Positivstellensatz Certificates for Containment of Polyhedra and Spectrahedra
- Containment problems belong to the classical problems of (convex) geometry. In the proper sense, a containment problem is the task to decide the set-theoretic inclusion of two given sets, which is hard from both the theoretical and the practical perspective. In a broader sense, this includes, e.g., radii or packing problems, which are even harder. For some classes of convex sets there has been strong interest in containment problems. This includes containment problems of polyhedra and balls, and containment of polyhedra, which have been studied in the late 20th century because of their inherent relevance in linear programming and combinatorics.
Since then, there has only been limited progress in understanding containment problems of that type. In recent years, containment problems for spectrahedra, which naturally generalize the class of polyhedra, have seen great interest. This interest is particularly driven by the intrinsic relevance of spectrahedra and their projections in polynomial optimization and convex algebraic geometry. Except for the treatment of special classes or situations, there has been no overall treatment of that kind of problems, though.
In this thesis, we provide a comprehensive treatment of containment problems concerning polyhedra, spectrahedra, and their projections from the viewpoint of low-degree semialgebraic problems and study algebraic certificates for containment. This leads to a new and systematic access to studying containment problems of (projections of) polyhedra and spectrahedra, and provides several new and partially unexpected results.
The main idea - which is meanwhile common in polynomial optimization, but whose understanding of the particular potential on low-degree geometric problems is still a major challenge - can be explained as follows. One point of view towards linear programming is as an application of Farkas' Lemma which characterizes the (non-)solvability of a system of linear inequalities. The affine form of Farkas' Lemma characterizes linear polynomials which are nonnegative on a given polyhedron. By omitting the linearity condition, one gets a polynomial nonnegativity question on a semialgebraic set, leading to so-called Positivstellensaetze (or, more precisely Nichtnegativstellensaetze). A Positivstellensatz provides a certificate for the positivity of a polynomial function in terms of a polynomial identity. As in the linear case, these Positivstellensaetze are the foundation of polynomial optimization and relaxation methods. The transition from positivity to nonnegativity is still a major challenge in real algebraic geometry and polynomial optimization.
With this in mind, several principal questions arise in the context of containment problems: Can the particular containment problem be formulated as a polynomial nonnegativity (or, feasibility) problem in a sophisticated way? If so, how are positivity and nonnegativity related to the containment question in the sense of their geometric meaning? Is there a sophisticated Positivstellensatz for the particular situation, yielding certificates for containment? Concerning the degree of the semialgebraic certificates, which degree is necessary, which degree is sufficient to decide containment?
Indeed, (almost) all containment problems studied in this thesis can be formulated as polynomial nonnegativity problems allowing the application of semialgebraic relaxations. Other than this general result, the answer to all the other questions (highly) depends on the specific containment problem, particularly with regard to its underlying geometry. An important point is whether the hierarchies coming from increasing the degree in the polynomial relaxations always decide containment in finitely many steps.
We focus on the containment problem of an H-polytope in a V-polytope and of a spectrahedron in a spectrahedron. Moreover, we address containment problems concerning projections of H-polyhedra and spectrahedra. This selection is justified by the fact that the mentioned containment problems are computationally hard and their geometry is not well understood.
Holocene sedimentary development and event sedimentation of a mid-ocean atoll lagoon, Maldives, Indian Ocean
- This study describes the Holocene sedimentary lagoonal deposition history, including event sedimentation and benthic foraminiferal analyzes, from about 10 kyrs BP until today. This is the first study describing the sedimentation of a Maldivian atoll lagoon in such detail. Thirty-nine sediment cores have been recovered from the deep Rasdhoo Atoll lagoon of the Maldives (4°N/73°W). Seventeen sediment cores were opened, described, and 296 sediment samples have been collected and analyzed. Different methods have been used to evaluate the coarse- and fine-grained carbonate components and a total of fifty-eight samples have been dated radiometrically by Beta Analytic Inc., Miami, Florida. In general, the Rasdhoo Atoll lagoon sediments can be divided into (1) a Late Pleistocene soil, (2) an early Holocene peat layer composed of mangrove deposits which mark the beginning inundation of the atoll lagoon by the rising Holocene sea-level at 10,320 ± 100 yrs BP, and (3) carbonate sediments starting to fill up the lagoon 7850 ± 140 yrs BP until today. The transition from peat to carbonate is characterized by a considerable hiatus. Six different carbonate sediment facies are classified by statistical analyses, listed in decreasing abundance:
(1) mollusk-coral-algal floatstone to rudstone (30%)
(2) mollusk-coral-red algae rudstone (23%)
(3) mollusk-coral-algal wackestone to floatstone (23%)
(4) mollusk-coral wackestone (13%)
(5) mollusk-coral mudstone to wackestone (9%)
(6) mollusk mudstone (2%)
Based on grain-sizes in combination with coral identification, the facies represent both lagoonal background sedimentation (mostly fine-grained sediments (matrix >50%)) and event sedimentation (coarse-grained sediment layers composing reefal components).
Six coarser grained layers in muddy background sediments of the Rasdhoo Atoll lagoon were interpreted as Holocene tsunami events, based on the increase of allochthonous skeletal material with shallow-water reef affinity such as fragments of shallow-water coral species, coralline red algae, and reef-dwelling foraminifera in these layers, as well as AMS dating:
• Event 1: 420 - 890 yrs BP (655 yrs BP)
• Event 2: 890 - 1560 yrs BP (1225 yrs BP)
• Event 3: 2040 - 2340 yrs BP (2190 yrs BP)
• Event 4: 2420 - 3380 yrs BP (2900 yrs BP)
• Event 5: 3890 - 4330 yrs BP (4110 yrs BP)
• Event 6: 5480 - 5760 yrs BP (5620 yrs BP)
Five of the six layers may be correlated to previously published tsunami events at adjacent coastal research sites. The mid-late Holocene atoll lagoon archive is incomplete though based on the assumption that major earthquakes at the Indonesian subduction zone generated more than six major tsunamis during the past 6.5 kyrs.
According to Gischler (2006), the sediments of the Rasdhoo Atoll lagoon can be divided into two areas: (1) a central to marginal deep lagoon with a lateral west-to-east gradient of sediment facies distribution, visible in sections <4 kyrs BP with sedimentary facies of mudstone to wackestone in the western part (e.g., cores 16, 18, and 34) and coarse-grained coral and algal-rich sediments in the eastern part of the lagoon (e.g., cores 30 and 31). (2) A northern enclosed and shallow area between the sand apron and the sand spit accumulating “sandy” sediments of wackestone facies (cores 2, 19, 25, and 26).
Comparing the sediment accumulation data of the lagoon with two reconstructed local sea-level curves, three different sequence-stratigraphical systems tracts are visible: (1) a lowstand systems tract (LST) >10 kyrs BP. Pleistocene brownish soil superposing subaerially exposed Pleistocene reef limestone. (2) A transgressive systems tract (TST) 10-6.5 kyrs BP. A peat layer marks the beginning of the inundation, and the carbonate sedimentation starts with very low sedimentation rates of 0.02 m/kyr. (3) A highstand systems tract (HST) 6.5-0 kyrs BP, further divided into three stages (6.5-3, 3-1, 1-0 kyrs BP). The sea-level rise slowed down, sedimentation rates are increasing continuously up to a maximum of 1.4 m/kyr, the sand spit developed some 4 kyrs BP, the lagoonal circulation got restricted, and the lateral west-to-east gradient of grain-size accumulation started. From 1-0 kyrs BP the sedimentation rates slowed down to modern mean sedimentation rates of 0.6 m/kyr.
Two cores, one core from the center of the lagoon (core 16) and one core from the northern margin of the lagoon (core 19), have been analyzed on diversity and assemblages of benthic foraminifera in high-resolution. The transitions of Ammonia spp. to a more even and diverse fauna marks a significant environmental change at 7.0 kyrs BP in core 16 (onset of a stable environment in the deep lagoon after the sea-level rise slowed down at HST stage 1) and at 4.0 kyrs BP in core 19. A continuing environmental change after 1.4 kyrs BP in core 16 caused the fauna to become more even, a recovery of diversity and a permanent decline of foraminiferal accumulation rate. The changes in the faunas at 4.0 kyrs BP and at 1.4 kyrs BP could be explained with the sand spit formation in the northwestern and western lagoon. The sand spit has apparently acted as an obstacle in lagoonal circulation and might have caused unstable environmental conditions due to a more rapid circulation at the shallow marine site of core 19 and a slowdown of bottom water circulation in the main lagoon (core 16) leading to higher residence times and to lower oxygen and higher nutrient concentrations.
Derivation and Characterization of a New Filter for Nonlinear High-Dimensional Data Assimilation
- Data assimilation (DA) combines model forecasts with real-world observations to achieve an optimal estimate of the state of a dynamical system. The quality of predictions in nonlinear and chaotic systems such as atmospheric or oceanic circulation is strongly sensitive to the initial conditions. Therefore, beyond the consistent reconstruction of past states, a primary relevance of advanced DA methods concerns the proper model initialization. The ensemble Kalman filter (EnKF) and its deterministic variants, mostly square root filters such as the ensemble transform Kalman filter (ETKF), represent a popular alternative to variational DA schemes. They are applied in a wide range of research and operations. Their forecast step employs an ensemble integration that fully respects the nonlinear nature of the analyzed system. In the analysis step, they implicitly assume the prior state and observation errors to be Gaussian. Consequently, in nonlinear systems, the mean and covariance of the analysis ensemble are biased and these filters remain suboptimal. In contrast, the fully nonlinear, non-Gaussian particle filter (PF) relies on Bayes' theorem without further assumptions, which guarantees an exact asymptotic behavior. However, it is exposed to weight collapse, particularly in higher-dimensional settings, known as the curse of dimensionality.
This work presents a new method to obtain an analysis ensemble with mean and covariance that exactly match the corresponding Bayesian estimates. This is achieved by a deterministic matrix square root transformation of the forecast ensemble, and subsequently a suitable random rotation that significantly contributes to filter stability while preserving the required second-order statistics. The forecast step remains as in the ETKF. The algorithm, which is fairly easy to implement and computationally efficient, is referred to as the nonlinear ensemble transform filter (NETF). The limitation with respect to fully-nonlinear filtering is that the NETF only considers the mean and covariance of the Bayesian analysis density, neglecting higher-order moments.
The properties and performance of the proposed algorithm are investigated via a set of experiments. The results indicate that such a filter formulation can increase the analysis quality, even for relatively small ensemble sizes, compared to other ensemble filters in nonlinear, non-Gaussian scenarios. They also confirm that localization enhances the applicability of this PF-inspired scheme in larger-dimensional systems. Finally, the novel filter is coupled to a large-scale ocean general circulation model with a realistic observation scenario. The NETF remains stable with a small ensemble size and shows a consistent behavior. Additionally, its analyses exhibit low estimation errors, as revealed by a comparison with a free ensemble integration and the ETKF. The results confirm that, in principle, the filter can be applied successfully and as simple as the ETKF in high-dimensional problems. No further modifications are needed, even though the algorithm is only based on the particle weights. Thus, it is able to overcome the curse of dimensionality, even in deterministic systems. This proves that the NETF constitutes a promising and user-friendly method for nonlinear high-dimensional DA.
The 'translational turn' in literary and cultural studies : the example of human rights
- Throughout the humanities, greater attention is being paid at present to the category of translation. More than ever before, the tradition al understanding of translation as the (philological and linguistic) translation of text and language is being expanded upon. Increasingly, translation is being spoken about as cultural translation. Yet often the use of this term is merely metaphorical, or even downright inflationary.
Ornament, Constellation, Flurries
- My point of departure is Benjamin's "Lehre vom Ähnlichen," since this text elaborates a theory of reading and writing based on the concept of "nonsensory similarity." The "strange ambiguity of the word reading in relation to both its profane and its magical meaning", which is often cited in Benjamin criticism, is derived from a precise figure, namely the constellation as a model for writing and the concomitant practices of anagrammatical dispersion.
Introduction : The translational turn
- It is no longer possible to ignore how crucial the processes of cultural translation and their analysis have become, whether for cultural contact or interreligious relations and conflicts, for integration strategies in multicultural societies, or for the exploration of productive interfaces between humanities and the natural sciences. The globalization of world society, in particular, demands increased attention to mediation processes and problems of transfer, in terms both of the circulation of global representations and "travelling concepts" and of the interactions that make up cultural encounters. Here, translation becomes, on the one hand, a condition for global relations of exchange ("global translatability"), and on the other, a medium especially liable to reveal cultural differences, power imbalances and scope for action. An explicit focus on translation processes something increasingly prevalent across the humanities may thus enable us to scrutinize more closely current and historical situations of cultural encounter as complex processes of cultural translation. Translation is opened up to a transnational cultural practice that in no way remains restricted to binary relationships between national languages, national literatures or national cultures.
Supporting remote collaborative problem-solving
- We propose a framework of individual problem-solving and communicative demands (IproCo) that bridges the gap between models from cognitive psychology and communication pragmatics. Furthermore, we present two experiments conducted to identify factors influencing the demands and to test possibilities for support. The experiments employed a remote collaborative picture-sorting task with concrete and abstract pictures and applied non-interactive conditions compared to interactive conditions. In a first experiment, the influence of the postulated demands on collaboration process and outcome was analysed, and the impact of shared applications was tested. In a second experiment, we evaluated instructional support measures consisting of model collaboration and a collaboration script. The collaboration process showed benefits of the support but the outcome did not. However, the support measures fostered the collaboration process even in the particularly difficult conditions with non-interactive communication. We discuss the impact of the IproCo framework and apply it to other tasks.
Supporting and hindering knowledge communication in a collaborative picture-sorting task
- Effective knowledge communication presupposes common ground (Clark & Brennan, 1991) that needs to be established and maintained. This is particularly difficult in remote communication as well as in non-interactive settings, because the speaker cannot use gestures or mimic and has to tailor his utterances to the addressee without receiving feedback. In these situations, the speaker may achieve mutual understanding for example by adopting the addressee’s perspective. We present a study conducted to test the impact of instructions that support and hinder individual problem solving and knowledge communication. We used a picture-sorting task requiring individual cognitive processes of feature search (Treisman & Gelade, 1980) in addition to referential communication. As our study focused on the design of utterances, all participants assumed the role of speaker. Participants were told that their descriptions would be recorded and then listened to later on by a participant in the role of addressee. Eight sets of pictures were used, which varied on two dimensions: the individual cognitive demands of detecting the relevant features (varied as between-subject factor) and the communicative demands (varied as within-subject factor). A further between-subject factor was the type of instructions: The participants received either a collaboration script as supporting instructions, or time pressure was applied to induce stress, or else they were given no additional instructions (control group). We used the speakers’ verbal utterances to examine the quality of the speakers’ descriptions. For both dimensions of difficulty, we found the expected effects. In the conditions with a collaboration script, there were fewer irrelevant features mentioned and fewer features were described with delay. In the conditions with time pressure, there were fewer irrelevant features described, but the number of correctly described pictures was impaired through the fact that relevant features were also neglected. Under time pressure, speakers tended to provide ambiguous descriptions regarding the frame of reference.
Integrative taxonomy and conservation status of amphibians in western Panama with an emphasis on the highlands of the Cordillera Central
- Amphibians have existed on the planet for over 300 million years and are today one of the most diverse vertebrate classes in the world with over 7000 known species and still many more to be discovered. However, several studies assume that approximately one third of the world´s known living amphibians are directly threatened with extinction, making it the most endangered vertebrate class. In relation to the relatively small land mass that is occupied by the state of Panama, it supports one of the most diverse amphibian faunas. However, in many cases the ecological role of single species in a wider context and their habitat preferences are still poorly understood and subject to ongoing research. Modern taxonomic approaches in other tropical regions have shown that former assumptions of amphibian diversity were distinct underestimations of the actual species diversity; a situation that is probably also true for Panama. Concurrently, the collection of amphibian diversity data and the description of new species is a race against time. The amphibian fauna of the world and that of Panama in particular, has suffered from an unprecedented loss of diversity over the last 30 years. The reasons are manifold and include destruction, alteration, and fragmentation of their natural habitats as the main causes, but also the deadly amphibian disease chytridiomycosis caused by the fungal pathogen Batrachochytrium dendrobatidis (Bd). In Panama and Costa Rica, this Emerging Infectious Disease (EID) spread in a wave-like manner from west to east causing mass die-offs and reduced amphibian diversity even in well-preserved habitats. The disease has primarily affected stream-associated highland species. The last large-scale evaluation of the conservation status of Panama´s amphibians through the IUCN Red List of Threatened Species in 2004 concluded that approximately 30% of the known species are acutely threatened with extinction. Furthermore, around 17% of the amphibian species that have been known back then lacked adequate data to be assessed. In view of Panama´s already overwhelming amphibian diversity, as well as the variety of habitats and the large number of sites that have not been examined with regard to amphibians before, I started this study with the conviction that the inventory of Panama´s amphibian diversity is far from being completed. Furthermore, when I started this study, it was uncertain if there would be any surviving amphibian species in areas where chytridiomycosis had emerged. The loss of whole amphibian communities in upland western Panama following Bd arrival led to a shift of amphibian research to lowland sites in central and eastern Panama aiming primarily on pathogen arrival and the documentation of epizootic outbreak and subsequent population decline. The situation of amphibian communities in areas post-decline was therefore largely unknown. Accordingly, the main goals of my study were to add to the taxonomic inventory of amphibians in Panama and to assess the situation of amphibian populations in habitats where chytrid-driven declines have been observed. To address these tasks I conducted fieldwork in western Panama with a focus on mountainous elevations between 1000 and 3475 m asl. Additionally, I visited different lowland sites between sea level and 1000 m asl to collect comparative material. In the period between 2008 and 2013, I conducted five collection trips to Panama that add up to a total of approximately 13 months in the field. I have sampled nine regions in western Panama and collected 767 specimens together with student collaborators, 531 of which were collected under my personal field number. Additional data obtained from those specimens include 68 male anuran call recordings, 102 standardized color descriptions of specimens in life, and 259 tissue samples that to date yielded 185 16S mtDNA sequences. This comprises the most comprehensive data set for amphibians of Panama and the first large-scale DNA barcoding approach for western Panama to date. After a preliminary DNA barcoding and subsequent comparative examination of morphological und bioacoustic data of all specimens collected, the number of taxonomic problems that needed to be addressed was higher than I previously anticipated. For most genetic lineages deeper taxonomic analyses were required to reach conclusive results. A selection had to be made with which lineages to proceed in the analyses, in view of the substantial financial and time expenditure that would be needed for a complete taxonomic revision. Therefore, I chose to run deeper analyses on one genus from each of the three amphibian orders in Panama. The genera selection depended largely on the availability of sufficient material and the scientific relevance of the respective genus.
I selected the genus Diasporus from the order Anura. These small frogs are omnipresent in many habitats and thus relatively easy to find. In addition, the genus is underrepresented in taxonomic studies. This is the first taxonomic study on the genus Diasporus to include a molecular phylogeny and the first comparison of advertisement calls between several populations from western Panama. In total, I collected 67 Diasporus specimens throughout western Panama and compared them morphologically with 49 additional specimens from Central America in collections, including the primary types of D. diasporus and D. hylaeformis. Additional comparative data were taken from literature. The DNA barcoding analysis of a fragment of the 16S rRNA gene included 43 own sequences that were complemented with 15 relevant GenBank sequences. In addition, I compared the advertisement calls of 26 male individuals among each other and with call descriptions from the literature. The DNA barcoding approach revealed several unnamed genetic lineages, but in some cases also resulted in the lumping of morphologically and bioacoustically distinct specimens. Generally, the morphological examination of the collected material revealed almost no specific characters that could be used to distinguish between genetic lineages. However, it was possible to identify species using a combination of several morphological characteristics. Which ones are relevant in the individual case depends on the respective species. My extensive collection of call recordings made it possible to test for the first time the intraspecific call variation of D. hylaeformis in dependency of various parameters. This analysis showed that the dominant frequency depends significantly on the body size of the calling male; the smaller the calling male, the higher the frequency of the call. A similar relationship was observed between the call rate and temperature: the lower the temperature during calling, the lower the call rate. I suppose that these general patterns, which have already been observed in other anuran genera, are also true in other Diasporus species that could not be tested in this study. Taking into account the intraspecific variation of Diasporus advertisement calls, I consider comparative call analyses to be the best way to distinguish between species. This is especially true in syntopic species. Integration of the three lines of evidence (i.e., morphology, DNA barcoding, and bioacoustics) led to the identification of four new species, two of which (i.e., D. citrinobapheus and D. igneus) colleagues and I have already formally described.
I conducted an integrative taxonomic analysis of the western Panamanian representatives of the genus Bolitoglossa from the order Caudata, the larger of the two Panamanian salamander genera. Bolitoglossa is very species-rich with a centre of diversification in the high mountains of Costa Rica and western Panama. I collected 53 Bolitoglossa specimens and compared them to twelve specimens in collection, including the holotype and one paratype of B. gomezi. The dataset was complemented with information from the literature. Among the sampled specimens were two species considered to be endangered that have not been collected or observed for several decades; B. magnifica has not been seen for 34 years and B. anthracina has not been seen for 22 years. Further, I collected salamanders at several new locations. To date, my 16S mtDNA barcoding analysis represents the densest taxon sampling for Panamanian Bolitoglossa composed of 21 own sequences that were combined in the final alignment with 47 GenBank sequences. Even though the molecular phylogeny is based only on a single marker, the received trees largely coincide with previous studies and the nodes received high statistical support. In these trees, I retrieve all previously defined subgenera and species groups. On the basis of this molecular phylogeny, I placed B. anthracina, here sequenced for the first time, in the B. subpalmata species group. Due to the fact that B. anthracina is a large and dark colored species it had previously been placed by implication in the B. schizodactyla species group along with other large black salamanders of the B. nigrescens species complex. Moreover, I found deep divergent genetic lineages among geographically separated populations of B. minutula. However, until now there were no additional morphological characteristics detectable to distinguish between these lineages. Additionally, my colleagues and I described a new deep divergent lineage in the B. robinsoni species group as B. jugivagans, a species new to science. In contrast, I found only minor genetic differences between specimens of B. sombra and B. nigrescens. After combining morphometric data and tooth counts from literature of both species with additional data from specimens of B. sombra that I collected near the type locality, the distinguishing features blurred. In particular, including much larger specimens of B. sombra, not yet known at the time of its description, showed that the tooth count difference is dependent on the size and age of the specimen examined. Larger specimens have more maxillary and vomerine teeth. Based on this evidence I regard B. sombra as a junior synonym of B. nigrescens. Further, I revised the Panamanian distribution of the two relatively common lowland salamanders, B. colonnea and B. lignicolor. Besides filling the gaps in the fragmentary known distributions of these species, I assessed the molecular and morphological variation of both species among populations in Panama. While there was little variation in B. lignicolor, I found divergent genetic lineages among geographically distinct populations of B. colonnea that require further taxonomic examination.
Caecilians (order Gymnophiona) are among the least investigated terrestrial vertebrates. After I received a first specimen of the predominantly South American genus Oscaecilia (family Caeciliidae) in western Panama, I started to work more extensively on the taxonomy of Caeciliidae in Central America. The specimens from western Panama were not readily assignable to a single described species, but shared characters with O. elongata and O. osae. While O. osae was only known from the holotype, the type material of O. elongata was destroyed during World War II. On the basis of the original description, the unique feature in O. elongata within Oscaecilia is the absence of subdermal scales in the posterior part of the body. In a referred specimen of O. elongata mentioned in the original description from eastern Panama, this characteristic cannot be examined as it consists of head and neck only. Therefore, I used non-destructive high-resolution, synchrotron-based X-ray micro CT imaging (HRμCT) to examine cranial characters in the specimens in question and took normal radiographs to count vertebrae and to make subdermal scales visible. I found that the fragmented specimen from eastern Panama likely belongs to the well-sampled species O. ochrocephala and has not much in common with O. osae or the specimens from western Panama. Contrarily, O. osae and the specimens from western Panama share many morphological characters, but also show some differences. Genetic barcoding revealed that both species are close relatives, but the genetic distance could not be finally resolved, because 16S sequences obtained from blood samples of living O. osae were of poor quality. Thus, I compare the Oscaecilia from western Panama to O. osae in this study, but postpone a taxonomic decision until further material becomes available. Further, I designate O. elongata a nomen dubium, because the type material is lost, the type locality is not defined in more detail than “Panama”, and the original description does not allow for a definite assignment. Since previous molecular studies only considered O. ochrocephala, the monophyly of Oscaecilia was never tested before. So far, the genus Oscaecilia is based largely on a single cranial character, the eyes covered with bone. Here, I combined two 16S mtDNA sequences of O. osae from Costa Rica and two sequences from O. sp. from western Panama with two sequences of O. ochrocephala and ten sequences of four species of the genus Caecilia, the sister genus of Oscaecilia. The resulted phylogeny contains two well-supported clades, one clade containing two species of Caecilia, one from Panama and one from western Ecuador and all species of Oscaecilia tested. The other clade consists of two species of Caecilia from the Amazon basin. I therefore assume that the split in both clades is due to the rise of the Andes, what led to today’s cis-trans-Andean distribution of the two clades. For now, to restore monophyly, I suggest to place Oscaecilia within the synonymy of Caecilia until more taxa have been tested. When assessing the conservation status of the amphibian species in mountainous western Panama, I first compiled a list of known species that I potentially could have found during my fieldwork. Using the IUCN categories, I analyzed how many of the endangered species I actually found and how these are distributed over families and species groups. Surprisingly, my rediscoveries of lost species were not equally distributed among the four families that comprise most endangered amphibian species (i.e., Bufonidae, Craugastoridae, Hylidae, and Plethodontidae). While I discovered ten of eleven endangered hylids and six of nine endangered plethodontids, I found only one of four endangered bufonids and none of the nine endangered craugastorids. I assume that the secretive living plethodontids, for which no Bd related declines have been documented, were just overlooked in the past decades. In contrast, I propose that hylids, in which Bd related population decline is well documented, developed distinct evolutionary solutions permitting coexistence with the pathogen. The situation is obviously different in bufonids and craugastorids, where I found no signs of population recoveries at present. So far, the only surviving populations of species from these families exist in climatic or physiographic niches that have probably shielded them from Bd. My data confirm the current view that the risk for naïve amphibian populations to decline during Bd epizootics is predicted by ecological traits (e.g., aquatic index, vertical distribution) and not dependent on taxonomic affiliation. However, I propose that only certain amphibian families (e.g., hylids and centrolenids) have the ability to acquire immunity solutions to coexist with the pathogen during enzootic stages. This is a very new perspective on the worst infectious disease in amphibians worldwide, allowing for new research approaches to understand the host-pathogen dynamics. Moreover, I examined where the share of surviving endangered amphibian species is particularly high in mountainous western Panama. As was to be expected, most of the endangered species are found within the boundaries of protected areas. One exception is the unprotected Cerro Colorado region in the Comarca Ngöbe-Buglé that provides habitat for a wide variety of endangered and undiscovered amphibian species. Nonetheless, planned open pit mining would destroy the forests in a large part of the area. This demonstrates once again that human activities are the biggest threat to amphibians in Panama and elsewhere.
Anthropogenic river flow alterations and their impacts on freshwater ecosystems in China
- In the past sixty years, excessive water consumption and dam construction have significantly influenced natural flow regimes and surface freshwater ecosystems throughout China, and thus resulted in serious environmental problems. In order to balance the competing water demands between human and environment and provide knowledge on sustainable water management, assessments on anthropogenic flow alterations and their impacts on aquatic and riparian ecosystems in China are needed.
In this study, the first evaluation on quantitative relationships between anthropogenic flow alterations and ecological responses in eleven river basins and watersheds in China was performed based on the data that could be obtained from published case studies. Quantitative relationships between changes in average annual discharge, seasonal low flow and seasonal high flow and changes in ecological indicators (fish diversity, fish catch and vegetation cover, etc.) were analyzed. The results showed that changes in riparian vegetation cover as well as changes in fish diversity and fish catch were strongly correlated with the changes in flow magnitude (r = 0.77, 0.66), especially with changes in average annual river discharge. In addition, more than half of the variations in vegetation cover could be explained by changes in average annual river discharge (r² = 0.63) and roughly 50 % changes in fish catch in arid and semi-arid region and 60% changes of fish catch in humid region could be related to alterations in average annual river discharge (r² = 0.53, 0.58).
In a supplementary analysis of this study, the first estimation on quantitative relationships between decreases in native fish species richness and anthropogenic flow alterations in 34 river basins and sub-basins in China was conducted. Linear relationships between losses of native fish species and five ecologically relevant flow indicators were analyzed by single and multiple regression models. For the single regression analysis, significant linear relationships were detected for the indicators of long-term average annual discharge (ILTA) and statistical low flow Q90 (IQ90). For the multiple regressions, no indicator other than ILTA has significant relationships with changes in number of fish species mainly due to collinearity. Two conclusions emerged from the analysis: 1) losses of fish species were positively correlated with changes in ILTA in China and 2) indicator of ILTA was dominant over other flow indicators included in this research for the given dataset. These results provide a guideline for the sustainable water resources management in rivers with high risk of fish extinction in China.