Does community-based forest ownership favour conservation of tree species diversity? A comparison of forest ownership regimes in the Sierra Madre Occidental, Mexico

Forest Ecology and Management 363 (2016) 218–228

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Does community-based forest ownership favour conservation of tree species diversity? A comparison of forest ownership regimes in the Sierra Madre Occidental, Mexico Ramón Silva-Flores a, José Ciro Hernández-Díaz b, Christian Wehenkel b,⇑ a Doctorado Institucional en Ciencias Agropecuarias y Forestales, Universidad Juárez del Estado de Durango, Boulevard del Guadiana No. 501, Ciudad Universitaria, C.P. 34120 Durango, Dgo., Mexico b Instituto de Silvicultura e Industria de la Madera, Universidad Juárez del Estado de Durango, Boulevard del Guadiana No. 501, Ciudad Universitaria, C.P. 34120 Durango, Dgo., Mexico

a r t i c l e

i n f o

Article history: Received 16 October 2015 Received in revised form 20 December 2015 Accepted 28 December 2015

Keywords: Communal forest Private forest Forest conservation Hill’s family Diversity profile Simpson diversity Silhouette interpretation Calinski–Harabasz criterion

a b s t r a c t It is not clear whether any particular type of forest land ownership is better than another regarding the quality of natural resource management. However, some researchers have found that communal ownership is efficient for this purpose, providing all members agree to establish operational rules and apply these in an atmosphere of cordiality and respect. In Mexico, 26% of the forests are privately owned, 4% are publicly owned and the remaining 70% are owned and managed by rural communities known as Ejidos and Comunidades. Studies of how forests and forest management may differ in relation to the type of land ownership in Mexico are scarce. Research on differences in tree species diversity in Mexican forests is desirable because species diversity is an important index in community ecology and may be affected by forest management. Moreover, tree species diversity is used as a biodiversity indicator in various monitoring schemes for sustainable forest management. In order to help resolve the lack of information regarding possible differences in forest management in relation to land ownership type in Mexico, the objectives of this study were as follows: (1) to identify groups of climatic, physiographical and social conditions that are almost homogeneous but widely separated from each other, and (2) to determine whether the type of forest land ownership affects tree species diversity within each group. Vegetationrelated data on 1592 plots in a forest area of about 6.33 million hectares were obtained from the Mexican National Forest and Soil Inventory. We used k-means clustering algorithms and the Affinity Propagation clustering, in an attempt to compare tree species diversity in communally and privately owned land. Finally, we used the Kruskal–Wallis rank sum test and a permutation test to compare the mean values of the tree species diversity in each cluster of similar, special conditions identified. There were no significant differences in the mean values of tree species diversity between the two types of forest land ownership. Thus, the study findings did not support the hypothesis that tree species diversity tends to be higher in communally owned forests than in the privately owned forests in the study area. Future research is needed to address the following: (1) the effect of land ownership regime on forest fragmentation, (2) agreements among diverse stakeholders about the type of benefits derived, and (3) improvement of public policies aimed at cost-effective sustainable forest management, considering land ownership. Ó 2015 Elsevier B.V. All rights reserved.

1. Introduction Mexico is one of the ten countries in the world with the largest area of primary forest. However, between 1990 and 2010 it was also one of the five countries with the largest net annual loss of ⇑ Corresponding author. E-mail addresses: [email protected] (R. Silva-Flores), [email protected] (J.C. Hernández-Díaz), [email protected] (C. Wehenkel). http://dx.doi.org/10.1016/j.foreco.2015.12.043 0378-1127/Ó 2015 Elsevier B.V. All rights reserved.

those forests, along with Brazil, Gabon, Papua New Guinea and Indonesia (Global Forest Resources Assessment, 2010). About 50% of the land in Mexico is degraded to some extent and is prone to soil erosion by the action of water or wind (SEMARNAT, 2005). The level of degradation is strongly related to deforestation and the selective extraction of timber species, among other anthropogenic causes (Global Forest Resources Assessment, 2010). Deforestation and degradation also lead to fragmentation and loss of biodiversity (Mas and Correa, 2000).

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In classical economics, four types of property ownership regimes are recognised: private, communal, public and free access (Tietenberg, 2000). In Mexico, 26% of the forests are privately owned, 4% are publicly owned and the remaining 70% are owned and managed by rural communities known as Ejidos and Comunidades, which manage these forests with some level of governmental control (Global Forest Resources Assessment, 2010; Thoms and Betters, 1998). An ejido in Mexico is a land owned and managed by a group generally comprising between 50 and 150 people; exceptionally large ejidos have more than 1000 shareholders (ejidatarios). The Comunidades system of land tenure is integrated and managed in a very similar way to the ejidos. Both groups (hereafter referred to as communal property owners) are represented by a governing board, appointed at a general assembly of the members. Communally owned forest land is usually managed for common use, and important decisions are only reached after discussions involving group members (Ley Agraria, 2012). By contrast, decisions regarding privately owned property are made by the individual owner and are therefore reached more easily. However, in Mexico, the same government forest policies apply to communally and privately owned land and the same technical advisers usually handle both types of properties, with similar technical criteria. Is usually thought that secure land tenure acts as an incentive to owners to invest time and resources in better forest management, which suggests the need to design and adopt efficient and secure mechanisms of land tenure that may contribute to reducing deforestation and degradation (Global Forest Resources Assessment, 2010). There is no evidence indicating that any particular type of land ownership is better than another in terms of management of natural resources over time (Baland and Platteau, 1996); however, some researchers in the field advocate the private ownership regime, indicating that this model will probably be efficient because of the smaller number of stakeholders usually involved (Tietenberg, 2000). In a very small study (184 ha) of soil and vegetation condition in Honduras, Tucker (1999) reported minor differences between four privately owned and two communally owned forests at the aggregate level. This author also found that, in some sites, communal ownership placed some limitations on residents’ use of the land and successfully prevented use of the forest by non-residents. At the same time, some private forest owners made decisions that restrained forest development or allowed exploitation. Studies of how forests and tree species diversity may differ in relation to the type of land ownership in Mexico are scarce. Research on differences in tree species diversity in Mexican forests is desirable because species diversity is an important index in community ecology (Myers and Harms, 2009) and may be affected by forest management (Lindenmayer et al., 2006; Nagaike, 2012). Moreover, tree species diversity is used as a biodiversity indicator in various monitoring schemes for sustainable forest management (Zilliox and Gosselin, 2014). In ecology, only a few diversity measures are commonly used, e.g. the Shannon index (Shannon, 1948), the Simpson index (Simpson, 1949) and species richness (Whittaker, 1972). In addition, several measures can be transformed into members of a family of explicit diversity indices, also known as Hill’s family (Hill, 1973; Gregorius, 1978) or Rényi-diversity (Zyczkowski, 2003; Jost, 2006, 2007; Gregorius, 2010). In order to help resolve the lack of information regarding possible differences in forest management in relation to land ownership type in Mexico, the objectives of this study were as follows: (1) to identify groups of climatic, physiographical and social conditions that are almost homogeneous but widely separated from each

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other, and (2) to determine whether the type of forest land ownership affects tree species diversity within each group. We tested the hypothesis (H0) that community-based forest ownership tends to conserve higher tree species diversity (characterised by three measures) than private land ownership in the Sierra Madre Occidental. In order to test this hypothesis, we assumed that the priority and degree of interest in the conservation and improvement of forest resources will differ between land ownership types. 2. Materials and methods 2.1. Study area The study area is located in the portion of the Sierra Madre Occidental (SMO) that crosses the west side of the state of Durango (Mexico) (22°200 4900 N–26°460 3300 N; 103°460 3800 W–107°110 3600 W) (Fig. 1). The SMO mountain range is situated between the Neotropical and Holarctic ecozones and occupies a forest area of about 6.33 million hectares in the state of Durango. It features a high diversity of flora and fauna (WWF, 2001; Rzedowski, 2006), including 21 different species of pine, 37 species of oak and many other tree species (Wehenkel et al., 2011; González-Elizondo et al., 2012). The elevation ranges between 390 and 3156 m (average 2244 m) above sea level in the study area. The climate ranges from temperate to tropical, with annual rainfall between 445 and 1450 mm and an annual average of 917 mm. The mean temperature varies from 8.2 to 26.2 °C, with an annual average of 13.3 °C (Rehfeldt, 2006; Sáenz-Romero et al., 2010; Rehfeldt et al., 2006). The predominant types of vegetation are pine-oak forests, often mixed with Pseudotsuga menziesii, Arbutus spp., Juniperus spp., and other tree species (González-Elizondo et al., 2012; SilvaFlores et al., 2014). 2.2. Sampling sites and variables The vegetation data were obtained from the National Forestry Commission (CONAFOR), which is the body responsible for carrying out the National Forest and Soil Inventory in Mexico. The sampling design included approximately 25,000 clusters of sampling sites throughout the whole country, distributed in a 5  5 km grid in forested areas (CONAFOR, 2004). Of the 1737 conglomerates located in the state of Durango, 1592 were located in forests in the SMO and were used as the main sampling plots in this study. Each of these plots consisted of four circular subplots, referred to as sampling sites; each site covers 400 m2 (Fig. 2). In each study site, we considered the following ten explanatory variables in order to test the hypothesis (Ho): longitude (LONG, degrees), latitude (LAT, degrees), elevation above sea level (ELEV, masl), geographical aspect (ASP, azimuth), slope (SLO, percent), mean annual precipitation (MAP, mm), degree days >5 °C (DD5, degree days), annual aridity index (AAI, fraction), total population in the nearest town (POB, number) and distance to the nearest town (DIST, m) (Table 1). The first five variables represent the site characteristics and location, while the other five describe climatic and social aspects. The dependent variable was the total number of trees per species. The trees considered in the inventory were of minimum height 3.0 m and minimum diameter of 7.5 cm at breast height (1.30 m) (DBH). In total 1289 conglomerates (81%) were located in 321 communally owned properties and 303 conglomerates (19%) were identified in 263 private properties. Each communally owned property in the study area typically covers an average of 14,473 ha and each privately owned property covers about 1379 ha.

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Fig. 1. Location of the study area in the Sierra Madre Occidental, Durango (Mexico). Geographical distribution and vegetation types in the sample plots (clusters) in the communally owned blue triangles) and privately owned (yellow circles) forest land. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

2.3. Climate variables

Fig. 2. Design of each sample plot (conglomerate) and corresponding sites in the National Forest and Soil Inventory (modified from CONAFOR, 2004). A conglomerate includes four sites (400 m2 each) distributed in a reverse ‘Y’ pattern. Abbreviations: Az = Azimuth, m = meter, N = North, SE = Southeast, SW = Southwest.

One of the most important patterns in ecology is in broad-scale variation in taxonomic richness in relation to climate and geography (Wright et al., 1993; Hawkins et al., 2003). The climatic variables at each conglomerate were estimated using the ANUSPLIN software, which is based on a model developed by Hutchinson (Hutchinson, 1991, 2004). We used Rehfeldt’s climate model (Rehfeldt, 2006; Sáenz-Romero et al., 2010; Rehfeldt et al., 2006), which produces standardised monthly estimates of total precipitation and mean, minimum and maximum temperature, using data from about 6000 weather stations (183 of which are in Durango). The data used to construct this model were collected over a period of 30 years (1961–1990), which is a sufficient length of time to enable estimation of the average values of the modelled climatic variables for each conglomerate. It also enables detection of any variations that may occur in these variables, which affect both communally and privately owned property in the same way and to the same extent. The software described can be used to predict the climatic variables at specific locations identified by latitude, longitude and elevation, and also to predict climate along gridded surfaces. Point estimates were obtained using a web interface (http://forest.moscowfsl.wsu.edu/climate/),

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Table 1 Physiographical, climate and social variables, the total number of tree species, the effective number of tree species, and the number of prevalent tree species considered in the study and the corresponding average, minimum and maximum values and standard deviations for each type of ownership.a Variablea

a

Unit

Communally owned forest

Privately owned forest

Mean

Standard deviation

Minimum value

Maximum value

Mean

Standard deviation

Minimum value

Maximum value

Longitude Latitude Elevation above sea level Geographical aspect Slope

LONG LAT ELEV ASP SLO

Degrees Degrees m Azimuth (degrees) Percent

105.60 24.51 2209 174.0 32.6

0.69 1.08 527 100.8 21.2

107.15 22.40 390 0.0 0.0

104.07 26.72 3156 359.5 120.2

105.45 24.64 2393 172 27.0

0.69 0.99 353 103.7 19.8

107.10 22.90 594 0.0 0.0

104.08 26.81 2981 358.3 126.1

Annual average precipitationb Degree days >5 °Cb Annual aridity indexb

MAP DD5 AAI

mm Degree days Degree days0.5 ⁄ mm1

928 3266 0.064

214 1375 0.019

445 1542 0.030

1448 7640 0.150

866 2852 0.066

229 921 0.023

452 1528 0.030

1450 6987 0.150

Total population in the nearest town Distance to the nearest town

POB

260

315

100

2908

369

578

100

4761

DIST

Number of residents m

7808

5394

355

31,315

9010

4450

727

29,044

v0 v2

– –

6.47 3.47

2.87 1.63

1 1

17 9.71

6.71 3.61

2.82 2.50

1 1

15 9.03

v1

–

2.40

0.98

1

5.87

1.61

1.02

1

6.92

Total number of tree species Effective number of tree species Number of prevalent tree species b

Abbreviation

Kruskal–Wallis test revealed differences in physiographical, climate and social variables between the communally and privately owned properties (P-value = 0.000006). Estimated for a 30-year period (1961–1990).

in which geographical coordinates and elevation were captured, for each conglomerate, to generate weather surfaces. The climatic variables considered in the present study included the annual aridity index (AAI), calculated as the ratio between the square root of degree days >5 °C (DD5) and the mean annual precipitation (MAP), and also LONG and ELEV (Table 1), for the following reasons: (i) these variables were significantly related to tree species diversity in the state of Durango and, (ii) there was no problem with collinearity between the variables (r < 0.8; SilvaFlores et al., 2014). Higher values of AAI indicate a more arid climate. Sáenz-Romero et al. (2010) noted that AAI is a powerful climatic variable for describing and predicting the distribution of pine species. 2.4. Social factors To analyse the impact that human population may have on the diversity of tree species, two variables were included in the database. The first is the total population of the nearest town (POB), including men and women of all ages. Only localities with more than 20 people were considered. The location of towns and the population data were obtained from topographic maps produced by the National Institute of Statistics, Geography and Informatics (http://www.inegi.gob.org.mx/geo/contenidos/topografia). The other social variable analysed was the distance to the nearest town (DIST), which refers to the shortest distance between a cluster and the closest town. This distance was measured with ARCGIS software by using the same source of information described for the previous variable. 2.5. Species diversity Species diversity was calculated with the range number of Hill, also called Hill’s family or diversity profile va (Hill, 1973; Gregorius, 1978), where a is a real number ranging from zero to infinity. The general concept underlying va is that the most frequent tree species determines the diversity of a collection to a greater degree than the less frequent tree species and that, the extent to which this is true increases with increasing values of the parameter a. Among the characteristics of a diversity measure, the most desirable is that va satisfies the following requirements, irrespective of

the value of a: (i) for a given number of tree species, va assumes its largest value exactly when all these tree species are equally frequent, and this value equals the number of tree species; (ii) va increases when two tree species approach equal frequencies; and (iii) va increases when one tree species is subdivided into several varieties. Considered as a function of a, va describes a diversity profile for each frequency distribution. The following are the most illustrative values of the subscript a in such diversity profiles: (i) a = 0, where the diversity is equivalent to the total number of tree species; (ii) a = 2 indicates the effective number of tree species, and (iii) a = 1, where only the most frequent (prevalent) tree species determines the diversity. In the present study, the diversity profiles are represented by the three diversity levels for each sample plot. Thus, each community was characterised by three measures: the total number of species (v0) known as tree richness, the effective number of tree P species (v2) inherent in Simpson diversity (D = pi2) (Simpson, 1949), and the number of prevalent tree species (v1) (Gregorius, 1978). All tree species are equally abundant when v0, v2 and v1 have the same value. The value of va is estimated using the following expression (where pi = relative frequency of a tree species i):

ma ¼ ma ðpÞ ¼

X pai

1 !1a

ð1Þ

i

2.6. Data analysis During construction of the database, all the sites without trees and sites of unknown ownership type (in total 40 conglomerates) were excluded from the analysis. The Spearman’s coefficient (rs) was first calculated to determine how tree species diversity is correlated with DIST, ASP, SLO, and POB. The relationships between ELEV, MAP, DD5, LONG and AAI and the three estimates of tree species diversity have been modelled and interpreted in a previous study (Silva-Flores et al., 2014). The two types of property ownership were unequally distributed in the study area (Fig. 1). Moreover, these two types were generally applied in areas with significantly different environmen-

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Table 2 Mean values and standard deviation of the ten variables studied within two, three and 13 clusters (of conditions that are almost homogeneous in each cluster but sufficiently different between clusters) calculated by the algorithms of k-means clustering, along with silhouette interpretation (SI), application of the Calinski–Harabasz Criterion (CHC) and use of Affinity Propagation (AP) clustering (with the input preference to the 0 quantile of the input similarities). ⁄

Cluster

COMM

PRIV

SI

1

282

17

2

1006

287

1

627

191

2

403

99

3

258

14

1

101

27

2

82

65

3

177

49

4

111

14

5

89

5

6

135

31

7

108

20

8

16

20

9

100

20

10

89

28

11

107

11

12

80

13

13

93

1

CHC

AP

STAT

LONG

LAT

ELEV

MAP

DD5

AAI

POB

ASP

SLO

Mean Std desv Mean Std desv

105.74 0.88 105.53 0.63

23.93 1.01 24.67 1.03

1381 445 2443 233

1095 158 875 209

5418 1096 2671 648

0.07 0.01 0.06 0.02

207 183 298 412

DIST 6441.3 4817.8 8406.5 5274.3

187 104 171 101

46.7 23.46 28.05 18.79

Mean Std desv Mean Std desv Mean Std desv

105.35 0.64 105.82 0.50 105.77 0.89

24.08 0.74 25.59 0.70 23.96 1.00

2446 219 2413 273 1323 422

987 175 703 129 1096 157

2612 626 2829 704 5578 1005

0.05 0.01 0.08 0.02 0.07 0.01

305 392 281 434 209 188

6808.2 3829.5 10976.0 6239.7 6310.5 4676.1

167 98 178 104 185 104

27.3 18.7 30.3 19.9 46.5 23.0

Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv Mean Std desv

105.68 0.36 104.91 0.32 105.12 0.32 106.10 0.25 106.24 0.21 105.78 0.36 104.44 0.21 105.67 0.52 106.09 0.44 105.70 0.36 106.55 0.40 105.99 0.38 104.85 0.35

25.66 0.70 24.05 0.44 23.68 0.40 25.81 0.42 25.49 0.28 24.77 0.51 23.05 0.29 24.51 0.90 24.62 0.62 25.75 0.67 24.79 0.54 24.44 0.66 22.91 0.33

2245 222 2484 171 2449 251 2710 182 2411 257 2537 153 2180 282 2437 221 2431 234 2295 226 1009 319 2136 276 1436 340

608 59 769 67 999 108 768 75 934 119 960 122 822 129 1017 247 1209 113 611 57 1178 102 1162 130 989 138

3332 528 2747 337 2610 541 2037 294 2504 678 2194 277 3922 547 2506 645 2423 633 3207 527 6230 613 3086 782 5521 901

0.10 0.02 0.07 0.01 0.05 0.01 0.06 0.01 0.05 0.01 0.05 0.01 0.08 0.01 0.05 0.02 0.04 0.01 0.09 0.02 0.07 0.01 0.05 0.01 0.08 0.01

205 131 253 212 262 224 217 188 171 106 222 179 306 333 2322 611 260 206 236 201 185 121 195 111 247 252

7719.2 3712.8 11033.6 4340.5 5487.8 2875.8 7556.0 3741.3 20996.9 4874.0 7783.9 3339.7 6520.4 3449.8 7069.6 4115.5 5041.7 2754.1 9787.8 4109.9 5790.5 4690.2 5929.6 3367.2 7031.5 4106.7

265 69 132 93 165 90 138 93 178 104 240 71 166 105 148 80 95 70 102 72 173 106 226 87 218 97

22.6 14.4 20.5 15.9 22.6 15.9 26.0 16.7 31.8 20.4 23.3 14.3 28.7 17.1 34.1 24.6 34.3 15.5 40.5 21.9 40.5 20.4 60.1 20.3 53.1 22.5

⁄

= Cluster method, Cluster = Number of the cluster, COMM = Number of conglomerates located in communal property, PRIV = Number of conglomerates located in privately owned property, STAT = Mean values and standard deviation for each variable studied by the cluster approach, LONG = Longitude in decimal degrees of the location of the conglomerate, LAT = Latitude in decimal degrees of the location of the conglomerate, ELEV = Elevation in metres above sea level, MAP = Annual average precipitation, DD5 = Degree days >5°C, AAI = Annual aridity index, POB = Total population in the nearest town, DIST = Straight distance in metres to the nearest town, ASP = Geographical aspect (Azimuth) and, SLO = Average slope, as a percentage.

tal conditions, which should promote different degrees of tree species diversity (Silva-Flores et al., 2014) irrespective of any differences in forest management (Table 1). Various types of cluster analyses were therefore carried out to ensure that comparison of the different tree species diversity measurements (in communally and privately owned land) were done under similar specific environmental conditions, defined by the variables LAT, LONG, ELEV, MAT, DD5, AAI, POB, DIST, ASP and SLO. The definitions of these variables and their mean, minimum and maximum values and standard deviations are included in Table 1. In order to detect groups of site conditions that are almost homogeneous inside each cluster but clearly different from any other clusters, we used k-means clustering algorithms (Hartigan and Wong, 1979) along with the recent Affinity Propagation (AP) clustering technique (with the input preference to the 0 and 0.5 quantile (q) of the input similarities) (Bodenhofer et al., 2011). We also applied silhouette interpretation (SI) (Rousseeuw, 1987) and the Calinski–Harabasz criterion (CHC) (Legendre and Legendre, 1998). The k-means is an iterative, data-partitioning algorithm and requires as input a matrix of points in n dimensions and a matrix of K initial cluster exemplars in n dimensions (determined using the Euclidean distance between point and cluster). The general

procedure is to search for a K-partition with locally optimal within-cluster sum of squares by moving points from one cluster to another (Hartigan and Wong, 1979). However, initial selection of exemplars strongly affects the results of k-means clustering. This algorithm works well only when the number of clusters is small and there is a high chance that at least one random initialization is close to a good solution (Frey and Dueck, 2007). By contrast, the conceptually new AP simultaneously considers all data points as potential exemplars. By viewing each data point as a node in a network, the algorithm recursively transmits realvalued messages along edges of the network until a good set of exemplars and corresponding clusters emerge. Messages are updated on the basis of simple formulas that search for minimal values of an appropriately chosen energy function. At any point in time, the magnitude of each message reflects the current affinity that one data point has for choosing another data point as its exemplar. AP has several advantages over related techniques that display some limitations: k-centres clustering, k-means clustering and the expectation maximisation (EM) algorithm store a relatively small set of estimated cluster centres at each step. Markov chain Monte Carlo techniques randomly search for good results, but do not share the Affinity Propagation’s advantage of simultaneous consideration of many possible solutions. Hierarchical agglomerative clustering and spectral clustering do not require that all

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Fig. 3. Results of the k-means clustering and silhouette interpretation. The silhouette interpretation identified two clusters as an optimal set. The 1592 objects (plots with attributes) can be subdivided in two groups under this criterion. The average silhouette width provides an evaluation of clustering validity and helps to select the optimal number of clusters. The average silhouette width is the average of the s(i) for all objects i belonging to that cluster. s(i) measures how well object i matches the cluster in question (that is, how well it has been classified). In the special case where there are only two clusters (k = 2), shifting object i from one cluster to the other will convert s(i) to s(i) (for details, see Rousseeuw, 1987).

points within a cluster are similar to a single centre and are thus not well-suited to many tasks. In particular, two points that should not be in the same cluster may be grouped together by an unfortunate sequence of pairwise groupings (Frey and Dueck, 2007). Finally, AP does not need a pre-defined number of clusters (Bodenhofer et al., 2011). In addition to AP search algorithms, SI and the CHC were used to determine the optimal number of clusters (Table 2). SI is a partitioning technique that uses tightness and separation of silhouettes representing different clusters. The silhouette graphs indicate which data lie well within their cluster and which merely lie somewhere in between clusters (Rousseeuw, 1987) (Fig. 3). CHC minimises the within-group sum of squares and maximises the between-group sum of squares. The highest CHC value corresponds to the optimal set (of most compact clusters). The optimal set can be recognised by a peak or at least an abrupt elbow on the linear plot of CHC values. By contrast, if the line is horizontal, smooth, ascending or descending, then is not possible to find an optimal set (Legendre and Legendre, 1998) (Fig. 4). A heat map with hierarchical clustering was also created (Fig. 5) to visualise the large amount of multi-dimensional data and to identify clusters of similar environmental conditions, shown as similarly coloured squares along the diagonal (Bodenhofer et al., 2011). All analyses were performed using the R Script for K-Means Cluster Analysis and ‘‘apcluster” software packages (Bodenhofer et al., 2011) implemented in the free statistical application, R (Development Core Team, 2014). The Kruskal–Wallis rank sum test (Kruskal and Wallis, 1952) and a permutation test based on randomly chosen reassignments (Manly, 1997) were used to test, for each cluster identified, whether the observed differences in the mean values of the tree

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Fig. 4. Results of the k-means clustering applied with the Calinski–Harabasz criterion (CHC). The CHC indicates that the 1592 objects (plots with attributes) can be subdivided into three clusters as an optimal set (marked as a red point), also recognised by the peak on the linear plot of CHC values. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Heat map with hierarchical clustering to visualise the large amount of multidimensional data and to identify clusters of similar environmental conditions based on the Affinity Propagation (AP) clustering, with the quantile = 0. This analysis indicates that the 1592 objects (plots with attributes) can be subdivided into 13 clusters, displayed as grey squares across the diagonal. The hierarchical clustering also identified 13 clusters, which are shown as 13 different colours. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

species diversity between the two types of ownership (communal and private) occur as random events rather than being caused by directed forces. Both are nonparametric tests that enable comparison of two groups in terms of mean values of a variable. However,

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Within each cluster with plots characterised by similar, particular environmental conditions and identified using different clustering methods, there were no significant differences between the communal and private ownership, in relation to any of the three measurements of tree species diversity considered. Although the total number of species (v0) and the effective number of tree species (v2) tended to be higher in privately owned forests (Table 1), this trend was not statistically significant either in the clusters or when clustering was not applied (Table 3). A comparison between the three clustering methods shows that the mean probability of error (P) for differences in v0, v2, and v1 between the two types of ownership in clusters calculated by Affinity Propagation (AP) clustering was much smaller (mean P = 0.30) than obtained in the other two methods (SI-k-means: mean P = 0.36; CHC-k-means: P = 0.40). However, the mean P value for differences in the diversity between the two property types without clustering was smaller than the mean P value obtained with clustering methods (Table 3). The largest (but not statistically significant) difference (P < 0.01) between v0 of communally and privately owned forests was detected in the seventh cluster (v0 was higher in communally owned forests). The most significant differences in relation to v2 and v1 between the two types of forest ownership were detected in clusters five (v2 was higher in community forests) and six (v1 was higher in private forests), all calculated by AP clustering (Fig. 8). In this approach, clusters five, six and seven represented intermediate environmental conditions (Tables 2 and 3). Figs. 6–8 and Table 1 show that total tree number (v0) varied from 1 to 17 (mean 6.47), the effective tree number (v2) increased from 1.00 to 9.71 (mean 3.47), and the number of prevalent tree species (v1) from 1.00 to 5.87 (mean 2.40) in the different clusters of the community forests. In the private forests, v0 ranged between 1 and 15 (mean 6.77), the effective tree number (v2) increased from 1.00 to 9.03 (mean 3.64), and the number of prevalent tree species (v1) from 1.00 to 6.92 (mean 2.52). In the two clusters identified by SI and calculated by k-means clustering, the mean highest v0, v2 and v1 (7, 3.67, and 2.55) were found in privately owned properties in the first cluster (Fig. 6). In the three clusters identified by CHC and computed by k-means clustering, the highest mean value

unlike the t test, the data are not required to fulfil the assumptions of normality and equal variances. Furthermore, parametric tests were not used because the central limit theorem cannot be applied due to the often small sample size within the calculated cluster. The permutation test essentially involves generating a large enough number of reassignments (permutations) of land ownership diversity and computing the values of the tree species diversity for each reassignment. The percentage of imitated differences greater than or equal to the respective observed differences in tree species diversity in the two types of ownership is calculated for each variable studied (P(Z P Diff)-values). If the P (Z P Diff) is not significant (P P 0.0003 after Bonferroni correction), we can expect random differences, otherwise the differences are directed by non-random forces between the two types of ownership (Wehenkel et al., 2009).

3. Results A weak, positive and statistically significant relationship between the distance to the nearest town (DIST) and the slope (SLO) was detected in relation to tree species diversity (rs = 0.06– 0.07, p < 0.01 (for v0, v2 and v1); rs = 0.05, p < 0.05 (only for v0 and v2)). Geographical aspect (ASP) and total population in the nearest town (POB) were not associated with any of the three measurements of tree species diversity. Silhouette interpretation (SI) identified two clusters, the Calinski–Harabasz criterion (CHC) identified three clusters, and the Affinity Propagation (AP) indicated 13 and 76 clusters respectively for q = 0 (Figs. 3–5) and q = 0.5. However, the identification of 76 clusters was not considered further due to the lack of a sufficient number (repetitions) of conglomerates located in private property in many clusters. Table 2 shows the two, three and 13 clusters and the almost homogeneous environmental plot conditions identified by the k-means and AP data-partitioning algorithms, with q = 0. The heat map also identified 13 clusters of similar, particular environmental conditions, shown as grey areas along the diagonal (Fig. 5).

Table 3 Probability of error for differences in the total number of species (v0), the effective number of tree species (v2), and the number of prevalent tree species (v1) between the two types of ownership in each cluster (similar environmental conditions) calculated by the Kruskal–Wallis rank sum test (P) and permutation test (P(Z P Diff)); the clusters were computed by the algorithms of k-means clustering, along with silhouette interpretation (SI), application of the Calinski–Harabasz Criterion (CHC) and use of Affinity Propagation (AP) clustering (with the input preference to the 0 quantile (q) of the input similarities). Note: no statistically significant differences were observed (all P > 0.0003). Cluster method

Cluster

P(Z P Diff) values of permutation test

P values of Kruskal–Wallis test

v0

v2

v1

Total

v0

v2

v1

without

1

0.0670

0.1110

0.1436

0.0629

0.0730

0.0997

0.0779

SI-k-means

1 2

0.9082 0.0819

0.6241 0.2575

0.6534 0.3134

0.6479 0.1279

0.3816 0.0264

0.4768 0.0531

0.3762 0.0480

CHC-k-means

1 2 3

0.6190 0.9941 0.0558

0.6831 0.5212 0.2771

0.7003 0.5240 0.3382

0.7622 0.7474 0.1101

0.2246 0.4647 0.0216

0.2356 0.2937 0.0484

0.3972 0.3409 0.0344

AP (q = 0)

1 2 3 4 5 6 7 8 9 10 11 12 13

0.1466 0.5344 0.6743 0.5542 0.1079 0.0397 0.0083 0.1515 0.4300 0.5517 0.1955 0.4219 0.2980

0.3269 0.8195 0.6180 0.7009 0.6396 0.0378 0.2073 0.0905 0.4556 0.4488 0.3042 0.8376 0.1454

0.4519 0.9984 0.7389 0.2313 0.7149 0.0403 0.3011 0.1412 0.4806 0.5617 0.3667 0.6657 0.2101

0.2071 0.5572 0.9370 0.9098 0.1962 0.0302 0.0418 0.1945 0.4722 0.5226 0.2081 0.6181 0.2310

0.0373 0.2281 0.4678 0.3562 0.0368 0.0084 0.0016 0.0718 0.2021 0.2430 0.0796 0.2466 0.2356

0.0303 0.3640 0.2790 0.3804 0.0868 0.0144 0.0467 0.0388 0.1437 0.2816 0.0696 0.3359 0.0845

0.0742 0.3376 0.3878 0.2047 0.0170 0.0195 0.0591 0.0883 0.1854 0.4286 0.0615 0.2927 0.1466

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Fig. 7. Box plots showing tree species diversity (v0, v2 and v1(inf) in 1600 m2) in the three clusters (c) (identified by the Calinski–Harabasz criterion (CHC) and calculated k-means clustering algorithm) and two forest properties (community forests (com), private forests (priv)).

privately owned properties and in the sixth and 13th clusters (Fig. 8).

4. Discussion and conclusions

Fig. 6. Box plots showing three diversity of tree species (v0, v2 and v1(inf) in 1600 m2) in the two clusters (c) (identified by the silhouette interpretation (SI) and calculated by k-means clustering algorithm) and two forest properties (community forests (com), private forests (priv)).

of v0 (7.21) was detected in privately owned property in the third cluster; however, the highest mean value of v2 (3.81) and v1 (2.60) were found in communally owned properties in the first cluster (Fig. 7). In the 13 clusters indicated by AP clustering, the highest mean values of v0, v2 and v1 (8.65, 5.10, and 3.03) were found in

The findings of the present study did not support the hypothesis that tree species diversity tends to be higher in communally owned forests than in privately owned forests in the Sierra Madre Occidental, Durango (Mexico), as there were no significant differences in the mean values of tree diversity between the two types of forest land ownership. Therefore, the degree of interest in the conservation and improvement of forest resources do not appear to be differ in relation to type of forest ownership. This is consistent with the conclusions reached by Ostrom and Nagendra (2006), who studied the number of stems, diameter at breast height and basal area of 42 forests in India, Kenya, Nepal, Uganda and USA and did not find any differences in the variables defining forest conditions in relation to the type of land ownership.

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Fig. 8. Box plots showing tree species diversity (v0, v2 and v1(inf) in 1600 m2) in the 13 clusters (c) (calculated by the Affinity Propagation clustering (with the input preference to the 0 quantile of the input similarities) and two forest properties (community forests (com), private forests (priv)).

In a study of the effects of government policies and property rights on forest conditions in privately and communally owned forests in Guatemala, Gibson (2002) obtained results consistent with the expectation that the private ownership regime is more efficient than communal ownership; however, the results did not apply when the main management aims were forest protection or when well-established communitary rules were strictly enforced. Moreover, some authors have shown that the communal system can also be efficient when members collaborate to establish operating rules and decisions are made in an atmosphere of cordiality and respect (Ostrom, 2001). The Rights and Resources Initiative (RRI, 2012) stated that ‘‘communities with strong management authority and sense of security tend to conserve forest resources, carbon and biodiversity and to enhance livelihoods”. The mean probability of error (P) for differences in the tree species diversity between the two types of ownership in different clusters (similar, specific environmental conditions) grouped by AP clustering was clearly smaller than that yielded by the other two methods (Tables 2 and 3). AP clustering allocated the 1592 objects (plots with attributes) to a greater number of different

environmental conditions (13) than the other two methods (Tables 2 and 3). This may increase the possibility of detecting differences (although not significant) in tree species diversity in some particular environmental conditions (such as in clusters five, six and seven) possibly caused by different forest management. However, the mean P with respect to differences in the tree species diversity between the two types of ownership without clustering was smaller than with clustering (Table 3). Those larger (although not significative) differences were probably due to significantly different environmental conditions (Table 1), because tree species diversity is associated with environmental variables (Hawkins et al., 2003; Silva-Flores et al., 2014) and the forest management methods are similar in the two ownership types. Hence, by detecting areas with similar environmental conditions, the clustering methods (Figs. 3–8) allowed to measure potential differences in tree diversity and helped to avoid misinterpretations, as could be to attribute those differences to forest management instead of environmental variables. In general, however, the ten explanatory variables including site characteristics, location and climatic and social aspects did not sig-

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nificantly influence the results, as no significant differences in the diversity of tree species were detected either overall or in the particular environmental conditions considered for clustering. The findings of the present study can probably be explained by the fact that the same forest consultancy firm usually handles both privately owned forests and communal forests, and the same technical criteria are applied in both cases (i) to prepare forest management plans and (ii) to predict timber harvests and select trees for harvesting. In addition, the same companies buy the timber from both types of forest owners. These companies are in charge of harvesting operations and decide which type of timber products to buy, which may affect selection of the species harvested and the working methods applied; however, these decisions do not appear to differ in relation to type of land ownership. In the same way, the federal and state laws and supervision that are applicable to forestry do not establish any difference between privately owned and communally owned forests, in relation to the requisites or specifications for silviculture and forest management. Besides, we did not find any reasons to assume any crucial differences in the level of knowledge of the two types of owners that could affect the way in which they manage the respective forests. Consequently, the general framework for the Durango forest land supports forest management in both types of ownership in a way that has had a similar influence on tree species diversity as a very important indicator for sustainable forest management (Zilliox and Gosselin, 2014). However, the aim of the study was not to explore whether forest management in Durango State has positively, negatively or marginally impacted the tree species diversity. If the effect of management were negative, improving these fundamental conditions would also represent a valuable starting point for improving forest management. All activities in these forests that enhance (i) correct selection of trees to be harvested, (ii) strict, independent and professional state supervision and (iii) levels of forest knowledge may be key factors in sustainable forest management in Durango. Obviously, these results alone do not demonstrate that the type of ownership is irrelevant to sustainable forest management. In the 80 years elapsed since the ejidos were first created in Mexico, marked differences have arisen between the private and the communal sectors, with reference to forestry. Traditionally the private sector has been identified as the main owner of forest industries (although not all of the private forest owners also own industries) and the communal owners have been identified as the principal holders of forested areas. This has historically led the two sectors to enter into contracts for the purchase of raw materials. The consequent conflicting interests have negatively affected the profitability and competitiveness of the forest production chain. In addition, the benefits of communal property ownership are more widely distributed among the population and are not limited to marketing of the respective goods and services. The benefits also include the general role of common property in development of the local economy derived from natural resource management (Bray et al., 2007). Additional research is required to clarify (1) the effect of the ownership regime on forest fragmentation; (2) the variables and agreements that interact with land tenure type in shaping the benefits to forest users and the amounts of these benefits (Tucker, 1999; Mas and Correa, 2000); and (3) the definition of public policies aimed at cost-effective sustainable management of forests and associated resources, taking into account the type of land ownership. Acknowledgement We thank Gustavo Perez-Verdin for his helpful suggestions regarding the study.

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References Baland, J.M., Platteau, J.P., 1996. Halting Degradation of Natural Resources: Is There a Role for Rural Communities? Oxford University Press, New York, 423p. Bodenhofer, U., Kothmeier, A., Hochreiter, S., 2011. APCluster: an R package for Affinity Propagation clustering. Bioinformatics 27 (17), 2463–2464. Bray, D.B., Merino-Pérez, L., Barry, D., 2007. Los bosques comunitarios de México. Manejo sustentable de paisajes forestales. Secretaría de Medio Ambiente y Recursos Naturales; Instituto Nacional de Ecología; Consejo Civil Mexicano para la Silvicultura Sostenible. Instituto de Geografía, UNAM; Florida International Institute. 444p. CONAFOR (Comisión Nacional Forestal), 2004. Inventario Nacional Forestal y de Suelos. Development Core Team, 2014. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Available: URL . Frey, B.J., Dueck, D., 2007. Clustering by passing messages between data points. Science 315 (5814), 972–976. Gibson, C.C., 2002. Does privatization protect natural resources? Property rights and forests in Guatemala. Soc. Sci. Quat. 83 (1), 206–225. Global Forest Resources Assessment, 2010. Main report. Food and Agriculture Organization of the United Nations. Rome, Italy. Available: (accessed 23.04.15). González-Elizondo, M.S., González-Elizondo, M., Tena-Flores, J.A., Ruacho-González, L., López-Enríquez, I.L., 2012. Vegetación de la Sierra Madre Occidental, México: Una Síntesis. Acta Botánica Mexicana 100, 351–403. Gregorius, H.R., 1978. The concept of genetic diversity and its formal relationship to heterozygosity and genetic distance. Math. Biosci. 41, 253–432. Gregorius, H.R., 2010. Linking diversity and differentiation. Diversity 2, 370–394. Hartigan, J.A., Wong, M.A., 1979. Algorithm AS 136: a k-means clustering algorithm. Appl. Stat., 100–108 Hawkins, B.A., Field, R., Cornell, H.V., Currie, D.J., Guégan, J.F., Kaufman, D.M., et al., 2003. Energy, water, and broad-scale geographic patterns of species richness. Ecology 84, 3105–3117. Hill, M.O., 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54, 427–432. Hutchinson, M.E., 1991. Continent-wide data assimilation using thin plate smoothing splines. In: Jasper, J.D. (Ed.), Data Assimilation Systems. Bureau of Meteorology, Melbourne, pp. 104–113. Hutchinson, M.E., 2004. Anusplin Version 4.3. Centre for Resource and Environmental Studies. The Australian National University, Canberra, Australia. Jost, L., 2006. Entropy and diversity. OIKOS 113, 363–375. Jost, L., 2007. Partitioning diversity into independent alpha and beta components. Ecology 88, 2427–2439. Kruskal, W.H., Wallis, W.A., 1952. Use of ranks in one-criterion variance analysis. J. Am. Stat. Assoc. 47 (260), 583–621. Legendre, P., Legendre, L., 1998. Numerical Ecology, second english edition. Elsevier Science B.V, Amsterdam. Ley Agraria, Congreso de los Estados Unidos Mexicanos, 2012. Diario Oficial de la Federación publicación del 09 Abril 2012. Lindenmayer, D.B., Franklin, J.F., Fischer, J., 2006. General management principles and a checklist of strategies to guide forest biodiversity conservation. Biol. Conserv. 131 (3), 433–445. Manly, B.F.J., 1997. Randomization, Bootstrap and Monte Carlo Methods in Biology. Chapman and Hall, London. Mas, J.F., Correa, S.J., 2000. Análisis de la fragmentación del paisaje en el área protegida ‘‘Los Petenes”, Campeche, México. Investigaciones geográficas Bol. del Instituto de Geografía. UNAM 43, 42–59. Myers, J.A., Harms, K.E., 2009. Seed arrival, ecological filters, and plant species richness: a meta-analysis. Ecol. Lett. 12 (11), 1250–1260. Nagaike, T., 2012. Review of plant species diversity in managed forests in Japan. ISRN Forestry. Ostrom, E., 2001. Reformulating the commons. In: Burger, J., Ostrom, E., Norgaard, R. B., Polcansky, D., Goldstein, B.D. (Eds.), Protecting the Commons. Island Press, Washington, DC, pp. 17–41. Ostrom, E., Nagendra, H., 2006. Insights on Linking Forests, Trees, and People From the Air, on the Ground, and in the Laboratory. National Academy of Sciences of the USA. Rehfeldt, G.E., 2006. A Spline Model of Climate for the Western United States. Gen. Tech. Rep. RMRS-GTR-165. U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station, Fort Collins, Colorado, USA. Rehfeldt, G.E., Crookston, N.L., Warwell, M.V., Evans, J.S., 2006. Empirical analyses of plant-climate relationships for the Western United States. Int. J. Plant Sci. 167 (6), 1123–1150. Rousseeuw, P.J., 1987. Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20, 53–65. RRI (Rights and Resource Initiative), 2012. What Rights? A Comparative Analysis of Developing Countries’ National Legislation on Community and Indigenous Peoples’ Forest Tenure Rights. Washington DC: Rights and Resources Initiative. Available: (accessed 17.12.14). Rzedowski, J., 2006. Vegetación de México. 1a. edición digital. Comisión Nacional para el Conocimiento y Uso de la Biodiversidad. México. 504p. Sáenz-Romero, C., Rehfeldt, G.E., Crookston, N.L., Duval, P., St-Amant, R., Beaulieu, J., Richardson, B.A., 2010. Spline models of contemporary, 2030, 2060 and 2090

228

R. Silva-Flores et al. / Forest Ecology and Management 363 (2016) 218–228

climates for Mexico and their use in understanding climate-change impacts on the vegetation. Climatic Change 102, 595–623. SEMARNAT (Secretaría de Medio Ambiente y Recursos Naturales), 2005. Indicadores Básicos del desempeño Ambiental. México, DF. Shannon, C.E., 1948. A mathematical theory of communication. Bell Syst. Tech. J. 27, 379–423 and 623–656. Silva-Flores, R., Pérez-Verdín, G., Wehenkel, C., 2014. Patterns of tree species diversity in relation to climatic factors on the Sierra Madre Occidental, Mexico. PLoS ONE 9 (8), e105034. http://dx.doi.org/10.1371/journal.pone.0105034. Simpson, E.H., 1949. Measurement of diversity. Nature 163, 688. Thoms, C.A., Betters, D.R., 1998. The potential for ecosystem management in Mexico’s forest Ejidos. For. Ecol. Manage. 103, 149–157. Tietenberg, T., 2000. Environmental and Natural Resource Economics. AddisonWesley Longman Inc., Reading, MA. Tucker, C.M., 1999. Private versus common property forests: forest conditions and tenure in a honduran community. Human Ecol. 27 (2), 201–230. Wehenkel, C., Corral-Rivas, J.J., Castellanos-Bocaz, H.A., Pinedo-Alvarez, A., 2009. Is there a positive relationship between naturalness and genetic diversity in forest tree communities? Investigación Agraria: Sistemas y Recursos Forestales. 18 (1), 20–27.

Wehenkel, C., Corral-Rivas, J.J., Hernández-Díaz, J.C., Gadow, K.V., 2011. Estimating balanced structure areas in multi-species forests on the Sierra Madre Occidental, Mexico. Ann. Forest Sci. 68, 385–394. Whittaker, R.H., 1972. Evolution and measurement of species diversity. Taxon 21, 213–251. Wright, D.H., Currie, D.J., Maurer, B.A., 1993. Energy supply and patterns of species richness on local and regional scales. In: Ricklefs, R.E., Schluter, D. (Eds.), Species Diversity in Ecological Communities: Historical and Geographical Perspectives. University of Chicago Press, Chicago II, pp. 66–74. WWF (World Wildlife Fund), 2001. Sierra Madre Occidental pine-oak forests (NA0302) Prepared by Valero, A., Schipper, J., Allnutt, T. and Burdette, Ch. Available: (accessed 14.12.11). Zilliox, C., Gosselin, F., 2014. Tree species diversity and abundance as indicators of understory diversity in French mountain forests: variations of the relationship in geographical and ecological space. For. Ecol. Manage. 321, 105–116. Zyczkowski, K., 2003. Rényi extrapolation of Shannon entropy. Open Sys & Information Dyn 10 (3), 297–310, Kluwer Academic Publishers, Netherlands.