Deforestation and local sustainable development in Brazilian Legal Amazonia : an exploratory analysis

We focus here on deforestation and human development dynamics among 211 small and medium-sized municipalities (in terms of population) in the Amazonian arc of deforestation, Brazil. First, we construct a typology of municipalities through principal component analysis and cluster analysis. Using this typology, we seek to identify changing deforestation frontiers in the study area based not only on forest loss levels, but also on sets of socioeconomic and demographic elements associated with human development. We find four well-defined macro-deforestation frontiers that exhibit distinct interactions between forest loss and human development levels. Our results show different levels of demographic and economic pressures in these frontiers while revealing some important trends such as the internalization of investments and demographic growth in the arc of deforestation. In addition, population growth and inmigration and out-migration patterns in the explored municipalities suggest a demographic complementarity among frontiers. Finally, we explore implications for public policies seeking to advance forest recovery and long-term conservation through sustainable development growth at the local and regional levels.


INTRODUCTION
In the Brazilian Amazon, regional and local sustainable development initiatives are vital to curb deforestation and forest degradation (Meir et al. 2011). Existing literature identifies sustainable development growth as a key element to forest recovery and long-term conservation in the tropics (Volpi 2007, UNDP 2014B. A. Jingwa and S. A. Asongu, unpublished manuscript: https://mpra.ub.uni-muenchen.de/35898/). Preserving the functioning of the Amazonian biome while promoting sustainable development is indispensable for regional and local ecological balance, as well as for climate change mitigation at a global scale (Meir et al. 2011). However, policies addressing deforestation and forest degradation in the Brazilian Amazon have not focused on regional and local sustainable development by integrating actions seeking social inclusion and economic growth without depleting natural resources. Instead, they were mainly concerned with short-and medium-term strategies such as law enforcement, the expansion of protected areas, and repression actions through monitoring and control (Volpi 2007, Soares-Filho et al. 2010, Pfaff et al. 2015; Instituto de Pesquisa Econômica Aplicada, Deutsche Gesellschaft fur Internationale Zusammenarbeit, and Comissão Econômica para a América Latina e Caribe, unpublished data: http://repositorio.ipea.gov.br/ bitstream/11058/885/1/Resultados%20avaliacao%20PPCDAm_seminario% 20avaliacao_JH03x.pdf).
Successful policies seeking to decrease deforestation and recover forest generally take into account multilevel efforts, multisector involvement, and bottom-up approaches, including all levels of government (local, state, and national). This approach responds to the fact that deforestation produces distinct effects according to the scale of analysis (Fearnside 2008, Guedes et al. 2011, and deforestation drivers are also different at the local, state, and national levels Moran 2012, Chakravarty et al. 2012). For optimum results, the private sector (soybean producers, ranchers, industries, and smallholders), public actors (executive, legislative, and judicial branches), and civil society (nongovernmental organizations and social and community groups) should work collectively by establishing goals regionally and locally (Sandbrook et al. 2010, Korhonen-Kurki et al. 2012, Sathler 2014. Lack of coordination among these stakeholders can hinder policies addressing deforestation and forest degradation (Gebara et al. 2014). In addition, long-term sustainable development strategies combining economic, social, and environmental initiatives can contribute to strengthen communities in facing deforestation and forest degradation (Steurer andTrattinig 2010, Meir et al. 2011).
Deforestation accelerated significantly during the 1990s and early 2000s in the Brazilian Amazon, reaching an annual rate of 27,423 km² in 2004 (INPE 2004). These high rates were mainly promoted by infrastructure expansion (roads, ports, and hydroelectric plants) and emergence of new economic activities such as logging, ranching, soybean producers, mining, and industry (Fearnside 2007, Fearnside and Graça 2009, Ebanyat et al. 2010). In addition, major changes in the regional demographic context and urbanization were strongly associated with deforestation and forest degradation in the region (Vicentini 2004, Monte-Mor 2013. In this context, the ecological effects of deforestation, such as increasing land degradation and changes in species composition and atmospheric parameters, are potentially large and strongly affect agriculture and ecological services in the Brazilian Amazon (Findell et al. 2006, Killeen and Solórzano 2008, Sheil and Murdiyarso 2009, Shukla et al. 1990). Moreover, deforestation and forest degradation in the region significantly affect the global climate system (Houghton et al. 2001, Houghton 2005, Soares-Filho et al. 2006, Berenguer et al. 2014, Busch and Ferretti-Gallon 2014, IPCC 2014, Song et al. 2015 (Popkin 2016); recent expansion of indigenous reserves and protected areas , Soares-Filho et al. 2010, Pfaff et al. 2015; enforcement of logging laws (UCS 2011); governmental interventions in beef and soy supply chains (Nepstad et al. 2014); and partnerships with nongovernmental organizations and the private sector (Greenpeace 2009).
The recent reduction of net deforestation and the strengthening of international initiatives such as Reducing Emissions from Deforestation and Forest Degradation and Enhancement of Carbon Stocks (i.e., REDD+), might suggest that the end of deforestation in the Brazilian Amazon is finally feasible (Nepstad et al. 2009). Empirical evidence observed in many developed and some developing forested countries support this argument by identifying a forest transition curve along which deforestation increases with development until it stabilizes, after which the process is reversed by forest growth (Meyfroidt et al. 2010, Elias et al. 2011. However, there is no guarantee that this recent deforestation reduction in the Brazilian Amazon will be a permanent pattern.  Macedo et al. 2012). In addition, there was a strong correlation between the availability of agricultural credit and deforestation rates in the Brazilian Amazon in this period (Andersen 1996, Silva 2009, Assunção et al. 2013). Despite Brazilian efforts in the past decade, these studies suggest that deforestation rates in the region are significantly associated with changes in investments and capital availability.
In 2008, the federal government launched the Sustainable Amazonia Plan (PAS), which proposed an integrated set of guidelines seeking to promote sustainable development in the Brazilian Amazon (Ministério do Meio Ambiente 2008). This plan incorporated many strategic policies at the state level, which might affect sustainable development at regional and local levels. However, municipalities of Brazilian Amazon are not deeply involved in projects for promoting sustainable development and forest preservation . In addition, conservation initiatives have spread more through top-down policies (PAS and PPCDAm) than through local interventions in the Brazilian Amazon (Madeira 2014).
Assessments of socioeconomic, demographic, and environmental changes are fundamental to support the implementation of public policies that take into account regional and local sustainable development in the Amazonian arc of deforestation, which comprises the area along the eastern, southern, and western edges of the forest (Barreto et al. 2008, Fearnside 2008. In this context, several studies have explored the regional levels of poverty, inequality, and social vulnerability in the Brazilian Amazon (Pinedo-Vasquez et al. 2001, Sears et al. 2007, Mangabeira 2010, Guedes et al. 2012, Garrett et al. 2017, as well as the negative social effects of deforestation in the region (Moran 1993, Celentano et al. 2012) and the interactions between forest loss and socioeconomic patterns in deforestation frontiers , Celentano et al. 2012). In general, these studies reveal that deforestation occurs on many fronts within the Amazonian arc of deforestation, which present distinct socioeconomic and demographic characteristics in a heterogeneous territory.
In the Brazilian Amazon, socioeconomic and environmental assessments of deforestation need to consider the whole urban hierarchy, which includes large cities, regional urban centers, and also the small and medium-sized (in terms of population) municipalities, highlighting their demographic, socioeconomic, and spatial specificities (IBGE 2008, Guedes et al. 2009, Sathler et al. 2009). Generally, small, medium, and large municipalities have distinct functions, synergies, and capacities to produce social and environmental changes in both urban and rural areas (Bolay and Rabinovich 2004), including deforestation (e.g., Aide et al. 2013, Brondizio andMoran 2012). In the arc of deforestation, public investments and the expansion of economic activities in small and medium-sized municipalities have caused important environmental and social changes (Becker 2005, Fearnside 2008, Ebanyat et al. 2010). However, deforestation and sustainable development dynamics in the small and medium-sized Amazonian municipalities are still understudied.
Here, we investigate the spatial patterns of deforestation and development between 2000 and 2010 (years of the two latest Brazilian demographic censuses) in the Amazonian small and medium-sized municipalities within the arc of deforestation. We focus on the following research questions. (1) Are there distinct and well-defined deforestation frontiers in the study area, and, if so, what are the main spatial patterns exhibited by forest loss and social variables in these frontiers? (2) How may our findings be used to improve the design of policies seeking regional and local sustainable development in the Brazilian Amazon?
To address these questions, we construct a typology of municipalities through principal component analysis (PCA) and cluster analysis (two-step cluster analysis). Using this typology, Ecology and Society 23(2): 30 https://www.ecologyandsociety.org/vol23/iss2/art30/ we seek to identify changing deforestation frontiers in the study area based not only on the forest loss levels, but also on sets of socio-demographic and economic characteristics associated with sustainable development. We conclude by discussing the major implications of our analysis for public policies seeking decreased deforestation and increased forest recovery through regional and local sustainable development initiatives in the Brazilian Amazon.

Data
We selected 211 small and medium-sized municipalities in the Amazonian arc of deforestation based on the following criteria: (1) deforested area > 200 km² between 2001 and 2010, which represents a significant amount of forest loss in this period, according to INPE (2014); (2) > 20% forested area in 2000 (baseline year); and (3) exclusion of state capitals and municipalities with > 140,000 inhabitants. These requirements took into account the regional specificities of small and mediumsized municipalities in the Brazilian Amazon, especially how cities and rural settlements are distributed in the territory, as well as previous studies about regional urban hierarchy (IBGE 2008, Sathler et al. 2010). In addition, our analysis also incorporates the northern edges of the Brazilian Amazon as part of the arc of deforestation. According to these criteria, unselected municipalities are necessarily not located in the arc of deforestation or did not have the minimal required amount of forest in the baseline year.
In this analysis, 27 initial variables represent the following dimensions: territory, deforestation and forest, demographic, education, human development, economic, inequality, poverty, and basic services (Table 1).
Deforestation and forest data were provided by INPE as part of the Amazon Deforestation Calculation Program (PRODES). Since 1988, PRODES has provided yearly open data at the municipal level, which allows researchers to integrate environmental information with multiple social and territorial dimensions. The accumulated deforestation in the Brazilian Amazon between 2001 and 2010, which was estimated by kriging interpolation, is shown together with the main physical and anthropic elements in the region (Fig. 1  of deforested area instead of absolute area of deforestation. Given the high heterogeneity of the selected municipalities in terms of territorial size and forest stock, the percentage of deforested area offers more appropriate information for comparability.
In tropical forest, deforestation rates have been associated with demographic parameters such as population growth, migration, and age structure changes (Amacher et al. 2009, Carr 2009, Caviglia-Harris et al. 2013. In our analysis, the demographic dimension is represented by 10 variables extracted from the Brazilian Microdata Population Censuses 2000 and 2010 (IBGE 2000(IBGE , 2010. These variables provided information about population stock, mortality, fertility, and age structure in 2010, and urban and rural population growth between 2000 and 2010. The percentage of migrants is also part of this dimension and was obtained by referring to migration flows in the 10 years preceding the census (Carvalho and Rigotti 1998).
Furthermore, human development characteristics are associated with forest loss and forest recovery at the local level (Meir et al. 2011. Education is represented by two variables: illiteracy rate and the percentage of poor people (defined as those with per capita household income ≤ R$ 140.00 per month in 2010) with no primary education (IBGE 2010). Other two variables are: the human development index (HDI) in 2010, and HDI variation between 2000 and 2010. This index was created by the United Nations and incorporates three indicators: per capita income, illiteracy rates, and life expectancy (PNUD 2013). Although HDI includes some information already present in Table 1, this index is a complementary measure with great potential for comparability.
Finally, most of the classic and recent literature on deforestation significantly addresses economic, inequality, poverty, and basic services aspects (Browder and Godfrey 1997, Fearnside and Graça 2009, Ebanyat et al. 2010, Hargrave and Kis-Katos 2013. The economic dimension is represented by gross domestic product (GDP) in 2010, GDP variation between 2000 and 2010, and percentage of agriculture, industry, and services in the GDP. The inequality dimension is addressed by the Gini index, and the

Multivariate methods
We used PCA and cluster analysis (Salvati andZitti 2009, Bell et al. 2015) to analyze the data. PCA was used to transform a set of original and interrelated variables into a new set of octagonal and unrelated components (Lima and Braga 2013). PCA seeks to reduce a large number of variables by a small number of linear functions, which best summarizes the large initial group of covariates (Mingoti 2007, Lima andBraga 2013). PCA is relevant for our study because the information vectors in the selected data sets are redundant, which might cause bias in further cluster analyses.
Before using PCA, we performed Kaiser Meyer Olkin (KMO) and Bartlett tests. The KMO test is a measure of adequacy that checks the fit of the data using all variables simultaneously. In this test, acceptable values range from 0.7 to 0.9. From the set of 27 variables, only two did not present a value > 0.7 (agricultural and industrial GDP). Therefore, we did not include these two variables in the PCA. In addition, the sphericity Bartlett's test examines the redundancy between variables by comparing the correlation matrix with the identity matrix, i.e., the main diagonal is equal to 1 and all other values are zero. Moreover, we applied the Varimax rotation method to minimize the number of variables in each component.
PCA transformed the original set of covariates into five standardized uncorrelated components with numerical values ranging from -∞ to + ∞, average centered on zero, and standard deviation equal to 1 (Mingoti 2007, Lima andBraga 2013). We then applied cluster analysis (using the two-step cluster algorithm) based on these five standardized and uncorrelated components to create a typology or classification of the municipalities included in the study. The cluster analysis subdivides data or objects into a number of different groups (clusters), which contain similar subjects (SPSS 2001, Everitt andHothorn 2011). In this analysis, the two-step algorithm preclusters the records into many small subclusters, and then it aggregates those subclusters into the desired number of clusters. We selected the number of optimal clusters according to the criterion suggested by Fraley and Raftery (1998), who proposed a Bayesian information criterion for the expected maximization clustering method (SPSS 2001). We performed these multivariate methods using R version 3.2.3 software.

RESULTS
The five standardized uncorrelated components are able to explain ~73% of the total variability in the original data set, which corresponds to approximately three-quarters of the information contained in the original set of variables (Table 2). These five components exhibit eigenvalues > 1 (Fig. 2). The first two components (PC1 and PC2) present the highest proportion of variance (0.380 and 0.132, respectively) while the other components also provided relevant information for cluster definition.    (Table 3).
We constructed a typology of municipalities through the PCA and cluster analysis (Table 4). Based on the Bayesian information criterion, four clusters are the best solution for the algorithm used. The spatial distribution of these clusters forms four deforestation frontiers in the study area: stagnated, dynamic deforestation, consolidated, and internal deforestation (Fig. 3, Table 5).  The consolidated frontier ( In addition, these municipalities present on average small populations and economies. Therefore, the internal deforestation frontier is characterized by municipalities presenting, on average, low economic growth and undiversified economy. The moderate level for the development challenges component shows that the internal deforestation frontier has, on average, higher fertility and dependency ratio levels than do the dynamic deforestation and consolidated frontiers. This typology of municipalities presents a well-defined pattern in terms of localization and contiguity (Fig. 3). Municipalities comprising the stagnated frontier (cluster 1) have the lowest territorial dispersion and are mainly located in the northern Maranhão state. In contrast, municipalities grouped in the dynamic deforestation frontier (cluster 2) present the highest territorial dispersion. These municipalities are located in the heart of the arc of deforestation, especially in the eastern and southern Pará state. These municipalities are also located in regions with important regional railways and massive agricultural projects such as in the central part of Mato Grosso and Maranhão, and in Rondônia state. The municipalities grouped in the consolidated frontier (cluster 3) are mainly located in Mato Grosso state, with little significant presence in Rondônia and eastern Pará. In Mato Grosso, municipalities grouped in the consolidated frontier surround the municipalities of cluster 2 located near the 153 road. Finally, the municipalities grouped in the internal deforestation frontier (cluster 4) were mainly located in the northern Brazilian Amazon, especially in areas where transportation is exclusively by river. These municipalities are also present in Acre state, as well as in southern Amazonas and southern Pará.

DISCUSSION
Spatial data integration and statistical analysis provided multiple results by exploring 25 environmental, socio-demographic, and economic variables at the municipal level in the Amazonian arc of deforestation. In the PCA, development challenges and forest components were decisive for cluster definition, whereas size, growth, and stagnation components provided relevant complementary information for understanding the sustainable developmental dynamics in the study area. Our typology of municipalities revealed four deforestation macro-frontiers, i.e., stagnated frontier, internal deforestation frontier, dynamic frontier, and consolidated frontier, which correspond to distinct interactions between deforestation and human development levels. We present here a discussion on the main characteristics of these frontiers.
In the stagnated frontier, municipalities have, on average, the lowest human developmental levels, high deforestation rates, and low percentage of forested areas. In the 1990s, Jha and Bawa (2006) found this same pattern by investigating 30 of the most important world deforestation hotspots in areas characterized by high population growth. However, the stagnated frontier exhibited high levels of environmental depletion between 2000 and 2010, even with low population growth and severe economic stagnation.
In the internal deforestation frontier, deforestation is also clearly associated with low levels of human development. In fact, the arc of deforestation traditionally encompasses areas characterized by low levels of human development (Ministério do Meio Ambiente 2008, Meir et al. 2011). Population growth between 2000 and 2010 in this frontier was not mainly driven by migration, as observed in the dynamic deforestation frontier and in the hotspots investigated by Jha and Bawa (2006). Our findings show that the significant population growth exhibited by municipalities grouped in the internal deforestation frontier might be explained by low out-migration and strong natural growth in the assessed period. In addition, these municipalities present, on average, significant percentages of forested area and huge territorial area, which contributes to the relatively low percentages of deforestation registered between 2001 and 2010. The absolute deforestation figures are significant in the internal deforestation https://www.ecologyandsociety.org/vol23/iss2/art30/ frontier, given its high values for the stagnation component and its low values for the size component.
The associations between forest loss and social variables are less clear in the dynamic deforestation frontier and in the consolidated frontier, in which the proliferation of economic activities and the historical advancement of the arc of deforestation were crucial for the cluster configurations. The dynamic deforestation frontier has presented significant economic growth between 2000 and 2010, which was mainly driven by agricultural and industrial activities Graça 2009, Ebanyat et al. 2010). However, human development levels and social variables did not grow to the same degree, which may have increased environmental vulnerability in these areas. In addition, municipalities grouped in the consolidated frontier exhibited significant deforestation levels between 2001 and 2010, even presenting, on average, the highest regional levels of human development.
Our analysis also indicates well-defined differences between the explored parameters, revealing some interesting patterns among the frontiers. Significant migratory attractiveness and economic dynamism exhibited by the dynamic deforestation frontier, as well as the high out-migration levels presented in the consolidated frontier, suggest complementarity in the demographic dynamism between these areas. This finding corroborates those of previous studies that demonstrate the predominance of internal migration in the region (e.g., Perz 2002, Becker 2005. In addition, the information regarding urban and rural population growth, fertility rate, and dependency ratio might indicate that municipalities grouped in the stagnated frontier and in the internal deforestation frontier are delayed in the demographic transition when compared to the other frontiers. Generally, the pace of the demographic transition is strongly related to human developmental levels and economic growth, with developed regions more advanced in this process than developing regions (Lee 2003, Reher 2011. Our results are consistent with demographic transition theory because human development levels are lower in the stagnated frontier and the internal deforestation frontier than in the other frontiers. Development levels are associated not only with more opportunities that assure forest conservation, but also with demographic changes that might cause negative environmental impacts such as increases in consumption and land demands in the region (Campos 2014, Mello and. Demographic transition and age structure changes are increasingly affecting the population distribution and are also creating environmental pressures in both urban and rural areas in the Brazilian Amazon (Perz et al. 2008). Changes in fertility and life expectancy have increased the proportion of adults and reduced the dependency rate, especially in the more developed municipalities (IBGE 2000(IBGE , 2010. In addition, young adults are likely to be relevant actors in labor migration (United Nations 2011, Kupiszewski et al. 2013), which can affect the population distribution and increase the pressure on natural resources in the Brazilian Amazon.
The related literature suggests that variations in the household life cycle and reductions in the dependency ratio driven by the demographic transition might threaten forest preservation in rural areas (Bilsborrow and Stupp 1997, Bilsborrow and Carr 2001, Moran et al. 2003, Guedes et al. 2011). According to complementary information provided by IBGE (2010), https://www.ecologyandsociety.org/vol23/iss2/art30/ municipalities grouped in the dynamic deforestation (63.30%) and consolidated (66.96%) frontiers have, on average, higher proportions of adults (15 to 64 years) than do municipalities grouped in the stagnated (61.43%) and internal deforestation (58.98%) frontiers, and these numbers are likely to increase in the next decade (Rigotti 2012).

Policy recommendations
Our results might assist in the design of policies seeking regional and local sustainable development for the preservation and regeneration of forests in the assessed municipalities. The stagnated frontier deserves special attention in the implementation of sustainable development initiatives, given its extremely low forest stocks and human development levels.
Policies need to focus on promoting forest recovery, starting from the most ecologically vulnerable areas such as those surrounding springs and streams. Local developmental policies that support economic diversification might attract more investments in nontraditional economic sectors and improve the existing services with no negative impact on forest regeneration. Currently, forest stocks do not provide significant environmental services for populations living in the stagnated frontier, which might hinder human development growth.
In the dynamic deforestation frontier, the continuous strengthening of environmental and control policies is vital in the short and medium terms. In the long term, policies seeking sustainable development can promote an important paradigm shift in the dynamic deforestation frontier, which would imply the reduction of expenditures on monitoring and control of deforestation and the increase in income supported by forestry ecological services. Otherwise, forest protection will indefinitely demand a significant amount of financial resources invested in monitoring and control initiatives (Angelsen 2008, Böttcher et al. 2009. In addition, public policies need to be aware of the intense economic and demographic changes in the dynamic frontier. Local governments will face the challenge of transforming economic growth in sustainable development, especially in mining areas that clearly require economic diversification policies, e.g., Canaã dos Carajás and Ourilândia do Norte in Pará state (SEICOM 2013). In addition, the immense distances between the main districts and areas presenting higher deforestation rates within some municipalities might hinder local actions in the dynamic deforestation frontier, especially those located in southern Amazonas (Apuí and Manicoré) and southern Pará (Novo Progresso, Altamira, and São Félix do Xingu).
The consolidated frontier presents the best social indicators among the frontiers in the arc of deforestation, which, in theory, can contribute to sustainable developmental growth by curbing Ecology and Society 23(2): 30 https://www.ecologyandsociety.org/vol23/iss2/art30/ deforestation. In the consolidated frontier, it is urgent for stakeholders to promote actions to regenerate the forest, especially in the areas most affected by cattle and soybean production. Policies seeking economic development must stop depleting natural resources by implementing local strategies to increase the eco-efficiency of agricultural activities in this frontier (Pacheco et al. 2013). Because the arc of deforestation has greatly damaged the forest stretching from the southern portion of the Brazilian Amazon into its interior, the results indicate the existence of some favorable conditions in these municipalities for the initiation of a strong movement for the recovery of forests and the enhancement of sustainable development, advancing also from the southern portion toward the interior of the region. Therefore, the consolidated frontier of deforestation might become the new frontier of sustainable development.
The internal deforestation frontier presents the lowest development level among clusters that still have significant stocks of forest such as the dynamic deforestation frontier and the consolidated frontier. In the internal deforestation frontier, deforestation has not been driven mainly by external economic forces, which generally follow a linear logic of territorial occupation in the arc of deforestation. Instead, deforestation has been strongly associated with demographic and socioeconomic characteristics such as age structure, household patterns, economic activities, and land occupation (Moran et al. 2003, Guedes et al. 2011). In the internal deforestation frontier, the municipalities located in the southern arc of deforestation require more attention in maintaining the forest stocks and improving living conditions, given the high deforestation rates presented by neighbors grouped in the dynamic deforestation frontier. In this frontier, conservation areas and indigenous lands play an important role in preserving the forest , Soares-Filho et al. 2010. Therefore, policies strengthening conservation areas and traditional communities in this frontier are critical to curb the expansion of deforestation, especially in Amazonas state.
For example, recent studies have explored the positive effects of conditional cash transfers and payments for environmental services on rainforest preservation at the local level (Rawlings and Rubio 2005, Zbnden and Lee 2005, Persson and Alpízar 2013. In Amazonas state, the Bolsa Floresta program clearly associates improvements in human development with preservation practices at the local level, which have been reducing forest loss in the small and isolated communities (Börner et al. 2013, Piperata et al. 2016. Our results suggest that other Amazonian states may achieve interesting results by replicating the Bolsa Floresta program, especially in municipalities located in the internal deforestation and dynamic deforestation frontiers. In addition, the federal government may require environmental compensation from the beneficiaries of this program by partially increasing this benefit in some selected areas within the arc of deforestation. Further studies should assess the effects of cash transfer programs designed with no environmental compensation in the Brazilian Amazon, such as Bolsa Família. As a complementary recommendation, municipalities must continually strengthen their interaction in projects developed at the regional and national levels. According to MacCarney (2006), the lack of interaction between local governments and regional and national efforts can lead to the failure of public policies. In the Brazilian Amazon, municipalities have the opportunity to take advantage of the mobilizations, plans, and actions developed for states and the national government. The Sustainable Amazonia Plan can assist municipalities to formulate and achieve their local developmental goals, and partnerships between municipalities and the national government can maximize the local results of PPCDAm.
Finally, public policies seeking regional and local sustainable development need to address the recent demographic changes in the Brazilian Amazon by taking into account both opportunities such as the positive effects of the high percentage of adult population on the economy, and challenges such as the regional increase in consumption and land demands arising from demographic transition, household changes, and migration trends in the region.

CONCLUSION
By exploring 211 small and medium-sized municipalities (in terms of population) in the Amazonian arc of deforestation, we find four well-defined macro-deforestation frontiers that exhibit distinct interactions between forest loss, sociodemographic and economic characteristics, and human development levels: the stagnated frontier, the dynamic deforestation frontier, the consolidated frontier, and the internal deforestation frontier. Our analysis shows different levels of population and economic pressures in these frontiers while revealing some important trends such as the internalization of investments and demographic growth in the arc of deforestation. In addition, population growth and in-and out-migration patterns suggest a demographic complementarity among frontiers.
Our results support public policies seeking to address deforestation and forest degradation through regional and local sustainable development initiatives in the Brazilian Amazon. In the stagnated frontier, which is formed by municipalities presenting the lowest levels of human development and a high proportion of deforested area, public policies will face the challenge of promoting economic diversification at the local level and forest recovery in the most ecologically vulnerable areas in Maranhão state. The dynamic deforestation frontier, which presents the highest economic growth between 2000 and 2010, needs to strengthen its environmental monitoring and control policies continuously in the short and medium terms. In the long term, regional and local governments can mitigate the negative effects of economic growth by developing sustainable practices in these areas. In the consolidated frontier, which groups municipalities presenting the most favorable social indicators among the explored clusters, public policies can reduce environmental impacts and promote forest regeneration by increasing the eco-efficiency in large areas affected by cattle and soybean production, especially in Mato Grosso state. Finally, the internal deforestation frontier comprises stagnated municipalities that presents large territorial dimensions and high proportions of forest. In this frontier, governments can protect the forest by strengthening conservation areas and fostering sustainable development initiatives among traditional communities. In the internal deforestation frontier, monitoring and control policies are important in municipalities located in the southern arc of deforestation. https://www.ecologyandsociety.org/vol23/iss2/art30/ Our investigation confirms the need for specific analysis in social and environmental studies for small and medium-sized municipalities within the arc of deforestation. In these municipalities, economic investments and the advancement of frontiers might cause significant local changes in some key explored variables, especially those presenting low levels in the base year. In fact, small and medium-sized municipalities serve as logistics bases for agro-industrial and mining projects, ensuring frontier expansion and the internalization of economic activities (Becker 2005, Monte-Mor 2013. In addition, the interpretation of some variables can change according to the population size or the level of importance of the municipality in the regional hierarchy. For example, high values of services in the GDP composition in the explored municipalities are strongly associated with lower levels of economic diversification and lack of investments in other economic sectors. This finding has a different meaning for the administrative capitals and large municipalities that have economies based on more specialized and diversified services (IBGE 2000(IBGE , 2010. Further research on topological relations among deforestation, forest stocks, and other mapped elements (main districts, roads, rivers, protected areas, economic activities, and urban agglomerations) might reveal relevant insights for this discussion. Spatial distribution and proximity are essential for understanding the interactions among socioeconomic, demographic, and environmental variables (Rindfuss and Stern 1998). In addition, time-series data could be useful to characterize the evolution of deforestation and social variables in the region.
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