Comparing spatial conservation prioritization methods with site- versus spatial dependency-based connectivity

Larval dispersal is an important component of marine reserve networks. Two conceptually different approaches to incorporate dispersal connectivity into spatial planning of these networks exist, and it is an open question as to when either is most appropriate. Candidate reserve sites can be selected individually based on local properties of connectivity or on a spatial dependency-based approach of selecting clusters of strongly connected habitat patches. The first acts on individual sites, whereas the second acts on linked pairs of sites. We used a combination of larval dispersal simulations representing different seascapes and case studies of biophysical larval dispersal models in the Coral Triangle region and the province of Southeast Sulawesi, Indonesia, to compare the performance of these 2 methods in the spatial planning software Marxan. We explored the reserve design performance implications of different dispersal distances and patterns based on the equilibrium settlement of larvae in protected and unprotected areas. We further assessed different assumptions about metapopulation contributions from unprotected areas, including the case of 100% depletion and more moderate scenarios. The spatial dependency method was suitable when dispersal was limited, a high proportion of the area of interest was substantially degraded, or the target amount of habitat protected was low. Conversely, when subpopulations were well connected, the 100% depletion was relaxed, or more habitat was protected, protecting individual sites with high scores in metrics of connectivity was a better strategy. Spatial dependency methods generally produced more spatially clustered solutions with more benefits inside than outside reserves compared with site-based methods. Therefore, spatial dependency methods potentially provide better results for ecological persistence objectives over enhancing fisheries objectives, and vice versa. Different spatial prioritization methods of using connectivity are appropriate for different contexts, depending on dispersal characteristics, unprotected area contributions, habitat protection targets, and specific management objectives. Comparación entre los métodos de priorización de la conservación espacial con sitio y la conectividad espacial basada en la dependencia     

Risk spreading, connectivity, and optimal reserve spacing

Two important processes determining the dynamics of spatially structured populations are dispersal and the spatial covariance of demographic fluctuations. Spatially explicit approaches to conservation, such as reserve networks, must consider the tension between these two processes and reach a balance between distances near enough to maintain connectivity, but far enough to benefit from risk spreading. Here, we model this trade-off. We show how two measures of metapopulation persistence depend on the shape of the dispersal kernel and the shape of the distance decay in demographic covariance, and we consider the implications of this trade-off for reserve spacing. The relative rates of distance decay in dispersal and demographic covariance determine whether the long-run metapopulation growth rate, and quasi-extinction risk, peak for adjacent patches or intermediately spaced patches; two local maxima in metapopulation persistence are also possible. When dispersal itself fluctuates over time, the trade-off changes. Temporal variation in mean distance that propagules are dispersed (i.e., propagule advection) decreases metapopulation persistence and decreases the likelihood that persistence will peak for adjacent patches. Conversely, variation in diffusion (the extent of random spread around mean dispersal) increases metapopulation persistence overall and causes it to peak at shorter inter-patch distances. Thus, failure to consider temporal variation in dispersal processes increases the risk that reserve spacings will fail to meet the objective of ensuring metapopulation persistence. This study identifies two phenomena that receive relatively little attention in empirical work on reserve spacing, but that can qualitatively change the effectiveness of reserve spacing strategies: (1) the functional form of the distance decay in covariance among patch-specific demographic rates and (2) temporal variation in the shape of the dispersal kernel. The sensitivity of metapopulation recovery and persistence to how covariance of vital rates decreases with distance suggests that estimating the shape of this function is likely to be as important for effective reserve design as estimating connectivity. Similarly, because temporal variation in dispersal dynamics influences the effect of reserve spacing, approaches to reserve design that ignore such variation, and rely instead on long-term average dispersal patterns, are likely to lead to lower metapopulation viability than is actually achievable.     

Dispersal per recruit: an efficient method for assessing sustainability in marine reserve networks.

Marine reserves are an increasingly important tool for the management of marine ecosystems around the world. However, the effects of proposed marine reserve configurations on sustainability and yield of populations are typically not estimated because of the computational intensity of direct simulation and uncertainty in larval dispersal and density-dependent recruitment. Here we develop a method for efficiently assessing a marine reserve configuration for persistence and yield of a population with sedentary adults and dispersing larvae. The method extends the familiar sustainability criteria of individual replacement for single populations based on eggs-per-recruit (EPR) to spatially distributed populations with sedentary adults, a dispersing larval phase, and limited carrying capacity in the settlement-recruit relationship. We refer to this approach as dispersal-per-recruit (DPR). In some cases, a single DPR calculation, based on the assumption that post-settlement habitat is saturated (i.e., at maximum recruitment), is sufficient to determine population persistence, while in other cases further iterative calculations are required. These additional calculations reach an equilibrium more rapidly than a full simulation of age- or size-structured populations. From the DPR result, fishery yield can be computed from yield-per-recruit (YPR) at each point. We assess the utility of DPR calculations by applying them to single reserves, uniformly distributed systems of reserves, and randomly sized and spaced systems of reserves on a linear coastline. We find that for low levels of EPR in fished areas (e.g., 10% or less of the natural, unfished EPR when post-settlement habitats are saturated by 35% of natural settlement), a single DPR calculation is sufficient to determine persistence of the population. We also show that, in uniform systems of reserves with finite reserve size, maximal fisheries yield occurs when the density of reserves is such that all post-settlement habitat is nearly saturated with settlers. Finally, we demonstrate the application of this approach to a realistic proposed marine reserve configuration.     

Evaluating the importance of demographic connectivity in a marine metapopulation

Recently researchers have gone to great lengths to measure marine metapopulation connectivity via tagging, genetic, and trace-elemental fingerprinting studies. These empirical estimates of larval dispersal are key to assessing the significance of metapopulation connectivity within a demographic context, but the life-history data required to do this are rarely available. To evaluate the demographic consequences of connectivity we constructed seasonal, size-structured metapopulation matrix models for two species of mytilid mussel in San Diego County, California, USA. The self-recruitment and larval exchange terms were produced from a time series of realized connectivities derived from trace-elemental fingerprinting of larval shells during spring and fall from 2003 to 2008. Both species exhibited a strong seasonal pattern of southward movement of recruits in spring and northward movement in fall. Growth and mortality terms were estimated using mark-recapture data from representative sites for each species and subpopulation, and literature estimates of juvenile mortality. Fecundity terms were estimated using county-wide settlement data from 2006-2008; these data reveal peak reproduction and recruitment in fall for Mytilus californianus, and spring for M. galloprovincialis. Elasticity and life-stage simulation analyses were employed to identify the season- and subpopulation-specific vital rates and connectivity terms to which the metapopulation growth rate (lambda) was most sensitive. For both species, metapopulation growth was most sensitive to proportional changes in adult fecundity, survival and growth of juvenile stages, and population connectivity, in order of importance, but relatively insensitive to adult growth or survival. The metapopulation concept was deemed appropriate for both Mytilus species as exchange between the subpopulations was necessary for subpopulation persistence. However, highest metapopulation growth occurred in years when a greater proportion of recruits was retained within the predominant source subpopulation. Despite differences in habitat and planktonic duration, both species exhibited similar overall metapopulation dynamics with respect to key life stages and processes. However, different peak reproductive periods in an environment of seasonal current reversals led to different regional (subpopulation) contributions to metapopulation maintenance; this result emphasizes the importance of connectivity analysis for spatial management of coastal resources.     

Integrating larval connectivity into the marine conservation decision-making process across spatial scales

Larval dispersal connectivity is typically integrated into spatial conservation decisions at regional or national scales, but implementing agencies struggle with translating these methods to local scales. We used larval dispersal connectivity at regional (hundreds of kilometers) and local (tens of kilometers) scales to aid in design of networks of no-take reserves in Southeast Sulawesi, Indonesia. We used Marxan with Connectivity informed by biophysical larval dispersal models and remotely sensed coral reef habitat data to design marine reserve networks for 4 commercially important reef species across the region. We complemented regional spatial prioritization with decision trees that combined network-based connectivity metrics and habitat quality to design reserve boundaries locally. Decision trees were used in consensus-based workshops with stakeholders to qualitatively assess site desirability, and Marxan was used to identify areas for subsequent network expansion. Priority areas for protection and expected benefits differed among species, with little overlap in reserve network solutions. Because reef quality varied considerably across reefs, we suggest reef degradation must inform the interpretation of larval dispersal patterns and the conservation benefits achievable from protecting reefs. Our methods can be readily applied by conservation practitioners, in this region and elsewhere, to integrate connectivity data across multiple spatial scales.     

Evaluating the Effects of Three Forms of Marine Reserve on Northern Abalone Populations in British Columbia, Canada

Abstract: Marine reserves have been suggested as tools for assisting the management of fisheries by protecting vulnerable marine species from overexploitation. Although there is a theoretical basis for believing that marine reserves may serve as management tools, there are few marine reserves in the world in which to test their effectiveness. My research evaluated three forms of marine reserve on the south coast of Vancouver Island, British Columbia, Canada. I used northern abalone ( Haliotis kamtschatkana ), a severely depleted shellfish in this region, as an indicator of the effectiveness of the reserves. Abalone populations in eight sites receiving different degrees of spatial protection were counted and measured in situ during the spring of 1996 and 1997. In all sites with enforced harvest closures, populations of abalone were greater, and one site with nearly 40 years of protection had on average much larger (older) abalone. Reproductive output, as a function of abundance and size, was also greater in the enforced reserve areas. Larval dispersal from reserves, and hence the benefit to exploited areas, was not formally surveyed. Nevertheless, the results of my study, combined with knowledge of present abalone populations, life history, and regional hydrodynamics, suggest that establishment of reserves is justified in the absence of perfect knowledge of larval dispersal.     

Connectivity or demography: Defining sources and sinks in coral reef fish metapopulations

The identity of an individual patch as a source or a sink within a metapopulation is a function of its ability to produce individuals and to disperse them to other patches. In marine systems patch identity is very often defined by dispersal ability alone—upstream patches are sources—while issues of variable habitat quality (which affects local production) are ignored. This can have important ramifications for the science of marine reserve siting. This study develops a spatially explicit source–sink metapopulation model for reef fish and uses it to evaluate the relative importance of connectivity versus demography and how this depends upon the level of local larval retention and the strength of density-dependent recruitment. Elasticity analyses indicated that patch contribution (source or sink) was more sensitive to demographic parameters (particularly survival) than connectivity and this effect was conserved even under strong levels of density-dependence and was generally strengthened as local retention increased. Variability in the relationship between parameter elasticity and local retention was shown to be dependent upon the magnitude of connectivity for an individual patch relative to a critical connectivity value. The proportion of larvae lost due to transport processes was an important parameter which directly affected the magnitude of this critical connectivity value. Patches with connectivity values less than the critical value contributed to the metapopulation largely via production (i.e., local demographics most important). As local retention increased, so did the importance of demographic parameters in these patches. Patches with connectivity values greater than the critical value contributed largely via dispersal of larvae and thus the importance of local demographics decreased as local retention increased.     

Developing Metapopulation Connectivity Criteria from Genetic and Habitat Data to Recover the Endangered Mexican Wolf

Restoring connectivity between fragmented populations is an important tool for alleviating genetic threats to endangered species. Yet recovery plans typically lack quantitative criteria for ensuring such population connectivity. We demonstrate how models that integrate habitat, genetic, and demographic data can be used to develop connectivity criteria for the endangered Mexican wolf (Canis lupus baileyi), which is currently being restored to the wild from a captive population descended from 7 founders. We used population viability analysis that incorporated pedigree data to evaluate the relation between connectivity and persistence for a restored Mexican wolf metapopulation of 3 populations of equal size. Decreasing dispersal rates greatly increased extinction risk for small populations (<150–200), especially as dispersal rates dropped below 0.5 genetically effective migrants per generation. We compared observed migration rates in the Northern Rocky Mountains (NRM) wolf metapopulation to 2 habitat‐based effective distance metrics, least‐cost and resistance distance. We then used effective distance between potential primary core populations in a restored Mexican wolf metapopulation to evaluate potential dispersal rates. Although potential connectivity was lower in the Mexican wolf versus the NRM wolf metapopulation, a connectivity rate of >0.5 genetically effective migrants per generation may be achievable via natural dispersal under current landscape conditions. When sufficient data are available, these methods allow planners to move beyond general aspirational connectivity goals or rules of thumb to develop objective and measurable connectivity criteria that more effectively support species recovery. The shift from simple connectivity rules of thumb to species‐specific analyses parallels the previous shift from general minimum‐viable‐population thresholds to detailed viability modeling in endangered species recovery planning. Desarrollo de Criterios de Conectividad Metapoblacional a Partir de Datos Genéticos y de Hábitat para Recuperar al Lobo Mexicano en Peligro de Extinción     

Assessing the current state of ecological connectivity in a large marine protected area system

The establishment of marine protected areas (MPAs) is a critical step in ensuring the continued persistence of marine biodiversity. Although the area protected in MPAs is growing, the movement of individuals (or larvae) among MPAs, termed connectivity, has only recently been included as an objective of many MPAs. As such, assessing connectivity is often neglected or oversimplified in the planning process. For promoting population persistence, it is important to ensure that protected areas in a system are functionally connected through dispersal or adult movement. We devised a multi-species model of larval dispersal for the Australian marine environment to evaluate how much local scale connectivity is protected in MPAs and determine whether the extensive system of MPAs truly functions as a network. We focused on non-migratory species with simplified larval behaviors (i.e., passive larval dispersal) (e.g., no explicit vertical migration) as an illustration. Of all the MPAs analyzed (approximately 2.7 million km²), outside the Great Barrier Reef and Ningaloo Reef, <50% of MPAs (46-80% of total MPA area depending on the species considered) were functionally connected. Our results suggest that Australia's MPA system cannot be referred to as a single network, but rather a collection of numerous smaller networks delineated by natural breaks in the connectivity of reef habitat. Depending on the dispersal capacity of the taxa of interest, there may be between 25 and 47 individual ecological networks distributed across the Australian marine environment. The need to first assess the underlying natural connectivity of a study system prior to implementing new MPAs represents a key research priority for strategically enlarging MPA networks. Our findings highlight the benefits of integrating multi-species connectivity into conservation planning to identify opportunities to better incorporate connectivity into the design of MPA systems and thus to increase their capacity to support long-term, sustainable biodiversity outcomes.     

A model for behavioral regulation of metapopulation dynamics

Habitat fragmentation can decrease local population persistence by reducing connectivity, which is a function of dispersal of individuals among habitat fragments. Dispersal is often treated as diffusion in population models, even though for many species it is a result of a series of behavioral decisions. We developed a metapopulation model to explore the potential importance of dispersal behaviors in driving metapopulation dynamics. We incorporated types of behavior that affect dispersal—colonization inhibiting, colonization enhancing, extinction inhibiting, extinction enhancing, rescue enhancing, rescue inhibiting—into Levins’ (1969) metapopulation model and projected occupancy rates for a variety of parameter values. Examples from the literature of behaviors associated with each of these parameters are provided. Our model simplifies into previously published metapopulation models that incorporate only a single behavior, and we present a density-dependent rescue function that leads to multiple non-zero equilibria. We found a variety of behavioral effects on metapopulations. Rescue enhancement fills patches faster than does colonization enhancement or extinction inhibition, and declines in patch occupancy are moderate with extinction enhancement, but colonization inhibition causes metapopulation extinction. We also found that with colonization and extinction inhibitions, equilibrium patch occupancy is inversely related to patch turnover rate. With density-dependent rescue, persistence depends not only on the strength of the strong rescue effect, but also on having a sufficient initial fraction of patches occupied; the stronger the rescue effect, the lower this fraction can be. This study suggests that dispersal behavior can have strong influences on metapopulation dynamics. It confirms the importance of understanding the relationship between landscape structure and dispersal behavior in understanding population persistence.     

A robust-design formulation of the incidence function model of metapopulation dynamics applied to two species of rails

The incidence function model (IFM) uses area and connectivity to predict metapopulation dynamics. However, false absences and missing data can lead to underestimates of the number of sites contributing to connectivity, resulting in overestimates of dispersal ability and turnovers (extinctions plus colonizations). We extend estimation methods for the IFM by using a hierarchical Bayesian model to account both for false absences due to imperfect detection and for missing data due to sites not surveyed in some years. We compare parameter estimates, measures of metapopulation dynamics, and forecasts using stochastic patch occupancy models (SPOMs) among three IFM models: (1) a Bayesian formulation assuming no false absences and omitting site-year combinations with missing data; (2) a hierarchical Bayesian formulation assuming no false absences but incorporating missing data; and (3) a hierarchical Bayesian formulation allowing for imperfect detection and incorporating missing data. We fit the models to multiyear data sets of occupancy for two bird species that differ in body size and presumed dispersal ability but inhabit the same network of sites: the small Black Rail (Laterallus jamaicensis) and the medium-sized Virginia Rail (Rallus limicola). Incorporating missing data affected colonization parameters and led to lower estimates of dispersal ability for the Black Rail. Detection rates were high for the Black Rail in most years but moderate for the Virginia Rail. Incorporating imperfect detection resulted in higher occupancy and lower turnover rates for both species, with largest effects for the Virginia Rail. Forecasts using SPOMs were sensitive to both missing data and false absences; persistence in models assuming no false absences was more optimistic than from robust models. Our results suggest that incorporating false absences and missing data into the IFM can improve (1) estimates of dispersal ability and the effect of connectivity on colonization, (2) the scaling of extinction risk with patch area, and (3) forecasts of occupancy and turnover rates.     

Reserve design to optimize functional connectivity and animal density

Ecological distance-based spatial capture–recapture models (SCR) are a promising approach for simultaneously estimating animal density and connectivity, both of which affect spatial population processes and ultimately species persistence. We explored how SCR models can be integrated into reserve-design frameworks that explicitly acknowledge both the spatial distribution of individuals and their space use resulting from landscape structure. We formulated the design of wildlife reserves as a budget-constrained optimization problem and conducted a simulation to explore 3 different SCR-informed optimization objectives that prioritized different conservation goals by maximizing the number of protected individuals, reserve connectivity, and density-weighted connectivity. We also studied the effect on our 3 objectives of enforcing that the space-use requirements of individuals be met by the reserve for individuals to be considered conserved (referred to as home-range constraints). Maximizing local population density resulted in fragmented reserves that would likely not aid long-term population persistence, and maximizing the connectivity objective yielded reserves that protected the fewest individuals. However, maximizing density-weighted connectivity or preemptively imposing home-range constraints on reserve design yielded reserves of largely spatially compact sets of parcels covering high-density areas in the landscape with high functional connectivity between them. Our results quantify the extent to which reserve design is constrained by individual home-range requirements and highlight that accounting for individual space use in the objective and constraints can help in the design of reserves that balance abundance and connectivity in a biologically relevant manner.     

Local disturbance cycles and the maintenance of heterogeneity across scales in marine metapopulations

In marine systems, the occurrence and implications of disturbance-recovery cycles have been revealed at the landscape level, but only in demographically open or closed systems where landscape-level dynamics are assumed to have no feedback effect on regional dynamics. We present a mussel metapopulation model to elucidate the role of landscape-level disturbance cycles for regional response of mussel populations to onshore productivity and larval transport. Landscape dynamics are generated through spatially explicit rules, and each landscape is connected to its neighbor through unidirectional larval dispersal. The role of landscape disturbance cycles in the regional system behavior is elucidated (1) in demographically open vs. demographically coupled systems, in relation to (2) onshore reproductive output and (3) the temporal scale of landscape disturbance dynamics. By controlling for spatial structure at the landscape and metapopulation levels, we first demonstrate the interaction between landscape and oceanographic connectivity. The temporal scale of disturbance cycles, as controlled by mussel colonization rate, plays a critical role in the regional behavior of the system. Indeed, fast disturbance cycles are responsible for regional synchrony in relation to onshore reproductive output. Slow disturbance cycles, however, lead to increased robustness to changes in productivity and to demographic coupling. These testable predictions indicate that the occurrence and temporal scale of local disturbance-recovery dynamics can drive large-scale variability in demographically open systems, and the response of metapopulations to changes in nearshore productivity.     

Dynamic reserve design with the union-find algorithm

When reserve networks are established over time, there is a risk that sites will be developed in areas planned for future reservation, reducing the effectiveness of reserves. We developed a dynamic reserve design model that maximizes the expected number of species conserved, taking account of the risk of future habitat loss and fragmentation. The model makes use of the union-find algorithm, which is an efficient method for maintaining a list of connected regions in a graph as nodes and edges are inserted. A simple extension of the algorithm allows us to efficiently determine, for each species, when a sequence of site selections results in a reserve in which the species can persist. The extension also allows us to determine when a sequence of deforestation events results in the species becoming non-viable. The dynamic reserve design model is much more effective than commonly used heuristics, particularly when multiple connected sites are required for species persistence. The model also is able to solve much larger problems with greater effectiveness than the only previous dynamic reserve design model that considered site connectivity relationships. The union-find algorithm has much scope for addressing ecological management problems in which dynamic connectivity needs to be considered.     

A Bioeconomic Model of Marine Reserve Creation

This paper employs a dynamic and spatial model of renewable resource exploitation to investigate the effects of marine reserve creation. The model combines a metapopulation model incorporating resource patch heterogeneity and dispersal with a behaviorally based spatially explicit harvesting model that assumes that fishermen choose location in a manner that eliminates spatial arbitrage opportunities. The combined spatial bioeconomic model is used to simulate the effects of reserve creation under various ecological structures. We identify parameter configurations and ecological dispersal processes that give rise to a double-payoff in which both aggregate biomass and harvest increase after an area of the fishery is set aside and protected from exploitation.     

Larval supply and juvenile recruitment of coral reef fishes to marine reserves and non-reserves of the upper Florida Keys,USA

For marine organisms, decoupling between the planktonic larval stage and the benthic-associated juvenile stage can lead to variable patterns of population replenishment, which have the potential to influence the effectiveness of marine reserves. We measured spatial and temporal variability in larval supply and recruitment of fishes to coral reefs of different protection levels and tested whether protection level influenced the relationship between supply and recruitment. We sampled pre-settlement larvae and newly settled recruits from four reefs (two reserves and two non-reserves) in the Florida Keys National Marine Sanctuary, USA. Replicate point measures of larval supply over 14 months and 17 monthly measurements of recruitment varied significantly among months and sites. Sites with the same protection level had significantly different patterns of larval supply as well as larval and recruit diversity, but recruitment magnitude differed only by protection level, where densities were greater at reserves. Differences in larval supply among sites included two particularly large peaks in larval abundance at one site, possibly associated with the observed passage of small-scale oceanographic features. To examine whether relationships between larval supply and recruitment varied by protection level, we selected one species that was present in both the light trap samples and the monthly recruitment surveys. Recruitment of the bicolor damselfish Stegastes partitus was significantly and positively related to larval supply at three of the four sites thus, protection level did not influence this linkage. Since local variability among sites can lead to spatial differences in population replenishment, characterization of larval supply and recruitment to potential marine reserve sites may help to identify optimal locations in a region and contribute to more effective reserve design.     

Effects of seascape connectivity on reserve performance along exposed coastlines

Seascape connectivity (landscape connectivity in the sea) can modify reserve performance in low-energy marine ecosystems (e.g., coral reefs, mangroves, and seagrass), but it is not clear whether similar spatial linkages also shape reserve effectiveness on high-energy, exposed coastlines. We used the surf zones of ocean beaches in eastern Australia as a model system to test how seascape connectivity and reserve attributes combine to shape conservation outcomes. Spatial patterns in fish assemblages were measured using baited remote underwater video stations in 12 marine reserves and 15 fished beaches across 2000 km of exposed coastline. Reserve performance was shaped by both the characteristics of reserves and the spatial properties of the coastal seascapes in which reserves were embedded. Number of fish species and abundance of harvested fishes were highest in surf-zone reserves that encompassed >1.5 km of the surf zone; were located < 100 m to rocky headlands; and included pocket beaches in a heterogeneous seascape. Conservation outcomes for exposed coastlines may, therefore, be enhanced by prioritizing sufficiently large areas of seascapes that are strongly linked to abutting complementary habitats. Our findings have broader implications for coastal conservation planning. Empirical data to describe how the ecological features of high-energy shorelines influence conservation outcomes are lacking, and we suggest that seascape connectivity may have similar ecological effects on reserve performance on both sheltered and exposed coastlines.     

Designing a Conservation Landscape for Tigers in Human-Dominated Environments

Abstract:  Wildlife populations in small, isolated reserves face genetic and demographic threats to their survival. To increase the probability of long-term persistence, biologists promote metapopulation management, in which breeding subpopulations are protected as source pools. Animals that disperse from the source pools increase the probability of persistence of the metapopulation across the greater landscape. We used a geographic information system (GIS)–based, cost-distance model to design a conservation landscape along the Himalayan foothills for managing a metapopulation of Asia's largest predator, the tiger ( Panthera tigris ). The model is based on data from 30 years of field research on tigers, recent satellite imagery, and a decade of buffer-zone restoration in this region. We used the model to (1) identify potential dispersal corridors for tigers; (2) identify strategic transit refuges; and (3) make recommendations for off-reserve land management and restoration to enhance the potential of corridors for tigers. This tool can aid the design of conservation landscapes for other endangered, wide-ranging species in human-dominated environments.     

Consistent scaling of persistence time in metapopulations

Recent theory and experimental work in metapopulations and metacommunities demonstrates that long-term persistence is maximized when the rate at which individuals disperse among patches within the system is intermediate; if too low, local extinctions are more frequent than recolonizations, increasing the chance of regional-scale extinctions, and if too high, dynamics exhibit region-wide synchrony, and local extinctions occur in near unison across the region. Although common, little is known about how the size and topology of the metapopulation (metacommunity) affect this bell-shaped relationship between dispersal rate and regional persistence time. Using a suite of mathematical models, we examined the effects of dispersal, patch number, and topology on the regional persistence time when local populations are subject to demographic stochasticity. We found that the form of the relationship between regional persistence time and the number of patches is consistent across all models studied; however, the form of the relationship is distinctly different among low, intermediate, and high dispersal rates. Under low and intermediate dispersal rates, regional persistence times increase logarithmically and exponentially (respectively) with increasing numbers of patches, whereas under high dispersal, the form of the relationship depends on local dynamics. Furthermore, we demonstrate that the forms of these relationships, which give rise to the bell-shaped relationship between dispersal rate and persistence time, are a product of recolonization and the region-wide synchronization (or lack thereof) of population dynamics. Identifying such metapopulation attributes that impact extinction risk is of utmost importance for managing and conserving the earth's evermore fragmented populations.     

Optimal design of compact and connected nature reserves for multiple species

When designing a conservation reserve system for multiple species, spatial attributes of the reserves must be taken into account at species level. The existing optimal reserve design literature considers either one spatial attribute or when multiple attributes are considered the analysis is restricted only to one species. We built a linear integer programing model that incorporates compactness and connectivity of the landscape reserved for multiple species. The model identifies multiple reserves that each serve a subset of target species with a specified coverage probability threshold to ensure the species' long‐term survival in the reserve, and each target species is covered (protected) with another probability threshold at the reserve system level. We modeled compactness by minimizing the total distance between selected sites and central sites, and we modeled connectivity of a selected site to its designated central site by selecting at least one of its adjacent sites that has a nearer distance to the central site. We considered structural distance and functional distances that incorporated site quality between sites. We tested the model using randomly generated data on 2 species, one ground species that required structural connectivity and the other an avian species that required functional connectivity. We applied the model to 10 bird species listed as endangered by the state of Illinois (U.S.A.). Spatial coherence and selection cost of the reserves differed substantially depending on the weights assigned to these 2 criteria. The model can be used to design a reserve system for multiple species, especially species whose habitats are far apart in which case multiple disjunct but compact and connected reserves are advantageous. The model can be modified to increase or decrease the distance between reserves to reduce or promote population connectivity.