Incorporating movement behavior into connectivity assessments

doi:10.21203/rs.3.rs-3962660/v1

Download PDF

Research Article

Incorporating movement behavior into connectivity assessments

https://doi.org/10.21203/rs.3.rs-3962660/v1

This work is licensed under a CC BY 4.0 License

Version 1

posted

You are reading this latest preprint version

Context

The number of publications that evaluate or utilize landscape connectivity has grown dramatically in recent years. In contrast, the biological realism and defensibility of common connectivity assessments has advanced slowly.

Objectives

I introduce a flexible methodology for evaluating landscape connectivity that accounts for potentially complex movement behavior and nuanced species-landscape interactions.

Methods

Making use of a forested landscape map, I develop the concepts and mechanics behind my connectivity assessment tools. I then describe a case study involving the Fender’s blue butterfly, and utilize this example to demonstrate the character and utility of my methods.

Results

My methods are able to identify clusters of connected resource patches, quantify and visualize movement rates between these patches, and identify connectivity-related opportunities and vulnerabilities. My results include an emergent dispersal kernel that captures the influence of movement behavior on connectivity.

Conclusions

The methods I introduce are capable of generating detailed yet practical connectivity analyses that can incorporate considerable biological and behavioral realism. My approach is straightforward, simple to implement, and the requisite data can be modest. Conclusions drawn using my methods will help identify limitations to connectivity analyses developed using circuit models.

Connectivity

Movement

Circuit theory

Graph theory

Dispersal kernel

Connectivity assessments are assertions about a landscape’s ability to facilitate or impede movement (Taylor et. al. 2006). In this context, the things doing the moving are typically living organisms, but could also include viral pathogens, inert objects, flows of energy, ideas, and so on. Connectivity can be a well-defined and objectively interpretable attribute of fractal-dimensioned networks (Schmadel et. al. 2018, Sarker et. al. 2019, Xingyuan et. al. 2023, Clauzel et. al. 2024), but tends to be difficult to assess in two or three dimensional landscapes (Guarenghi et. al. 2023, Iverson et. al. 2024, Riordan-Short et. al. 2023). Here, I describe new methods for quantifying landscape connectivity in two dimensions.

Relatively few researchers measure landscape connectivity directly, as empirical studies sufficient to do so are difficult to conduct (Ortega et. al. 2023, Carroll et. al 2024, Morin et. al. 2024), and nearly impossible to replicate. Instead, mathematical models and computer algorithms are frequently employed to obtain proxies for connectivity. Inferences used to be drawn from fragmentation indices, which are pattern metrics such as shape index, fractal dimension, or contagion (O'Neill et al. 1988, Turner 1989). But fragmentation indices have been shown to be poor predictors of connectivity when the latter is inferred from the outcome of movement simulators (Schumaker 1996). Since then, the methods we use to evaluate connectivity have improved dramatically (e.g. Mestre 2023), due largely to the development of tools that exploit graph and circuit theories (McRae 2006, McRae and Beier 2007, McRae et.al. 2008, Urban et. al. 2009, Perry et. al. 2017). Such studies have inferred patterns of animal movements across large landscapes (Carroll et. al. 2012, Severens et. al. 2013, Hromoda et. al. 2020, Finerty et. al. 2023), identified strengths and weaknesses of protected area networks (Carroll et. al. 2012), prioritized conservation and restoration activities (Dickson et. al. 2017, Pither et. al. 2023), and much more. Nonetheless, this new body of work is vulnerable to the limitation that compromised fragmentation indices; these methods are mostly unable to account for movement behavior (e.g. Iverson et. al. 2024).

Models building upon graph theory (Urban et. al. 2009), which I subsequently refer to as “graph models”, require access to a dispersal kernel (Fordham et. al. 2014, Proença-Ferreira et. al. 2023). Once a dispersal kernel has been formulated, the mathematics of graph theory can be deployed to reveal a great deal about network or landscape connectivity (e.g. Perry et. al. 2017). But the difficulty of collecting empirical movement data means that dispersal kernels are often derived from cost path estimates or similar measures (Fletcher et. al. 2023). Unsurprisingly, conclusions drawn from the use of these pattern-based dispersal kernels can suffer from biological oversimplification (Fordham et. al. 2014). Simulating movement can be an attractive solution, but regardless of the data source, easy-to-implement methods for extracting biologically nuanced dispersal kernels from movement data are lacking.

Circuitscape and Linkage Mapper (McRae et. al. 2008, McRae et. al. 2016), which I subsequently refer to as “circuit models”, have had an enormous impact on ecology and conservation (Dickson et. al. 2019). These tools use electrical theory to infer landscape connectivity from resistance surfaces (McRae 2006, McRae & Beier 2007, Pither et. al. 2023). Resistance surfaces are often assembled from extensive empirical data sets describing gene flow across complex landscapes (Peterman 2023, Calderón et. al. 2024), or from extrapolations based upon movement information (Finerty et. al. 2023). An advantage of resistance surfaces is their generality; these maps need not be species-specific, and the concept is extensible to the study of a wide variety of endpoints of interest (e.g. Tassi et. al. 2015, Tarkhnishvili et. al. 2016, Dickson et. al. 2019, Buchholtz et. al. 2023). A limitation stemming from the use of circuit models is that, regardless of the biological nuance embedded within a resistance surface, these tools cannot account for dispersal ability or behavior. Circuitscape and Linkage Mapper capture the potential for movement across complex landscapes, but are unable to condition these outcomes upon expected species-specific energetic constraints or ecological idiosyncrasies.

While fragmentation indices only evaluate pattern or structure, graph and circuit models attempt to capture functional connectivity by shifting the perspective from landscapes to organisms (Carroll et. al. 2012, Perry et. al. 2017, Dickson et. al. 2019, Finerty et. al. 2023, Guarenghi et. al. 2023, Pither et. al. 2023). But the term functional connectivity spans a continuum of biological and behavioral realism that is not thoroughly represented by these existing methods. For a simple illustration of what is missing, imagine a landscape composed of an array of cells, each having a score indicating its quality. An individual occupying a cell scored one (poor quality) might readily elect to move into a cell scored three (moderate quality). But, for an individual occupying a cell scored five (optimal quality), this option may appear undesirable. Similarly, behaviors that affect movement distance and path tortuosity might be uniquely influenced by an individual’s perception of its recent movement history. When incorporated, this type of biological detail is likely to alter estimates of functional landscape connectivity. Having methods that can capture a variety of movement-related information will give researchers the flexibility to design connectivity assessments that target a particular region of this analytic spectrum, which ranges from parsimony and generality to complexity and specificity.

Movement simulators can incorporate dispersal ability, account for species-landscape interactions and disturbance, and capture behaviors in which future decisions are influenced by past experience. Movement modeling therefore represents an efficient and widely-available research tool that should, in principle, aid in the evaluation of functional landscape connectivity. Nevertheless, little guidance has been available that illustrates how the output from simulation models can be used to generate connectivity assessments mirroring those obtained from graph or circuit models; but see Carroll et. al. (2012) and Hofmann et. al. (2023) for important exceptions. The present study illustrates one method for teasing such insights from simulation model output. Though my procedures are conceptually simple, they represent a culmination of many years of work designing, testing, and rejecting competing approaches.

My methods involve five principal steps: simulating movement within a spatially explicit landscape, extracting the portions of movement paths that link focal patches, forming an emergent dispersal kernel that quantifies the observed rates of movement between focal patches, visualizing connectivity by mapping movement paths, and identifying clusters of linked focal patches. I make use of a forested landscape to illustrate these concepts, and then apply them to explore functional connectivity for a population of Fender’s blue butterflies (Icaricia icarioides fenderi) occupying a small portion of the species’ range. My focus is on illustrating the methods I have developed, and the Fender's blue butterfly (FBB) case study is useful in this context. The FBB movement simulator I developed is plausible, as its design and parameters were informed by data obtained from empirical studies (Severns et. al. 2013, Cheryl Schultz, pers. comm.). Additional collaboration with species experts could produce rigorous, specific, and useful conservation management recommendations for this imperiled butterfly. Below, I use the FBB example to illustrate my methodology, and to explore how connectivity assessments that capture movement behavior might differ from those obtained using circuit models.

Software tools

I wrote a C-language software utility that performs connectivity analysis, which I’ll refer to as C3 — shorthand for the “Connectivity Cluster Constructor”. I also developed a suite of other algorithms that simplify the assessment of landscape connectivity. While the FBB movement simulations were conducted in HexSim (Schumaker and Brookes 2018) all of my other analyses utilized stand-alone utilities. This code-base is available to readers, and is accompanied by a step-by-step recreation of the forested landscape connectivity assessment (Appendix 1). HexSim is a popular platform for developing spatially-explicit, individual-based life history simulators (Heinrichs et. al. 2023, Lyons et. al. 2023, Mims et. al. 2023, Ransom et. al. 2023, White et. al. 2023).

The discussion that follows is, in large part, an exploration of the C3 utility and its potential for quantifying and visualizing landscape connectivity. Readers with some programming experience should be able to replicate my methods and tools without reliance on HexSim or C3. And those interested in quantifying connectivity in marine environments, forest canopies, or other spatially-complex systems could adapt my work to 3-dimensional spaces.

Study areas

To introduce my methods, I make use of a land cover map for a forested portion of the Oregon Cascades. In addition, my Fender’s blue butterfly case study runs within a map depicting a roughly 14,000 ha area situated in the approximate center of the species’ range. I refer to these respectively as the “forested” and “FBB” landscapes. Both maps are made up of arrays of hexagonal cells. The forested map was produced from Landsat Thematic Mapper data by Warren Cohen of the US Forest Service. The FBB map was derived from an ASCII Grid file exported from a geographical information system by staff at the US Fish and Wildlife Service.

The forested map is 736 hexagons wide × 1000 hexagons tall, containing 736K hexagons total. Each hexagon was assigned an integer score representing its resource quality (Fig. 1A). Non-forest areas were assigned the lowest values, while older forests were assigned the highest; hexagons falling outside of the imagery bounds were set to zero. Additional details for the forested landscape are available (Appendix 1), but not needed in the present context. I developed a separate map of focal patches to accompany the forested landscape. This binary image consists of a collection of regularly-spaced squares, though patches far from forested portions of the map were removed.

The Fender’s blue butterfly study area (Severens et. al. 2013) is located in the Cardwell Hills, to the west of Corvallis, Oregon, USA. This site contains one of the largest extant populations of the species. The ASCII Grid file representing FBB land cover has an extent of 10,896 columns × 15,231 rows, with each pixel representing a square 0.836 m² in size. This makes for a total landscape area of 13,876 ha. I resampled this raster image into a grid of hexagonal cells containing 9962 columns and 16,081 rows, slightly in excess of 160M hexagons total. The width (measured between parallel sides) and area of each hexagon are 1.000 m and 0.866 m². This fine-resolution map facilitated the simulation of individual FBB movements, which can be as short as three meters (see below). Each FBB land cover hexagon was assigned an integer score equal to the mode of the ASCII Grid pixels falling within that hexagon (Fig. 2). Subsequently, 1639 ha that had been assigned a “no data” classification in the ASCII grid file were merged into the “non-habitat” category in the hexagon grid. The resulting map of hexagonal cells contained six land cover categories (Table 1).

Table 1

Land cover types and areas from the Fender’s blue butterfly map.
Land Cover Type	Hexagons	Hectares
Non-habitat	23,847,287	2066
Dense forest	85,329,621	7390
Open forest	15,565,730	1348
Ag. and pasture	24,738,745	2143
Prairie	10,593,780	918
Kincaide’s lupine	123,759	11
TOTAL	160,198,922	13,876

Kincaide’s lupine (Lupinus oreganus) is the sole larval host plant for the Fender’s blue butterfly (Liston et. al 1995, Schultz and Dlugosch 1999, Schultz 2001), and there are 140 distinct Kincaide’s lupine patches in the FBB map. Of these, 65 are completely isolated by non-habitat, which the butterflies (real and simulated) will not enter. That leaves 75 accessible lupine patches that FBBs might potentially move between. These Kincaide’s lupine habitats comprise the focal patches for my butterfly connectivity analysis.

Movement models

My movement models incorporate behavior, and thus their output stores information about functional landscape connectivity. The C3 utility, which I used to extract this information, imposes minimal constraints on model design. Specifically, a suitable model must (a) simulate movement as a sequence of discrete “steps” in which individuals move from a cell to one of its immediate neighbors, and (b) write out all individual movement records in a predefined format (Appendix 1). Grids of hexagonal cells are ideal for simulating these types of movements because all neighbors are equidistant. Nonetheless, the analysis described here could be replicated using an array of square cells, though doing so would require modifying the C3 utility. Importantly, the application of C3 need not be limited to modeling studies; my methods can also be used to analyze movement data collected in field or laboratory settings (e.g. Finerty et. al., 2023).

My forested landscape example utilized 74 focal patches, each made up from 288 hexagonal cells (Fig. 1A). I initiated the movement process by randomly placing 1M individuals into the collection of focal patch hexagons. These movers were instructed to walk for a total of 50 steps. Each individual selected a preferred movement direction, but changed that direction if zero-valued hexagons or map edges were encountered. While in motion, individuals alternated between selecting a new hexagon based on their preferred direction, versus simply moving into the best neighboring site. Each individual generated a single movement record consisting of 50 steps. Portions of some individual movement paths can be seen in Fig. 1.

The FBB movement model was slightly more complex, and grew out of a series of conversations with species expert Dr. Cheryl Shultz, who had gathered empirical data describing Fender’s blue butterfly turning angles and path lengths as a function of land cover type. All simulated FBBs made a series of 250 separate movements, each characterized by a path length (number of steps), autocorrelation, and a probability of moving directly towards the species’ host plant, Kincaide’s lupine, referred to subsequently as “lupine”. In order to match the empirical information, the values used for these parameters were adjusted depending on the land cover class that each butterfly occupied at the time a movement was initiated (Table 2).

Table 2

HexSim FBB movement model parameters. The land cover classes have been sorted based on their anticipated desirability for the butterflies.
Land Cover Type	Path Length (in hexagons)	Autocorrelation (percent)	Go to Lupine (probability)
Non-habitat	Unused by Fender’s blue butterflies
Dense forest	7	68	0.75
Open forest	7	68	0.75
Ag. and pasture	11	71	0.25
Prairie	11	74	0.25
Kincaide’s lupine	3	35	0

In advance of each of the 250 separate movement events, every simulated FBB was placed into one of two behavior classes. Those not already located within lupine evaluated whether they were within 50 meters of a lupine patch. If so, these FBBs used a “go to lupine” probability to determine whether they should move directly towards lupine. FBBs presently within a lupine patch, those nearby who elect not to move directly towards lupine, and butterflies situated far from lupine all moved semi-randomly. Movement path lengths were imposed regardless of behavior class, but autocorrelation only influenced the behavior of butterflies moving semi-randomly. FBBs moving towards lupine walked up a gradient map, with ties being settled at random. Butterflies moving semi-randomly blended a correlated random walk with limited emergent taxis towards more “desirable” (Cheryl Schults, pers. comm.) land cover types (Table 2).

Because my goal was to evaluate inter-patch connectivity, introducing FBBs into the interior of lupine patches was computationally inefficient. Thus, I initially placed butterflies into every lupine patch edge, excepting those hexagons bordered strictly by lupine and/or non-habitat. Given this criteria, 2797 lupine hexagons qualified as valid starting locations. I ran 1000 model replicates, thus simulating roughly 2.8M butterflies, and generating 0.7B distinct movement records, each varying in length between 3 and 11 hexagons.

Connectivity metrics

The C3 utility ignores movement steps that precede an individual’s arrival at its first focal patch. Thus in both the forested landscape and FBB examples, I initially placed all simulated individuals into focal patches. C3 begins by aggregating all of the movement records associated with a specific individual into a single continuous movement path. This was trivial for the forested landscape simulations because those individuals only moved once. It was involved for the simulated FBBs, who each moved 250 times in a randomized order, meaning that individual movement records were scattered throughout > 200 gigabytes of model output. C3 next measures the rates at which individuals move between focal patches. To do so, it breaks each aggregate movement path into “connecting segments” that begin and end in separate focal patches. Movement steps in the interior of focal patches are not included in connecting segments, but C3 separately records the frequency with which individuals (a) begin and end in the same focal patch, and (b) begin in a focal patch but end in a different land cover type. C3 uses this information to construct a biologically-nuanced discrete dispersal kernel that captures the probability of moving between every pair of focal patches.

C3 also constructs a pair of maps that illustrate (a) “movement flux”, defined as the total number of times each hexagon was visited, and (b) “linkage flux", which only records visitations associated with connecting segments (Fig. 1). Movement flux may be thought of as an inverted resistance surface (high flux equaling low resistance) that conflates absence and avoidance. In contrast, linkage flux is a visual representation of a discrete dispersal kernel. Finally, C3 uses the connecting segments to construct a report describing “connectivity clusters", defined as collections of focal patches joined by movement. This report includes values for cluster traffic, the number of focal patches per cluster, and the IDs of every patch making up each cluster. A cluster’s traffic is defined as the number of connecting segments linking all of the focal patches it contains. For example, C3 identified seven separate connectivity clusters from the forested landscape simulations (Fig. 1C). All but one of the focal patches were included in a connectivity cluster. The number of focal patches per cluster ranged from 2 (the minimum) to 24, and the cluster traffic varied between 6 and 1199. The collection of focal patches formed a square lattice. This arrangement, along with the orientation of my hexagons, meant that a given patch would be functionally closer to its horizontal neighbors, and further from its vertical neighbors. This asymmetry explains the shape of the connectivity clusters that emerged from the forested landscape analysis.

While developed independently, the initial stages of my connectivity analysis are reminiscent of a portion of the methodology developed by Hofmann et. al. (2023). That being the case, our approaches for drawing conclusions about functional landscape connectivity are distinct yet complementary. Hofmann et. al. and others (e.g. Carroll et. al. 2012, Sarker et. al. 2019), utilize a graph theory metric termed “betweenness centrality” to infer connectivity from collections of simulated movement paths. In contrast, my strategy involves isolating the portions of movement paths that link resource patches, and using this information to identify and interrogate connectivity clusters.

C3’s analysis of the FBB movement data revealed the presence of nine separate connectivity clusters (Fig. 3), which ranged in size from 3 to 13 lupine patches. Cluster area and traffic varied across three and four orders of magnitude, respectively (Table 3). Of the 75 accessible lupine patches, 59 were included in the nine connectivity clusters. The remaining 16 accessible patches were functionally disconnected.

Table 3

The C3 connectivity cluster analysis for the FBB model. Lists of individual patch IDs have been replaced with cluster area, measured as the total number of lupine patch hexagons. C3 assigns cluster IDs in map order, from the upper-left to lower-right.
	Cluster Traffic	Lupine Patches	Cluster Area
Cluster 1	349	3	929
Cluster 2	346,486	13	2591
Cluster 3	496,290	10	25,818
Cluster 4	248,465	3	45
Cluster 5	368,602	5	943
Cluster 6	331,611	3	168
Cluster 7	1,025,837	13	2909
Cluster 8	540,085	3	50
Cluster 9	66,593	6	947

I used C3’s maps of movement and linkage flux to more closely examine clusters 1–3, 7–8, and 9 (Fig. 3). Based on movement flux, almost all of the lupine patches in the vicinity of clusters 1–3 would appear to be part of a single expansive “supercluster”. In contrast, the map of linkage flux (Fig. 4), and C3’s cluster analysis, suggest that functional connectivity is limited in this region. A direct comparison of the two flux maps (Fig. 4) indicates there is potential for reconnecting clusters 2 and 3, presumably via habitat restoration, as a large number of simulated butterflies explored the intervening landscape. In contrast, many fewer butterflies moved within the gap separating clusters 1 and 2. It is also apparent that potential exists to extend cluster 2 into the east. Finally, the linkage flux data suggests that cluster 3 itself is only tenuously connected, and likely vulnerable to future habitat loss.

Similarly, while the map of linkage flux suggests that clusters 7 and 8 are functionally distinct, the map of movement flux indicates that potential exists to tie this entire area into a single connected supercluster (Fig. 5). Given that clusters 7 and 8 exhibited the system’s largest cluster traffic (Table 3), the relative benefit of targeting this area for restoration may be high. A parallel inspection of cluster 9 (Fig. 6) suggests that restoration activities in the immediate vicinity of the existing functionally connected lupine patches might benefit the FBB population; but the creation of a robust new supercluster here may require substantial investment.

C3 generated an emergent FBB dispersal kernel in the form of a sparse square matrix with dimension 140 (the number of lupine patches) containing 19,600 cells. This matrix, which is not shown due to its size, has values that range between zero and 0.996. The value of the cell in column i and row k represents the probability that a FBB located in lupine patch i would subsequently move to patch k. The sum of column i equals the probability that a butterfly located in patch i would move to any lupine patch (including itself), while 1.0 minus this quantity is the likelihood that a FBB leaving that location would stop moving somewhere in the non-lupine matrix. The sum of row k represents the probability that a butterfly would travel to patch k from any other lupine patch, including itself.

Researchers commonly utilize graph and circuit models to quantify landscape connectivity. Graph models (e.g. Bastian et. al. 2009, Foltête et. al. 2012) assess the importance of network “nodes'' and “edges'' based on putative dispersal kernels. But by necessity, dispersal kernels are often derived from landscape geometry rather than movement data (Dickson et. al. 2019, Finerty et. al. 2023), and inferences based upon them can therefore lack realism (Fordham et al. 2014). And even when sufficient movement data are available, it can prove difficult to extract a dispersal kernel from this information. The Circuitscape family of tools (McRae et. al. 2008, McRae et. al. 2016) infer patterns of landscape connectivity from simulations of electrical current flowing across resistance surfaces. But electrical currents cannot represent behavior, are real-valued, and can only fall to zero when resistance becomes infinite. In contrast, the rate at which individuals move through landscape locations will reflect movement behavior, and can drop to zero in any location due to energetic constraints, perceived threats, and so on. The approach I have outlined above attempts to address all of these concerns.

My methods share commonalities with graph and circuit models, and this will facilitate direct comparisons. C3’s emergent dispersal kernels could be substituted directly into existing graph models (Fordham et. al 2014). And in spite of their methodological differences, my images of movement flux are reminiscent of the current flows obtained from circuit models. In contrast, C3’s movement and linkage flux maps are able to incorporate the individual behaviors and species-landscape interactions that circuit models must ignore. Further, the considerable differences between C3’s movement and linkage flux maps highlight the utility of discriminating between landscape locations that have been visited collectively and specific pathways successfully traversed by individuals. My maps of movement flux, and their circuit model analogs, both reveal a landscape’s potential connectivity (the former), whereas linkage flux reflects observed rates of movement between specific resource assets (the latter). Policy recommendations informed by potential versus observed connectivity assessments are likely to differ significantly.

I used the Fender’s blue butterfly case study to explore the differences between movement and linkage flux. Simulated FBBs frequently proved unable to move between lupine patches that exhibited high potential connectivity. For example, my maps of movement flux suggest the lupine patches in the vicinity of connectivity clusters 1, 2, and 3 might be a low priority for habitat restoration (Fig. 4). The results from my evaluation of linkage flux indicate exactly the opposite. Similar mismatches arose in the neighborhood of connectivity clusters 7 and 8 (Fig. 5) and cluster 9 (Fig. 6); they are likely ubiquitous across the FBB system.

Modern connectivity assessments are compelling and influential, but they incorporate little biological nuance. In contrast, spatial population models have been trending towards realism and defensibility (D’Elia et. al. 2022, Pili et. al. 2022, Heinrichs et. al. 2023), though this has been accompanied by increasing development times (e.g. Snyder et. al. 2019). Movement simulators provide a compromise; they can capture sophisticated individual behaviors, species-landscape interactions, and disturbance, while still being parsimonious and quick to assemble. And the data generated by these models have potential for catalyzing new insights into functional landscape connectivity. Nonetheless, previous attempts to extract useful connectivity metrics from simulation model output (e.g. Schumaker et. al., 2014) have exhibited neither the clarity we associate with circuit models, nor the inferential power we expect from graph theory. These deficiencies motivated the current study.

My Connectivity Cluster Constructor (C3) is designed to extract connectivity metrics from movement data, regardless of how this information was obtained. And as the above examples illustrate, the requisite data can be minimal. The analyses I’ve described involve five steps: (1) constructing a movement model and running simulations, (2) processing the simulation output, (3) generating a dispersal kernel, (4) mapping movement and linkage flux, and (5) performing a connectivity cluster analysis. The C3 utility automates steps 2–5, thus simplifying the workflow. Though I used HexSim for simulating FBB movement, all other pre- and post-processing steps were performed by stand-alone software utilities. To facilitate the transfer of this technology, I have provided a worked example of the entire process, beginning with a land cover map and ending with a full connectivity analysis (Appendix 1). This illustration does not require the use of HexSim, thus minimizing the investment required to replicate and improve upon my methods.

By isolating Fender’s blue butterfly movements that join distinct lupine patches, I was able to identify connectivity clusters and elucidate a multi-criteria framework suitable for informing recovery planning. My comparisons of movement and linkage flux can serve as a method for prioritizing efforts to reconnect fragmented landscapes, for identifying resources at risk of becoming functionally disconnected, and for exploring possible limitations of circuit models. Additionally, C3’s emergent dispersal kernels can serve as a practical means for bringing the power of graph theory to bear on complex conservation challenges such as Fender’s blue butterfly recovery. More generally, I developed these tools and methods to illustrate how future connectivity analyses might become increasingly defensible and actionable.

Author Contribution

Author NHS developed the concepts and methods, conducted the study, and wrote the manuscript.

Acknowledgements

The Fender’s blue butterfly case study grew out of a collaboration between Bruce Marcot of USFS, and Jennifer Siani, Michele St. Martin, and Mikki Collins of USFWS. I am indebted to Cheryl Shultz and Paul Severens for sharing data and insights into FBB movement behavior. Many thanks to Carlos Carroll, and Allen Brookes for reading and commenting on the manuscript.

The information in this document has been funded in part by the U.S. Environmental Protection Agency. It has been subjected to review by the Center for Public Health and Environmental Assessment, and approved for publication. Approval does not signify that the contents reflect the views of the Agency, nor does mention of trade names or commercial products constitute endorsement or recommendation for use.

Bastian M, Heymann S, Jacomy M. (2009). Gephi: An Open Source Software for Exploring and Manipulating Networks. In: AAAI. https://aaai.org/papers/00361-13937-gephi-an-open-source-software-for-exploring-and-manipulating-networks/. Accessed 22 Jan 2024
Buchholtz EK, Kreitler J, Shinneman DJ, et al (2023) Assessing large landscape patterns of potential fire connectivity using circuit methods. Landsc Ecol 38:1663–1676. https://doi.org/10.1007/s10980-022-01581-y
Calderón AP, Landaverde-Gonzalez P, Wultsch C, et al (2024) Modelling jaguar gene flow in fragmented landscapes offers insights into functional population connectivity. Landsc Ecol 39:12. https://doi.org/10.1007/s10980-024-01795-2
Carroll C, McRAE BH, Brookes A (2012) Use of Linkage Mapping and Centrality Analysis Across Habitat Gradients to Conserve Connectivity of Gray Wolf Populations in Western North America. Conservation Biology 26:78–87. https://doi.org/10.1111/j.1523-1739.2011.01753.x
Carroll SL, Schmidt GM, Waller JS, Graves TA (2024) Evaluating density-weighted connectivity of black bears (Ursus americanus) in Glacier National Park with spatial capture–recapture models. Mov Ecol 12:8. https://doi.org/10.1186/s40462-023-00445-7
Clauzel C, Godet C, Tarabon S, et al (2024) From single to multiple habitat connectivity: The key role of composite ecological networks for amphibian conservation and habitat restoration. Biological Conservation 289:110418. https://doi.org/10.1016/j.biocon.2023.110418
D’Elia J, Schumaker NH, Marcot BG, et al (2022) Condors in space: an individual-based population model for California condor reintroduction planning. Landsc Ecol 37:1431–1452. https://doi.org/10.1007/s10980-022-01410-2
Dickson BG, Albano CM, McRae BH, et al (2017) Informing Strategic Efforts to Expand and Connect Protected Areas Using a Model of Ecological Flow, with Application to the Western United States. Conservation Letters 10:564–571. https://doi.org/10.1111/conl.12322
Dickson BG, Albano CM, Anantharaman R, et al (2019) Circuit-theory applications to connectivity science and conservation. Conservation Biology 33:239–249. https://doi.org/10.1111/cobi.13230
Finerty GE, Cushman SA, Bauer DT, et al (2023) Evaluating connectivity models for conservation: insights from African lion dispersal patterns. Landsc Ecol 38:3205–3219. https://doi.org/10.1007/s10980-023-01782-z
Fletcher RJ, Iezzi ME, Guralnick R, et al (2023) A framework for linking dispersal biology to connectivity across landscapes. Landsc Ecol 38:2487–2500. https://doi.org/10.1007/s10980-023-01741-8
Foltête J-C, Clauzel C, Vuidel G (2012) A software tool dedicated to the modelling of landscape networks. Environmental Modelling & Software 38:316–327. https://doi.org/10.1016/j.envsoft.2012.07.002
Fordham DA, Shoemaker KT, Schumaker NH, et al (2014) How interactions between animal movement and landscape processes modify local range dynamics and extinction risk. Biology Letters 10:20140198. https://doi.org/10.1098/rsbl.2014.0198
Guarenghi MM, Walter A, dos Santos RF (2023) Integrating Habitat Availability, Permeability, and Configuration in a Model of Landscape Connectivity: The Contribution of Habitat’s Site-to-Site. Environmental Management 71:998–1010. https://doi.org/10.1007/s00267-022-01783-9
Heinrichs JA, Marcot BG, Linnell MA, Lesmeister DB (2023) Characterizing long-term population conditions of the elusive red tree vole with dynamic individual-based modeling. Conservation Science and Practice 5:e12938. https://doi.org/10.1111/csp2.12938
Hofmann DD, Cozzi G, McNutt JW, et al (2023) A three-step approach for assessing landscape connectivity via simulated dispersal: African wild dog case study. Landsc Ecol 38:981–998. https://doi.org/10.1007/s10980-023-01602-4
Hromada SJ, Esque TC, Vandergast AG, et al (2020) Using movement to inform conservation corridor design for Mojave desert tortoise. Movement Ecology 8:38. https://doi.org/10.1186/s40462-020-00224-8
Iverson AR, Waetjen D, Shilling F (2024) Functional landscape connectivity for a select few: Linkages do not consistently predict wildlife movement or occupancy. Landscape and Urban Planning 243:104953. https://doi.org/10.1016/j.landurbplan.2023.104953
Liston A, St. Hilaire K, Wilson MV (1995) Genetic Diversity in Populations of Kincaid’s Lupine, Host Plant of Fender’s Blue Butterfly. Madroño 42:309–322
Lyons AL, Gaines WL, Lewis JC, et al (2023) Climate change, wildfire, and past forest management challenge conservation of Canada lynx in Washington, USA. The Journal of Wildlife Management 87:e22410. https://doi.org/10.1002/jwmg.22410
McRae BH (2006) Isolation by Resistance. Evolution 60:1551–1561. https://doi.org/10.1111/j.0014-3820.2006.tb00500.x
McRae BH, Beier P (2007) Circuit theory predicts gene flow in plant and animal populations. Proceedings of the National Academy of Sciences 104:19885–19890. https://doi.org/10.1073/pnas.0706568104
McRae BH, Dickson BG, Keitt TH, Shah VB (2008) Using Circuit Theory to Model Connectivity in Ecology, Evolution, and Conservation. Ecology 89:2712–2724. https://doi.org/10.1890/07-1861.1
McRae BH, Popper K, Jones A, Schindel M, Buttrick S, Hall K, Unnasch RS, Platt J (2016) Conserving Nature’s Stage: Mapping Omnidirectional Connectivity for Resilient Terrestrial Landscapes in the Pacific Northwest. The Nature Conservancy, Portland Oregon. 47 pp. Available online at: http://nature.org/resilienceNW June 30, 2016.
Mestre F, Silva B (2023) lconnect R package: A versatile tool for evaluating landscape connectivity and prioritizing habitat patches in conservation research. Ecological Modelling 484:110489. https://doi.org/10.1016/j.ecolmodel.2023.110489
Mims MC, Drake JC, Lawler JJ, Olden JD (2023) Simulating the response of a threatened amphibian to climate-induced reductions in breeding habitat. Landsc Ecol 38:1051–1068. https://doi.org/10.1007/s10980-023-01599-w
Morin E, Razafimbelo NT, Yengué J-L, et al (2024) Are human-induced changes good or bad to dynamic landscape connectivity? Journal of Environmental Management 352:120009. https://doi.org/10.1016/j.jenvman.2023.120009
O’Neill RV, Krummel JR, Gardner RH, et al (1988) Indices of landscape pattern. Landscape Ecol 1:153–162. https://doi.org/10.1007/BF00162741
Ortega U, Ametzaga-Arregi I, Sertutxa U, Peña L (2023) Identifying a green infrastructure to prioritise areas for restoration to enhance the landscape connectivity and the provision of ecosystem services. Landsc Ecol 38:3751–3765. https://doi.org/10.1007/s10980-023-01789-6
Perry GLW, Moloney KA, Etherington TR (2017) Using network connectivity to prioritise sites for the control of invasive species. Journal of Applied Ecology 54:1238–1250. https://doi.org/10.1111/1365-2664.12827
Peterman WE (2023) One metric or many? Refining the analytical framework of landscape resistance estimation in individual-based landscape genetic analyses. Molecular Ecology Resources 24:e13876. https://doi.org/10.1111/1755-0998.13876
Pili AN, Tingley R, Chapple DG, Schumaker NH (2022) virToad: simulating the spatiotemporal population dynamics and management of a global invader. Landsc Ecol 37:2273–2292. https://doi.org/10.1007/s10980-022-01468-y
Pither R, O’Brien P, Brennan A, et al (2023) Predicting areas important for ecological connectivity throughout Canada. PLOS ONE 18:e0281980. https://doi.org/10.1371/journal.pone.0281980
Proença-Ferreira A, Borda-de-Água L, Porto M, et al (2023) dispfit: An R package to estimate species dispersal kernels. Ecological Informatics 75:102018. https://doi.org/10.1016/j.ecoinf.2023.102018
Ransom JI, Lyons AL, Hegewisch KC, Krosby M (2023) An integrated modeling approach for considering wildlife reintroduction in the face of climate uncertainty: A case for the North Cascades grizzly bear. Biological Conservation 279:109947. https://doi.org/10.1016/j.biocon.2023.109947
Riordan-Short E, Pither R, Pither J (2023) Four steps to strengthen connectivity modeling. Ecography 2023:e06766. https://doi.org/10.1111/ecog.06766
Sarker S, Veremyev A, Boginski V, Singh A (2019) Critical Nodes in River Networks. Sci Rep 9:11178. https://doi.org/10.1038/s41598-019-47292-4
Schmadel NM, Harvey JW, Alexander RB, et al (2018) Thresholds of lake and reservoir connectivity in river networks control nitrogen removal. Nat Commun 9:2779. https://doi.org/10.1038/s41467-018-05156-x
Schultz CB, Dlugosch KM (1999) Nectar and hostplant scarcity limit populations of an endangered Oregon butterfly. Oecologia 119:231–238. https://doi.org/10.1007/s004420050781
Schultz CB (2001) Restoring resources for an endangered butterfly. Journal of Applied Ecology 38:1007–1019. https://doi.org/10.1046/j.1365-2664.2001.00659.x
Schumaker NH (1996) Using Landscape Indices to Predict Habitat Connectivity. Ecology 77:1210–1225. https://doi.org/10.2307/2265590
Schumaker NH, Brookes A, Dunk JR, et al (2014) Mapping sources, sinks, and connectivity using a simulation model of northern spotted owls. Landscape Ecol 29:579–592. https://doi.org/10.1007/s10980-014-0004-4
Schumaker NH, Brookes A (2018) HexSim: a modeling environment for ecology and conservation. Landscape Ecol 33:197–211. https://doi.org/10.1007/s10980-017-0605-9
Severns PM, McIntire EJB, Schultz CB (2013) Evaluating functional connectivity with matrix behavior uncertainty for an endangered butterfly. Landscape Ecol 28:559–569. https://doi.org/10.1007/s10980-013-9860-6
Snyder MN, Schumaker NH, Ebersole JL, et al (2019) Individual based modeling of fish migration in a 2-D river system: model description and case study. Landscape Ecol 34:737–754. https://doi.org/10.1007/s10980-019-00804-z
Tarkhnishvili D, Gavashelishvili A, Murtskhvaladze M, Latsuzbaia A (2016) Landscape Complexity in the Caucasus Impedes Genetic Assimilation of Human Populations More Effectively than Language or Ethnicity. Hum Biol 88:287–300. https://doi.org/10.13110/humanbiology.88.4.0287
Tassi F, Ghirotto S, Mezzavilla M, et al (2015) Early modern human dispersal from Africa: genomic evidence for multiple waves of migration. Investig Genet 6:13. https://doi.org/10.1186/s13323-015-0030-2
Taylor PD, Fahrig L, With KA (2006) Landscape connectivity: a return to the basics. In: Crooks KR, Sanjayan M (eds) Connectivity Conservation. Cambridge University Press, Cambridge, pp 29–43
Turner MG (1989) Landscape Ecology: The Effect of Pattern on Process. Annual Review of Ecology and Systematics 20:171–197. https://doi.org/10.1146/annurev.es.20.110189.001131
Urban DL, Minor ES, Treml EA, Schick RS (2009) Graph models of habitat mosaics. Ecology Letters 12:260–273. https://doi.org/10.1111/j.1461-0248.2008.01271.x
White JM, Schumaker NH, Chock RY, Watkins SM (2023) Adding pattern and process to eco-evo theory and applications. PLOS ONE 18:e0282535. https://doi.org/10.1371/journal.pone.0282535
Xingyuan Z, Fawen L, Yong Z (2023) Impact of changes in river network structure on hydrological connectivity of watersheds. Ecological Indicators 146:109848. https://doi.org/10.1016/j.ecolind.2022.109848

No competing interests reported.

SchumakerAppendix1.pdf

Download PDF

Version 1

posted

You are reading this latest preprint version

Incorporating movement behavior into connectivity assessments

Status:

Version 1

Abstract

Context

Objectives

Methods

Results

Conclusions

Figures

Introduction

Methods

Software tools

Study areas

Movement models

Connectivity metrics

Results

Discussion

Conclusions

Declarations

Author Contribution

Acknowledgements

References

Additional Declarations

Supplementary Files

Status:

Version 1