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Ecological surveys risk incurring false negative and false positive detections of the target species. With indirect survey methods, such as environmental DNA, such error can occur at two stages: sample collection and laboratory analysis. Here we analyse a large qPCR based eDNA data set using two occupancy models, one of which accounts for false positive error by Griffin et al . (J R Stat Soc Ser C Appl Stat 69: 377–392, 2020), and a second that assumes no false positive error by Stratton et al . (Methods Ecol Evol 11: 1113–1120, 2020). Additionally, we apply the Griffin et al . (2020) model to simulated data to determine optimal levels of replication at both sampling stages. The Stratton et al . (2020) model, which assumes no false positive results, consistently overestimated both overall and individual site occupancy compared to both the Griffin et al . (2020) model and to previous estimates of pond occupancy for the target species. The inclusion of replication at both stages of eDNA analysis (sample collection and in the laboratory) reduces both bias and credible interval width in estimates of both occupancy and detectability. Even the collection of > 1 sample from a site can improve parameter estimates more than having a high number of replicates only within the laboratory analysis.

Protected areas are key to meeting biodiversity conservation goals, but direct measures of effectiveness have proven difficult to obtain. We address this challenge by using environmental DNA from leech-ingested bloodmeals to estimate spatially-resolved vertebrate occupancies across the 677 km 2 Ailaoshan reserve in Yunnan, China. From 30,468 leeches collected by 163 park rangers across 172 patrol areas, we identify 86 vertebrate species, including amphibians, mammals, birds and squamates. Multi-species occupancy modelling shows that species richness increases with elevation and distance to reserve edge. Most large mammals (e.g. sambar, black bear, serow, tufted deer) follow this pattern; the exceptions are the three domestic mammal species (cows, sheep, goats) and muntjak deer, which are more common at lower elevations. Vertebrate occupancies are a direct measure of conservation outcomes that can help guide protected-area management and improve the contributions that protected areas make towards global biodiversity goals. Here, we show the feasibility of using invertebrate-derived DNA to estimate spatially-resolved vertebrate occupancies across entire protected areas. Invertebrate-derived eDNA (iDNA) is an emerging tool for taxonomic and spatial biodiversity monitoring. Here, the authors use metabarcoding of leech-derived iDNA to estimate vertebrate occupancy over an entire protected area, the Ailaoshan Nature Reserve, China.

The distribution assessment and monitoring of species is key to reliable environmental impact assessments and conservation interventions. Considerable efort is directed towards survey and monitoring of great crested newts (Triturus cristatus) in England. Surveys are increasingly undertaken using indirect methodologies, such as environmental DNA (eDNA). We used a large data set to estimate national pond occupancy rate, as well as false negative and false positive error rates, for commercial eDNA protocols. Additionally, we explored a range of habitat, landscape and climatic variables as predictors of pond occupancy. In England, 20% of ponds were estimated to be occupied by great crested newts. Pond sample collection error rates were estimated as 5.2% false negative and 1.5% false positive. Laboratory error indicated a negligible false negative rate when 12 qPCR replicates were used. Laboratory false positive error was estimated at 2% per qPCR replicate and is therefore exaggerated by high levels of laboratory replication. Including simple habitat suitability variables into the model revealed the importance of fish, plants and shading as predictors of newt presence. However, variables traditionally considered as important for newt presence may need more precise and consistent measurement if they are to be employed as reliable predictors in modelling exercises.

(1) Background: Blastocystis is a microbial eukaryote inhabiting the gastrointestinal tract of a broad range of animals including humans. Several studies have shown that the organism is associated with specific microbial profiles and bacterial taxa that have been deemed beneficial to intestinal and overall health. Nonetheless, these studies are focused almost exclusively on humans, while there is no similar information on other animals. (2) Methods: Using a combination of conventional PCR, cloning and sequencing, we investigated presence of Blastocystis along with Giardia and Cryptosporidium in 16 captive water voles sampled twice from a wildlife park. We also characterised their bacterial gut communities. (3) Results: Overall, alpha and beta diversities between water voles with and without Blastocystis did not differ significantly. Differences were noted only on individual taxa with Treponema and Kineothrix being significantly reduced in Blastocystis positive water voles. Grouping according to antiprotozoal treatment and presence of other protists did not reveal any differences in the bacterial community composition either. (4) Conclusion: Unlike human investigations, Blastocystis does not seem to be associated with specific gut microbial profiles in water voles.

Environmental DNA (eDNA) surveys have become a popular tool for assessing the distribution of species. However, it is known that false positive and false negative observation error can occur at both stages of eDNA surveys, namely the field sampling stage and laboratory analysis stage. We present an RShiny app that implements the Griffin et al. (2020) statistical method, which accounts for false positive and false negative errors in both stages of eDNA surveys that target single species using quantitative PCR methods. Following Griffin et al. (2020), we employ a Bayesian approach and perform efficient Bayesian variable selection to identify important predictors for the probability of species presence as well as the probabilities of observation error at either stage. We demonstrate the RShiny app using a data set on great crested newts collected by Natural England in 2018, and we identify water quality, pond area, fish presence, macrophyte cover and frequency of drying as important predictors for species presence at a site. The state‐of‐the‐art statistical method that we have implemented is the only one that has specifically been developed for the purposes of modelling false negative and false positive observation error in eDNA data. Our RShiny app is user‐friendly, requires no prior knowledge of R and fits the models very efficiently. Therefore, it should be part of the tool‐kit of any researcher or practitioner who is collecting or analysing eDNA data.

Environmental changes in recent years have been linked to phenological shifts which in turn are linked to the survival of species. The work in this paper is motivated by capture-recapture data on blackcaps collected by the British Trust for Ornithology as part of the Constant Effort Sites monitoring scheme. Blackcaps overwinter abroad and migrate to the UK annually for breeding purposes. We propose a novel Bayesian nonparametric approach for expressing the bivariate density of individual arrival and departure times at different sites across a number of years as a mixture model. The new model combines the ideas of the hierarchical and the dependent Dirichlet process, allowing the estimation of site-specific weights and year-specific mixture locations, which are modelled as functions of environmental covariates using a multivariate extension of the Gaussian process. The proposed modelling framework is extremely general and can be used in any context where multivariate density estimation is performed jointly across different groups and in the presence of a continuous covariate

In this thesis, we present four manuscripts, described in the second to fifth chapter. Chapter 2 presents a Bayesian nonparametric model for capture-recapture (CR) data collected at different sites and for several years. To estimate arrival and departure patterns at the different sites and years, we build an extension of the Dirichlet process, the Hierarchical Dependent Dirichlet process, which allows us to perform density estimation jointly across different sites and in the presence of covariates. In this case, we use a year-specific covariate, and model the correlation structure of the covariate across years using a multivariate Gaussian process. In Chapter 3, we present a model for estimating entry and exit patterns, as well as the population size, using count data (CD), by employing a Polya Tree (PT) prior. In Chapter 4 we present several extensions of chapter 3. More specifically, we extend the model to CR and to ring-recovery data and develop a joint model for CR and CD. In addition, we consider the case when multiple data-sets are modelled at the same time, by defining a hierarchical extension of the PT, which we define as Hierarchical Logistic PT. Finally, we extend the model to the case of long time series, by borrowing ideas from the Optional PT. Chapter 5 presents a spatial model to estimate interactions between multiple species using CR data. The model uses a vector of interaction point process (IPP), which allows us to estimate interactions between and within species. The use of an IPP leads to an intractable ratio of normalising constants (RNC), and hence we use the Monte Carlo Metropolis Hastings algorithm to approximate the RNC with an importance sampling estimate. The supplementary material for each paper is presented in the appendix.

In recent years, a wide range of mortality models has been proposed to address the diverse factors influencing mortality rates, which has highlighted the need to perform model selection. Traditional mortality model selection methods, such as AIC and BIC, often require fitting multiple models independently and ranking them based on these criteria. This process can fail to account for uncertainties in model selection, which can lead to overly optimistic prediction interval, and it disregards the potential insights from combining models. To address these limitations, we propose a novel Bayesian model selection framework that integrates model selection and parameter estimation into the same process. This requires creating a model building framework that will give rise to different models by choosing different parametric forms for each term. Inference is performed using the reversible jump Markov chain Monte Carlo algorithm, which is devised to allow for transition between models of different dimensions, as is the case for the models considered here. We develop modelling frameworks for data stratified by age and period and for data stratified by age, period and product. Our results are presented in two case studies.

Hidden Markov models (HMMs) offer a robust and efficient framework for analyzing time series data, modelling both the underlying latent state progression over time and the observation process, conditional on the latent state. However, a critical challenge lies in determining the appropriate number of underlying states, often unknown in practice. In this paper, we employ a Bayesian framework, treating the number of states as a random variable and employing reversible jump Markov chain Monte Carlo to sample from the posterior distributions of all parameters, including the number of states. Additionally, we introduce repulsive priors for the state parameters in HMMs, and hence avoid overfitting issues and promote parsimonious models with dissimilar state components. We perform an extensive simulation study comparing performance of models with independent and repulsive prior distributions on the state parameters, and demonstrate our proposed framework on two ecological case studies: GPS tracking data on muskox in Antarctica and acoustic data on Cape gannets in South Africa. Our results highlight how our framework effectively explores the model space, defined by models with different latent state dimensions, while leading to latent states that are distinguished better and hence are more interpretable, enabling better understanding of complex dynamic systems.

DNA-based biodiversity surveys involve collecting physical samples from survey sites and assaying the contents in the laboratory to detect species via their diagnostic DNA sequences. DNA-based surveys are increasingly being adopted for biodiversity monitoring. The most commonly employed method is metabarcoding, which combines PCR with high-throughput DNA sequencing to amplify and then read `DNA barcode' sequences. This process generates count data indicating the number of times each DNA barcode was read. However, DNA-based data are noisy and error-prone, with several sources of variation. In this paper, we present a unifying modelling framework for DNA-based data allowing for all key sources of variation and error in the data-generating process. The model can estimate within-species biomass changes across sites and link those changes to environmental covariates, while accounting for species and sites correlation. Inference is performed using MCMC, where we employ Gibbs or Metropolis-Hastings updates with Laplace approximations. We also implement a re-parameterisation scheme, appropriate for crossed-effects models, leading to improved mixing, and an adaptive approach for updating latent variables, reducing computation time. We discuss study design and present theoretical and simulation results to guide decisions on replication at different stages and on the use of quality control methods. We demonstrate the new framework on a dataset of Malaise-trap samples. We quantify the effects of elevation and distance-to-road on each species, infer species correlations, and produce maps identifying areas of high biodiversity, which can be used to rank areas by conservation value. We estimate the level of noise between sites and within sample replicates, and the probabilities of error at the PCR stage, which are close to zero for most species considered, validating the employed laboratory processing.