Predicting connectivity, or how landscapes alter movement, is essential for understanding the scope for species persistence with environmental change. Although it is well known that movement is risky, connectivity modelling often conflates behavioural responses to the matrix through which animals disperse with mortality risk. We derive new connectivity models using random walk theory, based on the concept of spatial absorbing Markov chains. These models decompose the role of matrix on movement behaviour and mortality risk, can incorporate species distribution to predict the amount of flow, and provide both short‐ and long‐term analytical solutions for multiple connectivity metrics. We validate the framework using data on movement of an insect herbivore in 15 experimental landscapes. Our results demonstrate that disentangling the roles of movement behaviour and mortality risk is fundamental to accurately interpreting landscape connectivity, and that spatial absorbing Markov chains provide a generalisable and powerful framework with which to do so.

Quantifying landscape connectivity is fundamental to better understand and predict how populations respond to environmental change. Currently, popular methods to quantify landscape connectivity emphasize how landscape features provide resistance to movement. While many tools are available to quantify landscape resistance, these do not discern between two fundamentally different sources of resistance: movement behavior and mortality. To address this issue, we developed the samc R package that quantifies landscape connectivity using absorbing Markov chain theory. Within this mathematical framework, movements are represented as transient states in the Markov chain, while mortality is represented by transitions to absorbing states. Not only does this framework explicitly account for these different issues, it provides a probabilistic approach that can incorporate both short‐term and long‐term dynamics, as well as species distribution and abundance. The package includes functions to quantify life expectancy, long‐term visitation rates, and various spatially and temporally explicit measures of mortality and movement at the local and landscape scales. These functions in samc have been optimized to find computationally practical solutions in landscapes comprised of > 2 × 106 cells. Here, we illustrate the workflow of the samc package with publicly available movement and mortality data on the endangered Florida panther Puma concolor coryi. This analysis showed that movement and mortality are generally correlated except for locations near roads (areas of high mortality risk) that are within the dispersal range of source locations. This pattern would have been undetectable with current methods that quantify movement resistance. Overall, the samc package provides a means for implementing spatial absorbing Markov chains that can distinguish between movement behavior and mortality resulting in more reliable landscape connectivity measures.

Balancing the competing, and often conflicting, needs of people and wildlife in shared landscapes is a major challenge for conservation science and policy worldwide. Connectivity is critical for wildlife persistence, but dispersing animals may come into conflict with people, leading to severe costs for humans and animals and impeding connectivity. Thus, conflict mitigation and connectivity present an apparent dilemma for conservation. We present a framework to address this dilemma and disentangle the effects of barriers to animal movement and conflict-induced mortality of dispersers on connectivity. We extend random-walk theory to map the connectivity–conflict interface, or areas where frequent animal movement may lead to conflict and conflict in turn impedes connectivity. We illustrate this framework with the endangered Asian elephant Elephas maximus , a species that frequently disperses out of protected areas and comes into conflict with humans. We mapped expected movement across a human-dominated landscape over the short- and long-term, accounting for conflict mortality. Natural and conflict-induced mortality together reduced expected movement and connectivity among populations. Based on model validation, our conflict predictions that explicitly captured animal movement better explained observed conflict than a model that considered distribution alone. Our work highlights the interaction between connectivity and conflict and enables identification of location-specific conflict mitigation strategies that minimize losses to people, while ensuring critical wildlife movement between habitats. By predicting where animal movement and humans collide, we provide a basis to plan for broad-scale conservation and the mutual well-being of wildlife and people in shared landscapes.

Genetic connectivity lies at the heart of evolutionary theory, and landscape genetics has rapidly advanced to understand how gene flow can be impacted by the environment. Isolation by landscape resistance, often inferred through the use of circuit theory, is increasingly identified as being critical for predicting genetic connectivity across complex landscapes. Yet landscape impediments to migration can arise from fundamentally different processes, such as landscape gradients causing directional migration and mortality during migration, which can be challenging to address. Spatial absorbing Markov chains (SAMC) have been introduced to understand and predict these (and other) processes affecting connectivity in ecological settings, but the relationship of this framework to landscape genetics remains unclear. Here, we relate the SAMC to population genetics theory, provide simulations to interpret the extent to which the SAMC can predict genetic metrics and demonstrate how the SAMC can be applied to genomic data using an example with an endangered species, the Panama City crayfish Procambarus econfinae, where directional migration is hypothesized to occur. The use of the SAMC for landscape genetics can be justified based on similar grounds to using circuit theory, as we show how circuit theory is a special case of this framework. The SAMC can extend circuit‐theoretic connectivity modelling by quantifying both directional resistance to migration and acknowledging the difference between migration mortality and resistance to migration. Our empirical example highlights that the SAMC better predicts population structure than circuit theory and least‐cost analysis by acknowledging asymmetric environmental gradients (i.e. slope) and migration mortality in this species. These results provide a foundation for applying the SAMC to landscape genetics. This framework extends isolation‐by‐resistance modelling to account for some common processes that can impact gene flow, which can improve predicting genetic connectivity across complex landscapes.

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