (Lall et al.
2006), and (UNITAR 2010). Thus the variables of
percentage of the population living in localities with
less then 5000 people and percentage of the
indigenous population were introduced.
Figure 2: Graphs showing the input variables in blue and
the output variable in red.
Also, soil degradation, especially in the Mixteca
region, has caused the reduction in crop production,
leading to increase poverty and promoting migration
according to several non-profit organisations
(NGO’s) like Ecoinflexiones (Nuñez et al. 2013), the
World Wildlife Fund and government agencies such
as the Comisión Nacional Forestal (CONAFOR
2013).
According to the director, Rufino Domínguez, of
the Instituto Oaxaqueño de Atención al Migrante in
an interview with held in 2013 (Nssoaxaca 2013),
violence, within three municipalities, are causing
people to leave the communities where hundreds
have died and several have received death threats.
Many NGO’s, like Casa Collective, have reported
paramilitary violence, causing people to migrate to
safer areas (Jonathan 2008). The Drug War in
Mexico is an increasing factor of migration as
people flee the violence, this happens especially in
the region of the Itsmo de Tehuantepec region,
which is also the region were many migrates from
FuzzyModelingofMigrationfromtheStateofOaxaca,Mexico
847
Central America to cross to the USA (Basu et al.
2013), (Esteva 2007), and (Vogt 2013). The
information on homicides, provided by INEGI,
comes from the Secretariado Ejecutivo del Sistema
Nacional de Seguridad Pública (SESNSP), which
online database provides less information then the
one given by the INEGI’s online database, showing
inconsistencies and lack of information on different
crimes related to violence, such as rape, injuries
caused by knives and battery. The most complete
database was on homicides. The homicides index is
based on the proportion of the number of crimes on
the total population in each municipality.
4 RESULTS
The two models showed errors in the approximation
of the results. The Subtractive clustering method has
the lower training error of 0.1297 whilst the FCM is
0.1640. But the checking data error is higher for the
subtractive method with 0.1925 and the FCM is
0.1794. In figure 3, both results are compared to the
real values. The FCM model has five rules and the
subclustering model has six rules.
The two models show similar output surface,
when the EAP, who works in the primary sector,
tend to migrate more. This result was expected since
the working conditions have worsened with time. As
the workforce leaves, as the elderly and children stay
behind, the level of food production reduces, making
them more vulnerable and dependent on remittances
of their relatives working in other regions or abroad.
(Treviño-Siller et al. 2006). Another contributing
factor of migration of people working in the primary
sector is the degree of soil degradation, the tendency
shows that, the higher the level of degradation, the
higher the level of migration. It also shows that
when the index of marginalization is high, migration
will be high no matter which of the eight variables it
is paired with. The same tendency of higher level of
migration appears when the level of education is
higher, when the municipalities are under 5000
inhabitants since there are less services available
(also, municipalities with high percentage of
indigenous populations, as they tend to live in
smaller communities), and when municipalities have
higher percentage of remittances since there is
money to leave and a promise of a job somewhere
else. Homicides, in both models, also show a similar
surface, more homicides more migration.
Both the subtractive clustering model and the
FCM model were submitted to an improvement
using ANFIS. The training error for the subtractive
Figure 3: Graph showing both models, FCM in blue,
subtractive in red and the real data in green.
clustering model was 0.1239 but the checking error
increased 0.2171, for the FCM model the training
error to 0.1519, and the checking error is 0.1395.
The FCM model after being improved by ANFIS
recreated better the behaviour, see figure 4.
The rule six in the subclustering model and the
rule five in the FCM model are the same, if the
medium percentage of people occupied (40%) and a
lower percentage occupied in the primary sector
(30%) and a medium marginalization index (0.02)
and a higher education index (0.7) and low
percentage living in localities with less then 5000
habitants and a low percentage of indigenous
population and low soil degradation and a low
homicide rate and a low percentage of households
receiving remittances then there is a low inward
migration.
This analysis confirms the four conditions: the
higher the marginalization index, the smaller the
communities (rural areas), the tighter the social and
family network receiving remittances the higher the
percentage of migration and higher percentages of
the EAP working in the primary sector.
The results still show a significant error. Both
models had showed stabilization within the first 20
epochs in training, determining the need for more
variables to improve the index. Two municipalities
showed a greater outward migration index than the
one calculated, San Mateo Piñas and San Pedro
Jaltepetongo. In both municipalities, the loss of
productivity of agricultural lands has caused many to
migrate, due to the effects of floods (San Mateo
Piñas) and droughts (San Pedro Jaltepetongo)
causing damages both to the infrastructure and loss
of production. Both municipalities have violence
issues, which are mostly reported in the local news
and not reflected in the INGEI database. The
SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand
Applications
848
municipality of San Mateo Piñas has high levels of
corruption, their last municipality president was
charged several times by the magistrate for
embezzlement but remained free and was murdered
last year. Indices of flood and drought risk could be
introduced to improve the migration index. Both
municipalities have high grades of deforestation
making them vulnerable to climate impacts. Their
Municipality Development Plan considers
reforestation. Based on that information, the variable
of percentage of land without natural vegetation
could be added.
Corruption indices are at state level only. To
create a corruption index at municipality level would
require another study.
Figure 4: Graph showing the FCM model in red, the FCM
model after being trained in ANFIS in blue, the real data
in green.
The three municipalities that show the biggest
error in the inward migration index are San Miguel
Panixtlahuaca, San Pedro Comitancillo and San
Simón Zahuatlán. They receive more migrants then
calculated. The municipality of San Simón
Zahuatlán has the lowest percentage of labour
working in the primary sector, most work making
balls and hats providing them with a steady income.
It has one of the lowest homicide rates. It has a
temperate humid climate ideal for agriculture; many
are hired during the picking season as jornaleros.
Both San Miguel Panixtlahuaca and San Pedro
Comitancillo could be considered more urban
municipalities, both have higher-grade education
facilities and more health services. In San Miguel
Panixtlahuaca, the main crop is coffee. The
community is well organized and have certified their
coffee as organic. They sell their produce for export
getting better revenues even if the price of coffee has
fallen over the years. They hire jornaleros during the
picking season.
Other variables that could be included to
improve the index for high receiving municipalities
could be the number of schools at different levels,
health indexes such as child death rate and,
percentage of the EAP working in the other sectors
then the primary one.
5 CONCLUSION
The models show an innovative form to measure the
migration of the state of Oaxaca, Mexico. It is
important to note the tendencies that could help
develop adaptation plans to reduce the migration. Of
the four conditions stated by (Juarez 2008), one is
contradicted since the people with lower levels of
education are expected to be the ones who migrate
more, the analysis of the data shows otherwise, the
higher education level, the higher the migration rate.
This is due to lack of opportunities and well paid
jobs in the state as mentioned by (Contreras 2004).
This analysis confirms the four conditions: the
higher the marginalization index, the smaller the
communities (rural areas), the tighter the social and
family network receiving remittances the higher the
percentage of migration and higher percentage of the
EAP working in the primary sector.
Even with the lack of data on homicides, the
tendency clearly shows that higher levels of violence
will cause the population to migrate despite other
favourable conditions, as seen in figure 5.
Figure 5: Surface of the rules between the PEA and
homicides rates.
The model shows a tendency of people working
in the primary sector to migrate and the increasing
impact of soil degradation on migration patterns.
Land surface is an important part of the climate
FuzzyModelingofMigrationfromtheStateofOaxaca,Mexico
849
system. The interaction between land surface and the
atmosphere involves multiple processes and
feedbacks. It is frequently stressed that the changes
on vegetation type or cover can modify the
characteristics of the regional atmospheric
circulation and the large-scale external moisture
fluxes (Sivakumar et al. 2007). Climate change can
exacerbate the already hard conditions found in
regions, such as the Mixteca region, that have
deforested large areas and present high degrees of
soil degradation, causing violent agrarian and
political disputes, presenting the worst possible
scenario that could be attained in other regions of the
state of Oaxaca.
The downward spiral presented in the Mixteca
region, high degrees of soil degradation, high
percentage of the population working in the primary
sector, high levels of violence, high marginalization
index, result in high migration levels. This kind of
modelling can help design public policies and
adaptation measures to reduce vulnerability of the
remnant population and prevent the Mixtecan
scenario to be reproduced in other regions of the
state.
The introduction of variables of extreme events
could improve the models to better understand the
future impacts of climate change on migration.
Possible adaptation measures could be implemented
with the use of more environmental indices to
facilitate the understanding of the impacts on human
migration.
ACKNOWLEDGEMENTS
The present work was developed with the support of
the Programa de Investigación en Cambio Climático
(PINCC) of the Universidad Nacional Autónoma de
México and the University of Berkley California.
REFERENCES
Basu, S. and S. Pearlman (2013). "Violence and
Migration: Evidence from Mexico’s Drug War."
Available at SSRN.
Bautista, J. A. (2011) Globalizacion Y Estrategias De
Desarrollo Rural Sostenible En Las Unidades
Socioeconomicas Campesinas De Oaxaca México.
Bezdec, J. C. (1981). Pattern Recognition with Fuzzy
Objetive Function Algorithms. New York, Plenum
Press.
Chiu, S. L. (1994). "Fuzzy Model Identification Based on
Cluster Estimation." Journal of Intelligent & Fuzzy
Systems 2(3): 267-278.
CONAFOR, Comisón Nacional Forestal. (2013)
Degradación de suelos merma producción de
alimentos: Conafor.
CONAPO, Consejo Nacional de Población. (2014).
México en Cifras.
CONEVAL, Consejo Nacional de Evaluación de la
Política de Desarrollo Social (2012). Medición de la
Pobreza.
Contreras, A. N. (2004). "Migración, globalización y
perspectiva poblacional en la zona indígena Cuicateca,
Oaxaca." El cotidiano.
Esteva, G. (2007). "The Asamblea Popular de los Pueblos
de Oaxaca A Chronicle of Radical Democracy." Latin
American Perspectives 34(1): 129-144.
INEGI, Instituto Nacional de Estadística y Geografía
(2002). Land degration. Degradación del medio
ambiente. SEMARNAT and C. d. Postgraduados.
INEGI, Instituto Nacional de Estadística y Geografía.
(2013). México en Cifras. Oaxaca.
INEGI, Instituto Nacional de Estadística y Geografía
(2014). México en Cifras.
Jang, J.-S. R. (1993). "ANFIS: adaptive-network-based
fuzzy inference system." Systems, Man and
Cybernetics, IEEE Transactions on 23(3): 665-685.
Jeffrey, H. C. (2001). "Transnational Migration in Rural
Oaxaca, Mexico: Dependency, Development, and the
Household." American Anthropologist 103(4): 954-
967.
Jonathan (2008) Paramilitary Violence and Migration in
Rural Oaxaca: The View of Impunity from Vista
Hermosa. Analysis Derechos Humanos Immigration
Indigenous Rights Oaxaca.
Juarez, A. M. A. (2008). "Migracion y pobreza en
Oaxaca." El cotidiano 148: 85.
Kresge, L. (2007). "Indigenous Oaxacan Communities in
California: An Overview." California Institute for
Rural Studies, noviembre, en http://www. cirsinc.
org/Documents/Pub 1107.
Lall, S. V. and H. Selod (2006). Rural-urban migration in
developing countries: A survey of theoretical
predictions and empirical findings, World Bank
Publications.
MATLAB (2009). MATLAB. Natick, Massachusetts, The
MathWorks Inc.
nssoaxaca (2013). Violencia causa de migración en la
Mixteca. Mexico.
Nuñez, D. and G. Marten (2013) México - Región de la
Mixteca (Oaxaca) – Combatiendo la Desertificación
con Reforestación Comunitaria y Agricultura
Sustentable.
Perfilieva, I. and J. ô. Moƒçkoô (1999). Mathematical
principles of fuzzy logic, Springer.
Raveendranathan, K. (2011). Adaptive Filtering
Applications. L. Garcia.
SIM, S. d. I. M. (2014). Sistema de Información
Municipal, Gobierno de Oaxaca.
Sivakumar, M. V. and N. Ndiang'Ui (2007). Climate and
land degradation, Springer.
Treviño-Siller, S., B. Pelcastre-Villafuerte, et al. (2006).
"Experiencias de envejecimiento en el México rural."
SIMULTECH2014-4thInternationalConferenceonSimulationandModelingMethodologies,Technologiesand
Applications
850
salud pública de méxico 48(1): 30-38.
UNITAR (2010) Fact-Sheet on Climate Change and
Migration.
Wise, T. A. (2010) The impacts of US agricultural policies
on Mexican producers. Subsidizing Inequality.
Vogt, W. A. (2013). "Crossing Mexico: Structural
violence and the commodification of undocumented
Central American migrants." American Ethnologist
40(4): 764-780.
FuzzyModelingofMigrationfromtheStateofOaxaca,Mexico
851