Designing connected nature reserve networks using a graph theory approach

Habitat fragmentation has been cited as one of the critical reasons for biodiversity loss. Establishing connected nature reserve networks is an effective way to reduce habit fragmentation. However, the resources devoted to nature reserves have always been scarce. Therefore it is important to allocate our scarce resources in an optimal way. The optimal design of a reserve network which is effective both ecologically and economically has become an important research topic in the reserve design literature. The problem of optimal selection of a subset from a larger group of potential habitat sites is solved using either heuristic or formal optimization methods. The heuristic methods, although flexible and computationally fast, can not guarantee the solution is optimal therefore may lead to scarce resources being used in an ineffective way. The formal optimization methods, on the other hand, guarantees the solution is optimal, but it has been argued that it would be difficult to model site selection process using optimization models, especially when spatial attributes of the reserve have to be taken into account. This paper presents a linear integer programming model for the design of a minimal connected reserve network using a graph theory approach. A connected tree is determined corresponding to a connected reserve. Computational performance of the model is tested using datasets randomly generated by the software GAMS. Results show that the model can solve a connected reserve design problem which includes 100 potential sites and 30 species in a reasonable period of time. As an empirical application, the model is applied to the protection of endangered and threatened bird species in the Cache River basin area in Illinois, US. Two connected reserve networks are determined for 13 bird species.     

最优化设计连续的自然保护区

生境破碎是导致生物多样性损失的重要原因之一,避免生境破碎的一个有效方式是建立连续的自然保护区使物种可在保护区内自由移动。不加选择地把大片土地都转为保护区是实现连续的一个途径,但资源是有限的,应当以最优的方式分配。如何最优化设计生态上和经济上都有效的保护区成为生物保护领域一个重要议题。从一组备选地块中选择一部分组成自然保护区,这样的问题主要有两种解法:启发式方法和最优化方法。启发式方法虽然灵活且运算速度快但不能保证最优解因而可能导致稀缺资源的浪费,最优化方法保证得到的解是最优的但建模和运算存在困难。建立一个线性整数规划模型用于设计一个最小的连续保护区,用Dantzig剪切法消除循环确保形成一个连续的树,对应一个连续的保护区,检验了模型的计算效率。结果显示,模型可在合理时间内解决一个包含100个备选地块和30个物种的连续保护区设计问题,计算效率显著优于同类目的的其它方法。以美国伊利诺伊州Cache河流域11种濒危鸟类的保护区设计为例说明了该方法的应用,设计了两种情况下连续的保护区。讨论了模型的局限和数据问题。     

自然保护区空间特征和地块最优化选择方法

自然保护区是保护物种和生态系统的有效方式,用于建立自然保护区的资源却是稀缺的,这就提出这样的问题：1)自然保护区在空间上应具有什么特征才是有效的;2)如何从许多备选地块中选择一部分组成自然保护区对稀缺资源进行最优化分配。为促进物种生存繁衍,在地块选择时应考虑保护区空间特征。这篇文章综述了该领域最近的研究进展,重点介绍了结合各种空间特征的保护区地块最优化选择模型。介绍了4个主要的空间特征：1)连续,2)间隔和距离,3)边界和集约,4)面积以及核心区和缓冲区。以前用启发式算法求解这些问题,但研究已显示该法不能保证资源的最优化分配。空间特征也可用线性整数规划模拟,用最优化软件求得最优解。目前的线性整数规划模型和软件还不能有效解决大型的保护区地块选择问题,计算效率易成为实际应用的瓶颈。文章概括了我国目前自然保护区设计领域的研究状况和面临的问题,最后讨论了该领域新的研究方向。     

两种自然保护区设计方法——数学建模和计算机模拟

传统的自然保护区设计方法是打分法和Gap分析法,这两种方法简单易行但可靠性不高;地理信息系统(GIS)在保护区设计领域的应用也为人熟悉.关注近年来快速发展而国内使用不多的两种方法——数学建模和计算机模拟.数学建模主要用来从一组备选地块中选择一部分组成自然保护区,包括线性和非线性模型,用启发式算法或最优化算法求解.启发式算法具有速度快、灵活等优点,但解通常不是最优的,不能保证稀缺资源的最优化利用.最优化算法运算效率低,变量较多比如数百时就可能遇到计算困难,但解是最优的.预计两种算法都将继续发展.计算机模拟主要用于保护区评价、功能区划分、预测特定环境比如空间特征和气候变化对物种的影响等,多用启发式算法,与其它软件结合把结果以图画显示出来.两种方法特别是计算机模拟均要求保护区设计者有较强的专业知识.讨论了两种方法面临的问题和新的研究方向,至少包括:1)基础数据依然需要完善;2)一些新的因素比如动态性和不确定性如何在模型中考虑并与其它因素结合;3)气候变化预景下模拟参数如何评估和调整;4)如何协调保护与发展的关系;5)方法的实际应用需要研究者与决策者之间建立交流机制;6)多领域专家和相关利益方应有机会参与保护区设计.     

Designing a connected nature reserve using a network flow theory approach

Establishing nature conservation reserves is an effective and widely accepted practice to protect biodiversity. In order to promote the effectiveness and efficiency of the reserve, spatial attributes of the reserve should be considered. Connectedness (contiguity) is one of these important spatial attributes. Currently in the biological literature there are only a few formal/exact optimization approaches to endogenously designing a connected nature reserve. This article adds a new approach by adapting a spatial unit allocation model to the reserve design problem. Using concepts from network flow theory, the model defines a sink site from which no flow directs out and ensures contiguity by specifying the outflow and inflow relationship of the potential sites. Computational performance of the model is tested using hypothetical problems with various sizes including up to 400 potential sites. Results show that the time needed to solve the problem to optimality increases exponentially both as number of potential sites increases and as species distribution gets more sparse. An empirical application involving 80 potential sites and 15 bird species in part of Fox River watershed, Illinois USA is presented. Factors influencing an IP model’s computational performance and potential extensions of the model were discussed.     

鼎湖山的鸟类与考察研究历史

鼎湖山作为中国大陆第一个自然保护区,保存有完整的南亚热带季风常绿阔叶林,是华南生物多样性热点区域.保护区鸟类资源丰富,但历史研究资料较为零散,至今没有完整的鸟类编目.本文通过系统整理1913至2019年发表的文献,分析了保护区鸟类资源的变化情况以及受胁因素.区内共记录鸟类17目64科267种,其中国家重点保护鸟类45种...     

Frugivory on Persea lingue in temperate Chilean forests: interactions between fruit availability and habitat fragmentation across multiple spatial scales

Habitat degradation and fragmentation are expected to reduce seed dispersal rates by reducing fruit availability as well as the movement and abundance of frugivores. These deleterious impacts may also interact with each other at different spatial scales, leading to nonlinear effects of fruit abundance on seed dispersal. In this study we assessed whether the degradation and fragmentation of southern Chilean forests had the potential to restrict seed dispersal the lingue (Persea lingue) tree, a fleshy-fruited tree species. Of five frugivore bird species, the austral thrush (Turdus falcklandii) and the fire-eyed diucon (Xolmis pyrope) were the only legitimate seed dispersers as well as being the most abundant species visiting lingue trees. The results showed little or no direct effect of habitat fragmentation on seed dispersal estimates, possibly because the assemblage of frugivore birds was comprised habitat-generalist species. Instead, the number of fruits removed per focal tree exhibited an enhanced response to crop size, but only in the more connected fragments. In the fruit-richer fragment networks, there was an increased fragment-size effect on the proportion of fruits removed in comparison to fruit-poor networks in which the fragment size effect was spurious. We suggest that such nonlinear effects are widespread in fragmented forest regions, resulting from the link between the spatial scales over which frugivores sample resources and the spatial heterogeneity in fruiting resources caused by habitat fragmentation and degradation.     

Designing connected marine reserves in the face of global warming

Marine reserves are widely used to protect species important for conservation and fisheries and to help maintain ecological processes that sustain their populations, including recruitment and dispersal. Achieving these goals requires well‐connected networks of marine reserves that maximize larval connectivity, thus allowing exchanges between populations and recolonization after local disturbances. However, global warming can disrupt connectivity by shortening potential dispersal pathways through changes in larval physiology. These changes can compromise the performance of marine reserve networks, thus requiring adjusting their design to account for ocean warming. To date, empirical approaches to marine prioritization have not considered larval connectivity as affected by global warming. Here, we develop a framework for designing marine reserve networks that integrates graph theory and changes in larval connectivity due to potential reductions in planktonic larval duration (PLD) associated with ocean warming, given current socioeconomic constraints. Using the Gulf of California as case study, we assess the benefits and costs of adjusting networks to account for connectivity, with and without ocean warming. We compare reserve networks designed to achieve representation of species and ecosystems with networks designed to also maximize connectivity under current and future ocean‐warming scenarios. Our results indicate that current larval connectivity could be reduced significantly under ocean warming because of shortened PLDs. Given the potential changes in connectivity, we show that our graph‐theoretical approach based on centrality (eigenvector and distance‐weighted fragmentation) of habitat patches can help design better‐connected marine reserve networks for the future with equivalent costs. We found that maintaining dispersal connectivity incidentally through representation‐only reserve design is unlikely, particularly in regions with strong asymmetric patterns of dispersal connectivity. Our results support previous studies suggesting that, given potential reductions in PLD due to ocean warming, future marine reserve networks would require more and/or larger reserves in closer proximity to maintain larval connectivity.     

Elevation‐dependent effects of forest fragmentation on plant–bird interaction networks in the tropical Andes

Tropical forests harbor diverse ecological communities of plants and animals that are organized in complex interaction networks. The diversity and structure of plant–animal interaction networks may change along elevational gradients and in response to human‐induced habitat fragmentation. While previous studies have analyzed the effects of elevation and forest fragmentation on species interaction networks in isolation, to our knowledge no study has investigated whether the effects of forest fragmentation on species interactions may differ along elevational gradients. In this study, we analyzed main and interaction effects of elevation and forest fragmentation on plant–frugivore interaction networks at plant and bird species level. Over a period spanning two years, we recorded plant–frugivore interactions at three elevations (1000, 2000 and 3000 m a.s.l.) and in two habitat types (continuous and fragmented forest) in tropical montane forests in southern Ecuador. We found a consistent effect of elevation on the structure of plant–frugivore networks. We observed a decrease in the number of effective bird partners of plants and, thus, a decline in the redundancy of bird species with increasing elevation. Furthermore, bird specialization on specific plant partners increased towards high elevations. Fragmentation had a relatively weak effect on the interaction networks for both plant and bird species, but resulted in a significant increase in bird specialization in fragmented forests at high elevations. Our results indicate that forest fragmentation may have stronger effects on plant–frugivore interaction networks at high compared to low elevations because bird species richness declined more steeply towards high elevations than plant species richness. We conclude that conservation efforts should prioritize the maintenance of consumer diversity, for instance by maintaining stretches of continuous forest. This applies in particular to species‐poor communities, such as those at high elevations, as the ecological processes in these communities seem most sensitive towards forest fragmentation.     

Heuristic and optimal solutions for set-covering problems in conservation biology

Area-selection methods have recently gained prominence in conservation biology. A typical problem is to identify the minimum number of areas required to represent all species over some geographic region. Iterative heuristic methods have been developed by conservation scientists to solve these problems, although the solutions cannot be guaranteed to be optimal. Although optimal solutions can often be found, heuristics continue to be popular as they are perceived to be faster and more transparent as they are intuitively easy to understand. We used distributional data for 1921 bird species, 939 mammal species, 405 snake species, and 617 amphibian species compiled at the Zoological Museum, Univ. of Copenhagen for all 1° cells of mainland sub-Saharan Africa to compare the quality of the solutions found using two heuristic methods (simple-greedy algorithm and a progressive-rarity algorithm) with optimal solutions. We found that the heuristic methods considered here often provide solutions as good as optimal solutions. Even in those cases where the optimal solutions were better the difference was relatively small, with the heuristics providing solutions requiring a 2–10% increase in area selected compared with the optimal solution, which importantly, represented an increase of <1% of the total area. Our study also suggests that the heuristic algorithms performed least well for datasets with few single cell endemics and taxa that tend to have larger range sizes. Despite the good quality of solutions using heuristics there was no time penalty associated with finding optimal solutions for the problems considered here, suggesting that the major obstacle to their use is making optimal methods accessible to conservation biologists. We encourage conservation biologists to work with operations researchers and so gain the benefit of their expertise and experience in solving these kinds of problems.     

Threatened and endemic species: are they good indicators of patterns of biodiversity on a national scale?

Endemic and/or threatened species are often targeted to set conservation priorities. It is tempting to assume that a reserve network focusing on these species will be an effective umbrella for overall species richness of a country. For South Africa and Lesotho we tested whether complementary networks selected for threatened and/or endemic bird species satisfactorily represent all bird species, both in terms of capturing areas where other species are present or areas where they are more abundant (and, presumably, more viable). We found that areas selected for threatened and endemic species perform considerably better than areas selected at random. However, they do not guarantee the representation of overall bird species diversity, particularly not in peak abundance locations. Although nationally threatened and endemic species are important conservation targets, our results indicate that reserve networks focusing solely on these species may not be sufficient to preserve overall species diversity in a country.     

Multi-node selection of patches for protecting habitat connectivity: Fragmentation versus reachability

Landscape connectivity is of major importance in biodiversity conservation, and is one of the key aspects to be taken into consideration in the spatial design of networks of protected areas. Graph-theoretical approaches are useful in modelling habitat connectivity and defining priority areas for the protection of connectivity. This prioritization can be done based on rankings of the centrality (or importance) of individual habitat patches. Moreover, the centrality of a set of n habitat patches can also be calculated. Importantly, the most central single patch is not necessarily a member of the most central group of n patches (non-nested topology). Multi-node analyses identify groups of patches that maximally complement each other in order to increase the protection of connectivity for the whole network. We apply multi-node analyses to the prioritization of habitat patches for five vulnerable bird species in Catalonia, Spain, using two different approaches to connectivity, based on fragmentation and reachability. Groups of patches based on fragmentation are usually concentrated in core areas, while reachability groups are widely spread. Fragmentation sets have higher centrality value for low-mobility species, and reachability sets for long distance dispersers. The protection of the networks against fragmentation requires fewer patches, allows for more gradual implementation and is currently better accounted for by the Natura 2000 network of protected areas, while the protection of reachability is less costly and more efficient in terms of area requirements. Our work contributes to the development of landscape graph analysis for reserve design towards multi-node approaches.     

Habitat loss and connectivity of reserve networks in probability approaches to reserve design

Quantitative methods for the design of reserve networks often select over‐dispersed reserves, and consequently a number of species extinctions can be expected in such reserves, especially if unprotected surrounding habitat is lost. A novel approach that deals with this problem is presented by considering factors such as habitat quality and spatial configuration of reserves during the selection process. Species‐specific effects of habitat loss and fragmentation, together with habitat composition, are taken into account when computing species probabilities of local occurrence. Sites are then chosen to represent all species with a given target probability. The method is applied to a dataset of butterflies and moths from the Creuddyn Peninsula, North Wales, UK, which includes species with various responses to habitat quality and configuration. The results show that the resulting level of reserve clustering will depend on the number of species for which the spatial configuration plays an important role (at the scale under consideration), and on the pattern and amount of habitat loss that is expected to follow around the reserves. The method represents a step towards taking better into account species persistence when selecting reserve networks in a changing world.     

The impact of soybean expansion on mammal and bird,in the Balsas region,north Brasilian Cerrado

In order to analyse the impact of land use change, it is particularly important to know how organisms use resources distributed across a heterogeneous landscape. The main objective of this study is to analyse the potential impact of land use change on bird and mammal fauna, by using a coupled model approach. The CLUE (Conversion of Land Use and its Effects) model has been applied to obtain the spatial pattern of land use change for a scenario with soybean expansion in the Cerrado of Maranhão State in Brazil. These land use change maps were used as the input for the LEDESS (Landscape Ecological Decision and Evaluation Support System) model to evaluate the impact of habitat fragmentation on mammal and bird species. The scenarios demonstrated that high quality habitat for all studied species will be lost in the future when current trends in agricultural expansion continue, but these changes will have species-specific impacts. The most relevant ecological impact under the explored scenarios was habitat fragmentation expressed by the increase the number of habitat clusters. The coupled model approach of LEDESS and CLUE made it possible to project the spatial impact of soybean expansion on habitat dynamics in the studied region. This model approach can help to design effective ecological infrastructure to facilitate species survival and to implement an effective habitat network in the Balsas region.     

Spatially-Correlated Risk in Nature Reserve Site Selection

Establishing nature reserves protects species from land cover conversion and the resulting loss of habitat. Even within a reserve, however, many factors such as fires and defoliating insects still threaten habitat and the survival of species. To address the risk to species survival after reserve establishment, reserve networks can be created that allow some redundancy of species coverage to maximize the expected number of species that survive in the presence of threats. In some regions, however, the threats to species within a reserve may be spatially correlated. As examples, fires, diseases, and pest infestations can spread from a starting point and threaten neighboring parcels’ habitats, in addition to damage caused at the initial location. This paper develops a reserve site selection optimization framework that compares the optimal reserve networks in cases where risks do and do not reflect spatial correlation. By exploring the impact of spatially-correlated risk on reserve networks on a stylized landscape and on an Oregon landscape, this analysis demonstrates an appropriate and feasible method for incorporating such post-reserve establishment risks in the reserve site selection literature as an additional tool to be further developed for future conservation planning.     

Dynamics of extinction and the selection of nature reserves

Familiar quantitative reserve-selection techniques are tailored to simple decision problems, where the representation of species is sought at minimum cost. However, conservationists have begun to ask whether representing species in reserve networks is sufficient to avoid local extinctions within selected areas. An attractive, but previously untested idea is to model current species' probabilities of occurrence as an estimate of local persistence in the near future. Using distribution data for passerine birds in Great Britain, we show that (i) species' probabilities of occurrence are negatively related to local probabilities of extinction, at least when a particular 20-year period is considered, and (ii) local extinctions can be reduced if areas are selected to maximize current species' probabilities of occurrence We suggest that more extinctions could be avoided if even a simple treatment of persistence were to be incorporated within reserve selection methods.     

Efficient algorithms for protein sequence design and the analysis of certain evolutionary fitness landscapes.

Protein sequence design is a natural inverse problem to protein structure prediction: given a target structure in three dimensions, we wish to design an amino acid sequence that is likely fold to it. A model of Sun, Brem, Chan, and Dill casts this problem as an optimization on a space of sequences of hydrophobic (H) and polar (P) monomers; the goal is to find a sequence that achieves a dense hydrophobic core with few solvent-exposed hydrophobic residues. Sun et al. developed a heuristic method to search the space of sequences, without a guarantee of optimality or near-optimality; Hart subsequently raised the computational tractability of constructing an optimal sequence in this model as an open question. Here we resolve this question by providing an efficient algorithm to construct optimal sequences; our algorithm has a polynomial running time, and performs very efficiently in practice. We illustrate the implementation of our method on structures drawn from the Protein Data Bank. We also consider extensions of the model to larger amino acid alphabets, as a way to overcome the limitations of the binary H/P alphabet. We show that for a natural class of arbitrarily large alphabets, it remains possible to design optimal sequences efficiently. Finally, we analyze some of the consequences of this sequence design model for the study of evolutionary fitness landscapes. A given target structure may have many sequences that are optimal in the model of Sun et al.; following a notion raised by the work of J. Maynard Smith, we can ask whether these optimal sequences are "connected" by successive point mutations. We provide a polynomial-time algorithm to decide this connectedness property, relative to a given target structure. We develop the algorithm by first solving an analogous problem expressed in terms of submodular functions, a fundamental object of study in combinatorial optimization.     

How well do Important Bird Areas represent species and minimize conservation conflict in the tropical Andes?

Where high species richness and high human population density coincide, potential exists for conflict between the imperatives of species conservation and human development. We examine the coincidence of at‐risk bird species richness and human population in the countries of the tropical Andes. We then compare the performance of the expert‐driven Important Bird Areas (IBA) scheme against a hypothetical protected‐areas network identified with a systematic reserve selection algorithm seeking to maximize at‐risk bird species representation. Our aim is to assess the degree to which: IBAs contain a higher richness of at‐risk species than would be expected by chance, IBAs contain more people than would be expected by chance, and IBAs are congruent with complementary areas that maximize species representation with an equivalent number of sites. While the correlation of richness and population was low for the region as a whole, representation of all at‐risk bird species required many sites to be located in areas of high human population density. IBA sites contained higher human population densities than expected by chance (P < 0.05) and were markedly less efficient in representing at‐risk bird species of the region than sites selected using the reserve selection algorithm. Moreover, overlap between IBAs and these latter sites was very limited. Expert‐driven selection procedures may better reflect existing sociopolitical forces, including land ownership and management regimes, but are limited in their ability to develop an efficient, integrated network of sites to represent priority species. Reserve selection algorithms may serve this end by optimizing complementarity in species representation among selected sites, whether these sites are adopted independently or as a supplement to the existing reserve network. As tools of site selection, they may be particularly useful in areas such as the tropical Andes where complex patterns of species disjunction and co‐occurrence make the development of representative reserve networks particularly difficult. Furthermore, they facilitate making spatially explicit choices about how reserve sites are located in relation to human populations. We advocate their use not in replacement of approaches such as the IBA initiative but as an additional, complementary tool in ensuring that such reserve networks are developed as efficiently as practically possible.     

四川美姑大风顶国家级自然保护区鸟类物种及垂直多样性研究

2016年12月—2018年6月采用样带法和样点法对四川美姑大风顶国家级自然保护区的鸟类资源进行了调查,根据调查并结合相关文献记录,统计出保护区分布有鸟类268种,隶属17目56科。其中,留鸟146种(54.5%)、夏候鸟91种(34.0%)、冬候鸟18种(6.7%)、旅鸟13种(4.9%),以繁殖鸟为主。繁殖鸟类中,以东洋界物种为主(67.5%)。保护区的珍稀濒危鸟类物种数量较多,有国家Ⅰ级重点保护野生鸟类2种、国家Ⅱ级重点保护野生鸟类16种;列入濒危野生动植物种国际贸易公约附录Ⅰ1种、附录Ⅱ12种;列入世界自然保护联盟濒危物种红色名录濒危(EN)1种、易危(VU)3种、近危(NT)2种;中国特有种14种。各生境类型中的鸟类丰富度为针叶林>阔叶林>针阔混交林>灌丛及灌草丛>高山灌丛草甸>水域;针叶林、阔叶林、针阔混交林之间的鸟类群落结构相似性最高,水域与其他生境的最低。保护区鸟类物种丰富度在2600~3000m的中海拔地区最高,在高海拔和低海拔较低,物种垂直分布呈中峰模式。本研究丰富了保护区和凉山山系的鸟类资料,为鸟类垂直多样性研究提供了重要案例。     

Breaking functional connectivity into components: a novel approach using an individual-based model, and first outcomes

Landscape connectivity is a key factor determining the viability of populations in fragmented landscapes. Predicting 'functional connectivity', namely whether a patch or a landscape functions as connected from the perspective of a focal species, poses various challenges. First, empirical data on the movement behaviour of species is often scarce. Second, animal-landscape interactions are bound to yield complex patterns. Lastly, functional connectivity involves various components that are rarely assessed separately. We introduce the spatially explicit, individual-based model FunCon as means to distinguish between components of functional connectivity and to assess how each of them affects the sensitivity of species and communities to landscape structures. We then present the results of exploratory simulations over six landscapes of different fragmentation levels and across a range of hypothetical bird species that differ in their response to habitat edges. i) Our results demonstrate that estimations of functional connectivity depend not only on the response of species to edges (avoidance versus penetration into the matrix), the movement mode investigated (home range movements versus dispersal), and the way in which the matrix is being crossed (random walk versus gap crossing), but also on the choice of connectivity measure (in this case, the model output examined). ii) We further show a strong effect of the mortality scenario applied, indicating that movement decisions that do not fully match the mortality risks are likely to reduce connectivity and enhance sensitivity to fragmentation. iii) Despite these complexities, some consistent patterns emerged. For instance, the ranking order of landscapes in terms of functional connectivity was mostly consistent across the entire range of hypothetical species, indicating that simple landscape indices can potentially serve as valuable surrogates for functional connectivity. Yet such simplifications must be carefully evaluated in terms of the components of functional connectivity they actually predict.