The equivalence of two phylogenetic biodiversity measures: the Shapley value and Fair Proportion index

Most biodiversity conservation programs are forced to prioritise species in order to allocate their funding. This paper contains a mathematical proof that provides biological support for one common approach based on phylogenetic indices. Phylogenetic trees describe the evolutionary relationships between a group of taxa. Two indices for computing the distinctiveness of each taxon in a phylogenetic tree are considered here—the Shapley value and the Fair Proportion index. These indices provide a measure of the importance of each taxon for overall biodiversity and have been used to prioritise taxa for conservation. The Shapley value is the biodiversity contribution a taxon is expected to make if all taxa are equally likely to become extinct. This interpretation makes it appealing to use the Shapley value in biodiversity conservation applications. The Fair Proportion index lacks a convenient interpretation, however it is significantly easier to calculate and understand. It has been empirically observed that there is a high correlation between the two indices. This paper shows the mathematical basis for this correlation and proves that as the number of taxa increases, the indices become equivalent. Consequently in biodiversity prioritisation the simpler Fair Proportion index can be used whilst retaining the appealing interpretation of the Shapley value.     

Resource-aware taxon selection for maximizing phylogenetic diversity

Phylogenetic diversity (PD) is a useful metric for selecting taxa in a range of biological applications, for example, bioconservation and genomics, where the selection is usually constrained by the limited availability of resources. We formalize taxon selection as a conceptually simple optimization problem, aiming to maximize PD subject to resource constraints. This allows us to take into account the different amounts of resources required by the different taxa. Although this is a computationally difficult problem, we present a dynamic programming algorithm that solves it in pseudo-polynomial time. Our algorithm can also solve many instances of the Noah's Ark Problem, a more realistic formulation of taxon selection for biodiversity conservation that allows for taxon-specific extinction risks. These instances extend the set of problems for which solutions are available beyond previously known greedy-tractable cases. Finally, we discuss the relevance of our results to real-life scenarios.     

Assessment of impact of climate change on Rhododendrons in Sikkim Himalayas using Maxent modelling: limitations and challenges

Integration of climate change aspects in biodiversity management is one the fundamental requirements for long term biodiversity conservation. The explicit modelling of the biodiversity in response to climate change is the primary requirement for making any adaptation strategy. With Himalayan ecosystem in mind and Rhododendron as the species of concern, the current paper models the biogeography of the genera Rhododendron which are found intermixed in their spatial distribution in Sikkim Himalayas, mainly tree varieties, in response to climate change. The modelling algorithm used in the paper is Maxent (maximum entropy) which has estimated the target probability distribution by finding the probability distribution of Maxent. After projection of modelled bioclimatic layers to future climate scenario of SRES-A1B in Maxent, it was found that the suitable bioclimatic envelope for Rhododendron has shrunk considerably under the envisaged climate change scenario. The results on extent and locations of Rhododendron distributions in both the current and future climate scenarios provide a deep insight to the conservation planners about the kind of strategy that needs to be adopted for conserving Rhododendrons in the face of climate change. The challenges observed while doing this analysis highlight the gaps and set the agenda for further research to make the predictions of climate change driven impact on biodiversity scientifically more robust.     

Optimal taxonomic groups for biodiversity assessment: a meta‐analytic approach

A fundamental decision in biodiversity assessment is the selection of one or more study taxa, a choice that is often made using qualitative criteria such as historical precedent, ease of detection, or available technical or taxonomic expertise. A more robust approach would involve selecting taxa based on the a priori expectation that they will provide the best possible information on unmeasured groups, but data to inform such hypotheses are often lacking. Using a global meta‐analysis, we quantified the proportion of variability that each of 12 taxonomic groups (at the Order level or above) explained in the richness or composition of other taxa. We then applied optimization to matrices of pairwise congruency to identify the best set of complementary surrogate groups. We found that no single taxon was an optimal surrogate for both the richness and composition of unmeasured taxa if we used simple methods to aggregate congruence data between studies. In contrast, statistical methods that accounted for well‐known drivers of cross‐taxon congruence (spatial extent, grain size, and latitude) lead to the prioritization of similar surrogates for both species richness and composition. Advanced statistical methods were also more effective at describing known ecological relationships between taxa than simple methods, and show that congruence is typically highest between taxonomically and functionally dissimilar taxa. Birds and vascular plants were most frequently selected by our algorithm as surrogates for other taxonomic groups, but the extent to which any one taxon was the ‘optimal’ choice of surrogate for other biodiversity was highly context‐dependent. In the absence of other information – such as in data‐poor areas of the globe, and under limited budgets for monitoring or assessment – ecologists can use our results to assess which taxa are most likely to reflect the distribution of the richness or composition of ‘total’ biodiversity.     

Mollusc biodiversity in a European ancient lake system: lakes Prespa and Mikri Prespa in the Balkans

The spatial distribution of (endemic) biodiversity in ancient and potentially ancient lakes in Europe is poorly understood. Examples include Lakes Prespa and Mikri Prespa in the Central Balkans. Utilizing information of the most species-rich taxon in these lakes, the Mollusca, we therefore attempt to statistically assess and visualize the spatial distribution of biodiversity, to analyse biogeographical patterns, and to carry out a conservation assessment. We estimate that at least 40 (sub)species (29 gastropod and 11 bivalve taxa) occur in the lakes. For both lakes combined, 37.5% of the mollusc taxa are endemic. In general, the mollusc richness in Lake Mikri Prespa is lower than in Lake Prespa and less heterogeneously distributed. The highest species richness can be seen on the western and south eastern shores of Lake Prespa. Based on the presence/absence of genera, a minimum spanning tree analysis supports the sister lake relationship of both lakes, which, in turn, are most closely related to lakes in the western Balkans and not to nearby Lake Ohrid. The IUCN red list assessment revealed (A) a tendency towards mollusc faunal change, (B) a contemporary decline and potential loss of mollusc diversity, and (C) that all endemic species are of conservation concern.     

Elevational distribution of restricted range forest tree taxa in eastern Tanzania

The forests of eastern Tanzania are a globally important biodiversity hotspot. In this study 361 eastern Tanzanian restricted range forest tree taxa were assessed. Of these taxa, 223 occurred in the Eastern Arc, 150 in Coastal forests, 17 in Northern forests and 21 in the Lake Nyasa forests. The majority of the taxa had restricted elevational ranges with 76.3% occurring in no more than two 200 m elevational bands out of a total potential elevation range of 3000 m. The majority of the taxa occupied a small area in the eastern Tanzanian forests, with 201 taxa being only found at a few sites. In determining priority areas for conservation, selection of taxon definitions can have important effects. For example, tree size varies with elevation, so if only large trees are used then site selection will be biased towards particular areas.     

The culture of bird conservation: Australian stakeholder values regarding iconic,flagship and rare birds

Iconic, flagship and rare threatened bird taxa attract disproportionate amounts of public attention, and are often used to enable broader conservation strategies. Yet, little is known about why certain taxa achieve iconic or flagship status. Also unclear is whether the perception of rarity among those acting to conserve threatened birds is sufficient to influence attitudes and behaviour that lead to effective conservation action and, if so, which characteristics of rare birds are important to their conservation. We interviewed 74 threatened bird conservation stakeholders to explore perceptions about iconic, flagship and rare threatened birds and classified their attitudes using a new typology of avifaunal attitudes. There was a relationship between societal interest and conservation effort for threatened species characterised as iconic, flagship and rare. Iconic species tended to arouse interest or emotion in people due to being appealing and readily encountered, thereby attracting conservation interest that can benefit other biodiversity. Flagships tended to have distinguishing physical or cultural characteristics and were used to convey conservation messages about associated biodiversity. Attitudes about rarity mostly related to a taxon’s threatened status and small population size. Rarity was important for threatened bird conservation but not always associated with attitudes and behaviour that lead to effective conservation action. We conclude that conservation action for individual threatened bird taxa is biased and directly influenced by the ways taxa are socially constructed by stakeholders, which is specific to prevailing culture and stakeholder knowledge.     

The cost-effectiveness of biodiversity surveys in tropical forests

The identification of high-performance indicator taxa that combine practical feasibility and ecological value requires an understanding of the costs and benefits of surveying different taxa. We present a generic and novel framework for identifying such taxa, and illustrate our approach using a large-scale assessment of 14 different higher taxa across three forest types in the Brazilian Amazon, estimating both the standardized survey cost and the ecological and biodiversity indicator value for each taxon. Survey costs varied by three orders of magnitude, and dung beetles and birds were identified as especially suitable for evaluating and monitoring the ecological consequences of habitat change in our study region. However, an exclusive focus on such taxa occurs at the expense of understanding patterns of diversity in other groups. To improve the cost-effectiveness of biodiversity research we encourage a combination of clearer research goals and the use of an objective evidence-based approach to selecting study taxa.     

Indicator groups and congruence of assemblage similarity, species richness and environmental relationships in littoral macroinvertebrates

The rapid decrease of biodiversity and limited resources for surveying it have forced researchers to devise short-cuts for biodiversity surveys and conservation planning. These short-cuts include environmental surrogates, higher taxon surrogates, indicator species and indicator groups. We considered indicator groups as surrogates for wholesale biodiversity and cross-taxon congruence in biodiversity patterns in littoral macroinvertebrates of boreal lakes. Despite the fact that we considered indicator groups amongst a wide variety of taxa, such as two-winged flies, mayflies, caddisflies, beetles, bugs and molluscs, none of the proposed groups possessed all of the qualities of a good indicator taxon for biodiversity surveys and conservation planning. We found generally weak, yet typically significant, relationships between the proposed indicator groups and remaining taxa in both species richness and assemblage similarity. Low congruence was paralleled by somewhat differing relationships of the taxonomic groups to various environmental features of lakes. Furthermore, the relationships of most indicator groups to the environmental features of lakes were not particularly strong. The present findings are unfortunate, because indicator groups did not perform well in predicting the wholesale biodiversity of littoral macroinvertebrates. Thus, there appears to be no short-cut for considering all groups of macroinvertebrates in biodiversity surveys, conservation planning and characterisation of environmental relationships of lake littoral assemblages.     

Polyhedral Geometry of Phylogenetic Rogue Taxa

It is well known among phylogeneticists that adding an extra taxon (e.g. species) to a data set can alter the structure of the optimal phylogenetic tree in surprising ways. However, little is known about this “rogue taxon” effect. In this paper we characterize the behavior of balanced minimum evolution (BME) phylogenetics on data sets of this type using tools from polyhedral geometry. First we show that for any distance matrix there exist distances to a “rogue taxon” such that the BME-optimal tree for the data set with the new taxon does not contain any nontrivial splits (bipartitions) of the optimal tree for the original data. Second, we prove a theorem which restricts the topology of BME-optimal trees for data sets of this type, thus showing that a rogue taxon cannot have an arbitrary effect on the optimal tree. Third, we computationally construct polyhedral cones that give complete answers for BME rogue taxon behavior when our original data fits a tree on four, five, and six taxa. We use these cones to derive sufficient conditions for rogue taxon behavior for four taxa, and to understand the frequency of the rogue taxon effect via simulation.     

Budgeted Phylogenetic Diversity on Circular Split Systems

In the last 15 years, Phylogenetic Diversity (PD) has gained interest in the community of conservation biologists as a surrogate measure for assessing biodiversity. We have recently proposed two approaches to select taxa for maximizing PD, namely PD with budget constraints and PD on split systems. In this paper, we will unify these two strategies and present a dynamic programming algorithm to solve the unified framework of selecting taxa with maximal PD under budget constraints on circular split systems. An improved algorithm will also be given if the underlying split system is a tree.     

Evaluating tree wētā (Orthoptera: Anostostomatidae: <Emphasis Type="Italic">Hemideina</Emphasis> species) as bioindicators for New Zealand national biodiversity monitoring

Indicator taxa are increasingly being used to evaluate the natural environment because they provide both quantified and simplified information about complex phenomena and because they result in huge cost savings compared with monitoring entire biotas. In this paper, we examine the suitability of an iconic New Zealand invertebrate, the tree wētā (Orthoptera: Anostostomatidae: Hemideina species), as a bioindicator for invertebrates under a national biodiversity monitoring scheme in New Zealand. Tree wētā are common and widespread in New Zealand, comprising a distinctive component of the native invertebrate fauna, being large-bodied (up to 40 mm in length), relatively long-lived, flightless, and nocturnal. Arboreal tree wētā species are commonly monitored in conservation areas containing scrub or forest, particularly after mammal control, because they can be easily monitored using artificial roosts without harming them and they are readily identified by field workers. We evaluated whether data supported the use of tree wētā as a range of bioindicators for such monitoring and conclude that the arboreal species are good indicators for monitoring the effects of controlling the abundance of insectivorous mammals and that they are likely to be reliable population indicators of taxa sensitive to mammalian predation pressure, especially by rodents. However, it is unlikely that arboreal tree wētā are useful population indicators of habitat change (e.g. degradation and fragmentation) as they commonly survive in exotic vegetation and urban gardens throughout New Zealand. Although poorly studied for indicator value, tree wētā may not be good biodiversity indicators although there are insufficient data to establish this. We recommend further research be undertaken to develop standardised methods for monitoring so that conservation managers and researchers produce results that are consistent and comparable across different locations.     

Complementarity as a biodiversity indicator strategy

Richness, rarity, endemism and complementarity of indicator taxon species are often used to select conservation areas, which are then assumed to represent most regional biodiversity. Assessments of the degree to which these indicator conservation areas coincide across different taxa have been conducted on a variety of vertebrate, invertebrate and plant groups at a national scale in Britain, Canada, USA and South Africa and at a regional scale in Cameroon, Uganda and the USA. A low degree of spatial overlap among and within these selected indicator conservation areas has been demonstrated. These results tend to suggest that indicator conservation areas display little congruence across different taxa. However, some of these studies demonstrate that many conservation areas for indicator taxa capture a high proportion of non-target species. Thus it appears that indicator conservation areas might sample overall biodiversity efficiently. These indicator conservation areas may, however, exclude species essential for effective conservation, e.g. rare, endemic or endangered species. The present study investigated the value of indicator taxa as biodiversity surrogates using spatial congruence and representativeness of different indicator priority conservation areas. The conservation status of species excluded by the indicator approaches is also assessed. Indicator priority conservation areas demonstrate high land area requirements in order to fully represent non-target species. These results suggest that efficient priority area selection techniques must reach a compromise between maximizing non-target species gains and minimizing land-use requirements. Reserve selection procedures using indicator-based complementarity appear to be approaches which best satisfy this trade-off.     

Maximum parsimony on subsets of taxa

In this paper we investigate mathematical questions concerning the reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm for reconstructing the ancestral state given a phylogenetic tree and a character. In particular, we consider the question whether the maximum parsimony method applied to a subset of taxa can reconstruct the ancestral state of the root more accurately than when applied to all taxa, and we give an example showing that this indeed is possible. A surprising feature of our example is that ignoring a taxon closer to the root improves the reliability of the method. On the other hand, in the case of the two-state symmetric substitution model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that under a molecular clock the probability that the state at a single taxon is a correct guess of the ancestral state is a lower bound on the reconstruction accuracy of Fitch's method applied to all taxa.     

系统保护规划的理论、方法及关键问题

为了减缓生物多样性丧失的趋势、将有限的保护资源用于关键区域,Margules等提出了系统保护规划(Systematic Conservation Planning)概念和方法,目前该方法已成为国际主流保护规划方法。与传统基于专家决策的保护体系规划方法不同,系统保护规划拥有量化的保护目标、保护成本,并综合考虑保护体系连通性、人为干扰因素,使用优化算法计算,从而获得空间明晰的生物多样性保护体系。在阐述规划理念、规划流程与方法的基础上,重点评述了生物多样性替代指标的选择、保护规划成本的计算、保护目标的设置、规划结果的可靠性评估等关键问题,并结合我国的具体情况,探讨了该方法在我国的应用前景,以期为推进我国生物多样性与生态服务功能的保护做出贡献。     

Robust optimization for resource-constrained project scheduling with uncertain activity durations

The purpose of this paper is to propose models for project scheduling when there is considerable uncertainty in the activity durations, to the extent that the decision maker cannot with confidence associate probabilities with the possible outcomes of a decision. Our modeling techniques stem from robust discrete optimization, which is a theoretical framework that enables the decision maker to produce solutions that will have a reasonably good objective value under any likely input data scenario. We develop and implement a scenario-relaxation algorithm and a scenario-relaxation-based heuristic. The first algorithm produces optimal solutions but requires excessive running times even for medium-sized instances; the second algorithm produces high-quality solutions for medium-sized instances and outperforms two benchmark heuristics.     

Local scale prioritization of cost-efficient protection within the National Park Thy

This study applied MARXAN to identify cost-efficient areas for biodiversity protection, within the Thy National Park in Denmark. Public authorities have requested a more systematic approach to managing public land, which identifies cost-effective solutions and potential trade-offs between economic cost and biodiversity benefits. The aim of this study was to support the local management staff in setting conservation targets and prioritizing their management efforts. This was addressed through the creation of two primary scenarios: i) applying uniform conservation targets to all biodiversity features, and ii) heterogeneous targets addressing various degrees of conservation importance. Four sub-scenarios were established for each primary scenario to investigate the implications of various conservation targets on conservation cost. Local data on red-listed species and habitat types were used to assess biodiversity benefits. Detailed cost estimates of required conservation actions were included. The results indicated that scenarios with uniform conservation targets provided more flexible networks of protected areas but contributed less to target achievement and a smaller share of selected planning units overlapped with current protected areas. Applying heterogeneous targets based on threat status resulted in a higher degree of target achievement and compactness, but provided less flexible networks. However, these networks may be more suitable for efficient management due to a higher level of clustering and spatial overlap with threatened species distributions.     

The “dehesa”, a key ecosystem in maintaining the diversity of Mediterranean saproxylic insects (Coleoptera and Diptera: Syrphidae)

The “dehesa” is a traditional Iberian agrosilvopastoral ecosystem characterized by the presence of old scattered trees that are considered as “keystone-structures”, which favor the presence of a wide range of biodiversity. We show the high diversity of saproxylic beetles and syrphids (Diptera) in this ecosystem, including red-listed species. We analyzed whether saproxylic species distribution in the “dehesa” was affected by tree density per hectare, dominant tree species or vegetation coverage. Species diversity did not correlate with tree density; however, it was affected by tree species and shrub coverage but in a different way for each taxon. The highest beetle diversity was linked to Quercus pyrenaica, the most managed tree species, with eight indicator species. In contrast, Q. rotundifolia hosted more species of saproxylic syrphids. Regarding vegetation coverage, shrub coverage was the only variable that affected insect richness, again in a different way for both taxa. In contrast, beetle species composition was only affected by dominant tree species whereas syrphid species composition was not affected by tree species or shrub coverage. We concluded that the high diversity of saproxylic insects in the “dehesa” is related to its long history of agrosilvopastoral management, which has generated landscape heterogeneity and preserved old mature trees. However, the richness and composition of different taxa of insects respond in different ways to tree species and vegetation coverage. Consequently, conservation strategies should try to maintain traditional management, and different saproxylic taxa should be used to monitor the effect of management on saproxylic diversity.