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

 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

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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

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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‚Äôs 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. Moƒçko≈ô (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

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