Continuous versus binary representations of landscape heterogeneity in spatially-explicit models of mobile populations

How a landscape is represented is an important structural assumption in spatially-explicit simulation models. Simple models tend to specify just habitat and non-habitat (binary), while more complex models may use multiple levels or a continuum of habitat quality (continuous). How these different representations influence model projections is unclear. To assess the influence of landscape representation on population models, I developed a general, individual-based model with local dispersal and examined population persistence across binary and continuous landscapes varying in the amount and fragmentation of habitat. In binary and continuous landscapes habitat and non-habitat were assigned a unique mean suitability. In continuous landscapes, suitability of each individual site was then drawn from a normal distribution with fixed variance. Populations went extinct less often and abundances were higher in continuous landscapes. Production in habitat and non-habitat was higher in continuous landscapes, because the range of habitat suitability sampled by randomly dispersing individuals was higher than the overall mean habitat suitability. Increasing mortality, dispersal distance, and spatial heterogeneity all increased the discrepancy between continuous and binary landscapes. The effect of spatial structure on the probability of extinction was greater in binary landscapes. These results show that, under certain circumstances, model projections are influenced by how variation in suitability within a landscape is represented. Care should be taken to assess how a given species actually perceives the landscape when conducting population viability analyses or empirical validation of theory.     

Virtual Corridors for Conservation Management

Abstract:  Corridors are usually perceived as clearly visible, linear landscape elements embedded in a hostile environment that connect two or more larger blocks of habitat. Animal response to certain aspects of landscape heterogeneity, however, can channel their movements into specific routes that may appear similar to their surroundings. These routes can be described as "virtual corridors" (VCs). Here we contribute to the foundation of the concept of VCs and highlight their implications for conservation management. We used an individual-based model to analyze the formation of VCs in the case of hilltopping in butterflies—where males and virgin females ascend to hilltops and mate. We simulated butterfly movements in two different topographically heterogeneous landscapes. We analyzed the movement patterns with respect to one parameter, the intensity of response to topography. Virtual corridor structure depended on the behavioral parameter, landscape, and location of the source patch. Within a realistic range of the behavioral parameter and in a realistic landscape, VC structures may be complex and require individual-based models for their elucidation.     

Aphid population response to agricultural landscape change: A spatially explicit,individual-based model

A spatially explicit individual-based simulation model has been developed to represent aphid population dynamics in agricultural landscapes. The application of the model to Rhopalosiphum padi (L.) population dynamics is detailed, including an outline of the construction of the model, its parameterisation and validation. Over time, the aphids interact with the landscape and with one another. The landscape is modified by varying a simple pesticide regime, and the multi-scale spatial and temporal implications for a population of aphids is analysed. The results show that a spatial modelling approach that considers the effects on the individual of landscape properties and factors such as wind speed and wind direction provides novel insight into aphid population dynamics both spatially and temporally. This forms the basis for the development of further simulation models that can be used to analyse how changes in landscape structure impact upon important species distributions and population dynamics.     

Integrating functional connectivity and fire management for better conservation outcomes

Globally, the mean abundance of terrestrial animals has fallen by 50% since 1970, and populations face ongoing threats associated with habitat loss, fragmentation, climate change, and disturbance. Climate change can influence the quality of remaining habitat directly and indirectly by precipitating increases in the extent, frequency, and severity of natural disturbances, such as fire. Species face the combined threats of habitat clearance, changing climates, and altered disturbance regimes, each of which may interact and have cascading impacts on animal populations. Typically, conservation agencies are limited in their capacity to mitigate rates of habitat clearance, habitat fragmentation, or climate change, yet fire management is increasingly used worldwide to reduce wildfire risk and achieve conservation outcomes. A popular approach to ecological fire management involves the creation of fire mosaics to promote animal diversity. However, this strategy has 2 fundamental limitations: the effect of fire on animal movement within or among habitat patches is not considered and the implications of the current fire regime for long-term population persistence are overlooked. Spatial and temporal patterns in fire history can influence animal movement, which is essential to the survival of individual animals, maintenance of genetic diversity, and persistence of populations, species, and ecosystems. We argue that there is rich potential for fire managers to manipulate animal movement patterns; enhance functional connectivity, gene flow, and genetic diversity; and increase the capacity of populations to persist under shifting environmental conditions. Recent methodological advances, such as spatiotemporal connectivity modeling, spatially explicit individual-based simulation, and fire-regime modeling can be integrated to achieve better outcomes for biodiversity in human-modified, fire-prone landscapes. Article impact statement: Land managers may conserve populations by using fire to sustain or enhance functional connectivity.     

An Experimental Test of Matrix Permeability and Corridor Use by an Endemic Understory Bird

Abstract:  Because of widespread habitat fragmentation, maintenance of landscape connectivity has become a major focus of conservation planning, but empirical tests of animal movement in fragmented landscapes remain scarce. We conducted a translocation experiment to test the relative permeability of three landscape elements (open habitat, shrubby secondary vegetation, and wooded corridors) to movement by the Chucao Tapaculo ( Scelorchilus rubecula ), a forest understory bird endemic to South American temperate rainforest. Forty-one radio-tagged subjects were translocated (individually) to three landscape treatments consisting of small release patches that were either entirely surrounded by open habitat (pasture), entirely surrounded by dense shrubs, or linked to other patches by wooded corridors that were otherwise surrounded by open matrix. The number of days subjects remained in release patches before dispersal (a measure of habitat resistance) was significantly longer for patches surrounded by open habitat than for patches adjoining corridors or surrounded by dense shrubs. These results indicate that open habitat significantly constrains Chucao dispersal, in accord with expectation, but dispersal occurs equally well through wooded corridors and shrub-dominated matrix. Thus, corridor protection or restoration and management of vegetation in the matrix (to encourage animal movement) may be equally feasible alternatives for maintaining connectivity.     

Bright moonlight triggers natal dispersal departures

Upon leaving their natal area, dispersers are confronted with unknown terrains. Species-specific perceptual ranges (i.e. the maximum distance from which an individual can perceive landscape features) play a crucial role in spatial movement decisions during such wanderings. In nocturnal animals that rely on vision, perceptual range is dramatically enhanced during moonlight, compared to moonless conditions. This increase of the perceptual range is an overlooked element that may be responsible for the successful crossing of unfamiliar areas during dispersal. The information gathered from 143 radio-tagged eagle owl Bubo bubo juveniles in Spain, Finland and Switzerland shows that, although the decision to initiate dispersal is mainly an endogenous phenomenon determined by the attainment of a given age (～6 months), dispersers leave their birthplace primarily under the best light conditions at night, i.e. when most of the lunar disc is illuminated. This sheds new light into the mechanisms that may trigger dispersal from parental territory.     

Connecting today's climates to future climate analogs to facilitate movement of species under climate change

Increasing connectivity is an important strategy for facilitating species range shifts and maintaining biodiversity in the face of climate change. To date, however, few researchers have included future climate projections in efforts to prioritize areas for increasing connectivity. We identified key areas likely to facilitate climate‐induced species’ movement across western North America. Using historical climate data sets and future climate projections, we mapped potential species’ movement routes that link current climate conditions to analogous climate conditions in the future (i.e., future climate analogs) with a novel moving‐window analysis based on electrical circuit theory. In addition to tracing shifting climates, the approach accounted for landscape permeability and empirically derived species’ dispersal capabilities. We compared connectivity maps generated with our climate‐change‐informed approach with maps of connectivity based solely on the degree of human modification of the landscape. Including future climate projections in connectivity models substantially shifted and constrained priority areas for movement to a smaller proportion of the landscape than when climate projections were not considered. Potential movement, measured as current flow, decreased in all ecoregions when climate projections were included, particularly when dispersal was limited, which made climate analogs inaccessible. Many areas emerged as important for connectivity only when climate change was modeled in 2 time steps rather than in a single time step. Our results illustrate that movement routes needed to track changing climatic conditions may differ from those that connect present‐day landscapes. Incorporating future climate projections into connectivity modeling is an important step toward facilitating successful species movement and population persistence in a changing climate.     

Use of Empirically Derived Source-Destination Models to Map Regional Conservation Corridors

Abstract:  The ability of populations to be connected across large landscapes via dispersal is critical to long-term viability for many species. One means to mitigate population isolation is the protection of movement corridors among habitat patches. Nevertheless, the utility of small, narrow, linear features as habitat corridors has been hotly debated. Here, we argue that analysis of movement across continuously resistant landscapes allows a shift to a broader consideration of how landscape patterns influence connectivity at scales relevant to conservation. We further argue that this change in scale and definition of the connectivity problem improves one's ability to find solutions and may help resolve long-standing disputes regarding scale and definition of movement corridors and their importance to population connectivity. We used a new method that combines empirically derived landscape-resistance maps and least-cost path analysis between multiple source and destination locations to assess habitat isolation and identify corridors and barriers to organism movement. Specifically, we used a genetically based landscape resistance model for American black bears ( Ursus americanus ) to identify major movement corridors and barriers to population connectivity between Yellowstone National Park and the Canadian border. Even though western Montana and northern Idaho contain abundant public lands and the largest wilderness areas in the contiguous United States, moving from the Canadian border to Yellowstone Park along those paths indicated by modeled gene flow required bears to cross at least 6 potential barriers. Our methods are generic and can be applied to virtually any species for which reliable maps of landscape resistance can be developed.     

The effect of patch constellation on the exchange of individuals between habitat-islands

Metapopulation models assume that inter-patch dispersal dominantly depends on distance between patches and the dispersal capability of organisms in question. We used a spatially explicit, individual-based model to investigate the potential effect of patch constellation on the exchange of individuals between patches. We simulated migration of individuals from a start- into a target-patch with both patches having the same size and shape. Simulation experiments were carried out for four patch constellations and two different movement patterns. Our results demonstrate a substantial effect of patch constellation on the exchange of individuals. They also show that the magnitude and even the direction of this effect crucially depends on their movement pattern. We conclude that particularly for highly correlated movement patterns patch shape and constellation can not readily be ignored when modelling inter-patch dispersal between habitat-islands.     

Unveiling human-assisted dispersal mechanisms in invasive alien insects: Integration of spatial stochastic simulation and phenology models

Capturing the spread of biological invasions in heterogeneous landscapes is a complex modelling task where information on both dispersal and population dynamics needs to be integrated. Spatial stochastic simulation and phenology models have rarely been combined to assist in the study of human-assisted long-distance dispersal events.Here we develop a process-based spatially explicit landscape-extent simulation model that considers the spread and detection of invasive insects. Natural and human-assisted dispersal mechanisms are modelled with an individual-based approach using negative exponential and negative power law dispersal kernels and gravity models. The model incorporates a phenology sub-model that uses daily temperature grids for the prediction and timing of the population dynamics in each habitat patch. The model was applied to the study of the invasion by the important maize pest western corn rootworm (WCR) Diabrotica virgifera ssp. virgifera in Europe. We parameterized and validated the model using maximum likelihood and simulation methods from the historical invasion of WCR in Austria.WCR was found to follow stratified dispersal where international transport networks in the Danube basin played a key role in the occurrence of long-distance dispersal events. Detection measures were found to be effective and altitude had a significant effect on limiting the spread of WCR. Spatial stochastic simulation combined with phenology models, maximum likelihood methods and predicted versus observed regression showed a high degree of flexibility that captured the salient features of WCR spread in Austria. This modelling approach is useful because it allows to fully exploit and the often limited and heterogeneous information available regarding the population dynamics and dispersal of alien invasive insects.     

Using circuit theory to model connectivity in ecology, evolution, and conservation

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.     

The Application of Neutral Landscape Models in Conservation Biology

Neutral landscape models, derived from percolation theory in the field of landscape ecology, are grid-based maps in which complex habitat distributions are generated by random or fractal algorithms. This grid-based representation of landscape structure is compatible with the raster-based format of geographical information systems (GIS), which facilitates comparisons between theoretical and real landscapes. Neutral landscape models permit the identification of critical thresholds in connectivity, which can be used to predict when landscapes will become fragmented. The coupling of neutral landscape models with generalized population models, such as metapopulation theory, provides a null model for generating predictions about population dynamics in fragmented landscapes. Neutral landscape models can contribute to the following applications in conservation: (1) incorporation of complex spatial patterns in (meta)population models; (2) identification of species' perceptions of landscape structure; (3) determination of landscape connectivity; (4) evaluation of the consequences of habitat fragmentation for population subdivision; (5) identification of the domain of metapopulation dynamics; (6) prediction of the occurrence of extinction thresholds; ( 7) determination of the genetic consequences of habitat fragmentation; and (8) reserve design and ecosystem management. This generalized, spatially explicit framework bridges the gap between spatially implicit, patch-based models and spatially realistic GIS applications which are usually parameterized for a single species in a specific landscape. Development of a generalized, spatially explicit framework is essential in conservation biology because we will not be able to develop individual models for every species of management concern.     

Dispersal in Spatially Explicit Population Models

Abstract: Ruckelshaus et al. (1997) outlined a simulation model of dispersal between patches in a fragmented landscape. They showed that dispersal success—the proportion of dispersers successfully locating a patch—was particularly sensitive to errors in dispersal mortality and concluded that this limits the utility of spatially explicit population models in conservation biology. I contend that, although they explored error propagation in a simple dispersal model, they did not explore how errors are propagated in spatially explicit population models, as no consideration of population processes was included. I developed a simple simulation model to investigate the effect of varying dispersal success on predictions of patch occupancy and population viability, the conventional outputs of spatially explicit population models. The model simulates births and deaths within habitat patches and dispersal as the transfer of individuals between them. Model predictions were sensitive to changes in dispersal success across a restricted range of within-patch growth rates, which depended on the dispersal initiation mechanism, patch carrying capacities, and number of generations simulated. Predictions of persistence and patch occupancy were generally more sensitive to changes in dispersal success (1) under presaturation rather than saturation dispersal; (2) at lower patch carrying capacities; and (3) over longer time periods. The framework I present provides a means of assessing, quantitatively, the regions of parameter space for which differences in dispersal success are likely to have a large effect on population model outputs. Investigating the effect of the representation of dispersal behavior within the demographic and landscape context provides a more useful assessment of whether our lack of knowledge is likely to cause unacceptable uncertainty in the predictions of spatially explicit population models.     

Graph theory as a proxy for spatially explicit population models in conservation planning.

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.     

Controlling annual weeds in cereals by deploying crop rotation at the landscape scale: Avena sterilis as an example

Weed control through crop rotation has mainly been studied in a nonspatial context. However, weed seeds are often spread beyond the crop field by a variety of vectors. For weed control to be successful, weed management should thus be evaluated at the landscape level. In this paper we assess how seed dispersal affects the interactions between crop rotation and landscape heterogeneity schemes with regard to weed control. A spatially explicit landscape model was developed to study both short- and long-term weed population dynamics under different management scenarios. We allowed for both two- and three-crop species rotations and three levels of between-field weed seed dispersal. All rotation scenarios and seed dispersal fractions were analyzed for both completely homogeneous landscapes and heterogeneous landscapes in which more than one crop was present. The potential of implementing new weed control methods was also analyzed. The model results suggest that, like crop rotation at the field level, crop rotation implemented at the landscape level has great potential to control weeds, whereby both the number of crop species and the cropping sequence within the crop rotation have significant effects on both the short- and long-term weed population densities. In the absence of seed dispersal, weed populations became extinct when the fraction of each crop in the landscape was randomized. In general, weed seed densities increased in landscapes with increasing similarity in crop proportions, but in these landscapes the level of seed dispersal affected which three-crop species rotation sequence was most efficient at controlling the weed densities. We show that ignoring seed dispersal between fields might lead to the selection of suboptimal tactics and that homogeneous crop field patches that follow a specific crop rotation sequence might be the most sustainable method of weed control. Effective weed control through crop rotation thus requires coordination between farmers with regard to cropping sequences, crop allocation across the landscape, and/ or the fraction of each crop across the landscape.     

How complex do models need to be to predict dispersal of threatened species through matrix habitats?

Persistence of species in fragmented landscapes depends on dispersal among suitable breeding sites, and dispersal is often influenced by the "matrix" habitats that lie between breeding sites. However, measuring effects of different matrix habitats on movement and incorporating those differences into spatially explicit models to predict dispersal is costly in terms of time and financial resources. Hence a key question for conservation managers is: Do more costly, complex movement models yield more accurate dispersal predictions? We compared the abilities of a range of movement models, from simple to complex, to predict the dispersal of an endangered butterfly, the Saint Francis' satyr (Neonympha mitchellii francisci). The value of more complex models differed depending on how value was assessed. Although the most complex model, based on detailed movement behaviors, best predicted observed dispersal rates, it was only slightly better than the simplest model, which was based solely on distance between sites. Consequently, a parsimony approach using information criteria favors the simplest model we examined. However, when we applied the models to a larger landscape that included proposed habitat restoration sites, in which the composition of the matrix was different than the matrix surrounding extant breeding sites, the simplest model failed to identify a potentially important dispersal barrier, open habitat that butterflies rarely enter, which may completely isolate some of the proposed restoration sites from other breeding sites. Finally, we found that, although the gain in predicting dispersal with increasing model complexity was small, so was the increase in financial cost. Furthermore, a greater fit continued to accrue with greater financial cost, and more complex models made substantially different predictions than simple models when applied to a novel landscape in which butterflies are to be reintroduced to bolster their populations. This suggests that more complex models might be justifiable on financial grounds. Our results caution against a pure parsimony approach to deciding how complex movement models need to be to accurately predict dispersal through the matrix, especially if the models are to be applied to novel or modified landscapes.     

A Comparison of Corridors and Intrinsic Connectivity to Promote Dispersal in Transient Successional Landscapes

Low-vagility organisms that specialize on transitory successional habitats may be especially dependent upon habitat connectivity to maintain population viability. We analyzed the theoretical intrinsic connectivity of successional landscapes (i.e., the natural juxtaposition of similar habitats that allows dispersal) as a function of patch geometry coupled with the disperser's habitat specificity. Habitat specialists living in poorly connected landscapes (approximating hexagonal patches) have only a 26.5% chance of colonizing a new site when their resident patch becomes unsuitable. In contrast, generalists living in well connected landscapes can virtually always colonize a new site when needed. We infer from our simulation that for some habitat specialists, such as the rare, endemic Florida scrub lizard (Sceloporus woodi), anthropogenic control of successional dynamics for commercial logging may significantly reduce intrinsic connectivity. Lizard population viability may now depend upon the extrinsic connectivity provided by artificial corridors. However, the use of corridors will not serve as a general solution to the problem of anthropogenically reduced intrinsic connectivity until key logistical design problems have been resolved. Moreover, efforts to enhance intrinsic connectivity by modifying patch geometry may produce undesirable edge effects and conflict with old-growth preservation. Future research should focus on developing spatially explicit corridor models, documenting natural levels of intrinsic connectivity, quantifying anthropogenic disruption of natural connectivity, and describing species-specific mechanisms of inter-patch dispersal.     

An individual-based stochastic hazard model of eastern king prawn (Melicertus plebejus) migration with spatially and temporally varying fishing effort

This paper describes an individual-based stochastic model of eastern king prawn migration along the eastern Australian coast. Migration is treated as one-dimensional diffusion with drift. Capture of a prawn is seen as a failure event driven by movement through a spatially and temporally variable fishing mortality hazard. This hazard is combined with a uniform natural mortality hazard. We use a Monte Carlo method to estimate parameters by comparing expected numbers of tag-returns predicted from the model with previously published tag-release data. As the previous study used a discrete compartmental model, with compartments corresponding to zones of constant fishing effort, we used the same zones and fishing effort in our comparison. The marginal distribution of yield in each zone per single recruit is determined, providing more information compared with the deterministic approach to yield-per-recruit. Using our model we also derive the constant fishing mortality rate equivalent to a spatially variable fishing mortality rate in its impact on the proportion of prawns surviving the migration to reach spawning grounds. Determination of this proportion could contribute significantly to a sustainability assessment of the fishery. It is demonstrated using the AIC that better fits to the data of the previous study and greater parsimony are obtained using our model than were found in the deterministic compartmental analysis of that study. This improvement results from the ability of our model to account separately for average speed of movement and average dispersal rate, whereas in the previous deterministic compartmental model, movement is governed by just one parameter. Our individual-based model includes a parameter that explicitly accounts for dispersal of prawns in migration, so it can distinguish between speed effects and dispersal effects in the data. It also models both types of mortality as processes distinct from those of movement. This enables it to better separate movement and mortality effects compared to the compartmental approach, in which movement and mortality are treated as similar departure processes from a compartment. This separation reduces confounding of movement and mortality effects when parameters are estimated.     

Validating graph-based connectivity models with independent presence–absence and genetic data sets

Habitat connectivity is a key objective of current conservation policies and is commonly modeled by landscape graphs (i.e., sets of habitat patches [nodes] connected by potential dispersal paths [links]). These graphs are often built based on expert opinion or species distribution models (SDMs) and therefore lack empirical validation from data more closely reflecting functional connectivity. Accordingly, we tested whether landscape graphs reflect how habitat connectivity influences gene flow, which is one of the main ecoevolutionary processes. To that purpose, we modeled the habitat network of a forest bird (plumbeous warbler [Setophaga plumbea]) on Guadeloupe with graphs based on expert opinion, Jacobs’ specialization indices, and an SDM. We used genetic data (712 birds from 27 populations) to compute local genetic indices and pairwise genetic distances. Finally, we assessed the relationships between genetic distances or indices and cost distances or connectivity metrics with maximum-likelihood population-effects distance models and Spearman correlations between metrics. Overall, the landscape graphs reliably reflected the influence of connectivity on population genetic structure; validation R² was up to 0.30 and correlation coefficients were up to 0.71. Yet, the relationship among graph ecological relevance, data requirements, and construction and analysis methods was not straightforward because the graph based on the most complex construction method (species distribution modeling) sometimes had less ecological relevance than the others. Cross-validation methods and sensitivity analyzes allowed us to make the advantages and limitations of each construction method spatially explicit. We confirmed the relevance of landscape graphs for conservation modeling but recommend a case-specific consideration of the cost-effectiveness of their construction methods. We hope the replication of independent validation approaches across species and landscapes will strengthen the ecological relevance of connectivity models.