Choosing and using diversity indices: Insights for ecological applications from the German Biodiversity Exploratories

Biodiversity, a multidimensional property of natural systems, is difficult to quantify partly because of the multitude of indices proposed for this purpose. Indices aim to describe general properties of communities that allow us to compare different regions, taxa, and trophic levels. Therefore, they are of fundamental importance for environmental monitoring and conservation, although there is no consensus about which indices are more appropriate and informative. We tested several common diversity indices in a range of simple to complex statistical analyses in order to determine whether some were better suited for certain analyses than others. We used data collected around the focal plant Plantago lanceolata on 60 temperate grassland plots embedded in an agricultural landscape to explore relationships between the common diversity indices of species richness (S), Shannon's diversity (H'), Simpson's diversity (D1), Simpson's dominance (D2), Simpson's evenness (E), and Berger–Parker dominance (BP). We calculated each of these indices for herbaceous plants, arbuscular mycorrhizal fungi, aboveground arthropods, belowground insect larvae, and P. lanceolata molecular and chemical diversity. Including these trait-based measures of diversity allowed us to test whether or not they behaved similarly to the better studied species diversity. We used path analysis to determine whether compound indices detected more relationships between diversities of different organisms and traits than more basic indices. In the path models, more paths were significant when using H', even though all models except that with E were equally reliable. This demonstrates that while common diversity indices may appear interchangeable in simple analyses, when considering complex interactions, the choice of index can profoundly alter the interpretation of results. Data mining in order to identify the index producing the most significant results should be avoided, but simultaneously considering analyses using multiple indices can provide greater insight into the interactions in a system.

Invading and expanding: range dynamics and ecological consequences of the greater white-toothed shrew (Crocidura russula) invasion in Ireland

Establishing how invasive species impact upon pre-existing species is a fundamental question in ecology and conservation biology. The greater white-toothed shrew (Crocidura russula) is an invasive species in Ireland that was first recorded in 2007 and which, according to initial data, may be limiting the abundance/distribution of the pygmy shrew (Sorex minutus), previously Ireland’s only shrew species. Because of these concerns, we undertook an intensive live-trapping survey (and used other data from live-trapping, sightings and bird of prey pellets/nest inspections collected between 2006 and 2013) to model the distribution and expansion of C. russula in Ireland and its impacts on Ireland’s small mammal community. The main distribution range of C. russula was found to be approximately 7,600 km2 in 2013, with established outlier populations suggesting that the species is dispersing with human assistance within the island. The species is expanding rapidly for a small mammal, with a radial expansion rate of 5.5 km/yr overall (2008–2013), and independent estimates from live-trapping in 2012–2013 showing rates of 2.4–14.1 km/yr, 0.5–7.1 km/yr and 0–5.6 km/yr depending on the landscape features present. S. minutus is negatively associated with C. russula. S. minutus is completely absent at sites where C. russula is established and is only present at sites at the edge of and beyond the invasion range of C. russula. The speed of this invasion and the homogenous nature of the Irish landscape may mean that S. minutus has not had sufficient time to adapt to the sudden appearance of C. russula. This may mean the continued decline/disappearance of S. minutus as C. russula spreads throughout the island.

Correlation of phantom-based and log file patient-specific QA with complexity scores for VMAT

The motivation for this study was to reduce physics workload relating to patient- specific quality assurance (QA). VMAT plan delivery accuracy was determined from analysis of pre- and on-treatment trajectory log files and phantom-based ionization chamber array measurements. The correlation in this combination of measurements for patient-specific QA was investigated. The relationship between delivery errors and plan complexity was investigated as a potential method to further reduce patient-specific QA workload. Thirty VMAT plans from three treatment sites - prostate only, prostate and pelvic node (PPN), and head and neck (H&N) - were retrospectively analyzed in this work. The 2D fluence delivery reconstructed from pretreatment and on-treatment trajectory log files was compared with the planned fluence using gamma analysis. Pretreatment dose delivery verification was also car- ried out using gamma analysis of ionization chamber array measurements compared with calculated doses. Pearson correlations were used to explore any relationship between trajectory log file (pretreatment and on-treatment) and ionization chamber array gamma results (pretreatment). Plan complexity was assessed using the MU/ arc and the modulation complexity score (MCS), with Pearson correlations used to examine any relationships between complexity metrics and plan delivery accu- racy. Trajectory log files were also used to further explore the accuracy of MLC and gantry positions. Pretreatment 1%/1 mm gamma passing rates for trajectory log file analysis were 99.1% (98.7%-99.2%), 99.3% (99.1%-99.5%), and 98.4% (97.3%-98.8%) (median (IQR)) for prostate, PPN, and H&N, respectively, and were significantly correlated to on-treatment trajectory log file gamma results (R = 0.989, p < 0.001). Pretreatment ionization chamber array (2%/2 mm) gamma results were also significantly correlated with on-treatment trajectory log file gamma results (R = 0.623, p < 0.001). Furthermore, all gamma results displayed a significant correlation with MCS (R > 0.57, p < 0.001), but not with MU/arc. Average MLC position and gantry angle errors were 0.001 ± 0.002 mm and 0.025° ± 0.008° over all treatment sites and were not found to affect delivery accuracy. However, vari- ability in MLC speed was found to be directly related to MLC position accuracy. The accuracy of VMAT plan delivery assessed using pretreatment trajectory log file fluence delivery and ionization chamber array measurements were strongly correlated with on-treatment trajectory log file fluence delivery. The strong corre- lation between trajectory log file and phantom-based gamma results demonstrates potential to reduce our current patient-specific QA. Additionally, insight into MLC and gantry position accuracy through trajectory log file analysis and the strong cor- relation between gamma analysis results and the MCS could also provide further methodologies to both optimize the VMAT planning and QA process. 

Root Cause Analysis by a Combined Sparse Classification and Monte Carlo Approach

Classification methods with embedded feature selection capability are very appealing for the analysis of complex processes since they allow the analysis of root causes even when the number of input variables is high. In this work, we investigate the performance of three techniques for classification within a Monte Carlo strategy with the aim of root cause analysis. We consider the naive bayes classifier and the logistic regression model with two different implementations for controlling model complexity, namely, a LASSO-like implementation with a L1 norm regularization and a fully Bayesian implementation of the logistic model, the so called relevance vector machine. Several challenges can arise when estimating such models mainly linked to the characteristics of the data: a large number of input variables, high correlation among subsets of variables, the situation where the number of variables is higher than the number of available data points and the case of unbalanced datasets. Using an ecological and a semiconductor manufacturing dataset, we show advantages and drawbacks of each method, highlighting the superior performance in term of classification accuracy for the relevance vector machine with respect to the other classifiers. Moreover, we show how the combination of the proposed techniques and the Monte Carlo approach can be used to get more robust insights into the problem under analysis when faced with challenging modelling conditions.

Pseudomonas aeruginosa exhibits frequent recombination, but only a limited association between genotype and ecological setting

Pseudomonas aeruginosa is an opportunistic pathogen and an important cause of infection, particularly amongst cystic fibrosis (CF) patients. While specific strains capable of patient-to-patient transmission are known, many infections appear to be caused by unique and unrelated strains. There is a need to understand the relationship between strains capable of colonising the CF lung and the broader set of P. aeruginosa isolates found in natural environments. Here we report the results of a multilocus sequence typing (MLST)-based study designed to understand the genetic diversity and population structure of an extensive regional sample of P. aeruginosa isolates from South East Queensland, Australia. The analysis is based on 501 P. aeruginosa isolates obtained from environmental, animal and human (CF and non-CF) sources with particular emphasis on isolates from the Lower Brisbane River and isolates from CF patients obtained from the same geographical region. Overall, MLST identified 274 different sequence types, of which 53 were shared between one or more ecological settings. Our analysis revealed a limited association between genotype and environment and evidence of frequent recombination. We also found that genetic diversity of P. aeruginosa in Queensland, Australia was indistinguishable from that of the global P. aeruginosa population. Several CF strains were encountered frequently in multiple ecological settings; however, the most frequently encountered CF strains were confined to CF patients. Overall, our data confirm a non-clonal epidemic structure and indicate that most CF strains are a random sample of the broader P. aeruginosa population. The increased abundance of some CF strains in different geographical regions is a likely product of chance colonisation events followed by adaptation to the CF lung and horizontal transmission among patients.

Probabilistic Inference in Credal Networks: New Complexity Results

Credal networks are graph-based statistical models whose parameters take values in a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The computational complexity of inferences on such models depends on the irrelevance/independence concept adopted. In this paper, we study inferential complexity under the concepts of epistemic irrelevance and strong independence. We show that inferences under strong independence are NP-hard even in trees with binary variables except for a single ternary one. We prove that under epistemic irrelevance the polynomial-time complexity of inferences in credal trees is not likely to extend to more general models (e.g., singly connected topologies). These results clearly distinguish networks that admit efficient inferences and those where inferences are most likely hard, and settle several open questions regarding their computational complexity. We show that these results remain valid even if we disallow the use of zero probabilities. We also show that the computation of bounds on the probability of the future state in a hidden Markov model is the same whether we assume epistemic irrelevance or strong independence, and we prove an analogous result for inference in Naive Bayes structures. These inferential equivalences are important for practitioners, as hidden Markov models and Naive Bayes networks are used in real applications of imprecise probability.

On the complexity of solving polytree-shaped limited memory influence diagrams with binary variables

Influence diagrams are intuitive and concise representations of structured decision problems. When the problem is non-Markovian, an optimal strategy can be exponentially large in the size of the diagram. We can avoid the inherent intractability by constraining the size of admissible strategies, giving rise to limited memory influence diagrams. A valuable question is then how small do strategies need to be to enable efficient optimal planning. Arguably, the smallest strategies one can conceive simply prescribe an action for each time step, without considering past decisions or observations. Previous work has shown that finding such optimal strategies even for polytree-shaped diagrams with ternary variables and a single value node is NP-hard, but the case of binary variables was left open. In this paper we address such a case, by first noting that optimal strategies can be obtained in polynomial time for polytree-shaped diagrams with binary variables and a single value node. We then show that the same problem is NP-hard if the diagram has multiple value nodes. These two results close the fixed-parameter complexity analysis of optimal strategy selection in influence diagrams parametrized by the shape of the diagram, the number of value nodes and the maximum variable cardinality.

On the Complexity of Strong and Epistemic Credal Networks

Credal networks are graph-based statistical models whose parameters take values on a set, instead of being sharply specified as in traditional statistical models (e.g., Bayesian networks). The result of inferences with such models depends on the irrelevance/independence concept adopted. In this paper, we study the computational complexity of inferences under the concepts of epistemic irrelevance and strong independence. We strengthen complexity results by showing that inferences with strong independence are NP-hard even in credal trees with ternary variables, which indicates that tractable algorithms, including the existing one for epistemic trees, cannot be used for strong independence. We prove that the polynomial time of inferences in credal trees under epistemic irrelevance is not likely to extend to more general models, because the problem becomes NP-hard even in simple polytrees. These results draw a definite line between networks with efficient inferences and those where inferences are hard, and close several open questions regarding the computational complexity of such models.

Complexity of Inferences in Polytree-shaped Semi-Qualitative Probabilistic Networks

Semi-qualitative probabilistic networks (SQPNs) merge two important graphical model formalisms: Bayesian networks and qualitative probabilistic networks. They provide a very general modeling framework by allowing the combination of numeric and qualitative assessments over a discrete domain, and can be compactly encoded by exploiting the same factorization of joint probability distributions that are behind the Bayesian networks. This paper explores the computational complexity of semi-qualitative probabilistic networks, and takes the polytree-shaped networks as its main target. We show that the inference problem is coNP-Complete for binary polytrees with multiple observed nodes. We also show that inferences can be performed in linear time if there is a single observed node, which is a relevant practical case. Because our proof is constructive, we obtain an efficient linear time algorithm for SQPNs under such assumptions. To the best of our knowledge, this is the first exact polynomial-time algorithm for SQPNs. Together these results provide a clear picture of the inferential complexity in polytree-shaped SQPNs.

New Complexity Results for MAP in Bayesian Networks

This paper presents new results for the (partial) maximum a posteriori (MAP) problem in Bayesian networks, which is the problem of querying the most probable state configuration of some of the network variables given evidence. It is demonstrated that the problem remains hard even in networks with very simple topology, such as binary polytrees and simple trees (including the Naive Bayes structure), which extends previous complexity results. Furthermore, a Fully Polynomial Time Approximation Scheme for MAP in networks with bounded treewidth and bounded number of states per variable is developed. Approximation schemes were thought to be impossible, but here it is shown otherwise under the assumptions just mentioned, which are adopted in most applications.

The Complexity of Approximately Solving Influence Diagrams

Influence diagrams allow for intuitive and yet precise description of complex situations involving decision making under uncertainty. Unfortunately, most of the problems described by influence diagrams are hard to solve. In this paper we discuss the complexity of approximately solving influence diagrams. We do not assume no-forgetting or regularity, which makes the class of problems we address very broad. Remarkably, we show that when both the treewidth and the cardinality of the variables are bounded the problem admits a fully polynomial-time approximation scheme.

The Inferential Complexity of Bayesian and Credal Networks

This paper presents new results on the complexity of graph-theoretical models that represent probabilities (Bayesian networks) and that represent interval and set valued probabilities (credal networks). We define a new class of networks with bounded width, and introduce a new decision problem for Bayesian networks, the maximin a posteriori. We present new links between the Bayesian and credal networks, and present new results both for Bayesian networks (most probable explanation with observations, maximin a posteriori) and for credal networks (bounds on probabilities a posteriori, most probable explanation with and without observations, maximum a posteriori).