Assessing Environmental Criteria to Support Forest Connectivity

Establishing forest connection in landscapes under urban sprawl is essential for maintaining the ecological processes and ensuring biodiversity conservation. However, the major challenge is incorporated the ecological network in the land-use/land-cover planning. This way, the main objective of the study was the evaluation of environmental criteria for prioritizing areas to obtain forest functional connectivity in a landscape subject to the urban sprawl. The second objective was to understand how the criteria are associated with the structural forest attributes represented by traditional landscape ecology metrics. The criteria were dened through the literature review, representing the landscape characteristics as the topographic, conicts, and biotics. The metrics used to characterize the forest structure were perimeter, shape index, and distance to the nearest neighbor. They were generated to a selected group of forest remnants, which represent the landscape forest structure. Sampling the criteria and forest fragments maps (i.e., different maps representing the metrics-values) through the hexagon network, we assessed how the criteria are associated with the structural forest attributes. The statistical analysis used to evaluate these sampled values were The Moran Global (Moran I) and Moran Local (LISA). We obtained that the urban expansion process is diffuse, although it does not occur randomly in our landscape. The criteria slope, TWI, distance from drainage network, distance from highways, distance from the low-density urban area, and distance from forest patches have characteristics that support this process. Furthermore, our results indicated a spatial autocorrelation among metrics and after, among metrics and these criteria. Also, we obtained that the external inuences on the fragments did not occur randomly and that the criteria act on the landscape. This way, through these criteria, we can identify regions where it is possible to have the persistence of forest fragments, even though in places under the impact of urban sprawl.


Introduction
The urban sprawl has been worldwide discussed in terms of its negative consequence as the loss of natural habitat, forest fragmentation, and increased barriers to gene ow, that has in uenced the ecological connectivity of different species (Mimet, Clauzel and Foltête, 2016; Semper-Pascual et al., The major challenge is the selection of an adequate metric set, which can be done through a literature review (Frank et al., 2013;Lechner et al., 2013). In the case of ecological analysis prevails the metrics of area, edge, and connectivity (Cheung, Brierley and O'Sullivan, 2016;Senzaki and Yamaura, 2016;Schindler et al., 2015), that re ect the forest fragments characteristics in terms of biodiversity (Pereira et al., 2013).
In this context, the main objective of the study was the evaluation of environmental criteria for prioritizing areas to obtain forest functional connectivity, in landscape subject to the urban sprawl. The second objective was to understand how the criteria are associated with the structural forest attributes, represented by traditional landscape ecology metrics. Newbold et al. (2015) cited that the maintenance of forest functional connectivity is an important component for biodiversity conservation, in landscapes under urban sprawl, especially when the ecological network is incorporated into the land-use/land-cover planning (Huang et

Study Area
The landscape studied (Fig. 1) is in the Green Belt Biosphere Reserve (GBBR) of São Paulo (SP), which is one of the largest cities in the South America (IBGE, 2021). The city has suffering with the urban sprawl, resulting in pressure in its surrounding area, in terms of conversion to urban use and to agriculture.
The GBBR-SP region is an example of this situation, considering that its agricultural production has as main destination São Paulo city. This way, the urban sprawl occurs in areas originally occupied by Atlantic Studies have been conducted to minimize these negative effects (Newbold et al. 2015; Ayram et al., 2016;Ribeiro et al. 2020); and we focus on one SE, that is forest connectivity, thinking in the importance of the GBBR areas. According to Unesco (2019), in these areas the human and environmental con icts should be solved through the efforts of the local and scienti c communities, aiming at the sustainable use of natural resources.
The study area is characterized by an urban-rural transition, however, has 34.9% of its area (165099.25 ha) covered by Atlantic Forest remnants belongs to Ombrophilous Dense Forestry (IBGE, 2012). Some remnants belong to Protected Area as the Cabreúva Environmental Protection Area (EPA) in the North, Morro Grande Forest Reserve (FR) in the South, and Itupararanga EPA in the Southwest (Fig. 1). In this scenario, the studied area was considered of extreme importance for the biodiversity conservation and to design ecological corridor (MMA, 2019).
Other remnants are scattered through the matrix composed predominantly by pastures (i.e. anthropic elds) and urban areas, that occupy 36.3% and 22.4% of the total study, respectively. Furthermore, in the area there is 3.4% of planted forests (Eucalliptus sp), 1.4% of farmlands, 1.0% water and 0.6% of roads (highways and rural roads), as show Fig.1

Conceptual Model
The conceptual framework model (Fig. 2), for our study area in GBBR-SP, includes the environmental criteria and landscape ecology metrics at fragment level, that were spatialized in the Geographic Information System (GIS).
Environmental criteria were group according the landscape characteristic as follow: Topographic: slope, aspect, and Topographic Wetness Index (TWI).
Con icts: distance from highways, distance from drainage network, and distance from low-density urban area; and Biotics: Normalized Difference of Vegetation Index (NDVI) and distance from forest patches.
The database used to produce the criteria as well as the justi cation of them, in the context of connectivity analysis, will be described in the section below.
The landscape metrics used to characterize the forest structure were perimeter, shape index, and distance to the nearest neighbor. They were generated to a selected group of forest remnants, which represent the landscape forest structure.
Sampling the criteria and forest fragments maps, (i.e. different maps representing the metrics-values) through the hexagon network, we assessed how the criteria are associated with the structural forest attributes. The statistical analysis used to evaluate these sampled values were The Moran Global (Moran I) and Moran Local (LISA) (Fig. 2).

criteria selection
The criteria were de ned through the literature review in the period from 2015 to 2019, using platforms as Scielo, Scopus, Web of Science, and Google Scholar. We de ned a combination of search terms with su cient comprehensiveness to maximize the nding of environmental criteria. Since they represented the integration of forest functional connectivity and conservation principles.
The most mentioned criteria, despite differences in nomenclatures, were related to forest cover, topography, water resources, urban area, highways, and soils (Table 1). agglomerations or farms characterized by a horizontal, dispersed, and polycentric growth. Conversely, the highly dense urban areas were classi ed as constraints, considering their low quality for support he functional connectivity, have a compact, vertical and monocentric shape (Ojima, 2007).
The NDVI index considers the relation between the energy re ected in the red and near-infrared wavelengths to represents the vegetation biomass. The index varies from -1 to +1, with the last value indicating vegetation denser, moist, and well-developed (Melo et al., 2011). In this context, we used NDVI to represent the forest vegetation vigor (Anatoly, Peng, and Huemmrich, 2014).
The principal component analysis (PCA) was used to explain the organization and variability of criteria in the landscape.
PCA is a linear method for the exploratory data analysis of multidimensional statistical series, that aimed the reduction of variables (no signi cant) without information loss (Borcard, Gillet, and Legendre, 2011).

Forest patches metrics
The metrics used to characterize a selected group of patches, that represented the landscape forest structure, were area, perimeter, shape index, and distance to the nearest neighbor. According to Pereira et al., 2013; Mello, Toppa and Cardoso-Leite, 2016; Palmero-Iniesta et al., 2020 these metrics also support the forest patches description in terms of connectivity and conservation.
Firstly, we divided the forest remnants into size classes, having the prerogative that the forest area represented by these classes should be similar. The analysis guaranteed the representativeness of patches with different sizes, excluding the speci cs categories in uence as those that occupied a small area or that contained a large area concentrated on restricted patches. This way, the actual condition of the landscape under study was represented, as illustrated in Fig. 1.
After, the patches were identi ed individuality in a map, that was used to calculate the metrics through the Vector Based Landscape Analysis Tools Extension (V-Late), in the GIS environmental.
The metrics values were associated with their respective patches to compose maps, representing their perimeters, shapes, and distances to their nearest neighbor.

Criteria and forest structure Evaluation
We assessed how the criteria are associated with the forest patches metric (representing the structural forest attributes) based on a hexagon network sampling (Fig. 3).
Through this network, we sampled the maps of criteria and metrics, considering hexagons that covered more than 50% of the patch size (Fig. 3.) As the size of hexagon-unit was 2 ha, at least two sample points by patch were obtained.
These sampled values supported the statistical analyses. Using Moran Global (Moran I) (Moran, 1950) and Moran Local (LISA) indexes (Anselin, 1995), we evaluated the spatial autocorrelation of the criteria, metrics, and nally among the criteria and metrics.
The rst index varies from 0 to +1, indicating a direct correlation, and from 0 to −1, that re ected an inverse correlation. Otherwise, LISA asses the autocorrelation degree, weighted by geographic proximity and it indicates regional grouping.
For the two indexes, the signi cance level considered was p < 0.05, that was calibrated for the Euclidean distance from the average point of the sample space.
The canonical correspondence analysis (CCA) tested the hypothesis that the metrics can indicate the criteria importance rank to the forest functional connectivity, revealing these criteria in uence under the forest patches. The vegan package (R software) supported the canonical correspondence analysis, after the preveri cation of multicollinearity for values greater than 5 (James et al., 2014) and the validation of product with p < 0.05 through permutation and ANOVA tests.

Results
The environmental criteria, selected from the literature review (from 2015 to 2020), considering terms as forest functional connectivity, connectivity and forest conservation, and landscape subject to urban sprawl, among others are listed in Table 2. The distribution pattern of mature forests, combined with the disturbance, and replacement of old forests, can in uence the dispersion of species, movement and processes at the population level and de ne whether species adapt or perish in altered forest ecosystems (Ruffell, Clout, and Didhan, 2017).
Habitat reduction, with subsequent increased edge effects, changes the behavior of individuals and habitat use patterns, also reducing movement between fragments (Ramesh, Kalle and Downs, 2015).
Proximity to nature reserve areas also affects how people perceive the importance of forest conservation. As they move away from core areas, the opportunities and level of anthropic disturbance increase (Deng et al., 2015).
Con icts Distance from the lowdensity urban area In the urban expansion area, there is an increase for work and housing, a rapid regional economic development ( This riparian vegetation continues offers an opportunity to establish an integrated network of forest remnants, which can serve as habitat and connectors at the regional or local scale, especially when reduced as sources that cause environmental degradation (Zimbres et al., 2018).
The riverside areas are dynamic, biologically rich ecosystems, with a high content of nutrients, humidity and the presence of unique microclimates for species of invertebrates (Ramey and Richardson, 2017) terrestrial mammals (Zimbres et al., 2018) and birds (Mitchell et al., 2018).

Distance from Highways
Disturbances caused by highways increase the forest patches edge effects, decreasing the fauna species presence (Avalos and Bermúdez, 2016). In addition, highways contribute to increased landscape fragmentation, as they cut through continuous areas with high connectivity and create barriers to movement between habitats (Carvalho et al., 2015).
The group represents landscape features relating to their topography and biotic components that can support the prioritization of areas to obtain forest function connectivity in the forest conservation context. They also have characteristics representing con icts for this objective, which can threaten the process ( Fig. 4).
This way, the main reason or importance that drove the authors (from the literature review) to include the criteria in their studies are presented in Table 2.
According to the slope criterion ( Fig. 4A), approximately 91% of the study area showed declivity at most 20%. Nearly 47% of this total presented at most 8% of declivity and they are concentrated in the South region of the study area (Fig. 4A).
This concentration was also appointed by the LISA index, that classi ed the region by low-low, indicating the spatial proximity between lowest slope values (Fig. 5A).
In this context, the slope was the criterion associated with the higher According to the LISA index results for the criterion, the study area was classi ed in 20% as high-high and 21% as low-low, having signi cant spatial autocorrelation.
The TWI criterion (Fig. 4B) indicated the South region also associated with the high moisture-retention ability, having values varying from 12 to 27, that occupy 16% of the study area.
Re ecting this spatial pattern of the most features distributed randomly across the landscape, the Moran Index for TWI was 0.190, which was the lowest value obtained among the criteria (Fig. 5B).
In the same way, the LISA index did not identify a signi cative regional grouping (Fig. 5B), showing only a tendency in the Central-North region of lowest TWI values, which were classi ed as low-low (with 15.4% of spatial autocorrelation) (Fig. 5B). However, this tendency is not statistically signi cant, taking into account the great variability of the criterion features.
The Central-North region was associated with relief Heavily-Undulating (20-45%) and Hilly (> 45%) (Fig.   4AB), having a spatial distribution signi cantly positive (Fig. 5C). As mentioned, the LISA index indicated groupings in those regions, that were classi ed as high-high because of the high spatial correlations between near features (Fig. 5C).
The LISA index also showed groupings for the aspect criterion in the Central-North region classi ed as high-high (16.2%) and low-low (16.3%) (Fig. 5C), considering the predominance of faces oriented for east-west direction (Fig. 4C).
However, Fig. 4C illustrated these faces spread across the landscape and interacting with others, resulting in a low value of Moran Index (I = 0.292), as we observed for TWI. The east-west faces occupied 65.3% of the landscape and north-south faces 34.7% (Fig. 4C).
Similarly, the distance from the drainage network showed its watercourses spread by the landscape (Fig.   4D), obtaining the Moran index of 0.477. The value was superior to the TWI and aspect, indicating a positive autocorrelation in the spatial distribution of the watercourses, although with a low level, having only 18% classi ed as high-high and 23% as low-low (Fig. 5D).
The maximum distance from the drainage network was 800m, although values at most 200m from watercourses represented 56% of total area and between 200-400m approximately 36% (Fig. 5D).
Basing on the low-density urban areas and highways, the maximum distances obtained were, respectively, 8200 m and 16482 m, mainly in the function of the values present in the extremes of North and Southeast ( Fig. 4E and Fig. 4F).
This way, those features presented more in uence in the Central-to-South-west portion of the landscape, where we can also observe the great urban areas, which were classi ed as a restriction to functional connectivity because of their low quality. Due the presence of these con icts features the region was classi ed as low-low (LISA index), showing signi cant spatial autocorrelation of 41.5% for low-density urban area and 41.4% for distance from highway.
Consequently, this region has signi cant positive spatial autocorrelation with regions classi ed as highhigh represented 14.0% (low-density urban area) and 16.8% (distance from highways) ( Fig. 5E and Fig.   5F). However, the spatial autocorrelation of distance from highway is slightly higher than the distance from low-density urban areas, considering their Moran index values of 0.992 and 0.976.
The urban areas and highways in uenced on the forest patches spatialization through the landscape, that presented 11268 m as the maximum distance among them (Fig. 4h).
The criterion showed Moran index value of the 0.992, that re ects the high and positive correlation among the distances from forest patches. Thus, the LISA index showed region grouping (with high autocorrelation degree) classi ed as high-high (29.2% spatial autocorrelation) (Fig. 5h) and located in the central region of the landscape.
The high-high class indicates place associated with a high probability to occur the great distance values, near other places in the same condition. For the study, in the same region that the LISA index indicated the low-low (38.6% of spatial autocorrelation) groupings for the distances from low-density urban areas and highways (i.e. concentration of places near to the con icts features).
This way, the spatial autocorrelation analysis indicated that the great distance from the forest patches occurred in places occupied by urban areas and highways.
Finally, Fig. 4g showed the NDVI index, having its highest values associated with the largest forest patches.
Although, its Moran Index was 0.50, indicating that the criterion has a minor autocorrelation degree than the criterion distance from the forest patch. Figure 5g illustrated the groupings detected through the LISA analysis, that were classi ed as high-high (23.7% of spatial autocorrelation) and were in similar regions of the distance from forest patches criterion. However, the spatial autocorrelation of this criterion is smaller than the last.
Relating to the criteria variability, PCA analysis explained 42.58% of the data (Fig. 6) According to the rst axis the slope decreases as the distance from the drainage network and aspect values also decrease.
Conversely, TWI values increase (Fig. 6). Figure 6 showed in the second axis that, as the forest patches are coming toward the low-density urban areas and highways, there is a decrease in the distance value among forest patches and the NDVI index.

Forest structure evaluation
The study area has 57665.75 ha covered by 10428 Atlantic Forest remnants with sizes varying from 0.04 ha to 11248.31 ha.
According to Table 3, 92.5% of these remnants have less than 5 ha, however, they represented only 5.9% of the total native forest area. Where: NP = number of forest patches; AREA -habitat size; PERIM -perimeter; SHAPE -shape index; NEAR -distance of the nearest neighbor edge; * mean value; and **SD: standard deviation value.
Otherwise, we observed that 0.2% of the total patches (i.e. 21 patches) occupying 50% of the total forest area. Most of these restricted group belongs to three Protect Areas, located inside the study area i.e.
This way, the pattern of forest patches that are distributed through the landscape studied have sizes varying from 5 ha to 300 ha. As prede ned for this study, their size classes are occupying similar percentage of the native cover ( Table 3).  (Table 3).
Similarly, the PERIM and SHAPE metric values (mean and SD) increased as the patch sizes were increased ( Conversely, the NEAR metrics value (mean and SD) decreased as the mean patch size increased. According to According to the Moral Index (Fig. 7), the metrics presented signi cant and positive spatial autocorrelation. Although, the spatial autocorrelation of NEAR (1.000) was slightly higher than the AREA (0.971), PERIM (0.968), and SHAPE (0.963).
Consequently, the LISA index indicated groupings in regions with spatial proximity between similar characteristics (Fig. 7).
In the case of the NEAR metric (Fig. 7), we can highlight groupings classi ed as low-low in the central portion of the study area. They represented the concentration of areas with high distance values from forest patches.
For the other metrics, we can highlight the small low-low groupings, representing the concentration of the largest patches, characterized by the greatest perimeters and irregular shapes ( Fig. 7b-d).

Criteria and Forest Structure Analysis
The patches, representing the forest structure of the study area, were associated with criteria characteristics, as described in Table 4.
Relating to the slope criterion, they were predominately associated with regions varying from 6.66-17% declivity (Slope mean = 11.83%), that compound the 91% of the study area with declivity at most 20% (Fig.   4A). However, there is forest patches associated reliefs ats (Slope min = 0.002%) as well as Heavily-Undulating (Slope max = 36.36%) ( Table 4). We de ned the predominant pattern for the criterion based on its low standard deviation value. Table 4 also indicated TWI and NDVI in the same situation.
This way, regions associated with the forest patches showed TWI varying from 4.81 to 9.35 (TWI mean = 7.08). Values that integrated this more range frequently of moisture-retention ability were observed in the landscape (Fig. 4B) Relating the aspect criterion, the mean value indicates a tendency of the patches to be placed on the East-West face (Aspect mean = 177.03). Although, the high variation value of SD (Aspect sd = 70.67) cannot support the pattern de nition for those regions. Especially, when we consider its spatial pattern of the majority features distributed randomly across the landscape, which was indicated by the Moran Index (I = 0.292) and the LISA index (Fig. 4e 5C).
Otherwise, we can a rmative that the great part of forest remnants is at mostly 325.75 m from the watercourses (drainage mean = 7.08) ( Table 4), that in 92% of the landscape are at closest 400 m from the rivers (Fig. 4D).
The forest patches also presented mean distance from the low-density urban area and highways of 829.44 m (SD: ± 878.10m) and 1680.86 m (SD: ± 1844.85m) ( Table 4) (Table 4).
According to Table 4, the forest patches showed mean distance among then of 2440.01m (SD: ± 1671.40 m). As the last two criteria, the mean values and standard deviation values re ects the presence of the patches through the landscape (Fig. 4g). The same way, the criterion presented the highest spatial autocorrelation values (Moran I: 0.992) among the criteria, supporting the concentration of remnants in same regions of the landscape. Where the NEAR metric (Table 3) indicated values varying from 21.56 m to 107.67 m for patches grouped in similar size classes. Still, the minimum distance indicated in Table 4 was 59.12 m.
This way, the criterion re ected the forest patches scattered across the landscape, having a mean distance among them of 2440.01 m, but with some remnants near to each other (Dist_patch min = 59.12m).
The mean NDVI index of these patches varies from 0.55 to 0.61 (NDVI mean =0.58), which was the minor range of SD, among the criteria (Table 4). We obtained these values based on a hexagon network sampling, obtaining the NDVI values inside of the patches.
The criterion map presented Moran index of 0.500, indicating these small groupings. However, for the landscape prevailed its mainly characteristics, that is the low spatial autocorrelation (Fig. 4h) Concerning the Canonical correspondence analysis (CCA), Fig. 8 illustrates that the forest patches metrics explain in 84.10% the criteria ordering.
The data variability was explained in 66% by the axis 1 and 18.10 by the axis 2. Through the rst, we observed the greatest in uence of the metrics NEAR and PERIMETER. While in the second, the main ordering variables were SHAPE and NEAR. However, the area variability was not signi cant (Fig. 8).
The CCA analysis (Fig. 8) also indicated that the forest patches perimeters values increase as the distance value from the highways increases too. Conversely, decreasing the distance from the low-density urban areas decrease, the distance among forest patches (NEAR) also decreases. Such happens because low-density urban areas are composed of small urban agglomerations, which are scattered among the forest fragments.
In the same way, the aspect, TWI, NDVI, slope, and distance from the drainage network showed variation in their values associated with the metrics SHAPE and PERIMETER. The criteria values decrease when the rst metric decrease and the second increase.
Finally, we observed a no-signi cant relation between the metric AREA and the criterion distance from the forest patches.

Discussion
The environmental criteria, that were selected through the literature review (Tables 1 and 2 As we mention in Table 2, the criteria have different importance for the functional connectivity and forest conservation, representing a part of the process to obtain the main objective. Importance that has been In the case of criteria selected for the study area in the GBBR-SP, Brazil, they are not spatially correlated and no have information overlap (Figs. 4 and 5). Thus, they can be used to prioritize areas to functional connectivity.
Relating the main characteristics bring for the criteria, we obtain through the slope that 91% of the study area showed declivity at most 20% (mean value of 11.83%; ± 5.17) ( Table 4 and Fig. 4A). This predominance of declivity value associated with the low variation of its standard deviation supports the de nition of a spatial pattern for the criterion, which was identi ed by LISA index (I = 0.457) (Fig. 5A). Authors as Adams, Barnard and Loomis (2014) complement that tree growth and forest productivity can be affected by slope, as well as for the TWI and aspect due to in uences on runoff and wind exposure. Thus, these factors allow the elaboration of forest connectivity models based on relief, as the species have different habitat requirements (Czarnecka, Rysiak, and Chabudzinski, 2017).
Relating to TWI criterion, we obtained approximately 62.1% of the total area varying from 5-12, including soils classi ed as well-drained (TWI of 4-5), moderately drained (TWI of 5-7), and poorly drained soils (TWI of 7-12) (Li et al., 2006). Approximately 43% of this total is associated with the moderately drained soils, contributing to classi cation of this areas as low-low by LISA Index (Fig. 5B), since they are showed a scattered distribution through the landscape.
According to our results, regions associated with the 5-12 TWI range are occupied by forest fragments, showing an average of 7.08 and a low standard deviation (± 2.27) ( Table 4).
This way, TWI was characterized as a heterogeneous criterion, having Moran Index (I) of 0.190) as also mentioned by Da Silva, Santos and Oka-Fiori (2019).
Similarly, the aspect also was de ned as heterogeneous, having an I value of 0.292, however with a standard deviation of ± 70.67, (Table 4). This criterion behavior occurs in our study area, even it characterized by has a topographic divider of water ow and, having 65.3% of its area associated with East-West slopes facing (Fig. 4C). These facings are associated with forest patches groups (LISA index, Fig. 5C), which are the most regular patches of the landscape placed in faces with the lowest aspect values (CCA analysis, Fig. 8). This can be explained by the predominance of anthropic land-use on the east landscape face (Victor et al., 2004).
Aspect reveals a tendency to coming toward the slope values because they came from DEM. However, we cannot establish a statistical and signi cant pattern between them. Adding the fact, that the criterion does not present high spatial correlation, it cannot be considered adequate for a model of prioritization areas, aiming the functional connectivity. This justi ed by the uncertainties in connectivity analysis, that the aspect can bring to the model. According to our results, the aspect is the only environmental criterion not adequate for prioritizing areas to obtain forest functional connectivity, in landscape subject to the urban sprawl.
In the same way that the slope and TWI, the distances from forest patches and drainage network criteria are essential to model of the prioritization of areas subject to urban sprawl (Fig. 4D).
According to these maps the average distance of forest patches from the water courses was 199.27 m, with 56% of them at most 200 m. Considering that 36% of the total forest patches is between 200m and 400 m from the river and ± 126.48m as maximum value of deviation standard (Table 4), we obtained that the majority patches (including the 56%) is from 325.75 m from a watercourse.
The distances from the drainage network criterion supported these results. Firstly, because the watercourses are adequately distributed throughout the study area (I = 0.477) (Figs. 4 and 5D), that resulted in a high spatial autocorrelation with a value superior to the topographic criteria. Second, because the autocorrelation supported the clusters structuration in regions, where there were the minor distances of the patches from watercourses (LL in LISA), as well as there were the highest (HH) distances ( Fig. 5D).
Observing the criterion results, we noticed that they were predominately supported by the relation with the proximity to watercourses, which is the most important region for the main objective. This way, the most adequate name for the criterion is proximity to the drainage network instead of the distances from the While the watercourses are scattered through the landscape, the main features of the distance from the low-density urban area and highways criteria showed concentrated, mainly, in its Central-to-South-west portion ( Fig. 4E and Fig. 4F). Due the presence of the great urban areas and roads, the forest patches cluster of this regions presented spatial autocorrelation classi ed as LL ( Fig. 5E; I = 0.976 and Fig. 5F; I = 0.992). It is noted in the Fig. 4E that a restricted area was created over consolidated urban agglomerations, to analyze only the effects of urban sprawl on forest remnants. However, the features of criteria (roads and urban) and consequently theirs respectively distance maps showed an effect in the forest fragments spatialization. Around 71% of the forest patches are 2000 m from an urban area and 86% of them are 2000 m from a road.
Anthropogenic disturbance in the landscape favors generalist species that are able to explore environments, such as disturbed habitats (Magioli et al., 2019). Consequently, there is an increase in con ict factors, such running over wildlife (Abra et al., 2021), predation of farm animals (McPherson, Brown, and Downs, 2016), and animals lethal control (Blackwell, et al., 2016), being essential to de ne the most bene cial actions of conservation planning and implementation (Abra et al., 2021).
Con ict features that showed high spatial correlation (PCA analysis, Fig. 6), indicating that they can compose a unique criterion in future studies. Criterion that brings information related with the connectivity, since that urbans areas and road have crossed landscapes subject to urban sprawl, which have become one of the greatest threats to biodiversity conservation (Scriven et  Relating the importance to maintain the criteria distance from forest patches, our results indicate that we have forest patches supporting the native fauna and ora, especially the group formed by patches with sizes greater than 300 ha (Table 4 and Fig. 4H). As we mentioned, this group is formed by 21 patches, belong to three Protect Areas, located inside the study area, and occupy 50% of the total forest area. Even more, these forest patches are integrated with others, considering that the minor than they are scattered across the landscape (Table 3).
According to Magioli et al. (2019), the large and continuous habitats support populations with more complex trophic structures, acting as a source for biodiversity maintenance in modi ed habitats. Gibson et al., (2011) complemented that these habitats are essential refuges for wildlife, assuming that their similarity to natural areas (i.e, without anthropic actions).
The Brazilian environmental legislation has been encouraged the conservation of areas as patches greater than 300 ha, however, it is not enough to minimize the urban pressure effect (Romero et al., 2020). In our study areas is not only this group that has potential for connectivity in the studied landscape. We can include the group having medium size too, highlighting the importance of the criterion distances from forest patches. Considering these proximity relations among the forest patches, we can suggest for next studies the name proximity to forest cover as proposed by author as Mello et al., 2018. Showing different behavior of other criteria, we have the NDVI. The traditional index represents the forest patches in terms of their status and/or quality (Fig. 4H) i.e., the conditions inside the remnants. Consequently, it is not a criterion that represents the conditions of the natural vegetation on the landscape, as our objective requires.
However, patches-level data are important to support the decision-makers discussion, which guided us to includes our second objective.
For the study area, the patches-level metrics showed coherent resultants, considering the classes areas, that we proposed. The largest forest remnants showed great values of perimeter and shape than the smallest, but minor values of distance among their components (Table 3).
Furthermore, the class areas supporting the evaluation of the spatial autocorrelation among metrics and after, among metrics and criteria.
The results were a high Moran index value for metrics (Fig. 7), which supported in their correspondence with the criteria since these results re ected that the external in uences on the fragments did not occur randomly and that the criteria act on the landscape (with 84.1% of explanation in CCA, Fig. 8). The CCA analysis (Fig. 8) also indicated that the reduction in the distance from low-density urban areas was associated with a reduction in the distance among forest fragments (NEAR). While the distance from the highways was associated with an increase in the perimeter of the forest patches, and consequently their respective areas. According to Pirnat and Hladink (2018), new diffuse urban areas are not subject to signi cant changes in terms of habitat size and this seems to happen regardless of population changes (Organization of United Nations Habitat, 2016).
Otherwise, the drier regions of the landscape, on the atter terrains, near to the rivers, and facing to the east face were associated with our smallest and most irregular patches, that were isolated and presented the lowest NDVI values. Thus, in these landscape regions, the condition related to the urban infrastructure and topography were favorable to human occupation, as also observed by Torres, Jaeger, and Alonso, 2016.

Conclusions
This study evaluated environmental criteria for prioritizing areas to obtain forest functional connectivity in a landscape subject to the urban sprawl.
Our study area, the GBBR-SP region, brings the theme importance since its urbanization occurs in areas originally occupied by Atlantic Forest. However, that has its agricultural production destinated to São Paulo city, one of the largest cities in the world. This way, our major challenge is to incorporate a forest network in the land-use/land-cover planning.
Our results indicated that we obtained robust criteria through the literature review, decreasing the intrinsic subjectivity commonly associated with their de nition in the participatory technique context. Criteria set composed by slope, TWI, distance from drainage network, distance from highways, distance from a lowdensity urban area, and distance from forest patches. Also, they are not spatially correlated or have information overlap.
In this context, these criteria support identifying regions where it is possible to have the persistence of forest fragments, even though in places under the impact of urban sprawl. Highlighting that we obtained a diffuse urban expansion process in the GBBR-SP region that does not occur randomly.
However, thinking that the criteria names re ect their respective features and importance to the study, the adequate name could be proximity to drainage network and proximity to forest patches instead of distance.
Otherwise, we concluded that aspect and NDVI (originally selected) are not adequate criteria, thinking in prioritize forest areas to functional connectivity, considering that the rst showed a heterogeneous behavior through the landscape, revealing a tendency to coming toward the slope values because they came from Digital Elevator Model. The second re ects the patches' quality instead of their potential for forest connectivity.
In this context, we can a rm that the selected criteria re ect the forest structure. Furthermore, they support identifying areas near to watercourses, associated with the deep slope, the greatest moisture retention potential. Areas covered by the great forest patches are the most irregular and connected of the study area.
In this sense, the most distant locations from the highways re ect areas with more preserved forest structure characteristics. However, in areas under diffuse urban expansion, large and connected forest fragments are close to low-density urban environments. Highlighting that these regions are also important for functional connectivity.
This way, our ndings indicated a spatial autocorrelation among metrics and after, among metrics and criteria. Also, we obtained that the external in uences on the fragments did not occur randomly and that the criteria act on the landscape.
Finally, our results reveal value ranges more suitable for each criterion in the environment under urban sprawl to indicate the occurrence of forest fragments, aiming for functional forest connectivity.   Forest patches and hexagonal network, that was used to criteria evaluation of the study area in the GBBR-SP, Brazil.