# Landscape graphs as tools for modelling and managing spatial ecological networks: current limits and new challenges

Jean-Christophe Foltête, Gilles Vuidel

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Jean-Christophe Foltête, Gilles Vuidel. Landscape graphs as tools for modelling and managing spatial ecological networks: current limits and new challenges. Environmental Modelling and Software, 2025, 193, pp.106594. 10.1016/j.envsoft.2025.106594. hal-05173130

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# Landscape graphs as tools for modelling and managing spatial ecological networks: current limits and new challenges

Jean-Christophe Foltête*, Gilles Vuidel

Université Marie et Louis Pasteur, CNRS, ThèMA, Besançon, France

## ARTICLE INFO

### Keywords:

- Landscape graph

- Least-cost distance

- Resistance distance

- Individual-based models

## ABSTRACT

Among the approaches to modelling habitat connectivity, landscape graphs have been widely used in conservation and land planning for two decades. However, their relevance is challenged by methods derived from circuit theory and individual-based models (IBMs). We identify the limitations of landscape graphs in light of the advantages provided by competing methods. The focus falls first on link weighting, hindered by the shortcomings of least-cost distances (LCDs), and second on the inconsistencies of the standard connectivity metrics. Faced with these limitations, circuit theory may partly remedy the drawbacks of LCDs without providing any clear advantage. Conversely, IBMs are an interesting way to overcome both the problems of link weighting and their integration into connectivity metrics by directly providing flux estimates. Consequently, a major challenge of landscape graphs is to renew their design by including a parsimonious IBM.

## 1. Introduction

Habitat connectivity is acknowledged to be crucial for conserving wildlife in fragmented landscapes (Baguette et al., 2013; Forman, 1995; Taylor et al., 2006). The importance of connectivity in ecology and biological conservation has led to the development, over several decades now, of numerous methodological approaches by which to evaluate and quantify habitat connectivity (Correa Ayram et al., 2016; Diniz et al., 2020; Dutta et al., 2022; Hesselbarth et al., 2024; Martínez-Richart et al., 2024). However, in this extensive literature, it is no longer easy to gain a clear overview since “connectivity” may take on various meanings according to the context. Considering habitat connectivity as a property emerging from the interaction between individual movements of a given species and landscape structures (Taylor et al., 2006), i.e. putting aside structural connectivity, we can broadly distinguish: (1) field methods designed to measure actual connectivity directly (movement and population tracking) or indirectly (genetic data); (2) modeling methods designed to evaluate potential connectivity. The latter approach is of great importance when addressing conservation issues and decision support, because spatially-explicit models are suitable for dealing with location questions pertaining to land planning and development.

The modelling methods for handling connectivity differ in their complexity according to the amount of input data they require and their

capacity to represent actual fluxes (Liczner et al., 2024). Among these modelling approaches, graph-theoretic methods named landscape graphs (or habitat networks or also patch-based graphs) are widely used both in academic research and in operational applications, e.g. Berges et al. (2020); Foltête et al. (2014); Kosma et al. (2023); Lechner et al. (2015); Tarabon et al. (2019, 2020). In short, landscape graphs combine a set of habitat patches hosting individuals, considered as nodes, and a set of potential movements between them, considered as links. The key movements represented by the links mostly pertain to the dispersal process. These graphs are suitable for computing numerous connectivity metrics at different levels and for characterizing network properties. Ever since the seminal paper of Urban and Keitt (2001), their usage has been facilitated by syntheses (Galpern et al., 2011; Hashemi et al., 2024; Rayfield et al., 2011; Urban et al., 2009) and by the diffusion of specific tools such as Conefor Sensinode (Saura and Torné, 2009), Graphab (Foltête et al., 2012) and Iconnect (Mestre and Silva, 2023). Prior to the development of these tools, Calabrese and Fagan (2004) provided arguments for graph-based methods when comparing the methods available for habitat connectivity. On the one hand, methods restricted to structural connectivity are unsuitable for representing potential movements; on the other hand, Incidence Function Metapopulation models are powerful tools but prove to be less easily reproducible because they require specific field data. Considering this, Calabrese and Fagan (2004) argue that in the balance between complexity and capacity to evaluate

<footnote>* Corresponding author. Jean-Christophe Foltête 32, rue Mégevand, F-25030 Besançon, France
*E-mail address: jean-christophe.foltete@univ-fcomte.fr* (J.-C. Foltête).</footnote>
actual connectivity, landscape graphs offer a trade-off, requiring few input data while producing a realistic representation of spatial ecological networks.

However, 20 years on, this trade-off can no longer be viewed in the same way. During this period, case studies and technical refinements of landscape graphs have proliferated, e.g. Clauzel et al. (2024); Duflot et al. (2018); Foltête et al. (2021); Savary et al. (2024). But meanwhile, criticisms of landscape graphs have been voiced (Moilanen, 2011) and other modelling approaches, that were not widely disseminated at the time of the comparison of Calabrese and Fagan (2004), now compete with landscape graphs in evaluating connectivity. What makes this comparison outdated is (1) the dissemination of methods based on circuit theory (Dickson et al., 2019); and (2) the development of individual-based models (IBMs) targeted at connectivity (Diniz et al., 2020). Circuit theory is applied mainly through the Circuitscape application (McRae et al., 2008) both for mapping corridors and computing effective distances as alternatives to the standard least-cost distances (Dickson et al., 2019). IBMs rely on the simulation of virtual individuals across the landscape, using rules for representing movement, behavior and often demographic dynamics (Grimm, 2019). Pioneering work was done in the 1990–2000s (Gardner and Gustafson, 2004; Grimm et al., 1999; Tischendorf, 1997; Tischendorf and Fahrig, 2000) with many other studies being published thereafter, e.g. Hauenstein et al. (2019); Kanagaraj et al. (2013); Palmer et al. (2011); Pauli et al. (2013); Unni-than Kumar et al. (2022a).

Landscape graphs, circuit-theory applications and IBMs all relate to specific approaches that differ in their purpose, design and computational requirements. This explains why reviews of habitat connectivity often present them as separate approaches (Hesselbarth et al., 2024). The first two approaches are now familiar enough and are often compared, while IBMs are not so widespread (Dutta et al., 2022) and not yet indexed among the methods dedicated to habitat connectivity in certain specific environments such as urban landscapes (Lookingbill et al., 2022). However, with growing computing capacity facilitating the implementation of simulation platforms, it is likely that IBMs will soon take on greater importance (Unnithan Kumar et al., 2022b), potentially calling into question the relevance of landscape graphs. Rare empirical comparisons have been made (Lumia et al., 2024; Minor and Urban, 2007), but a more formal comparison is still awaited. Specifically, such a comparison could lead researchers to revisit the main limitations of landscape graphs in light of the advantages provided by competing methods like IBMs and those derived from circuit theory.

With this in mind, we propose here to identify the main shortcomings of landscape graphs and the way these shortcomings might be overcome. We examine the three main components that make up these methods (i. e. patches, links and connectivity metrics), and for each of them, we question their relevance in relation to circuit-theory applications and IBMs applied to habitat connectivity. This leads us to propose a new challenge for the design of advanced landscape graphs.

## 2. Defining patches

Habitat patches are the very basic elements of any landscape graph and the first ones to be defined. These elements serve as sources and targets in the movements represented by graph computations. They can be designed in several ways but, in the initial applications, they simply correspond to the patches shaped by the land cover categories representing the optimal habitat of the species under study (Urban and Keitt, 2001). The assumption is that the analysis is focused on specialist species dependent on a habitat that is easy to map, for example a forest species. The growing number of applications of landscape graphs has rapidly enhanced this simple definition of habitat patches, making for a better representation of the spatial usages of certain species, either to specify the habitat quality by including additional data (e.g. micro-topographic data) or to account for specific life cycles implying habitat complementation. Amphibians, for example, require a

combination of aquatic and terrestrial habitats, so not all ponds can be considered as optimal habitat (Clauzel et al., 2015). More recently, habitat patches have also been defined as the outputs of species distribution or suitability models combining geo-environmental data and presence data acquired in the field (Duflot et al., 2018; Foltête et al., 2020). Species distribution models are useful for including several environmental gradients associated with the needs of the species, giving greater validity to the patches. Another possibility encountered in conservation is to consider protected areas as initial patches for connectivity analyses, as in Diniz et al. (2018).

The methods for defining habitat patches in landscape graphs are thus positioned at a certain level on a gradient of complexity. The other methods of connectivity modelling are often applied to points rather than surfaces, e.g. McClure et al. (2016), but may also be applied in the same spatial framework as landscape graphs. Circuit-theory applications can be applied between land cover patches (Fagan et al., 2016), suitability patches (Ahmadi et al., 2017) or protected areas (Gantchoff and Belant, 2017). Similarly, IBMs may be applied from land-cover patches (Coulon et al., 2015; Lumia et al., 2024), patches or cells derived from suitability models (Hauenstein et al., 2019; Kanagaraj et al., 2013) or protected areas (Hofmann et al., 2023). Finally, compared to the other modelling methods, the definition of the nodes in landscape graphs does not suffer specific weaknesses and can be adapted to each study context.

## 3. Weighting links: standard and alternative designs

The links to be drawn between patches may also be defined in many ways including options and computation settings that we cannot list exhaustively here (Foltête et al., 2020; Galpern et al., 2011). The standard case is to measure an edge-to-edge distance between patches, given a complete or a planar topology (Fall et al., 2007). Two key points should be examined: the spatial metric used to weight the links and the way this weighting is integrated into connectivity metrics.

Links may be weighted by a simple Euclidean distance, either because the species is generalist, or because of the possible lack of information about its movement behavior across the landscape matrix. However, in most cases, the starting framework is a resistance surface used to account for matrix heterogeneity, as in many other connectivity models (Lumia et al., 2024). This leads to the computing of least-cost distances (LCDs), a classical spatial metric associated with least-cost paths (Adriaensen et al., 2003). As LCDs are not specific to landscape graphs and were used for two decades in many contexts including landscape genetics (Ray, 2005), much has been said about them (Diniz et al., 2020; Sawyer et al., 2011) and two main weaknesses have been identified. The first is to consider a single path linking two patches (Moilanen, 2011), whereas in reality, the landscape matrix separating two patches may provide a set of possible paths that could vary the probability of making a crossing for one and the same LCD value. The second weakness is the gap between the computational process and the type of movement to be represented. While Dijkstra's algorithm (Jungnickel, 2008) works on the underlying assumption that the organism has complete knowledge of its environment so as to minimize the cost of its movement, natal dispersal events take the form of exploratory movements without any predefined target.

Another key point to examine when evaluating the links of landscape graphs is how LCDs are integrated into connectivity metrics. It may be recalled that measuring connectivity has produced many indices or metrics (Laita et al., 2011; Rayfield et al., 2011). As a landscape graph relies on nodes of various sizes (i.e., containing varying numbers of individuals) located in a landscape matrix of varying permeability, quantifying connectivity has proved to be more relevant when including both the weight of habitat patches and links. This explains the wide use of “weighted metrics” including patch area and distance in calculating them. These metrics are based on a dispersal kernel expressing the probability of a dispersal movement from a source patch to another patch. As in metapopulation models (Hanski, 1994) and diffusion
models (Clark et al., 1998), the dispersal kernel is defined as a negative function applied to the distance value weighting the link, usually a negative exponential function (Urban and Keitt, 2001):

$$p_{ij} = e^{-ad_{ij}}$$

where $p_{ij}$ is the probability that individuals move from patch i to patch j, $d_{ij}$ is the distance between patches, and $\alpha$ is a distance-decay parameter.

This operation needs to set the parameter $\alpha$ representing the braking effect of distance on movement. When using a Euclidean distance, knowledge of the key-distance of dispersal for the species under study is sufficient (Urban and Keitt, 2001). But when using an LCD, this setting presents a difficulty because the key distance is usually expressed in a metric unit. This difficulty may be overcome by statistically estimating the key-distance from a regression model fitting cost distances from metric distances as in Tarabon et al. (2022). However, the statistical relationship between these distances is often non-linear when strong barriers occur in the landscape, making the estimation unreliable.

Considering these conceptual and technical difficulties, several strategies have been proposed. To address the problem of the single path, variants were imagined as multiple shortest paths (Pinto and Keitt, 2009), but the main way to address the weaknesses of LCDs was paved by the resistance distances known through the Circuitscape application (McRae et al., 2008). From the same resistance surface as input data, resistance distances result from the use of a circuit-theory algorithm diffusing a current from points considered as sources across the resistance surface. This operation is similar to a set of random walks triggered from the sources, that can be considered as explanatory movements thus adapted to the modelling of natal dispersal events. Moreover, the resulting resistance distance between sources and targets is shorter when numerous pathways are possible and vice versa. These interesting properties could have made resistance distances a suitable alternative to LCDs in landscape graphs, as in some experimentations with them (Foltête et al., 2016; Rayfield et al., 2016). However, they also present several drawbacks that make them less relevant in this context. First, the systematic search for all possible paths often makes their computation costly for quantifying distances between a large number of patches, not only in computation time but also in memory resources because of the calculations applied to large matrices (Pelletier et al., 2014). These computational difficulties have led to several strategies (Hall et al., 2021) including first the splitting of the input data using a moving window before combining the results, with the Circuitscape application (Landau et al., 2021). They have also led to successive updates of Circuitscape being proposed to improve computation speed, specifically with the implementation in Julia (Hall et al., 2021), and to the development of Gflow, a tool running on high performance clusters

(Leonard et al., 2017). In any case, the implementation of circuit-theory applications requires large processing capacities. Second, resistance distances attribute greater importance to the number of possible paths than to the crossed cost (Van Moorter et al., 2021), making them hard to interpret, even if they are supposed to represent commuting times. Consequently, they cannot be converted into metric units like LCDs and their transformation into movement probability for computing weighted connectivity metrics is challenging.

Least-cost and resistance distances therefore have their own drawbacks when it comes to properly representing individual movements while providing distance units that can be converted into movement probability. Moreover, comparison of their respective relevance according to biological responses fails to reveal a clear advantage for resistance distances (Marrotte and Bowman, 2017). The randomized shortest paths proposed as an intermediate strategy between least-cost and resistance distances (Van Moorter et al., 2021) are another possibility, but they also raise the issue of implementation for efficient application to a large number of patches, specifically because of the memory resources required.

Let us now examine IBMs from the perspective of weighting the links of a landscape graph. IBMs cannot directly yield a set of distances between habitat patches, but they can provide a set of explanatory paths for characterizing the dispersal movements from a given patch considered as a source. First, as they are built from movement rules, these spatial simulations do not have the shortcomings of the least-cost computation, i.e., the single path, the assumption of prior knowledge of the destination and perfect knowledge of the environment (Coulon et al., 2015). Second, if IBMs are used for characterizing the dispersal from every patch in a systematic manner, they may provide flux directly including the movement probability noted $p_{ij}$ previously. In Tischendorf and Fahrig (2000) for example, “immigration” can serve as a patch-level measure of successful dispersal events. Thus, in a landscape graph, what results from an indirect process combining the measurement of distances followed by a generic distance-decay effect converting the distances into probabilities, could correspond in IBMs to a direct measure following the simulation process. On the computation side, IBMs do not require large memory resources and may benefit from parallelization, e.g. using manicore architectures, making them suitable for large-scale applications although they may be time-consuming.

The main criteria for comparing the methods likely to be used to weight the links in landscape graphs are summarized in Table 1. LCPs have practical advantages but are limited by their low level of realism. Conversely, IBMs present several features that can overcome the limitation of LCDs, especially if we consider the transformation of distances into flux estimates in connectivity metrics and the memory resources

<caption>**Table 1**</caption>

Main comparison criteria between LCDs, resistance distances, randomized shortest paths and IBMs in the weighting of the links in a landscape graph. LCDs are the standard method today while the other methods, used in contexts other than landscape graphs, offer alternative approaches. It should be observed that the conversion of resistance distances into metric units can be difficult because of their double dependence on the number of paths and on the cost values.

<table><thead><tr><th>Method</th><th>Least-cost distances (LCDs)</th><th>Resistance distances</th><th>Randomized Shortest Paths</th><th>IBMs</th></tr></thead><tbody><tr><td>Type of paths</td><td>Single shortest path</td><td>Multiple paths</td><td>Multiple paths</td><td>Multiple paths</td></tr><tr><td>Underlying assumption about knowledge of the environment</td><td>Complete knowledge</td><td>No knowledge</td><td>Intermediate knowledge (customizable)</td><td>Intermediate knowledge (customizable)</td></tr><tr><td>Dispersal movement probability</td><td>Conversion of distances by a negative exponential function<br>Setting of the function using a log-log regression of LCDs fitted by Euclidean distances</td><td>Challenging operation</td><td>Challenging operation</td><td>Direct<br>No function to be set</td></tr><tr><td>Computation time</td><td>Low</td><td>High</td><td>High</td><td>High</td></tr><tr><td>Required memory resources</td><td>Low</td><td>Variable according to the implementation</td><td>High</td><td>Low</td></tr><tr><td>Other constraints</td><td></td><td>Possible biases linked to the size heterogeneity of patch area as sources</td><td></td><td>Sensitivity analyses to be made for the setting of movement rules</td></tr></tbody></table>
required.

## 4. Connectivity metrics: can we go beyond generalized accessibility?

Connectivity metrics are a highlight of landscape graphs, being widely used to diagnose habitat connectivity. They can be applied to the global level of the whole graph and also to the local level of the patches and the links (Rayfield et al., 2011). The weighted metrics mentioned above mainly include the Area Weighted Flux (AWF) (Urban and Keitt, 2001), the Probability of Connectivity (PC) family (Saura and Pascual-Hortal, 2007; Saura and Rubio, 2010) and the weighted Betweenness Centrality index (BC) (Foltête et al., 2012). Each of these three metrics has several variants, and more specifically, the “PC-family” encompasses the PC index and its delta version dPC (Saura and Pascual-Hortal, 2007), the partitioning of the dPC into three components (Saura and Rubio, 2010), the equivalent connectivity area ECA (Saura et al., 2011), Protected Connected (ProtConn) (Saura et al., 2017) and spatio-temporal connectivity (Martensen et al., 2017).

Despite the great number of weighted connectivity metrics, we can note their common computation principle combining areas (or another proxy of individual amount) and dispersal probabilities. AWF, for example, sums for a given source patch *i* the area of the connected patches *a*<sub>*j*</sub> weighted by the dispersal probability *p*<sub>*ij*</sub> from the source:

$$AWF_i = \sum_{j \neq i} a_j p_{ij}$$

Similarly, the contribution of a source patch *i* to the PC index amounts to the sum of the product of the area of the habitat source *a*<sub>*i*</sub> with the area of other patches *a*<sub>*j*</sub>, multiplied by the maximum product probability *p*<sub>*ij*</sub><sup>*</sup> of the shortest path separating them:

$$PC_i = \frac{1}{A^2} \sum_j a_i a_j p_{ij}^*$$

with A the total study area and PC = $\sum_i PC_i$

The principle of computation combining a number of moving elements and the brake of distance refers to the spatial interaction models encountered in quantitative human geography. AWF, specifically, is similar to the generalized accessibility applied in Stewart's seminal model (Pooler, 1987; Stewart, 1942). In this model, population potentials (e.g., potential customers for a commercial offer) are calculated by summing local populations weighted by a movement kernel including a term of distance *d*. As with AWF, the computation represents individuals moving from a source to all potential targets successively. Similarly, the interaction models devoted to the modelling of the migration flux, proposed by Stewart (1948) and based on an analogy with Newton's gravitation law, take the same form as the PC index, with a product of populations weighted by a movement kernel. In all these geographical models, the movement kernel was initially set with $d^{-2}$ but later came to be based on a negative exponential function as in spatial ecology.

Let us now examine the implicit consequences of these spatial models in terms of individuals' movements in ecology. Given a source patch that is home to a local population and other patches considered as potential destinations for dispersers (Fig. 1a), the conversion of distances into probabilities (Fig. 1b) leads to determining the number of dispersers according to the distance, as in computing AWF (Fig. 1c), and also to quantifying the spatial interaction between the source and each destination, as in the PC-family indices (Fig. 1d). As expected, the distance-decay effect means the number of dispersers falls as the distance increases, but the computation involves certain individuals making several successive trips from the same source patch, i.e. the total number of individuals moving exceeds the initial population. Such a process can be suitable for analyzing commercial fluxes in economic geography, because in this case, the movements linked to purchases do not entail a relocation of individual residences, but instead round trips from the

<figure><img src="image_3.png" /><figcaption>Fig. 1. How individuals represented by the patch areas are multiplied in weighted connectivity metrics. (a) A source patch of area $a_0$ is distant from potential destination patches 1 and 2 by $d_1$ and $d_2$ respectively. (b) These distances are converted into movement probabilities using a negative exponential function. (c) Probabilities are multiplied by the source population to quantify dispersal fluxes. (d) The potential interactions of the source patch are formulated as the addition of the local population remaining in the source patch, plus a fraction of this population reaching patch 1 and another smaller fraction reaching patch 2. This is as if some of the same individuals are simultaneously not dispersers (or intra-patch dispersers) but also dispersers to other destination patches.</figcaption></figure>

residence locations. However, in the case of dispersal events in ecology, individuals do not return to the source patch but settle in another patch. The calculation is thus not fully consistent with the process it is intended to represent. Theoretically, an appropriate model should distribute dispersers in the potential hosting patches exclusively rather than multiply them.

The artificial multiplication of the individuals in weighted connectivity metrics should now be questioned if we are to move beyond a measurement of generalized accessibility. These metrics may help when comparing the amount of reachable habitat from each focal patch and they have proved their worth as conservation decision support tools in many studies, although they represent an unrealistic process in terms of the movements of individuals. In the early stages of the application of landscape graphs, these generic measurements provided considerable added value compared to simpler methods for quantifying connectivity. But we should also concede that today, graph-based connectivity metrics have significant limitations with respect to the way individuals' movements are represented.

If we now look at IBMs applied to dispersal movements, how is connectivity measured following individual simulations? As in landscape graphs, the metrics apply either at the global level to quantify the connectivity of the entire network, or to characterize local connectivity at the patch level or at the cell level. At the global level, dispersal success (i.e., the number of successful dispersal events) and the ratio between dispersal success and the total number of simulated individuals are the most common metrics (Coulon et al., 2015; Tischendorf and Fahrig, 2000). At the local level, two main measurements appear in studies using IBMs. The first is the movement density calculated at the cell level for the entire landscape as in Allen et al. (2016); Hofmann et al. (2023);
Kanagaraj et al. (2013); Lumia et al. (2024); Unnithan Kumar et al. (2022a). The second is the ratio of dispersal success from one given patch (or source) to the others, as in Day et al. (2025); Hofmann et al. (2023); Kanagaraj et al. (2013); Schippers et al. (1996). In all cases, the principle of individual simulations is to distribute the dispersers among the potential target patches without resorting to multiple trips by the same individuals. This constitutes a fundamental difference between landscape graphs and IBMs with respect to the way habitat connectivity is quantified. In IBMs, the modelling of the dispersal process at the individual level ensures the consistency of the connectivity quantification in relation to the individual nature of the dispersal movements. Conversely in landscape graphs, the aggregation of individuals within patches leads to measurements that are globally logical but incoherent at the individual level. This emphasizes the limits of the aggregated scale of landscape graphs for representing individual processes, and it challenges the integration of an individual rationale in these methods without forfeiting their main qualities.

# 5. Towards advanced landscape graphs

There are many arguments explaining why landscape graphs have been used extensively for more than 20 years now, with numerous studies illustrating the scope of this powerful method (Foltête et al., 2021). One of these arguments is the easy access to generic tools. Another is the potential of spatial analyses made possible by the graph format, in the form of connectivity metrics that cannot be applied in the same way in other modelling approaches. In this paper, we have pointed out several shortcomings of these methods: some are familiar enough, such as the weaknesses of LCPs (Moilanen, 2011; Sawyer et al., 2011), whereas others are rarely mentioned, such as the way the link weights are included in connectivity metrics, and the limits of the standard connectivity metrics themselves. This does not invalidate the current landscape graphs as suitable tools for modelling habitat connectivity, but it should lead us to better identify their limitations, as with every modelling approach based on spatial indicators (Li and Wu, 2004).

## 5.1. Potential contribution of individual-based models to landscape graphs

When examining the potential alternative methods capable of addressing these drawbacks, resistance distances fail to provide a clear advantage, although they do remedy the problems of LCPs concerning the single path and the underlying assumption in the distance computations (Van Moorter et al., 2021). Their computational limits and the difficulty in integrating them into connectivity metrics are significant impairments. Conversely, IBMs open up interesting approaches when it comes to redefining some of the components of landscape graphs. The first reason is the flexibility in the modelling enabled by the individual-level approach. The movement rules used in IBMs may thus be more consistent with the main assumptions concerning the behavior of individuals than LCPs (Allen et al., 2016), even if all modelling approaches are based on a simplification of reality. Faced with the usual combination of distance computations and the transformation of these distances into movement probabilities in connectivity metrics, IBMs could provide a direct means of estimating the potential flux among habitat patches, and so escape the intricate problem of distance conversion. Considering all these advantages, the flux estimates from IBMs are expected to be more realistic than those derived from LCPs. Some features already reinforce this view, such as the poor correlation between the flux resulting from IBMs and the usual exponential decay applied to distances (Schippers et al., 2024), or again the added value of IBMs compared to LCPs in fitting biological responses in the study of Coulon et al. (2015).

Patch-level simulations including a graph approach may be integrated into metapopulation models, as in Mestre et al. (2016). But to our knowledge, to date no IBM has been implemented within a

methodological framework to produce a landscape graph. We think this coupling could make a significant change in the design of new landscape graphs, to break free of the limits inherent in LCPs and to provide more interpretable metrics. This way of upgrading landscape graphs could help tackle the realism issues, considered as the first questions and needs by Liczner et al. (2024) among the current challenges addressed in connectivity science. More broadly, the integration of an individual-based dispersal module instead of an aggregate model of movement can be viewed as a choice to switch from a KISS (Keep It Simple Stupid) modelling approach to a KIDS (Keep It Descriptive Stupid) approach, following Edmonds and Moss (2005). This means that the use of LCPs is only justified by practical arguments of simplicity and rapidity, and that a model based on a better representation of actual movements is now needed.

However, the coupling of an IBM with a landscape graph presents its own difficulties because the individual level of modelling and the stochastic nature of the simulations make the approach more complex. Our proposal is not to fully replace the patch-based model by process-based models in all biological dimensions, but rather to maintain an adequate compromise between the ease of application and the capacity to represent actual fluxes. The barriers to easy use are for example the difficulty in managing multiple parameters without controlling their interactions, the need for many sensitivity analyses for testing the stability of simulations and the limit inherent in computation time. If we are mindful of the trade-off advocated by Calabrese and Fagan (2004), this would mean slightly increasing the input setting of landscape graphs without getting into an overly complex model. Since a major challenge of conservation planning is to have versatile tools that can be applied in operational contexts, it seems to us important to maintain the relevant position of landscape graphs for this purpose. As IBMs may correspond to simulations with various levels of complexity (DeAngelis and Mooij, 2005), only parsimonious IBMs focused on the dispersal process, namely the individual-based dispersal models (IBDMs) following Diniz et al. (2018), can be usefully coupled with landscape graphs (Fig. 2). We thus assume that simple dispersal modules like those in Allen et al. (2016); Coulon et al. (2015); Hofmann et al. (2023); Schumaker (2024); Unnithan Kumar et al. (2022a) are sufficient to improve landscape graphs significantly. Conversely, models including many details such as the sex of individuals and their interactions (Pauli et al., 2013; Valle et al., 2024), or including demographic and genetic dynamics, e.g. Bocedi et al. (2014); Day et al. (2025); Hauenstein et al. (2019), ensure greater biological realism but move the cursor towards complex approaches requiring a large amount of input data. Moreover, parsimonious IBDMs may easily conform with the need for transparent and reproducible tools in connectivity modelling, as claimed by Liczner et al. (2024).

A parsimonious IBDM designed to provide a significant update of a landscape graph should be restricted to movement rather than dealing with demographic aspects. It should thus specifically focus on the transfer and settlement phases of the dispersal process, and set aside the pre-emigration and emigration phases, although all these phases are interdependent (Travis et al., 2012). In practice, this implies positioning the IBDM after the definition of the nodes in the landscape graph workflow. Three main steps could be considered: (1) the definition of the disperser individuals at the initial step, including their numbers and their distribution among the habitat patches, (2) the movement step whereby these individuals either reach another patch or die, (3) the measurement of the pairwise movement probabilities resulting from the simulated individual paths. These three steps can replace both the LCPs computations and the part of the connectivity metrics calculation designed to convert the LCPs into movement probabilities. Consequently, the integration of an IBDM into a landscape graph will modify the way the connectivity metrics are calculated. This is a significant shift and not just a minor change, if we consider current tools such as Conefor Sensinode, Graphab or Iconnect.
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Elements contributing to biological realism according to the methodological approaches for modelling connectivity. While the shortcomings of LCPs in representing dispersal movements are partly governed by resistance distances derived from circuit theory, only IBMs (and specifically IBDMs) can support the design of advanced landscape graphs by directly providing dispersal fluxes made up of multiple explanatory paths. It should be noticed that this figure focuses on realism and omits other comparison criteria such as connectivity metrics, which are a clear advantage afforded by landscape graphs.</figcaption></figure>

## 5.2. *The consequences of integrating and IBDM into a landscape graph*

In any event, IBDMs cannot be thought of as magic wands that will overcome all the difficulties in modelling connectivity. First, it should be observed that their starting framework is common to the other modelling approaches since a cost (or resistance) surface needs to be designed. Users of IBDMs thus face the same challenge of defining cost values from the available data according to the context (Zeller et al., 2012). Second, the choice and the setting of the simulation parameters liable to produce a satisfactory level of realism may be challenging. In an IBDM, these parameters are designed to represent the choices and behaviors leading to a movement step in a dispersal event. Using the “right” values of these parameters involves a calibration stage relying on comparisons between the outcomes of the simulations and real data acquired in the field. In the present case, the calibration requires records be obtained of actual paths taken by individuals, such as GPS tracks. With these data, several strategies are available for parameter calibration, for example Pattern-Oriented-Modelling (Grimm et al., 2005; Topping et al., 2012) or Approximate Bayesian Computing (ABC) (Beaumont, 2010; Csilléry et al., 2010). Whatever the strategy implemented, the approach includes three components (Hartig et al., 2011): (1) the choice of statistical indicators intended to summarize the observed and simulated movement data (e.g., distance crossed after a given number of steps, indicator of directional persistence, etc.), (2) the calculation of the likelihood of obtaining the observed data from a given set of parameters in the IBDM using a parametric approximation, (3) the exploration of the parameters using optimization or sampling algorithms. This approach may be complex and time-consuming, but in the case of a parsimonious IBDM, it could be facilitated by the limited number of parameters. Beyond the exploration of the parameter space, the stochastic nature of the movement simulations requires a clear view of the way settings affect outcomes, compelling users to carry out sensitivity analyses in order to ensure stable results. This was done for example in Gold et al. (2024); Kanagaraj et al. (2013). Finally, computation time must not be overlooked when implementing massive simulations, so as to obtain significant enough flux to provide suitable connectivity estimates.

Another aspect that should be investigated when integrating an IBDM into a landscape graph is the evaluation of the added value compared to the usual approach based on LCPs. This relates to empirical studies where connectivity criteria are considered as potential drivers of biological responses. The vast literature based on classic landscape graphs includes, for example, studies focused on community richness

(Foltête et al., 2025; Mony et al., 2018), genetic diversity (Bertin et al., 2017; Savary et al., 2022), and roadkills (Girardet et al., 2015; Kim et al., 2019). These studies open up a promising avenue for research comparing the respective explanatory power of classic and advanced landscape graphs. With the advent of advanced landscape graphs, it can be hoped that the proliferation of such comparisons will confirm the hypothesis that IBDMs will contribute significantly to connectivity modelling.

## 6. Conclusion

Landscape graphs figure among the standard methods for modelling habitat connectivity. Many studies designed to provide decision support in land planning and conservation have shown these methods to be effective. But compared to other approaches such as circuit theory and IBMs, landscape graphs are limited by the way dispersal links are weighted. On reviewing the key components of these methods and referring to other methodological approaches dealing with habitat connectivity, we conclude that individual-based models devoted to dispersal movements (IBDMs), if designed parsimoniously, could provide significant added value for building advanced landscape graphs. This promising coupling implies new tasks, such as parameter calibration using, say, the ABC method, but it will mean least-cost distances can be set aside and more realistic connectivity models can be designed.

### CRediT authorship contribution statement

Jean-Christophe Foltête: Writing – original draft, Methodology, Conceptualization. Gilles Vuidel: Writing – original draft, Methodology.

### Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

### Data availability

No data was used for the research described in the article.
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