Local Deforestation Patterns in Mexico

An Approach using Geographiccally Weighted Regression

Jean Francois Mas and Gabriela Cuevas

Centro de Investigaciones en Geografía Ambiental, Universidad Nacional Autónoma de México,

Antigua carretera a Pátzcuaro # 8701, Col. Ex Hacienda de San José de la Huerta,

C.P. 58190, Morelia, Michoacán, Mexico

{jfmas, gcuevas}@ciga.unam.mx

Keywords: Deforestation, Geographically Weighted Regression, Mexico.

Abstract: This study identifies drivers of deforestation in Mexico by applying Geographically Weighted Regression

(GWR) models to cartographic and statistical data. A wall-to-wall multitemporal GIS database was

constructed incorporating digital data from Global Forest Change (2000-2012); along with ancillary data

(road network, settlements, topography, socio-economical parameters and government policies). The

database analysis allowed assessing the spatial distribution of deforestation at the municipal level. The

statistical analysis of deforestation drivers presented here was focused on the rate of deforestation during the

period 2007-2011 as dependent variable. In comparison with the global model, the use of GWR increased

the goodness-of-fit (adjusted R

) from 0.46 (global model) to 0.58 (average R

of GWR local models), with

individual GWR models ranging from 0.52 to 0.64. The GWR model highlighted the spatial variation of the

relationship between the rate of deforestation and its drivers. Factors identified as having a major impact on

deforestation were related to topography (slope), accessibility (road and settlement density) and

marginalization. Results indicate that some of the drivers explaining deforestation vary over space, and that

the same driver can exhibit opposite effects depending on the region.

1 INTRODUCTION

Mexico, with a total area of about two million

square kilometres, is a megadiverse country, but it

presents high rates of deforestation (FAO, 2001).

Various studies have attempted to assess land use /

cover change (LUCC) over the last decades (Mas et

al., 2004) but there have been few attempts to assess

the main causes of deforestation at national level

(Figueroa et al., 2009); (Pineda Jaimes et al., 2010);

(Bonilla-Moheno et al., 2013). Given the complexity

of Mexico territory, the processes of change and its

factors are expected to be different depending on the

region. Geographically Weighted Regression

(GWR) has been applied in exploring spatial data in

the social, health and environmental sciences. The

goal of this study is to evaluate the spatial patterns

of deforestation with respect to drivers reported to

influence LUCC using Geographically Weighted

Regression (GWR).

2 MATERIAL AND METHODS

2.1 Material

In order to elaborate the GIS database, the following

data were used:

 Map of forest loss from the Global Forest

Change 2000–2012 data base at 30 m resolution

(Hansen et al., 2013).

 Maps of ancillary data (digital elevation model,

slope, roads maps, human settlements, climate,

soils, municipal boundaries). (Figure 1)

 Socio-economic data from the National Institute

of Geography, Statistics and Informatics (INEGI

for its Spanish acronym) organized by

municipality (Population census for 2005 and

2010). (Figure 2)

 Government policies (rural and cattle-rearing

subsidies, and protected areas). (Figure 3)

GIS operations were carried out with the following

programs: ArcGIS (ESRI, 2011) and Q-GIS

(www.qgis.org/). Statistical analysis and graphs

Mas J. and Cuevas G..

Local Deforestation Patterns in Mexico - An Approach using Geographiccally Weighted Regression.

DOI: 10.5220/0005349000540060

In Proceedings of the 1st International Conference on Geographical Information Systems Theory, Applications and Management (GISTAM-2015), pages

54-60

ISBN: 978-989-758-099-4

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

were created using R (R Development Core Team,

2009). Geographically weighted regressions (GWR)

were carried out using the packages: gwrr (Wheeler,

2007 and 2012) and spgwr (Bivand and Yu, 2012) in

Figure 1: Average elevation of the municipalities.

Figure 2: Municipal population density in 2010.

Figure 3: Cattle-rearing subsidies (2007-2011).

2.2 Deforestation Rates and GIS

Database Elaboration

Deforestation rates were calculated at municipality

level (2456 municipalities) based in the Global

Forest Change 2000-2012 database (Hansen et al.,

2013). In this study, the rate of deforestation was

computed as the total area of forest loss during

2007-2011 normalized by the municipality area.

In order to determine which ancillary variables

are most likely to be indirect drivers of

deforestation, we calculated, for each municipality

various indices describing: population, economic

activities and the resources accessibility. These

indices were: a) Population density in 2010 (people

per km

); b) Density settlements (number of

settlements per km

); c) Index of marginalization,

which takes into account incomes, level of schooling

and housing conditions (CONAPO, 2010), d) Cattle

density, e) Goat density, f) Mean slope (degrees), g)

Mean elevation, h) Road density (km of road per

), i)Amount of governmental subsidies for

agriculture and cattle ranching (thousand of Mexican

pesos per km

), j) Proportion of municipality with

protected areas.

2.3 Statistical Analysis

Geographically Weighted Regression is a local

spatial statistical technique for exploring spatial

nonstationarity (Fotheringham et al., 2002). It

supports locally modelling of spatial relationships by

fitting regression models. Regression parameters are

estimated using a weighting function based on

distance in order to assign larger weights to closer

locations. Different from the usual global regression,

which produces a single regression equation by

summarizing the overall relationships among the

explanatory and dependent variables (for the whole

Mexican territory in that case), GWR produces

spatial data that express the spatial variation in the

relationships among variables. Maps that present the

spatial distribution of the regression coefficient

estimates along with the level of significance (e.g. t-

values) have an essential role in exploring and

interpreting spatial nonstationarity. Fotheringham et

al., (2002) provide with a full description of GWR,

and Mennis (2006) gives useful suggestions to map

GWR results.

The first stage of the study was correlation

analysis between explanatory variables using the

Spearman coefficient in order to discard highly

correlated variables. Due to the uneven distribution

and size of the municipalities, the weighting

LocalDeforestationPatternsinMexico-AnApproachusingGeographiccallyWeightedRegression

function used an adaptive kernel which selects a

proportion of the observations (k-nearest

neighbours) assigned to each municipality and

calculates the weights using a Gaussian model. The

optimal size of the bandwidth (in this case the

proportion of observations) was evaluated by

minimizing the root mean square error. A map was

elaborated for each explanatory variable showing the

value of the regression’s coefficients (color scaling

of the symbol) and statistical significance (gray

mask).

3 RESULTS

3.1 LUCC Monitoring

As shown in Figure 4: The rate of deforestation

varies over space. The coastal floodplains of the

Gulf of Mexico and the southern part of the country

exhibits high rates of deforestation.

Figure 4: Per municipality deforestation (2007-2011).

3.2 Geographically Weighted

Regression (GWR)

In this paper, we report the results of the GWR using

as dependent variable the rate of deforestation in the

period of 2007-2011. The weighting function was

based on a 5% of the observations. A global model

was fitted and obtained an adjusted-R

of 0.46. The

use of GWR slightly increased the strength in the

relationship in terms of the goodness-of-fit (adjusted

) to 0.58 (average R

of GWR local models), with

local GWR models with adjusted R

ranging from

0.52 to 0.64. Figure 5 presents the spatial

distribution of the goodness of fit.

Figure 5: Distribution of local R

Some variables such as population and road

density and slope exhibit a significant relationship

with the rate of deforestation for the whole territory.

As expected, the first two variables have a positive

effect on this proportion while slope presents a

negative relationship (steeper slope less

deforestation) also there is a "stronger" relationship

in flat regions, or with more recent deforestation

(Figure 6). Other explanatory variables have a more

contrasted pattern. In example, the marginalization

index presents a significant relationship with the rate

of deforestation. It presents a positive relationship in

the Baja California states, the border with the USA

and the north strip along the Gulf of Mexico and a

negative relationship in the center of Mexico (Figure

7).

Many studies have associated poverty and

deforestation (Rudel and Horowitz, 2013). The

region in the center south, where the relationship

between marginalization and deforestation is

negative is related to indigenous regions where

municipalities with higher marginalization indices

present lower deforestation rates. Previous

researches have reported that the most conserved

natural areas in Mexico are often located in poor

rural areas and/or community lands (Klooster 2000);

(Alix-Garcia de Janvry and Sadoulet, 2005);

(Figueroa et al., 2009); (García-Barrios et al., 2009).

With respect to the government policy variables,

protected areas (PAs) have no relationship to

deforestation in most of the territory, but where the

relation exists, it indicates that there is less

deforestation in municipalities with more protected

areas (Figure 8). Various studies reported

contrasting effects of PAs on changes (Pineda et al.,

2010); (Bray et al., 2008).

GISTAM2015-1stInternationalConferenceonGeographicalInformationSystemsTheory,ApplicationsandManagement

Figure 6: GWR coefficient and significance values for mean slope.

Figure 7: GWR coefficient and significance values for marginalization.

LocalDeforestationPatternsinMexico-AnApproachusingGeographiccallyWeightedRegression

Figure 8: GWR coefficient and significance values for protected areas.

4 DISCUSSION

Some limitations of this study have been identified.

Some of them are related with input data and with

the way information is summarized at municipality

level: i) Change data is based only on a drastic

change of land cover (forest loss), it does not

consider cover degradation. This factor has to be

considered during the results interpretation. For

example in some regions goat density is associated

with lower levels of deforestation, however it is

likely related with vegetation cover degradation

rather than deforestation. ii) The rate of

deforestation shows change from 2007 to 2011, but

the drivers variables (population, marginalization,

government subsidies) are from a particular date at

different times of the period depending on data

availability. The temporal issue cannot be totally

addressed due to the lack of information.

Additionally, in some cases, it could be interesting

to calculate rates of change of these indices. For

instance deforestation may be more related to the

increase of population density than to population

itself, iii) Another limitation is the averaging of

indices at municipality level which may end up with

a figure that does not reflect the actual situation over

much of the area. For instance, a municipality with

flat and steep slopes will present the average value

corresponding to moderate slope. Moreover,

deforestation can occur in small regions which

present very different features from the average

figure. A way to minimize those effect could be to

calculate the indices taking into account only the

forested area. For instance, average slope of

municipality forest area is used to explain

deforestation instead of the slope average over the

entire municipality, iv) Finally, as depicted in figure

4, the set of explanatory variables we used did not

allow to explain the dependent variable in a

satisfactory manner for the entire territory. More

drivers have to be taken into account for future

analysis.

Other limitations are related with the method

used and the deforestation process itself:

Deforestation is a complex process that depends on

interacting environmental, social, economic and,

cultural drivers. Some of them cannot be used into

the model because they are unable to be mapped.

Moreover, the GWR uses municipality information

to explain deforestation but is unable to take into

account shifting effects (deforestation in a given

GISTAM2015-1stInternationalConferenceonGeographicalInformationSystemsTheory,ApplicationsandManagement

municipality is due to the actions from inhabitants

from other municipalities) and effects at different

scale (as the GWR use the same bandwidth for all

the explanatory variables). It worth noting that some

drivers cannot act with very fuzzy spatial pattern or

no pattern at all (e.g. global economy effect such as

import/export of agriculture goods).

It is likely that the effect of a driver on a given

region is related to the time such driver has been

shaping the landscape and that different drivers have

affect at different temporal and spatial scales, which

makes the interpretation of the results difficult.

Considering the rate of deforestation during different

past periods of time will enable us to analyze the

dynamic of deforestation in its temporal and spatial

dimensions.

5 CONCLUSIONS

Some limitations of this study have been identified

and will be addressed in forthcoming researches.

However, results clearly show the advantages of a

local approach (GWR) over a global one, to assess

different drivers’ effect on LUCC over such a

complex and diverse territory as Mexico.

In future researches, alternative deforestation

rates will be computed, new explanatory variables

such as land tenure will be integrated into the model,

the effect of correlation between explanatory

variables at local scale will be tested and a workshop

will be organized to carry out deep interpretation of

the results.

ACKNOWLEDGEMENTS

This research has been funded by the Consejo

Nacional de Ciencia y Tecnología (CONACyT) and

the Secretaría de Educación Pública (grant

CONACYT-SEP CB-2012-01-178816) and

CONAFOR project: “Construcción de las bases para

la propuesta de un nivel nacional de referencia de las

emisiones forestales y análisis de políticas públicas”.

The authors would like to thank the four reviewers

for their careful review of our manuscript and

providing us with their comments and suggestion to

improve the quality of the manuscript.

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GISTAM2015-1stInternationalConferenceonGeographicalInformationSystemsTheory,ApplicationsandManagement