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In this paper we analyse gender-based biases in the language within complex legal judgments. Our aims are: (i) to determine the extent to which purported biases discussed in the literature by feminist legal scholars are identifiable from the language of legal judgments themselves, and (ii) to uncover new forms of bias represented in the data that may promote further analysis and interpretation of the functioning of the legal system. We consider a large set of 2530 judgments in family law in Australia over a 20 year period, examining the way that male and female parties to a case are spoken to and about, by male and female judges, in relation to their capacity to provide care for children subject to the decision. Structural topic modelling is used to develop coherent topics for sentences that fall under the notion of “capacity”, which are further differentiated by the gender of both the target of the sentence and the gender of the judge. The analysis reveals significant gendered differences in the language used in these documents, determined by both the gender of the target and the gender of the judge.

Dispersal biology at an invasion front differs from that of populations within the range core, because novel evolutionary and ecological processes come into play in the nonequilibrium conditions at expanding range edges. In a world where species' range limits are changing rapidly, we need to understand how individuals disperse at an invasion front. We analyzed an extensive dataset from radio-tracking invasive cane toads (Rhinella marina) over the first 8 y since they arrived at a site in tropical Australia. Movement patterns of toads in the invasion vanguard differed from those of individuals in the same area postcolonization.Our model discriminated encamped versus dispersive phases within each toad's movements and demonstrated that pioneer toads spent longer periods in dispersive mode and displayed longer, more directed movements while they were in dispersive mode. These analyses predict that overall displacement per year is more than twice as far for toads at the invasion front compared with those tracked a few years later at the same site. Studies on established populations (or even those a few years postestablishment) thus may massively underestimate dispersal rates at the leading edge of an expanding population. This, in turn, will cause us to underpredict the rates at which invasive organisms move into new territory and at which native taxa can expand into newly available habitat under climate change.

Global species richness is a key biodiversity metric. Concerns continue to grow over its decline due to overexploitation and habitat destruction by humans. Despite recent efforts to estimate global species richness, the resulting estimates have been highly uncertain and often logically inconsistent. Estimates lower down either the taxonomic or geographic hierarchies are often larger than those above. Further, these estimates have been typically represented in a wide variety of forms, including intervals (a, b), point estimates with no uncertainty, and point estimates with either symmetrical or asymmetrical bounds, making it difficult to combine information across different studies. Here, we develop a Bayesian hierarchical approach to estimate global species richness (we estimate 22.02 m species; 95% highest posterior density (HPD) interval (10.43 million, 35.28 million)) that combines 50 estimates from published studies. The data mix of intervals and point estimates are reconciled using techniques from symbolic data analysis. This approach allows us to recover interval estimates at each species level, even when data are partially or wholly unobserved, while respecting logical constraints, and to determine the effects of estimation on the whole hierarchy of obtaining future estimates for particular taxa at various levels in the hierarchy.

Robust conclusions regarding changes in the temperature distribution rely on the accuracy and reliability of the input datasets used. Differences between methodologies and datasets in previous studies add uncertainty when comparing and quantifying findings. Here, the authors investigate the sensitivity of assessing global and regional temperature variability and extremes over 1980–2014 in gridded datasets of daily temperature anomalies. A gridded in situ–based dataset, Hadley Centre Global Historical Climatology Network–Daily (HadGHCND), is compared against several commonly used reanalysis products by assessing both the entire distribution and the tails of the distribution. Empirical probability distribution functions show sensitivity to the input dataset when estimating aspects such as standard deviation and skewness, with the mean showing robust results for most regions, irrespective of dataset choice. Standard deviation is especially sensitive, with larger disagreements between datasets for some regions more than others, such as Africa and the Mediterranean region, and with larger differences in minimum temperatures compared with maximum temperatures. Estimates of extreme parameters also show sensitivity to dataset choice, particularly in the lower tails and for daily minimum temperature anomalies. Comparing changes in the means and the extremes of the temperature distributions, the cold extremes in the lower tails have been warming at a faster rate than the mean of the entire distribution for much of the Northern Hemisphere extratropics, with warm extremes warming at a faster rate than the mean in some subtropical regions. These documented sensitivities call for caution when assessing changes in temperature variability and extremes, as dataset choice can have substantial effects on results.

The emergence of antibiotic resistance in Mycobacterium tuberculosis has raised the concern that pathogen strains that are virtually untreatable may become widespread. The acquisition of resistance to antibiotics results in a longer duration of infection in a host, but this resistance may come at a cost through a decreased transmission rate. This raises the question of whether the overall fitness of drug-resistant strains is higher than that of sensitive strains--essential information for predicting the spread of the disease. Here, we directly estimate the transmission cost of drug resistance, the rate at which resistance evolves, and the relative fitness of resistant strains. These estimates are made by using explicit models of the transmission and evolution of sensitive and resistant strains of M. tuberculosis, using approximate Bayesian computation, and molecular epidemiology data from Cuba, Estonia, and Venezuela. We find that the transmission cost of drug resistance relative to sensitivity can be as low as 10%, that resistance evolves at rates of [almost equal to]0.0025-0.02 per case per year, and that the overall fitness of resistant strains is comparable with that of sensitive strains. Furthermore, the contribution of transmission to the spread of drug resistance is very high compared with acquired resistance due to treatment failure (up to 99%). Estimating such parameters directly from in vivo data will be critical to understanding and responding to antibiotic resistance. For instance, projections using our estimates suggest that the prevalence of tuberculosis may decline with successful treatment, but the proportion of cases associated with resistance is likely to increase.

The analysis of unperturbed tumor growth kinetics, particularly the estimation of parameters for S-shaped equations used to describe growth, requires an appropriate likelihood function that accounts for the increasing error in solid tumor measurements as tumor size grows over time. This study aims to propose suitable likelihood functions for parameter estimation in S-shaped models of unperturbed tumor growth. Five different likelihood functions are evaluated and compared using three Bayesian criteria (the Bayesian Information Criterion, Deviance Information Criterion, and Bayes Factor) along with hypothesis tests on residuals. These functions are applied to fit data from unperturbed Ehrlich, fibrosarcoma Sa-37, and F3II tumors using the Gompertz equation, though they are generalizable to other S-shaped growth models for solid tumors or analogous systems (e.g., microorganisms, viruses). Results indicate that error models with tumor volume-dependent dispersion outperform standard constant-variance models in capturing the variability of tumor measurements, particularly the Thres model, which provides interpretable parameters for tumor growth. Additionally, constant-variance models, such as those assuming a normal error distribution, remain valuable as complementary benchmarks in analysis. It is concluded that models incorporating volume-dependent dispersion are preferred for accurate and clinically meaningful tumor growth modeling, whereas constant-dispersion models serve as useful complements for consistency and historical comparability.

Modelling exchangeable relational data can be described appropriately in graphon theory. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we overcome these two shortcomings by smoothing piecewise-constant graphons, which permits continuous intensity values for describing relations, without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We first propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. Then, we further develop the Latent Feature Smoothing Graphon (LFSG), which improves the ISG, by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.

Variable numbers of tandem repeats (VNTR) typing is widely used for studying the bacterial cause of tuberculosis. Knowledge of the rate of mutation of VNTR loci facilitates the study of the evolution and epidemiology of Mycobacterium tuberculosis. Previous studies have applied population genetic models to estimate the mutation rate, leading to estimates varying widely from around 10⁻⁵ to 10⁻² per locus per year. Resolving this issue using more detailed models and statistical methods would lead to improved inference in the molecular epidemiology of tuberculosis. Here, we use a model-based approach that incorporates two alternative forms of a stepwise mutation process for VNTR evolution within an epidemiological model of disease transmission. Using this model in a Bayesian framework we estimate the mutation rate of VNTR in M. tuberculosis from four published data sets of VNTR profiles from Albania, Iran, Morocco and Venezuela. In the first variant, the mutation rate increases linearly with respect to repeat numbers (linear model); in the second, the mutation rate is constant across repeat numbers (constant model). We find that under the constant model, the mean mutation rate per locus is 10⁻²·⁰⁶ (95% CI: 10⁻²·⁶¹,10⁻¹·⁵⁸)and under the linear model, the mean mutation rate per locus per repeat unit is 10⁻²·⁴⁵ (95% CI: 10⁻³·⁰⁷,10⁻¹·⁹⁴). These new estimates represent a high rate of mutation at VNTR loci compared to previous estimates. To compare the two models we use posterior predictive checks to ascertain which of the two models is better able to reproduce the observed data. From this procedure we find that the linear model performs better than the constant model. The general framework we use allows the possibility of extending the analysis to more complex models in the future.

Future climate is typically projected using multi-model ensembles, but the ensemble mean is unlikely to be optimal if models’ skill at reproducing historical climate is not considered. Moreover, individual climate models are not independent. Here, we examine the interplay between the benefits of optimising an ensemble for the performance of its mean and the the effect this has on ensemble spread as an uncertainty estimate. Using future Australian precipitation change as a case study, we perform optimal subset selection based on present-day precipitation, sea surface temperature and/or 500 hPa eastward wind climatologies. We use either one, two, or all three variables as predictors. Out-of-sample projection skill is assessed using a model-as-truth approach (rather than observations). For multiple variables, multi-objective optimisation is used to obtain Pareto-optimal subsets (an ensemble of model subsets), to gauge the uncertainty in optimisation arising from the multiple constraints. We find that the spread of climate model subset averages typically under-represents the true projection uncertainty (overconfidence), but that the situation can be significantly improved using mixture distributions for uncertainty estimation. The single best predictor, present-day precipitation, gives the most accurate results but is still overconfident—a consequence of calibrating too specifically. It is only when all three constraints are used that projection skill is improved and overconfidence is eliminated, but at the cost of a poorer best estimate relative to one predictor. We thus identify an important trade-off between accuracy and precision, depending on the number of predictors, which is likely relevant for any subset selection or weighting strategy.

1. Floodplain vegetation states (communities) exhibit spatiotemporal dynamics in vegetation structure and composition, which reflect unique hydrological and connectivity patterns. Shifts in inundation regimes can drive succession and establish new stable states, determined by the magnitude and duration of the hydrological perturbation. 2. We aimed to develop a modelling approach that is able to capture ecosystem dynamics, identify and quantify the main drivers of change, and provide a tool for conservation decision-making. We developed state and transition models for floodplain vegetation states based on surveys in 1991 and 2008 in the Macquarie Marshes (Australia), a Ramsar wetland of international importance. We used a Bayesian logistic regression approach to model state and transitions between vegetation states and investigated how flood frequency, distance to stream and fire frequency were associated with vegetation dynamics during this period. 3. During 1991-2008, significant transitions have occurred towards drier states. Semi-permanent wetland vegetation had the lowest persistence probability (ppsis = 0·456) and a significant threshold response of transitioning to terrestrial vegetation (ptran = 0·505). Transition to drier states was driven by lower inundation probabilities followed by increased fire probability, and distance to nearest stream. 4. Using developed models, we predicted persistence probabilities of vegetation states under an unregulated (i.e. no dams or diversions) and regulated water availability system. Under a regulated system, semi-permanent wetland vegetation had an average persistence of ppsis = 0.67 and 0·08 in the northern and southern sections of the nature reserve, respectively. Under an unregulated system, the predicted persistence of semi-permanent wetland vegetation was considerably higher: ppsis = 0·87 and 0·38, respectively. 5. Synthesis and applications. Developing quantitative models of state transitions significantly improved our understanding of ecosystem dynamics, identifying sensitive indicators for monitoring and thus supporting conservation decision-making. This helps managers understand potential trajectories of change in ecosystems in response to management options. For example, increasing environmental flows in the Macquarie Marshes is predicted to shift the community towards more of a wetland than the terrestrial state, resulting from river regulation. State and transition models identified how key ecological assets respond to drivers of change, particularly where these can be managed. This is critical for ensuring that all ecosystem components are managed and that these do not shift into undesirable states.