ARC Centre of Excellence for Mathematical and Statistical Frontiers

Surveying threatened and invasive species to obtain accurate population estimates is an important but challenging task that requires a considerable investment in time and resources. Estimates using existing ground-based monitoring techniques, such as camera traps and surveys performed on foot, are known to be resource intensive, potentially inaccurate and imprecise, and difficult to validate. Recent developments in unmanned aerial vehicles (UAV), artificial intelligence and miniaturized thermal imaging systems represent a new opportunity for wildlife experts to inexpensively survey relatively large areas. The system presented in this paper includes thermal image acquisition as well as a video processing pipeline to perform object detection, classification and tracking of wildlife in forest or open areas. The system is tested on thermal video data from ground based and test flight footage, and is found to be able to detect all the target wildlife located in the surveyed area. The system is flexible in that the user can readily define the types of objects to classify and the object characteristics that should be considered during classification.

have indoor sources; and for offices, outdoor air is the source of all three particle size fractions. While each individual building is different, leading to differences in exposure and ideally necessitating its own assessment (which is very rarely done), our findings point to the existence of generalizable trends for the main types of indoor environments where people spend time, and therefore to the type of prevention measures which need to be considered in general for these environments.

Summary Bayesian experimental design is a fast growing area of research with many real‐world applications. As computational power has increased over the years, so has the development of simulation‐based design methods, which involve a number of algorithms, such as Markov chain Monte Carlo, sequential Monte Carlo and approximate Bayes methods, facilitating more complex design problems to be solved. The Bayesian framework provides a unified approach for incorporating prior information and/or uncertainties regarding the statistical model with a utility function which describes the experimental aims. In this paper, we provide a general overview on the concepts involved in Bayesian experimental design, and focus on describing some of the more commonly used Bayesian utility functions and methods for their estimation, as well as a number of algorithms that are used to search over the design space to find the Bayesian optimal design. We also discuss other computational strategies for further research in Bayesian optimal design.

Abstract Thermal regimes are fundamental determinants of aquatic ecosystems, which makes description and prediction of temperatures critical during a period of rapid global change. The advent of inexpensive temperature sensors dramatically increased monitoring in recent decades, and although most monitoring is done by individuals for agency‐specific purposes, collectively these efforts constitute a massive distributed sensing array that generates an untapped wealth of data. Using the framework provided by the National Hydrography Dataset, we organized temperature records from dozens of agencies in the western U.S. to create the NorWeST database that hosts >220,000,000 temperature recordings from >22,700 stream and river sites. Spatial‐stream‐network models were fit to a subset of those data that described mean August water temperatures (AugTw) during 63,641 monitoring site‐years to develop accurate temperature models ( r 2 = 0.91; RMSPE = 1.10°C; MAPE = 0.72°C), assess covariate effects, and make predictions at 1 km intervals to create summer climate scenarios. AugTw averaged 14.2°C (SD = 4.0°C) during the baseline period of 1993–2011 in 343,000 km of western perennial streams but trend reconstructions also indicated warming had occurred at the rate of 0.17°C/decade (SD = 0.067°C/decade) during the 40 year period of 1976–2015. Future scenarios suggest continued warming, although variation will occur within and among river networks due to differences in local climate forcing and stream responsiveness. NorWeST scenarios and data are available online in user‐friendly digital formats and are widely used to coordinate monitoring efforts among agencies, for new research, and for conservation planning.

Abstract Ecological data often exhibit spatial pattern, which can be modeled as autocorrelation. Conditional autoregressive (CAR) and simultaneous autoregressive (SAR) models are network‐based models (also known as graphical models) specifically designed to model spatially autocorrelated data based on neighborhood relationships. We identify and discuss six different types of practical ecological inference using CAR and SAR models, including: (1) model selection, (2) spatial regression, (3) estimation of autocorrelation, (4) estimation of other connectivity parameters, (5) spatial prediction, and (6) spatial smoothing. We compare CAR and SAR models, showing their development and connection to partial correlations. Special cases, such as the intrinsic autoregressive model (IAR), are described. Conditional autoregressive and SAR models depend on weight matrices, whose practical development uses neighborhood definition and row‐standardization. Weight matrices can also include ecological covariates and connectivity structures, which we emphasize, but have been rarely used. Trends in harbor seals ( Phoca vitulina ) in southeastern Alaska from 463 polygons, some with missing data, are used to illustrate the six inference types. We develop a variety of weight matrices and CAR and SAR spatial regression models are fit using maximum likelihood and Bayesian methods. Profile likelihood graphs illustrate inference for covariance parameters. The same data set is used for both prediction and smoothing, and the relative merits of each are discussed. We show the nonstationary variances and correlations of a CAR model and demonstrate the effect of row‐standardization. We include several take‐home messages for CAR and SAR models, including (1) choosing between CAR and IAR models, (2) modeling ecological effects in the covariance matrix, (3) the appeal of spatial smoothing, and (4) how to handle isolated neighbors. We highlight several reasons why ecologists will want to make use of autoregressive models, both directly and in hierarchical models, and not only in explicit spatial settings, but also for more general connectivity models.

Having the ability to work with complex models can be highly beneficial. However, complex models often have intractable likelihoods, so methods that involve evaluation of the likelihood function are infeasible. In these situations, the benefits of working with likelihood-free methods become apparent. Likelihood-free methods, such as parametric Bayesian indirect likelihood that uses the likelihood of an alternative parametric auxiliary model, have been explored throughout the literature as a viable alternative when the model of interest is complex. One of these methods is called the synthetic likelihood (SL), which uses a multivariate normal approximation of the distribution of a set of summary statistics. This article explores the accuracy and computational efficiency of the Bayesian version of the synthetic likelihood (BSL) approach in comparison to a competitor known as approximate Bayesian computation (ABC) and its sensitivity to its tuning parameters and assumptions. We relate BSL to pseudo-marginal methods and propose to use an alternative SL that uses an unbiased estimator of the SL, when the summary statistics have a multivariate normal distribution. Several applications of varying complexity are considered to illustrate the findings of this article. Supplemental materials are available online. Computer code for implementing the methods on all examples is available at <i>https://github.com/cdrovandi/Bayesian-Synthetic-Likelihood</i>.

Ecosystem monitoring is central to effective management, where rapid reporting is essential to provide timely advice. While digital imagery has greatly improved the speed of underwater data collection for monitoring benthic communities, image analysis remains a bottleneck in reporting observations. In recent years, a rapid evolution of artificial intelligence in image recognition has been evident in its broad applications in modern society, offering new opportunities for increasing the capabilities of coral reef monitoring. Here, we evaluated the performance of Deep Learning Convolutional Neural Networks for automated image analysis, using a global coral reef monitoring dataset. The study demonstrates the advantages of automated image analysis for coral reef monitoring in terms of error and repeatability of benthic abundance estimations, as well as cost and benefit. We found unbiased and high agreement between expert and automated observations (97%). Repeated surveys and comparisons against existing monitoring programs also show that automated estimation of benthic composition is equally robust in detecting change and ensuring the continuity of existing monitoring data. Using this automated approach, data analysis and reporting can be accelerated by at least 200x and at a fraction of the cost (1%). Combining commonly used underwater imagery in monitoring with automated image annotation can dramatically improve how we measure and monitor coral reefs worldwide, particularly in terms of allocating limited resources, rapid reporting and data integration within and across management areas.

Physiological variability manifests itself via differences in physiological function between individuals of the same species, and has crucial implications in disease progression and treatment. Despite its importance, physiological variability has traditionally been ignored in experimental and computational investigations due to averaging over samples from multiple individuals. Recently, modelling frameworks have been devised for studying mechanisms underlying physiological variability in cardiac electrophysiology and pro-arrhythmic risk under a variety of conditions and for several animal species as well as human. One such methodology exploits populations of cardiac cell models constrained with experimental data, or experimentally-calibrated populations of models. In this review, we outline the considerations behind constructing an experimentally-calibrated population of models and review the studies that have employed this approach to investigate variability in cardiac electrophysiology in physiological and pathological conditions, as well as under drug action. We also describe the methodology and compare it with alternative approaches for studying variability in cardiac electrophysiology, including cell-specific modelling approaches, sensitivity-analysis based methods, and populations-of-models frameworks that do not consider the experimental calibration step. We conclude with an outlook for the future, predicting the potential of new methodologies for patient-specific modelling extending beyond the single virtual physiological human paradigm.

Molecular sequence data that have evolved under the influence of heterotachous evolutionary processes are known to mislead phylogenetic inference. We introduce the General Heterogeneous evolution On a Single Topology (GHOST) model of sequence evolution, implemented under a maximum-likelihood framework in the phylogenetic program IQ-TREE (http://www.iqtree.org). Simulations show that using the GHOST model, IQ-TREE can accurately recover the tree topology, branch lengths, and substitution model parameters from heterotachously evolved sequences. We investigate the performance of the GHOST model on empirical data by sampling phylogenomic alignments of varying lengths from a plastome alignment. We then carry out inference under the GHOST model on a phylogenomic data set composed of 248 genes from 16 taxa, where we find the GHOST model concurs with the currently accepted view, placing turtles as a sister lineage of archosaurs, in contrast to results obtained using traditional variable rates-across-sites models. Finally, we apply the model to a data set composed of a sodium channel gene of 11 fish taxa, finding that the GHOST model is able to elucidate a subtle component of the historical signal, linked to the previously established convergent evolution of the electric organ in two geographically distinct lineages of electric fish. We compare inference under the GHOST model to partitioning by codon position and show that, owing to the minimization of model constraints, the GHOST model offers unique biological insights when applied to empirical data.

Understanding the mechanisms that reduce the many degrees of freedom in the musculoskeletal system remains an outstanding challenge. Muscle synergies reduce the dimensionality and hence simplify the control problem. How this is achieved is not yet known. Here we use network theory to assess the coordination between multiple muscles and to elucidate the neural implementation of muscle synergies. We performed connectivity analysis of surface EMG from ten leg muscles to extract the muscle networks while human participants were standing upright in four different conditions. We observed widespread connectivity between muscles at multiple distinct frequency bands. The network topology differed significantly between frequencies and between conditions. These findings demonstrate how muscle networks can be used to investigate the neural circuitry of motor coordination. The presence of disparate muscle networks across frequencies suggests that the neuromuscular system is organized into a multiplex network allowing for parallel and hierarchical control structures.

= 98) (7000-3000 BCE). Using the genetic substructure observed in European hunter-gatherers, we characterize diverse patterns of admixture in different regions, consistent with both routes of expansion. Early western European farmers show a higher proportion of distinctly western hunter-gatherer ancestry compared to central/southeastern farmers. Our data highlight the complexity of the biological interactions during the Neolithic expansion by revealing major regional variations.

The partially observable Markov decision process (POMDP) provides a principled general framework for planning under uncertainty, but solving POMDPs optimally is computationally intractable, due to the "curse of dimensionality" and the "curse of history". To overcome these challenges, we introduce the Determinized Sparse Partially Observable Tree (DESPOT), a sparse approximation of the standard belief tree, for online planning under uncertainty. A DESPOT focuses online planning on a set of randomly sampled scenarios and compactly captures the "execution" of all policies under these scenarios. We show that the best policy obtained from a DESPOT is near-optimal, with a regret bound that depends on the representation size of the optimal policy. Leveraging this result, we give an anytime online planning algorithm, which searches a DESPOT for a policy that optimizes a regularized objective function. Regularization balances the estimated value of a policy under the sampled scenarios and the policy size, thus avoiding overfitting. The algorithm demonstrates strong experimental results, compared with some of the best online POMDP algorithms available. It has also been incorporated into an autonomous driving system for real-time vehicle control. The source code for the algorithm is available online.

Abstract Many inland waters exhibit complete or partial desiccation, or have vanished due to global change, exposing sediments to the atmosphere. Yet, data on carbon dioxide (CO 2 ) emissions from these sediments are too scarce to upscale emissions for global estimates or to understand their fundamental drivers. Here, we present the results of a global survey covering 196 dry inland waters across diverse ecosystem types and climate zones. We show that their CO 2 emissions share fundamental drivers and constitute a substantial fraction of the carbon cycled by inland waters. CO 2 emissions were consistent across ecosystem types and climate zones, with local characteristics explaining much of the variability. Accounting for such emissions increases global estimates of carbon emissions from inland waters by 6% (~0.12 Pg C y −1 ). Our results indicate that emissions from dry inland waters represent a significant and likely increasing component of the inland waters carbon cycle.

Europe's prehistory oversaw dynamic and complex interactions of diverse societies, hitherto unexplored at detailed regional scales. Studying 271 human genomes dated ~4900 to 1600 BCE from the European heartland, Bohemia, we reveal unprecedented genetic changes and social processes. Major migrations preceded the arrival of "steppe" ancestry, and at ~2800 BCE, three genetically and culturally differentiated groups coexisted. Corded Ware appeared by 2900 BCE, were initially genetically diverse, did not derive all steppe ancestry from known Yamnaya, and assimilated females of diverse backgrounds. Both Corded Ware and Bell Beaker groups underwent dynamic changes, involving sharp reductions and complete replacements of Y-chromosomal diversity at ~2600 and ~2400 BCE, respectively, the latter accompanied by increased Neolithic-like ancestry. The Bronze Age saw new social organization emerge amid a ≥40% population turnover.

Climate change is impacting coral reefs now. Recent pan-tropical bleaching events driven by unprecedented global heat waves have shifted the playing field for coral reef management and policy. While best-practice conventional management remains essential, it may no longer be enough to sustain coral reefs under continued climate change. Nor will climate change mitigation be sufficient on its own. Committed warming and projected reef decline means solutions must involve a portfolio of mitigation, best-practice conventional management and coordinated restoration and adaptation measures involving new and perhaps radical interventions, including local and regional cooling and shading, assisted coral evolution, assisted gene flow, and measures to support and enhance coral recruitment. We propose that proactive research and development to expand the reef management toolbox fast but safely, combined with expedient trialling of promising interventions is now urgently needed, whatever emissions trajectory the world follows. We discuss the challenges and opportunities of embracing new interventions in a race against time, including their risks and uncertainties. Ultimately, solutions to the climate challenge for coral reefs will require consideration of what society wants, what can be achieved technically and economically, and what opportunities we have for action in a rapidly closing window. Finding solutions that work for coral reefs and people will require exceptional levels of coordination of science, management and policy, and open engagement with society. It will also require compromise, because reefs will change under climate change despite our best interventions. We argue that being clear about society's priorities, and understanding both the opportunities and risks that come with an expanded toolset, can help us make the most of a challenging situation. We offer a conceptual model to help reef managers frame decision problems and objectives, and to guide effective strategy choices in the face of complexity and uncertainty.

Abstract In the face of increasing cumulative effects from human and natural disturbances, sustaining coral reefs will require a deeper understanding of the drivers of coral resilience in space and time. Here we develop a high‐resolution, spatially explicit model of coral dynamics on Australia's Great Barrier Reef (GBR). Our model accounts for biological, ecological and environmental processes, as well as spatial variation in water quality and the cumulative effects of coral diseases, bleaching, outbreaks of crown‐of‐thorns starfish ( Acanthaster cf. solaris ), and tropical cyclones. Our projections reconstruct coral cover trajectories between 1996 and 2017 over a total reef area of 14,780 km 2 , predicting a mean annual coral loss of −0.67%/year mostly due to the impact of cyclones, followed by starfish outbreaks and coral bleaching. Coral growth rate was the highest for outer shelf coral communities characterized by digitate and tabulate Acropora spp. and exposed to low seasonal variations in salinity and sea surface temperature, and the lowest for inner‐shelf communities exposed to reduced water quality. We show that coral resilience (defined as the net effect of resistance and recovery following disturbance) was negatively related to the frequency of river plume conditions, and to reef accessibility to a lesser extent. Surprisingly, reef resilience was substantially lower within no‐take marine protected areas, however this difference was mostly driven by the effect of water quality. Our model provides a new validated, spatially explicit platform for identifying the reefs that face the greatest risk of biodiversity loss, and those that have the highest chances to persist under increasing disturbance regimes.

Abstract After decades of extensive surveying, knowledge of the global distribution of species still remains inadequate for many purposes. In the short to medium term, such knowledge is unlikely to improve greatly given the often prohibitive costs of surveying and the typically limited resources available. By forecasting biodiversity patterns in time and space, predictive models can help fill critical knowledge gaps and prioritise research to support better conservation and management. The ability of a model to predict biodiversity metrics in novel environments is termed “transferability,” and models with high transferability will be the most useful in this context. Despite their potentially broad utility, little guidance exists on what confers high transferability to biodiversity models. We synthesise recent advances in biodiversity model transfers to facilitate increased understanding of what underpins successful model transferability, demonstrating that a consistent approach has so far been lacking but is essential for achieving high levels of repeatability, transparency and accountability of model transfers. We provide a set of guidelines to support efficient learning and the improvement of model transferability.

Hepatitis B virus (HBV) has been infecting humans for millennia and remains a global health problem, but its past diversity and dispersal routes are largely unknown. We generated HBV genomic data from 137 Eurasians and Native Americans dated between ~10,500 and ~400 years ago. We date the most recent common ancestor of all HBV lineages to between ~20,000 and 12,000 years ago, with the virus present in European and South American hunter-gatherers during the early Holocene. After the European Neolithic transition, Mesolithic HBV strains were replaced by a lineage likely disseminated by early farmers that prevailed throughout western Eurasia for ~4000 years, declining around the end of the 2nd millennium BCE. The only remnant of this prehistoric HBV diversity is the rare genotype G, which appears to have reemerged during the HIV pandemic.

Climate change and human pressures are changing the global distribution and the extent of intermittent rivers and ephemeral streams (IRES), which comprise half of the global river network area. IRES are characterized by periods of flow cessation, during which channel substrates accumulate and undergo physico-chemical changes (preconditioning), and periods of flow resumption, when these substrates are rewetted and release pulses of dissolved nutrients and organic matter (OM). However, there are no estimates of the amounts and quality of leached substances, nor is there information on the underlying environmental constraints operating at the global scale. We experimentally simulated, under standard laboratory conditions, rewetting of leaves, riverbed sediments, and epilithic biofilms collected during the dry phase across 205 IRES from five major climate zones. We determined the amounts and qualitative characteristics of the leached nutrients and OM, and estimated their areal fluxes from riverbeds. In addition, we evaluated the variance in leachate characteristics in relation to selected environmental variables and substrate characteristics. We found that sediments, due to their large quantities within riverbeds, contribute most to the overall flux of dissolved substances during rewetting events (56%-98%), and that flux rates distinctly differ among climate zones. Dissolved organic carbon, phenolics, and nitrate contributed most to the areal fluxes. The largest amounts of leached substances were found in the continental climate zone, coinciding with the lowest potential bioavailability of the leached OM. The opposite pattern was found in the arid zone. Environmental variables expected to be modified under climate change (i.e. potential evapotranspiration, aridity, dry period duration, land use) were correlated with the amount of leached substances, with the strongest relationship found for sediments. These results show that the role of IRES should be accounted for in global biogeochemical cycles, especially because prevalence of IRES will increase due to increasing severity of drying events.

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability , we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically motivated synthetic data and Markov chain Monte Carlo methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github .