Landscape and connectivity metrics as a spatial tool to support invasive annual grass management decisions

The spatial patterns and context of invasions are increasingly recognized as important for successful and efficient management actions. Beyond mapping occurrence or percent cover in pixels, spatial summary information that describes the size and arrangement of patches in the context of a larger landscape (e.g., infested regions, connected patch networks) can add a depth of information for managing invasive grasses that threaten native ecosystems. Few invasive annual grass analyses have explored the use of landscape and circuit-based connectivity metrics to characterize and compare spatial patterns of invasion. To assess the transferability and applicability of these landscape ecology analyses, we calculated landscape metrics (4 area-based, 3 configuration) and a connectivity metric (circuit-based centrality), using a weighted-average map of invasive annual grass cover in the Great Basin, USA. We calculated metrics at local and regional scales, allowing invasion statistics to be compared across the landscape and illustrating varying patterns of invasion extent and connectedness. We found the metrics provided additional, complementary information at the sampled local and regional scales beyond abundance measures alone. We also illustrated how key metrics could be used to categorize and map areas needing different management strategies, for example, where strategies could proactively protect uninvaded cores, disconnect fine fuel patches, or contain established invasions. The landscape and connectivity metric approach can be applied across scales to spatially target patches locally, provide broader context within a single region, as well as to compare metrics and spatial variation in patterns among different regions.


Introduction
As ecosystems change, standardized approaches are valuable for quantifying spatiotemporal patterns and informing subsequent management actions. Habitat loss and restoration studies, for example, have long benefited from landscape metrics methods to characterize fragmentation and compare patterns across space and time (Uuemaa et al. 2009;Fardila et al. 2017). However, this metrics-based approach from landscape ecology has yet to be broadly applied to grass invasions at the landscape scale. Invasive annual grasses alter vegetation communities and pose many challenges for conservation and management. Where invasive grasses outcompete native species, they can fragment wildlife habitat and effect human land uses (Davies et al. 2021). Invasive grasses, as fine fuels, also influence fire regimes and are an important consideration in wildfire management (D'Antonio and Vitousek 1992;Brooks et al. 2004). Total eradication is impossible for widespread invasive species such as cheatgrass (Bromus tectorum), which is found across millions of hectares in North America (Davies et al. 2021). Instead, management actions focus on strategically reducing invasion risk or increasing resistance to invasion (Lodge et al. 2016;Crist et al. 2019;Maestas et al. 2022).
Management decisions about where to invest in monitoring, control, and treatment of invasive annual grasses often rely on presence and abundance of the invasive species (Tarbox et al. 2022). Despite increased accuracy in mapping invasive grasses (Pastick et al. 2021), few analyses have characterized spatial patterns and context of invasion (Crist et al. 2019). Landscape metrics can fill this need by providing standardized, comparable measurements at multiple spatial scales (McGarigal 1995) to quantify the area and configuration of terrestrial invasions. Whereas abundance estimates can quantify the amount of invasion, landscape metrics can additionally characterize the spatial patterns of invasion and provide more information and context needed to inform targeted management decisions. Areas that have similar abundances of invasive grasses may differ, for example, in the configuration of invaded patches, or the size and aggregation of those patches. Abundance additionally cannot capture the connectedness and linkages among invaded patches, but these can be measured using connectivity metrics (Keeley et al. 2021). By bringing together a metrics-based approach from landscape ecology with an understanding of invasion ecology, landscape and connectivity metrics are well-suited to provide valuable information about invasion patterns that would otherwise be lost in abundance-only measurements.
Scientists and practitioners have recognized the importance of spatial patterns and context for invasive grass management, identifying a need that landscape and connectivity metrics can fill. Partnerships and associations across the western United States (i.e., the Idaho Cheatgrass Challenge, SageCon West's Invasives Initiative, the Western Governors' Association Invasive Annual Grass Toolkit, and the U.S. Department of Agriculture Natural Resources Conservation Service Working Lands for Wildlife, among others) have developed a cohesive, geographic strategy for invasive grasses to "defend and grow the core", prioritizing proactive management around intact, uninvaded "core" areas (Creutzburg et al. 2022;Maestas et al. 2022). Landscape and connectivity metrics can be leveraged to both identify and to monitor areas that fit within this strategy and support specific management objectives. For example, metrics about patch number and size could be used to identify and monitor "cores". Another management concern, wildfire, could be supported with connectivity metrics used to determine regions where invasive grasses are highly connected as fine fuels, and where intentional disconnection or fuel reduction may be desired to reduce potential for fire spread. The standardized nature of metrics also makes them particularly useful as they can be calculated at a variety of spatial extents (Frazier and Kedron 2017), compared across regions, repeated through time, and updated as needed with different inputs.
We applied a metric-based approach to characterize area, configuration, and connectivity of invasive annual grasses as a proof of concept using the Great Basin region in the United States of America. We developed examples of how landscape and connectivity metric outputs could support invasion management that considers both local and regional invasion severity and patterns.

Methods
The Great Basin region of the western United States is approximately 502,615 km 2 and has extensive existing annual grass invasion (Fig. 1a). As the input for our metric calculations, we used an annual herbaceous cover synthesis map (weighted-average of 3 spatial data products over multiple years) that primarily describes cheatgrass (30 m resolution; Maestas et al. 2020). We considered all pixels with > 10% abundance to be invaded, and invaded pixels were used to define patches. We calculated landscape and connectivity metrics within defined spatial extents at the local level (15 × 15 km grid cells; n = 2408). Summarized metric values within and across grid cells were then used for broad-scale regional visualization and comparison of spatial invasion patterns. We also calculated the dominant percent grass (hereafter, cover class) for each grid cell and total abundance across the Great Basin, following convention to classify invasion into low (0-10%), mild (11-25%), moderate (26-50%), and high (51-100%) cover (Maestas et al. 2020).
We calculated seven landscape metrics at the local level. Area-based metrics included the number of invaded patches, mean patch size, total invaded area per grid cell, and largest patch index (percent of the grid cell occupied by the largest patch). Configuration metrics included the Euclidean distance to the nearest neighbor invaded patch, patch contiguity (the spatial connectedness within a patch), and aggregation index (based on the number of like adjacencies within the class compared with the maximum possible number of like adjacencies) (McGarigal 1995;Hesselbarth et al. 2019).
We chose this subset of the many available landscape metrics in order to represent information that is relevant to invasion proliferation and easily interpretable. We calculated the metrics (based on FRAGSTATS; McGarigal 1995) using the 'landscapemetrics' package (Hesselbarth et al. 2019) in R version 3.6.2 (R Core Team 2019).
To characterize connectivity of annual invasive grasses, we calculated betweenness centrality (hereafter, centrality). We used this connectivity metric to represent the relative contribution of pixels within each grid cell in facilitating connectivity across the landscape (Estrada and Bodin 2008). Using annual herbaceous cover (Maestas et al. 2020) as our conductance surface and pixels invaded with > 10% abundance as our source threshold, we calculated the normalized cumulative current density based on omnidirectional circuit connectivity using Omniscape (Landau et al. 2021) in Julia v1.5.4 (Bezanson et al. 2017). Centrality was calculated as the sum of current density for all pixels within each grid cell (Gray and Dickson 2016).
We used the Pearson correlation to identify which metrics were likely to provide relevant information and were not redundant with each other or with abundance values. We created map summaries of metric results to visualize similarities and differences in invasion characteristics among grid cells.
We developed examples that thresholded landscape metric results by quartiles to compare invasion status and patterns across a large landscape.

Results
The presence of annual invasive grass is extensive in the sagebrush biome of the Great Basin (Fig. 1a), but the percent cover varied. About half of this landscape (200,033 km 2 ; ~ 55% of landscape area) had no or low cheatgrass cover, with 104,687 km 2 (29%) at mild abundance and 54,848 km 2 (15%) at moderate abundance. Only 2510 km 2 (0.7%) of the Great Basin rangeland was classified as high abundance cover of invasive annual grasses. Beyond abundance, we used landscape and connectivity metrics to better understand how annual invasive grasses are distributed. The metrics provided additional detail unavailable in pixel-based occurrence or cover maps, such as the number, size, and configuration of patches, even within areas of relatively low abundance (Table 1; see Fig. 2c, f, i for visualization of 3 sampled cells). We summarized the metric values and found considerable local variation in the abundance, area, configuration, and connectivity of invasive annual grasses in the Great Basin ( Fig. 1; Table 1, data generated in this study are available as a USGS data release, Buchholtz and Heinrichs 2022). Mapped values illustrate how the standard measure of cover class (Fig. 1a) can be contrasted and complemented with area-based (Fig. 1b), configuration (Fig. 1c), and connectivity metrics (Fig. 1d). Dominant cover class was positively correlated with invaded class area (Pearson correlation r = 0.72) and largest invaded patch index (r = 0.70). It was not correlated with other metrics (r < 0.70). Invaded class area and largest patch index were strongly correlated (r = 0.96).
The aggregation index indicated that invaded pixels were more likely to be adjacent to other invaded pixels. In contrast, mean patch contiguity was relatively low, with regional variation in spatial connectedness of patches (Fig. 1c). No configuration metrics were strongly correlated with each other (r < 0.70). The centrality connectivity metric identified where linkages among invaded areas were important in connecting potential invasion across the broader landscape (Fig. 1d); the centrality connectivity metric was not strongly correlated with landscape metrics or abundance (r < 0.70).
To highlight how metrics can provide valuable information in the context of management objectives, we explored three examples. These illustrate scenarios in which landscape and connectivity metric values are used to divide the landscape into categories for different management priorities. (1) Protect non-invaded areas: to prioritize protecting core areas, we used metric thresholds to identify grid cells that had limited invaded area and invaded pixels were far apart (Fig. 2a); (2) Disconnect fine fuels: for fire management, we used the thresholded metric values to identify grid cells with contiguous local patches and landscape-level central linkages (Fig. 2b); (3) Contain invasion: to identify areas with low likelihood of treatment success, we used thresholds to identify grid cells that were dominated by large patches and moderately high or high invasive abundance (Fig. 2c). We used the quartile divisions of metric values to set thresholds for illustration purposes, however, management will want to set these thresholds based on specific objectives, ecological context, and local knowledge.

Discussion
These metrics provide an accessible and intuitive approach for characterizing the spatial extent and connectivity of invasive grasses that can be applied to local areas of interest, while also being standardized and comparable across space and time. We characterized invasive annual grasses in the Great Basin using landscape and connectivity metrics to illustrate a scalable approach to quantifying invasion patterns and severity. We found considerable local and regional variation in the extent and connectivity of invasive annual grasses in the Great Basin, and that many landscape metrics can complement abundance measurements by providing additional information about spatial context and patterns of invasion. There are many ways in which invasive grasses can be distributed in patches and across a landscape, requiring the use of area, configuration, and connectivity-based measures to more fully describe. Using a selection of landscape and connectivity metrics, we characterized the spatial patterns of annual grass invasion at local and broad scales in the Great Basin. When compared with existing abundance estimates of invasive grass, most of the metrics we calculated were not strongly correlated with dominant cover class, indicating the potential for metrics to provide complementary information about spatial context and patterns of invasion. The metric values also highlighted high variability at the local scale. Patch sizes within each grid averaged 157.0 ha but had a large mean standard deviation (1498 ha); some grids were entirely covered by one large, invaded patch. Configuration and connectivity metrics also varied widely, with local differences in how close, contiguous, or aggregated invaded patches were. Invaded patches were on average only 151 m apart (SD ± 324 m, summarized at the grid level), emphasizing the proximity among invaded areas across the region. In general, this spatial variation underscores the importance of assessing and comparing local patterns, even among areas with similar abundance of invasive grasses.
Beyond simply measuring invasion with landscape and connectivity metrics, metric values can be used to categorize the landscape and support prioritizing, spatial planning, and targeted management. In our example scenarios for the Great Basin, we illustrated how metrics could be used to categorize patterns and identify opportunities for different management strategies. For instance, protecting core uninvaded areas is a key priority for invasive grass management. We used landscape metric values to identify the regions on the landscape that met specific metric-based thresholds that would indicate "core" uninvaded status. Area and configuration metrics, such as the total number of patches, average patch size, largest patch index, and distance between patches, could also be monitored over time to track potentially increasing invasion. Management planners could set thresholds to align with their capacity to intervene and actively manage invasion and use trends in landscape metrics to trigger actions (Creutzburg et al. 2022). For example, an action threshold based on mean patch size and nearest neighbor distance could be used in the southern Great Basin to prioritize action where limited herbicide or chemical treatments may be impactful on smaller, clustered patches of invasion.
In areas that are already invaded, management strategies will vary based on the spatial patterns and context of the invasion. Our second illustrative example identified regions that have more contiguous patches and are important, high-centrality hubs for potential fire spread via invasive grass connectivity. Where invasive grasses are both abundant and well-connected, fuel reduction can be targeted to intentionally fragment and limit potential fire spread; in contrast, high-abundance areas that are isolated may be targeted for containment to reduce risk of invasives spread to neighboring uninvaded areas. Additionally, calculating metrics before and after management actions could help quantify the impact of local treatments on landscape-level invasion. Landscape and connectivity metrics provide additional information to help target specific management actions in specific locations. Across the larger landscape, comparison of invasion using landscape and connectivity metrics (e.g., among grid cells) can identify broad patterns and action zones that require regional coordination among invasives managers. These applications of the landscape metric approach are facilitated by the relatively straightforward and fast calculations of metrics using freely available software resources.
We focused on a handful of key metrics for this proof of concept, yet additional metrics can be relevant for characterizing invasion and planning specific management strategies. Future work could calculate metrics related to interspersion and the length of patch edges, representing the interface between intact, non-invaded areas and invaded areas that are relevant for targeting actions to 'grow the core'. Landscape metric calculations use discrete thresholds of invasive cover maps to define patches and classes of invasive percent cover and result in statistics and patterns that are straightforward to interpret and compare. Each threshold can be defined based on ecologically-or management-relevant thresholds to suit specific objectives. Follow-up research could additionally explore the calculation of landscape and connectivity metrics to more fully express a gradient of invasive cover conditions, without the need for thresholds to define patches and classes (Frazier and Kedron 2017;McGarigal and Cushman 2005). Further applications could pair this information with local expertise, priorities, and other data to provide a broader ecological, practical, and decision-making context. This landscape and connectivity metrics approach to characterizing invasion seeks to simplify a complex, heterogenous, and dynamic invasion of annual grasses, to support multi-scale understanding of the invasion problem. Characterizing variation in spatial pattern and ecological context is crucial for successful management of invasive grasses (Crist et al. 2019;Maestas et al. 2022) across spatial and temporal scales (Magness et al. 2021). Standardized approaches such as landscape and connectivity metrics provide repeatable, comparable tools to quantify and address challenges of changing ecosystems such as those affected by invasive annual grasses.