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Spatially explicit population models (SEPMs) are often considered the best way to predict and manage species distributions in spatially heterogeneous landscapes. However, they are computationally intensive and require extensive knowledge of species' biology and behavior, limiting their application in many cases. An alternative to SEPMs is graph theory, which has minimal data requirements and efficient algorithms. Although only recently introduced to landscape ecology, graph theory is well suited to ecological applications concerned with connectivity or movement. This paper compares the performance of graph theory to a SEPM in selecting important habitat patches for Wood Thrush (Hylocichla mustelina) conservation. We use both models to identify habitat patches that act as population sources and persistent patches and also use graph theory to identify patches that act as stepping stones for dispersal. Correlations of patch rankings were very high between the two models. In addition, graph theory offers the ability to identify patches that are very important to habitat connectivity and thus long-term population persistence across the landscape. We show that graph theory makes very similar predictions in most cases and in other cases offers insight not available from the SEPM, and we conclude that graph theory is a suitable and possibly preferable alternative to SEPMs for species conservation in heterogeneous landscapes.

Connectivity among populations and habitats is important for a wide range of ecological processes. Understanding, preserving, and restoring connectivity in complex landscapes requires connectivity models and metrics that are reliable, efficient, and process based. We introduce a new class of ecological connectivity models based in electrical circuit theory. Although they have been applied in other disciplines, circuit-theoretic connectivity models are new to ecology. They offer distinct advantages over common analytic connectivity models, including a theoretical basis in random walk theory and an ability to evaluate contributions of multiple dispersal pathways. Resistance, current, and voltage calculated across graphs or raster grids can be related to ecological processes (such as individual movement and gene flow) that occur across large population networks or landscapes. Efficient algorithms can quickly solve networks with millions of nodes, or landscapes with millions of raster cells. Here we review basic circuit theory, discuss relationships between circuit and random walk theories, and describe applications in ecology, evolution, and conservation. We provide examples of how circuit models can be used to predict movement patterns and fates of random walkers in complex landscapes and to identify important habitat patches and movement corridors for conservation planning.

Context The impact of construction land expansion on regional landscape sustainability received significant attention, but the habitat isolation caused by such expansion across the urban-rural continuum calls for a closer examination. Objective This study aims to use the ecological network approach to assess the isolation effect imposed by urban areas and rural settlements on habitat patches in the Nanjing Metropolitan Area during 2000, 2010, and 2020. Methods We first extracted the habitat patches by applying morphological spatial pattern analysis (MSPA), then identified the ecological networks based on the comprehensive resistance surface and circuit theory. Finally, we constructed two indices, the isolation effect index (IEI) and isolation degree (ID), and evaluated the differential contributions of urban areas and rural settlements to habitat isolation. Results Our results showed a total of 129 habitat patches within our study area. These patches were linked by 188, 186, and 183 ecological corridors in the years 2000, 2010, and 2020, respectively. Further analysis revealed that habitat patches were strongly isolated by the expansion of construction land and increasing human activities. Remarkably, both urban areas and rural settlements played pivotal roles in exacerbating this isolation, with urban areas showing a striking surge in their isolation impact, while rural settlements continued to be the predominant driver of habitat isolation. Conclusions Sustainable landscape planning should consider how land uses may cause habitat isolation. Our study utilizes the ecological network approach to evaluate habitat isolation and introduces applicable indicators for estimating the isolation effects attributed to construction land expansion. Our findings hold significant implications for informing landscape planning and shaping ecological conservation policies.

Connectivity losses lead to a reduction of the amount of habitat resources that can be reached and used by species, and hence to a decline in the ranges and abundance of multiple taxa. Despite the recognized important role of small habitat patches for many species inhabiting fragmented landscapes, their potential contribution as stepping stones for maintaining overall landscape connectivity has received less attention. Using connectivity metrics based on a graph-theoretic approach we (i) quantified the connectivity of grassland patches in a sector of the Pampa region in Argentina, using a range of dispersal distances (from 100 to 10,000 m) representative of the scale of dispersal of different species; (ii) identified the most relevant patches for maintaining overall connectivity; and (iii) studied the importance of small patches (defined for different area thresholds of 5, 20, and 50 ha) as connectivity providers in the landscape. Although grassland patches were in general poorly connected at all distances, some of them were critical for overall connectivity and were found to play different crucial roles in the patch network. The location of small patches in the grassland network allowed them to function as stepping stones, yielding significant connectivity gains for species that move large distances (>5000 m) for the three area thresholds considered. Thus, under the spatial pattern of the studied landscape, species that move long distances would benefit from stepping stones, while less mobile organisms would benefit from, and mostly rely on the largest patches. We recommend that future management activities should (i) aim at preserving the grassland patches with the highest potential as stepping stones to promote landscape-level connectivity; and (ii) pay more attention to the conservation of key small patches, particularly given that usually they are those more vulnerable to land clearing for agriculture.

Habitat loss leads to habitat fragmentation. Habitat connectivity, however, could mitigate effects of habitat fragmentation on wildlife populations. This study was carried out to assess habitat suitability and connectivity of a brown bear population located along the Iran-Iraq border in the Zagros Mountains, at the southernmost extreme of the species range. A total of 34 presences of brown bear and seven environmental variables were used for habitat modeling using MaxEnt, and connectivity among habitat patches was assessed by electrical-circuit methods using Circuitscape. Distance from villages, elevation, slope, and distance from roads were respectively the most important variables in habitat modeling of the brown bear in the study area. In total, 33 habitat patches were identified for the brown bear, which covered about 12% of the study area. Results of connectivity revealed high connectivity among habitat patches in the Iran section, whereas in the Iraq section, only low connectivity was observed in areas close to the Iran-Iraq border. Systematic monitoring is recommended to assess potential habitat patches and habitat connectivity of the brown bear in future research as a first step towards cooperative management efforts between wildlife managers of Iran and Iraq. Moreover, establishing a transboundary protected area is highly recommended along the Iran-Iraq border to provide safety and connectivity for the brown bear in this region and reduce the effect of the country border as a separating factor.

Though landscape corridors increase dispersal of many animals and plants, it remains unknown whether these positive effects extend to the process of colonization and establishment of new populations in fragments. Working in experimentally fragmented landscapes, we tested how two aspects of habitat fragments altered by corridors – connectivity and edge‐to‐area ratio – determine patterns of colonization by a solitary, cavity‐nesting bee Megachile rotundata. We found that though connectivity initially affected rates of nest‐site occupation, edge‐to‐area ratio ultimately determined the final patterns of patch occupation and nest building, likely due to habitat selection by our focal species. Bee colonization was also higher in patches with higher abundances of their preferred food resources, flowers from the Fabaceae family. Our results show the importance of considering the effects of both connectivity and edge on population dynamics in habitat‐based conservation.

Context The effective delineation of habitat is crucial for understanding drivers of habitat loss and fragmentation, and their effects on biodiversity outcomes at local to global scales. The concept of the habitat patch is central to this process but presents both theoretical and methodological challenges related to the seemingly irreconcilable tendency of habitat to simultaneously exhibit characteristics of both gradation and aggregation. This apparent contradiction, recently described as the continuity-contiguity problem in landscape ecology, presents a problem of classification in which the associated ambivalence is analogous to that surrounding the fate of Schrödinger’s Cat. Objectives This is the first of a pair of papers that aim to address the theoretical and methodological challenges associated with the habitat patch concept. This first paper aims to (a) articulate the theoretical and practical limitations of working with the habitat patch concept and (b) set out a framework based on a functional definition of habitat that captures the tendency of resources to exhibit both discrete and continuous spatial characteristics. The second paper (Dennis et al. this issue) presents a demonstration of this framework applied to a real-world landscape, in which the impact of adopting alternative perspectives on habitat delineation on potential functional connectivity is revealed. Methods We present a new methodological approach that integrates alternative gradient and patch-based models of habitat in landscape ecology. We achieve this integration by leveraging the notion of geographical vagueness and the application of fuzzy set theory to land cover classification. We apply this approach to simulated landscapes that contain information on membership values to different land cover classes and their associated uncertainty. We then demonstrate the functional delineation of habitat from these landscapes based on the use of species-specific parameters, the leveraging of spatial kernels, and type-1 and type-2 fuzzy sets. The possibility of incorporating this approach into subsequent workflows is then described using estimates of between-patch distances and potential functional connectivity as examples. Results Our method provides a functional spatial delineation of habitat that reflects both resource-based and patch-based habitat perspectives and can be applied to any gradient or patch-based landscape modelling method. This approach achieves the integration of multiple resource types, habitat complementarity associated with neighbouring cover types, and negative edge effects. We refer to this measure of habitat as Functional Habitat so-called as it reflects the total availability of habitat accounting for the influence of all land cover types and positive and negative neighbourhood effects. Conclusion This paper describes a functional approach to habitat delineation and its integration into the computation of fragmentation-related metrics. This methodological framework achieves, for the first time, (1) a multivariate delineation of habitat based on type-1 fuzzy membership and the operationalising of neighbourhood effects and (2) the harnessing of uncertainty in land cover classification ( type-2 fuzzy membership) to achieve a distribution of possible outcomes that resolves the continuity-contiguity problem . This new methodology provides a long-awaited functional definition of habitat patches for those seeking to understand the role of habitat fragmentation in biodiversity outcomes.

Fragmentation transforms natural habitats into a set of structurally and functionally differentiated small and separated patches, and causes the loss of connectivity among populations. In this study, we used a multi-temporal approach (1986, 2011 and 2016), to analyze the patterns of habitat fragmentation and to identify critical zones for the maintenance of habitat connectivity of two focal pine species (Pinus pseudostrobus and P. montezumae) with the broadest distribution and highest economic importance in the temperate forests of the Meseta Purépecha, in Michoacán, Mexico. This eco-region is currently one of the most threatened in terms of habitat degradation and extinction of forest communities. From a supervised classification of satellite images, land use coverage classes were selected and used as a basis to analyze the degree of landscape fragmentation using configuration and composition metrics and landscape connectivity based on the graph-theory approach. The fragmentation metrics suggested an increase in agricultural coverage (10.81%; fruits crop, mainly avocado), while the coverage of the forest showed a reduction (15.06%) and fragmentation throughout the study period. The landscape connectivity is lower (16.3% on average) and showed two highly important zones (Uruapan and Tancítaro) and one zone of high importance (Pátzcuaro) to maintain connectivity, considering three different dispersion distances (0.5, 5.0 and 10 km) for the species analyzed. We propose these three zones as potential habitat stepping stones to promote overall landscape connectivity, offering primary habitats and possible ecological resilience for this important forest ecosystem.

AimOur aim was to test whether species richness patterns are best explained by the effect of the total amount of habitat within the landscape, or instead by a combination of patch size and patch isolation effects. To this end, we jointly contrast the habitat amount hypothesis and countryside biogeography with patch size and isolation concepts from island biogeography.LocationThree multi‐habitat landscapes in Peneda‐Gerês National Park, NW Portugal.TaxonMacro‐moths (Lepidoptera).MethodsLight‐trapping using a semi‐nested design at 84 fixed sites which were each repeatedly sampled six times.ResultsAutocovariate models show that sampling sites with a higher number of forest and meadow macro‐moth species (alpha diversity) were surrounded by a higher amount of forest and meadow habitat, respectively within a 160 and 320 m radius (scale of effect). These top‐ranked models, containing only habitat amount as a significant variable, had lower Akaike's information criteria (AIC) than models (only) containing patch size and/or isolation. Complementary to this, the countryside species–area relationship (SAR) model outperforms the classic SAR model, so that the effective area of habitat explains landscape species richness (gamma diversity) across spatial scales (beta diversity) better than the classic SAR. Specifically, we show that forest macro‐moths have a higher spatial turnover than meadow macro‐moths and that, on average, there are more species in forest than in meadow habitat.Main conclusionsThe habitat amount hypothesis predicts alpha species richness in multi‐habitat landscapes better than do patch size and isolation while the countryside SAR predicts beta and gamma diversity better than the classic SAR. We suggest that evidence is mounting to revise the application of the classical approaches of island biogeography and metapopulation theory to conservation biogeography.

Habitat fragmentation involves habitat loss concomitant with changes in spatial configuration, confounding mechanistic drivers of biodiversity change associated with habitat disturbance. Studies attempting to isolate the effects of altered habitat configuration on associated communities have reported variable results. This variability may be explained in part by the fragmentation threshold hypothesis, which predicts that the effects of habitat configuration may only manifest at low levels of remnant habitat area. To separate the effects of habitat area and configuration on biodiversity, we surveyed fish communities in seagrass landscapes spanning a range of total seagrass area (2-74% cover within 16000-m² landscapes) and spatial configurations (1-75 discrete patches). We also measured variation in fine-scale seagrass variables, which are known to affect faunal community composition and may vary with landscape-scale features. We found that species richness decreased and the community structure shifted with increasing patch number within the landscape, but only when seagrass area was low (< 25% cover). This pattern was driven by an absence of epibenthic species in low-seagrass-area, highly patchy landscapes. Additional tests corroborated that low movement rates among patches may underlie loss of vulnerable taxa. Fine-scale seagrass biomass was generally unimportant in predicting fish community composition. As such, we present empirical support for the fragmentation threshold hypothesis and we suggest that poor matrix quality and low dispersal ability for sensitive taxa in our system may explain why our results support the hypothesis, while previous empirical work has largely failed to match predictions.