patterns of soil degradation in Mexico
Xanat Antonio-Nemiga2, Jose Alberto
and Martín Alfonso Mendoza-Briseño3
of Forest Sciences. Juarez University of Durango State.
Río Papaloapan and Blvd. Durango; Col. Valle del Sur; CP
34120; Durango, Dgo., México.
of Geography. Autonomus University of México State,
Cerro de coatepec s/n, Ciudad Universitaria. C.P. 50100.
de Postgraduados. Campus Veracruz. Carr Federal Km 88.5,
Accepted 31 January, 2011
The spatial pattern of soil degradation in México was
evaluated to test the hypothesis of non-random correlation.
For this purpose, data on the degree of soil degradation in
the 16,040 ecological systems in which the country is
divided was used to calculate the Moran coefficient. A
graphical analysis, based on the dispersion diagram and the
local indicator of spatial association, was also applied.
Soil degradation showed a positive and statistically robust
pattern of spatial auto-correlation, since the Moran
coefficient was able to synthesize 42.8% of the global
structure of linear correlation among the degrees of
degradation. The underlying variables that explain the
relationship remain to be identified.
Spatial autocorrelation, geostatistics, Geoda.
is a natural resource that is considered non renewable because of
the cost and difficulty involved in recovering it once it has been
degraded. As soil loss endangers ecological balance, investigation
of soil degradation processes is essential in order to develop
scientifically based plans for soil conservation. Recent studies
show that 64% of the soils in Mexico are degraded to a greater or
(CONAFOR, 2006). Soil degradation is one of the major threats to
ecosystem conservation worldwide, because it reduces the soil
potential for food production and leads to desertification and soil
Although, there are numerous technical reports concerning soil
degradation (Evelyn et al., 2008; Christopher et al., 2009),
spatial distribution aspects are often ignored, thus reducing the
ecological and practical importance of this information with regard
to future trends, constraint factors and environmental policies (Pompa,
Spatial information about the phenomenon enables identification of
spatial correlation patterns among data, and revelation of whether
the spatial distribution is random or auto-correlated (clustered or
dispersed). In order to design suitable strategies and actions for
soil management, robust information regarding the nature of soil
degradation is required, especially with regard to the causal agents
and conditions that induce erosion. Research on causal agents is of
prime importance because the design and operation of prevention
programs, based on awareness of risk and danger factors, requires
strong background knowledge and represents economic advantages for
large areas of land.
Autocorrelation can be defined as the influence of the coincidence
of similar values of a variable on nearby geographical spaces (Anselin,
2004). To test for autocorrelation in the spatial distribution of
soil degradation in Mexico, we chose the statistical method
developed by Moran (Moran, 1950), since several of the indexes used
to obtain a global estimation of this pattern are based on this
method (Greig, 1964; Pielou, 1969; Diggle, 1983; Upton and Fingleton,
1985; Krahulec et al., 1990; Condés and Martínez, 1998; Dale, 1999;
Liu, 2001). In addition, authors such as Acevedo and Velásquez
(2008) have stated that Moran’s index is still the most commonly
used. It had been applied in several different types of study, such
as the study of demographic trends (Martori and Hoberg,
2008), economic development of regions (Vilalta, 2003) and
electoral behavior (Vilalta, 2005).However, its application to soil
degradation patterns has been limited, especially in Mexico. We
therefore considered it appropriate to describe the characteristics
of the spatial distribution of soil degradation in México, to
provide a better interpretation of intrinsic factors that are
perhaps not visible in the field. The null hypothesis considered was
that the phenomenon of soil degradation is subject to non random
Vicinity criteria types.
Description of the study area
Mexico is located between latitudes of 14º32’ and 32º43’N
and longitudes of 86º42’ and 118º27’W. To the north, it
borders with the United States of America, to the south with
Guatemala and Belize, to the east with the Gulf of Mexico
and to the west with the Pacific Ocean (Figure 3).
The database was obtained from the National Forestry
Commission (CONAFOR, 2006) in a shapefile from 2006.
This shapefile contains data on the 16,040 terrestrial
systems of Mexico, which includes a classification of the
degree of soil erosion, evaluated in terms of the reduction
in the biological productivity of the land. The
classification considers the following levels:
1. Slight degradation: This land is optimal for forestry,
agriculture and livestock rearing and shows a slight,
perceivable reduction in productivity.
2. Moderate degradation: Land suitable for forestry,
agriculture and livestock rearing, although there is also a
perceivable reduction in land productivity.
3. Strong degradation: At farm level, degradation of this
land is so severe that its productivity is considered
irreversible, unless huge restoration efforts are applied.
4. Extreme degradation: Land productivity is unrecoverable
and it is not possible to restore the land, even with the
best management practices for soil erosion.
In order to detect and measure the spatial autocorrelation
of the deforested surfaces, I Moran’s coefficient
(1950) was applied. The values of the coefficient vary from
-1 to 1, although several authors recognize that it may
surpass both limits (Cliff and Ord, 1981; Upton and
Fingleton, 1985). The first value implies a perfect negative
correlation, whereas the second implies a
perfect positive correlation. A value of zero indicates
a totally random spatial pattern. To calculate the value of
the coefficient, the following equation was applied:
where Xi and Xj are the values taken
by X at i and j points, N is the data
population and Wij is the weight of the class at
distance d, which can be 1 if j is within the
class of distance d from the point i, or can
be 0 if said condition is not fulfilled (Camarero and Rozas,
In the ratio established in 1, the numerator shows the
covariance, whilst the denominator indicates variance, which
makes it a similar design to the Pearson coefficient of
correlation (Pearson, 1896). However, in this ratio, the
association of values at the data set is determined by a
matrix of distances (2), or by contiguity, which predefines
the neighboring values (the values for the coefficient
calculation); that is, the weights define the proximity of
each point evaluated.
To determine the vicinity within spatial units, the “Queen”
criteria was used (Figure 1), because of its contact
proximity in all directions (a maximum of eight neighbors).
To test the hypothesis of absence of a spatial pattern, I
Moran’s coefficient was located within a normal
curve of probabilities Z(I), and a test was carried
out to determine whether the spatial distribution of values
was random within n possible distributions (Vilalta, 2005).
A non-significant value of Z(I) will lead to acceptance of
such hypothesis, while a significant positive value reflects
a spatial pattern of positive autocorrelation. GEODA
software was used to implement this test. In addition, the
Scatter diagram of Moran was applied as an instrument of
graphical analysis (Anselin, 2003). The Local Indicator of
spatial association was also calculated to ensure that each
statistic obtained for each section provides information
related to the relevance of similar surrounding values.
According to Anselin (1995), the statistic used to test the
contrast of Local Spatial Association is defined as:
and where the added value j refers to the cluster of
neighboring units of i with respect to sample mean
the horizontal axis, Moran’s dispersion diagram of soil erosion
presents the observation of a normalized degree of soil erosion, and
over the vertical axis it shows the spatial delay in the same
variable, defined as the product between the observation vector of X
and the matrix of spatial weights (Figure 2).
that most observations are concentrated over the diagonal line that
crosses the upper right and lower left quadrants, it is evident that
there is a positive autocorrelation of 0.4276, which indicates that
the Moran statistic comprises 42.76% of the global structure of
linear association between the degrees of soil degradation. Although
the coefficient is not very high, the positive trend must be taken
into account, given the great diversity in the study area.
significance map of the local indicator associated with Moran’s
dispersion diagram (Figure 3) enables identification of regions with
numerous highly degraded areas, surrounded by zones with a similar
degree of degradation (high-high correspondence at Moran’s graph).
This correspondence is very common in Baja California and Nuevo
Leon, and may be related to the arid conditions in these states,
where the highest rates of degradation normally occur (Conafor,
2006; Pompa, 2008).
some regions, there is also a low degree of degradation associated
with similar neighbors (low-low situation); this is particularly
common in the Sierra Madre Occidental and the Central highlands.
However, low-high (which is a common pattern in the tropics at the
Gulf of Mexico) and high-low situations are also encountered.
Finally, regions without any association are also found (Figure 3).
positive association is not observed throughout the entire region,
and is restricted to certain regions. The Local Indicator of
Spatial Association is shown Figure 4 to reveal those regions with
high values of local spatial association. The intensity of this
indicator depends on the associated significance of these
Moran’s dispersion diagram for the degree of soil degradation in
The results indicate positive and significant autocorrelation,
and therefore a tendency for areas to be aggregated by the
degree of soil degradation. We can therefore assert with a
confidence level of 99% that this correlation is not random,
under the assumption of a normal distribution of Z probable
values. Furthermore, the legend of the cluster map in Figure 3
includes five categories: Not significant (Areas that are not
significantly degraded at a default
pseudo-significance level of
0.05), high-high (Highly degraded areas surrounded by other
highly degraded areas), low-low (Slightly degraded areas
surrounded by slightly degraded areas), low-high (Slightly
degraded areas surrounded by highly degraded areas), and
high-low (Highly degraded areas values surrounded by slightly
Soil is an important component of terrestrial ecosystems, which
justifies the search for the causes of its degradation. The
techniques applied reveal the spatial association in the degree
of soil degradation, providing new insight into soil erosion
association, as well as the location where said associations are
important: regions where the activities of soil recovery and
erosion control should be directed, as a function of the
spatiality correlated causative variables. The results of the
study verify how incorporation of the spatial dimension in the
evaluation of soil erosion improves comprehension of the nature
of the phenomenon. Further studies are required, according to an
observation by Zhang and Chaosheng (2008), who state that
spatial analysis of the data at several scales must be a vital
part of the search for the underlying reasons for the spatio-temporal
distribution of this process.
The results show how spatial association within highly degraded
areas is common in arid regions, which indicates the association
between climate variation and soil erosion (Conafor, 2006; Pompa,
2008), although further research is required to verify this. On
the other hand, low-low associations appeared to be associated
with the presence of dense forest coverage, which is an
important finding for the design of national soil conservation
The spatial pattern of soil degradation occurrence is a key
factor in understanding its dynamics, and presence of soil
erosion is determined by several biotic and non biotic factors,
however, the effects of each factor vary between ecosystems and
within spatial and temporal. Understanding the causal factors
and conditions in the geographical areas in which soil
degradation occurs is a key step in the development of
conservation and rehabilitation strategies.
Cluster map showing the associations between different degrees
of soil degradation in the study area.
Local Indicator of spatial association for the degree of soil
degradation in Mexico.
Spatial analysis has rarely been applied to soil degradation studies
and has more often been used to analyze trends in soil pollution (Zhang
2008; Chang and Heejun, 2008), spatial autocorrelation
of soil properties (Dray and Stéphane, 2008; Iqbal
2005; Buscaglia and Varco, 2003; Ducarme and Lebrun, 2004), soil
and Zartman, 2004),
spatial patterns of weeds and plague severity and occurrence in
several types of soil
Toepfer et al., 2007).
In all these cases, the studied units have shown some type of
spatial autocorrelation, thus confirming the law of Tobler (1970).
The findings of the present study are consistent with the
interactions revealed suggest the need to apply regression
procedures to search for the variables that may explain the
associations, since only the magnitude and localization of the
spatial autocorrelation has been described. This will lead to
hypotheses regarding the causal agents of the spatial pattern.
Nonetheless, careful revision of the procedure is required, because
several ecological processes may produce similar patterns of spatial
Acevedo I, Velásquez E (2008). Some concepts of
and exploratory analysis of spatial data. Ecos of Economy. 27.
Medellín, pp. 9- 34.
Anselin L (1995). Local indicators of
spatial association- LISA. Geogr Anal 27, pp. 93-115.
Anselin L (2003). GeoDa 0.9 User's
Guide. Spatial Analysis Laboratory, University of Illinos,
Urbana-Champaign, IL. USA.
Anselin L (2004). GeoDa 0.9.5-i
Release Notes. Spatial Analysis Laboratory department of
Agricultural and Consumer Economics, University of Illinois.
Buscaglia H, Varco J (2003).
Comparison of sampling designs in the detection of spatial
variability of Mississippi delta soils. Soil Sci. Soc. Am Diario,
Camarero JJ, Rozas V (2006). Spatial
surface-pattern analyses and boundary detection techniques applied
in forest ecology. Invest Agrar: Sist Recur For., 15(1): 66-87.
Chang H (2008). Spatial analysis of
water quality trends in the Han River basin, South Korea. Water
Research, KOREA (South), 42: 13.
Christopher D, Gormally MJ, Knutson
V, Vala J, Moran J, Doherty O, Mc Donnell R (2009). Factors
affecting Sciomyzidae (Diptera) across a transect at Skealoghan.
Ecología Springer, Ireland, 43(1): 117-133.
Cliff AD Ord JK (1981). Spatial
Processes: Models and Applications. Pion Ltd., London, p. 260.
Condés S, Martínez MJ (1998).
Comparative of most used Index´s for spatial analysis of trees in
forest issues. Invest. Agr: Sist. Recur. For. 7: 173-187.
Dale MR (1999). Spatial pattern
analysis in plant ecology. Cambridge University Press, Cambridge,
Dessaint F, Chadoeuf R, Rarralis O
(1991). Spatial Pattern Analysis of Weed Seeds in the cultivated
soil seed bank. J. Appl. Ecol., 28(2): 721-730.
Diggle PJ (1983). Statistical Analysis
of Spatial Point Patterns. Academic Press, London.
Dray S (2008). Spatial
ordination of vegetation data using a generalization of
Wartenberg’s multivariate spatial correlation, J. Veget. Sci.,
Ducarme X, Lebrun (2004). Spatial
microdistribution of mites and organic matter in soils and caves.
Biol. Fertil. Soils, 39(6): 457-466.
Efron D, Nestel D, Glazer I (2001).
Spatial analysis of entomopathogenic nematodes and insect hosts in a
citrus grove in a semi-arid region in Israel. Environ. Entomol.,
Evelyn R, Jüri K. Arno M (2008).
Spatial correlograms of soil cover as an indicator of landscape
heterogeneity. Ecol. Indic., 8(6): 783-794.
Greig SP (1964). Quantitative Plant
Ecology. Butterworth and Co., London.
Iqbal, Javed, Thomasson, John A
(2005). Spatial variability analysis of soil physical properties of
alluvial soils. Soil Sci. Soc. Am. J., 69(4): 1338-1350.
Krahulec F, Agnew AD, Agnew S, Willems
JH (1990). Spatial Processes in Plant Communities. SPB Academic
Publishers, The Hague.
Liu C (2001). A comparison of five
distance-based methods for spatial pattern analysis. J. Veg. Sci.,
Martori JC, Hoberg K (2008). News
spatial statistical techniques for detection of residential clusters
of inmigrant population. Scripta Nova, 263(12): 98.
Moran PA (1950). Notes on continuous
stochastic phenomena. Biometrika, 37: 17-23.
Mueller O, George W, Young, William C,
Whittaker, Gerald W (2008). GIS analysis of spatial clustering and
temporal change is weeks of grass seed crops. Weed Sci., 56(5):
Pompa GM (2008). Spatial distribution
of vegetation loss in Mexico´s arid ecosystems. Methods in ecology
and sistematic, 3(3): 13-22.
Pearson K (1896). Mathematical
contributions to the theory of evolution: III. Regression, heredity,
and panmixia. Philosophical Trans. Royal Soc., 187: 253-318.
Pielou EC (1969). An Introduction to
Mathematical Ecology. Wiley, New York.
Ping J, Zartman B (2004). Exploring
spatial dependence of cotton yield using global and local
autocorrelation statistics. Field Crops Res., 89 (2/3): 219-236.
Shaukat SS, Siddiqui I Ali (2004).
Spatial pattern analysis of seeds of an arable soil seed bank and
its relationship with aboveground vegetation in an arid region. J.
Arid. Environ., 57(3): 311.
Tobler W (1970). A computer movie
simulation urban growth in the Detroit region. Econ. Geogr., 46(2):
Toepfer SE, Michael E, Ren K, Ulrich U
(2007). Spatial clustering of Diabrotica virgifera virgifera and
Agriotes ustulatus in small-scale maize fields without topographic
relief drift. Entomol. Experi. Appl. U.S.A., 124(1): 61-75
Upton GJ, Fingleton B (1985). Spatial
data analysis by example, Vol. 1. Point Pattern and interval data,
John Wiley. UK.
Vilalta CJ (2003). Survey of regionals
differences of income in Mexico: an application of spatial analysis.
Economy, society and territory, 4(14): 317-340.
Vilalta CJ (2005). Spatial analysis of
urban electoral process and comparative approach on OLS and SAM
techniques regression. Demographic and Urban Surveys.
Zhang C (2008). Use of local Moran's I
and GIS to identify pollution hotspots of Pb in urban soils of
Galway, Ireland. Science of the Total Environment, Ireland,
WEB PAGES CONSULTED
Conafor, 2006. e-mapas system. Office of Forest Inventories and
Geomatics of CONAFOR.
http://www.cnf.gob.mx:81/emapas/SystemPolitics.aspx; consulted on
May 22nd, 2007.