Encyclopedia
Please note this is a comparison between Version 1 by Marcelo Miranda and Version 2 by Beatrix Zheng.
Graph metrics allow the description of landscape heterogeneity in the same way as classical metrics, and they consider compositional, configurational, and topological characteristics. Some graph metrics that consider topology provide new information owing to the application of topological relationships that are not necessarily based on a Euclidian space. A graph analytical perspective enables the incorporation of new biophysical information related to ecological processes beyond the conventional LULC categories applied in classical landscape analysis. Consequently, more complex ecological questions can be addressed, for example, relationships between ecological processes at the level of topology or topological relationships between processes beyond the traditional dimensions.
- landscape graph metrics
- landscape heterogeneity
- spatial graph
- landscape characterization
1. Introduction
Landscape ecology appraises the interactions between spatial patterns and ecological processes, analyzing causes and consequences of spatial heterogeneity in ecosystems across a range of scales [1]. To understand the role of landscape heterogeneity in biodiversity, the habitat-matrix framework based on the theory of island biogeography [2] and the patch-mosaic model have been developed [3][4][5][6][7][3,4,5,6,7]. The first regards natural or seminatural habitat patches containing all resources necessary for organisms as being embedded in a homogeneous and hostile matrix usually composed of agricultural land cover [8]. The second considers the interactions between habitat patches as being dependent on mosaic properties such as resistance to the movement/dispersal of organisms [9]. One of the most important ideas to emerge from these approaches is that relationships at a local scale can produce effects at large spatial scales and vice versa, affecting the dynamics of the whole ecosystem [10][11][12][13][14][15][10,11,12,13,14,15]. Nevertheless, classical metrics do not directly account for these dynamics. More recently, Fahrig et al. suggested describing landscape heterogeneity on the basis of the composition (amount and diversity) and configuration (spatial arrangement) of landscape features [4].
To elucidate the impact of landscape heterogeneity on ecological process, many patch-based metrics have been developed to measure and synthesize the attributes and geometric characteristics (form, spatial relationship, and connectivity) of different patches associated with both single landscape elements and whole landscapes. Despite being extensively applied to relate landscape heterogeneity to ecological patterns, these metrics show limited integration of mosaic properties/functions (e.g., resistance to movement of organisms) [7][16][7,16].
Landscape ecologists have turned to graph theory driven by a desire for a more functional approach to landscape quantification. In this framework, the landscape is represented by a set of nodes (habitat patches) connected by links or edges formed by potential ecological fluxes (e.g., dispersal or movement); together, these nodes result in a landscape graph [7][17][7,17]. Graph theory provides a formal foundation for studying the effects of landscape graph structure on ecological patterns. It also represents a powerful and effective way to analyze landscape connectivity [5][18][19][20][5,18,19,20]. Nevertheless, empirical ecological studies applying this framework are still scarce.
Graph theory has mostly been used in areas such as chemistry, physics [21][22][21,22], social sciences [23][24][23,24], and computer science [25]. Since its introduction to landscape ecology by Urban and Keitt in 2001 [26], it has been increasingly used to measure multiple aspects of connectivity in the context of conservation biology, land-use planning, and biogeography [12][20][27][12,20,27]. Consequently, a wide variety of metrics have been developed to characterize landscape graphs. These metrics involve either local descriptions related to structures, movements, and fluxes at the level of nodes and edges or global descriptions at the level of the entire graph (for reviews, see [20][28][20,28]. Consequently, the selection of appropriate measures that can explain the phenomenon being studied poses a challenge to landscape ecologists [20].
Most landscape ecological studies using graph theory treat landscapes from a habitat-matrix perspective [10][20][26][10,20,26], are dedicated to one species or groups of species, and use dispersal strategies as the link between nodes [6][29][30][6,29,30]. However, because some species or groups of species are associated with (1) particular land-cover types (i.e., specialist species), (2) use different land-cover types to complete their life cycles (complementation/supplementation processes), and (3) can move between habitat patches (e.g., through neighboring or mass effects; [31][32][31,32], it is necessary to jettison the habitat-matrix perspective and consider the whole landscape mosaic. In addition, among the growing number of studies analyzing landscape connectivity with graphs of biodiversity [33], most are dedicated to animals (e.g., [5][6][5,6] whose nodes are habitat patches and whose links are migration or movement routes [10]. Studies investigating the effects of landscape connectivity on plants are scarce (see [34] for a review). Depending on their dispersal strategies, plants can spread and make connections between habitat patches, creating a landscape network [11].
2. Graph Metric Analyses
Landscape metrics are quantitative indices that describe compositional and configurational aspects of landscapes, the latter being typically described as discrete entities or patches [7]. The release of the FRAGSTATS program [35][103] in 2012 revolutionized landscape structure analysis and made landscape metrics the most common tool to understand biodiversity, ecological processes, and functions at the landscape scale [7][36][7,104]. Today, hundreds of different metrics are used to measure landscape patterns [37][105]. However, some of them present problems such as redundancy and high correlation, limited consideration of spatial patterns, and difficulties in interpretation leading to inappropriate inferences [7][36][38][7,104,106]. Although some of these problems are also apparent in graph metrics, graph theory presents great potential for understanding processes and functions at the landscape scale and considering the type of landscape phenomenon (plant dispersal, animal movements, fire propagation, etc.). Calabrese and Fagan highlighted the potential of graph theory due to its low data requirement given the benefits it can deliver [39][107]. Kupfer showed that, for a selection of landscape metrics, there is a tradeoff between (1) data requirements and ease of calculation of the metrics, (2) their basis in structural versus functional properties, and (3) their ease of interpretation [7]. In this sense, graph metrics are at the midpoint between structure and function, but they are usually more difficult to calculate and interpret than the commonly used structural metrics [7].
As demonstrated here, graph metrics must be used according to the type of information provided by the metric. While there are some metrics that can be applied at the landscape scale and provide a single value for the whole landscape, others are informative about the role of one node in relation to its neighbors or the rest of the landscape. Among the metrics used to characterize the whole landscape, those that appraise the heterogeneity, connectivity, atomization, or assortativity of the landscape can be differentiated. On the other hand, among the metrics used to characterize the landscape at the local scale, it is possible to distinguish between metrics that are informative about node importance and those that explain its local heterogeneity (compositional and configurational).
Graph/landscape heterogeneity metrics provide information similar to that offered by classic compositional metrics, such as the number of patches and total edge. They can easily be incorporated into a characterization and evaluation of a given landscape, consequently facilitating the analysis by providing both points of view (classical and graph theory analyses).
Several metrics available for graph connectivity at the landscape scale provide information about the quantity of interactions between nodes (maximum degree and mean and median node degree). These descriptive metrics can be complemented by observing the complete distribution of the degrees of the landscape nodes.
On the other hand, the number of edges, mean node distance, and graph density provide information about the number of connections and their density or degree of topological aggregation/disaggregation that are not necessarily in a Euclidean plane. Given that the three metrics are correlated with the number of nodes in the landscape, which in turn could hide important patterns, thwe researchers rececommend modifying these metrics so that their values are independent of the number of nodes. In addition, a particular value of these metrics may be obtained either from a rather “uniform” network or from a network consisting of a very cohesive region (with points of high degree) and a very sparse region (with points of low degree; ref. [40][67]), which could also hide landscape patterns.
Graph diameter, which represents the topological distance between the two farthest nodes, is an easily interpretable metric, which allows consideration of processes associated with connectivity that are not necessarily Euclidean. However, it is necessary to account for its value being influenced by differences in any of the edges that make up the diameter, rendering changes or differences in other parts of the graph invisible.
Cluster metrics are probably the most dissimilar to the classic metrics of landscape ecology. The number of communities based on “greedy optimization of modularity” and “the leading eigenvector of the community matrix” are mainly metrics measuring the configurational heterogeneity of the landscape, while the number of communities based on “propagating labels” is related to both configurational and compositional heterogeneity.
The last metric at the landscape scale, the degree of assortativity, is also very different from any other classic metric of landscape ecology. It allows relating connectivity between nodes to some external property. Here, the number of connections is used to measure their assortativity, but any other characteristics of the nodes can potentially be used. For example, if information is available on patches with a certain disease, it is possible to evaluate the degree to which the disease clusters or whether it is dispersed in the landscape, which could provide valuable information for its management.
At the local scale, metrics associated with node importance, which indicates the extent of connectivity of the nodes, are configurational metrics that demonstrate their significance in relation to others, revealing local flow capacity. The different methods for measuring them represent the different ways to see their topology. These methods may be related to the compositional metric, edge density (which measures the m/ha of a class per patch, class of land use/land cover (LULC), or landscape), but the methods themselves do not measure the flow between patches.
Compositional heterogeneity is one of the newest measures, along with cluster metrics, which identifies communities or groups in the landscape on the basis of LULC and the amount of connectivity between nodes. It describes heterogeneity at the local scale as a function of the first-order neighborhood. In the configurational heterogeneity group, patch area and perimeter are metrics that provide the same information as the classic configurational metrics obtained from raster data. This occurs because the configuration of each node of the graph contains the area and perimeter information of each patch as an attribute. This is useful since it is possible to add other patch attributes, such as temperature, primary productivity, and type of management. On the other hand, the other two metrics in this group measure the number of communities surrounding each node. It is not possible to obtain this information by classic metrics of landscape ecology.
3. Implementation of Graph Metrics
As Kupfer stated, graph metrics are more difficult to calculate and interpret than commonly used structural metrics [7]. This calculation difficulty is in part due to the lack of software that can construct and analyze graphs [7]. However, the development of new packages in open-source software, such as R, is providing the opportunity to overcome this barrier by using them in conjunction with other tools, such as sf, raster, and landscape metrics, to analyze landscapes [36][41][42][43][104,108,109,110] or specific to graphs such as graph4lg, Makurhini, and igraph [44][45][46][44,111,112]. Unlike other software for calculating graph-based metrics, R allows integration of large workflows and reproducibility of analyses, as it is available for the most common operating systems [41][108]. Given the many approaches to quantify spatial patterns (e.g., landscape, graph, and surface metrics) and that there is no one-size-fits-all solution [37][105], different complementary approaches may be required for the same study, and R is the program with the highest potential to offer them.
However, by reducing technological barriers, the same problems that occurred with FRAGSTATS development, i.e., the use and misuse of metrics due to the problems mentioned by Gustafson, Kupfer, and Li and Wu are possible [7][36][38][7,104,106]. One of these problems is the assumption that the matrix is homogeneous, when, in fact, it may neither be uniformly uninhabitable nor serve as a total barrier to the movement of a certain organism [7]. Many graph metrics are based on this binary perspective of the landscape. For instance, Rayfield et al. identified 63 graph metrics, of which 29 are calculated using simple connections between habitat patches, i.e., topological relationships or the “Euclidean nearest neighborhood” metric [20]. The other 34 metrics are calculated by including node and/or edge weights characterizing some functional factor, such as patch area, the distance between patches, or the cost to move between patches. However, both types of metric (weighted and unweighted) are analyzed from the perspective that habitat patches are nodes and ignore the heterogeneity of the matrix.
In addition, one of the criticisms of the classic metrics obtained from landscapes viewed as mosaics is that many tend to characterize the landscape in a structural rather than a functional way, and they do not necessarily have a relationship with the processes that occur in the landscape [7][38][7,106]. Although the graphs in this researchtudy are based on mosaics, nodes can incorporate qualitative and quantitative information, and the links can incorporate weights, allowing the graphs to better represent the relationships between the structure and function of the landscape [47][113]. For example, edges between nodes can be weighted on the basis of patch similarity in terms of genetics, species richness, agricultural practices, or another relevant ecological factor [37][105]. Using graphs to analyze the processes and functions of landscapes through their metrics offers an opportunity to go beyond the emphasis on structural properties inherent in most traditional landscape metrics; however, the degree to which this can be accomplished with graphs is determined by the way in which nodes and edges are defined and how metrics are calculated [7][18][20][48][7,18,20,114]. To the extent that information and/or resources are available, mark–recapture studies or species-specific cost surfaces can be used to estimate the movement of organisms between patches. In this way, edges between patches can be more realistically characterized for analysis.
