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Ecological research is becoming increasingly quantitative, yet students often opt out of courses in mathematics and statistics, unwittingly limiting their ability to carry out research in the future. This textbook provides a practical introduction to quantitative ecology for students and practitioners who have realised that they need this opportunity. The text is addressed to readers who haven't used mathematics since school, who were perhaps more confused than enlightened by their undergraduate lectures in statistics and who have never used a computer for much more than word processing and da

Infectious diseases are often transmitted through local interactions. Yet, both surveillance and control measures are implemented within administrative units. Capturing local transmission processes and spatial coupling between regions from aggregate level data is therefore a technical challenge that can shed light on both theoretical questions and practical decisions. Fox rabies has been eliminated from much of Europe through oral rabies vaccination (ORV) programmes. The European Union (EU) co-finances ORV to maintain rabies freedom in EU member and border states via a cordon sanitaire. Models to capture local transmission dynamics and spatial coupling have immediate application to the planning of these ORV campaigns and to other parts of the world considering oral vaccination. We fitted a hierarchical Bayesian state-space model to data on three decades of fox rabies cases and ORV campaigns from Eastern Germany. Specifically, we find that (i) combining regional spatial coupling and heterogeneous local transmission allows us to capture regional rabies dynamics; (ii) incursions from other regions account for less than 1% of cases, but allow for re-emergence of disease; (iii) herd immunity achieved through bi-annual vaccination campaigns is short-lived due to population turnover. Together, these findings highlight the need for regular and sustained vaccination efforts and our modelling approach can be used to provide strategic guidance for ORV delivery. Moreover, we show that biological understanding can be gained from inference from partially observed data on wildlife disease.

The balance between economic growth and wildlife conservation is a priority for many governments. Enhancing realism in assessment of population‐level impacts of anthropogenic mortality can help achieve this balance. Population Viability Analysis (PVA) is commonly applied to investigate population vulnerability, but outcomes of PVA are sensitive to formulations of density‐dependence, environmental stochasticity and life history. Current practice in marine assessments is to use precautionary models that assume no compensation from density‐dependence or rescue‐effects via "re‐seeding" from other colonies. However, if we could empirically quantify regulatory population processes, the responses of populations to additional anthropogenic mortality may be assessed with more realism in PVA. Using Bayesian state‐space models fitted to population time series from three sympatric seabird populations, selected for varied life histories, we inferred the extent to which their dynamics are driven by environmental stochasticity and density‐dependence. Based on these inferences, we conducted an exhaustive PVA across credible parameterizations for intrinsic and extrinsic population regulation, simulated as a closed and re‐seeded system. Scenarios of anthropogenic mortality, along a sliding scale of precaution, were applied both proportionally and as a fixed quota using Potential Biological Removal (PBR). Baseline results from fitting revealed clear environmental regulation in two of our three species. Crucially, we found that for our empirically derived, realistic model parameterizations there are risks of decline to real populations even under very precautionary mortality scenarios. We find that PBR is dubious in application as a sustainable tool for population assessment when we account for regulation. Closed versus re‐seeded models showed a large divergence in outcomes, with sharper declines in closed simulations. Fixed‐quota mortality typically induced greater population declines comparative to proportional mortality, subject to regulation and re‐seeding. Synthesis and applications. Practitioners using arbitrary formulations of population regulation risk over‐precaution (economic constraint) or under‐precaution (endangering populations). The demands of increased economic development and preservation of wildlife require that methodologies apply techniques that confer reality and rigour to assessment. The current practice of employing models lacking density‐dependence and empirical environmental information imposes limitations in the efficacy of estimating impacts. Here, we provide a method to quantify the conditions that predominantly regulate a population and exacerbate the risk of decline from anthropogenic mortality. It is in the interests of both developers and conservationists to apply methods in population impact assessments that capture realism in the processes driving population dynamics.

Infectious diseases are often transmitted through local interactions. Yet, both surveillance and control measures are implemented within administrative units. Capturing local transmission processes and spatial coupling between regions from aggregate level data is therefore a technical challenge that can shed light on both theoretical questions and practical decisions. Fox rabies has been eliminated from much of Europe through oral rabies vaccination (ORV) programmes. The European Union (EU) co-finances ORV to maintain rabies freedom in EU member and border states via a cordon sanitaire. Models to capture local transmission dynamics and spatial coupling have immediate application to the planning of these ORV campaigns and to other parts of the world considering oral vaccination. We fitted a hierarchical Bayesian state-space model to data on three decades of fox rabies cases and ORV campaigns from Eastern Germany. Specifically, we find that (i) combining regional spatial coupling and heterogeneous local transmission allows us to capture regional rabies dynamics; (ii) incursions from other regions account for less than 1% of cases, but allow for re-emergence of disease; (iii) herd immunity achieved through bi-annual vaccination campaigns is short-lived due to population turnover. Together, these findings highlight the need for regular and sustained vaccination efforts and our modelling approach can be used to provide strategic guidance for ORV delivery. Moreover, we show that biological understanding can be gained from inference from partially observed data on wildlife disease.

Summary As part of global efforts to reduce dependence on carbon‐based energy sources there has been a rapid increase in the installation of renewable energy devices. The installation and operation of these devices can result in conflicts with wildlife. In the marine environment, mammals may avoid wind farms that are under construction or operating. Such avoidance may lead to more time spent travelling or displacement from key habitats. A paucity of data on at‐sea movements of marine mammals around wind farms limits our understanding of the nature of their potential impacts.Here, we present the results of a telemetry study on harbour seals Phoca vitulina in The Wash, south‐east England, an area where wind farms are being constructed using impact pile driving. We investigated whether seals avoid wind farms during operation, construction in its entirety, or during piling activity. The study was carried out using historical telemetry data collected prior to any wind farm development and telemetry data collected in 2012 during the construction of one wind farm and the operation of another.Within an operational wind farm, there was a close‐to‐significant increase in seal usage compared to prior to wind farm development. However, the wind farm was at the edge of a large area of increased usage, so the presence of the wind farm was unlikely to be the cause.There was no significant displacement during construction as a whole. However, during piling, seal usage (abundance) was significantly reduced up to 25 km from the piling activity; within 25 km of the centre of the wind farm, there was a 19 to 83% (95% confidence intervals) decrease in usage compared to during breaks in piling, equating to a mean estimated displacement of 440 individuals. This amounts to significant displacement starting from predicted received levels of between 166 and 178 dB re 1 μPa(p‐p). Displacement was limited to piling activity; within 2 h of cessation of pile driving, seals were distributed as per the non‐piling scenario. Synthesis and ...

Knowledge gaps in spatiotemporal changes in mangrove diversity and composition have obstructed mangrove conservation programs across the tropics, but particularly in the Sundarbans (10,017 km(2)), the world's largest remaining natural mangrove ecosystem. Using mangrove tree data collected from Earth's largest permanent sample plot network at four historical time points (1986, 1994, 1999 and 2014), this study establishes spatially explicit baseline biodiversity information for the Sundarbans. We determined the spatial and temporal differences in alpha, beta, and gamma diversity in three ecological zones (hypo-, meso-, and hypersaline) and also uncovered changes in the mangroves' overall geographic range and abundances therein. Spatially, the hyposaline mangrove communities were the most diverse and heterogeneous in species composition while the hypersaline communities were the least diverse and most homogeneous at all historical time points. Since 1986, we detect an increasing trend of compositional homogeneity (between-site similarity in species composition) and a significant spatial contraction of distinct and diverse areas over the entire ecosystem. Temporally, the western and southern hypersaline communities have undergone radical shifts in species composition due to population increase and range expansion of the native invasive species Ceriops decandra and local extinction or range contraction of specialists including the globally endangered Heritiera fomes. The surviving biodiversity hotspots are distributed outside the legislated protected area network. In addition to suggesting the immediate coverage of these hotspots under protected area management, our novel biodiversity insights and spatial maps can form the basis for spatial conservation planning, biodiversity monitoring and protection initiatives for the Sundarbans.

Knowledge gaps in spatiotemporal changes in mangrove diversity and composition have obstructed mangrove conservation programs across the tropics, but particularly in the Sundarbans (10,017 km2), the world's largest remaining natural mangrove ecosystem. Using mangrove tree data collected from Earth's largest permanent sample plot network at four historical time points (1986, 1994, 1999 and 2014), this study establishes spatially explicit baseline biodiversity information for the Sundarbans. We determined the spatial and temporal differences in alpha, beta, and gamma diversity in three ecological zones (hypo-, meso-, and hypersaline) and also uncovered changes in the mangroves' overall geographic range and abundances therein. Spatially, the hyposaline mangrove communities were the most diverse and heterogeneous in species composition while the hypersaline communities were the least diverse and most homogeneous at all historical time points. Since 1986, we detect an increasing trend of compositional homogeneity (between-site similarity in species composition) and a significant spatial contraction of distinct and diverse areas over the entire ecosystem. Temporally, the western and southern hypersaline communities have undergone radical shifts in species composition due to population increase and range expansion of the native invasive species Ceriops decandra and local extinction or range contraction of specialists including the globally endangered Heritiera fomes. The surviving biodiversity hotspots are distributed outside the legislated protected area network. In addition to suggesting the immediate coverage of these hotspots under protected area management, our novel biodiversity insights and spatial maps can form the basis for spatial conservation planning, biodiversity monitoring and protection initiatives for the Sundarbans.

DJFR, GH, VMJ and BM were funded by the UK Department of Energy and Climate Change (DECC) as part of their Offshore Energy Strategic Environmental Assessment programme. DT and GH were also funded by NERC/Defra EBAO NE/J004243/1. ELJ was funded under Scottish Government grant MMSS001/01. This work was also supported by National Capability funding from the Natural Environment Research Council to SMRU (grant no. SMRU1001). Tags and their deployment in the Thames in 2006 and The Wash were funded by DECC. Tags and their deployment in the Thames in 2012 were commissioned by Zoological Society London, with funding from BBC Wildlife Fund and Sita Trust. ; 1. As part of global efforts to reduce dependence on carbon-based energy sources there has been a rapid increase in the installation of renewable energy devices. The installation and operation of these devices can result in conflicts with wildlife. In the marine environment, mammals may avoid wind farms that are under construction or operating. Such avoidance may lead to more time spent travelling or displacement from key habitats. A paucity of data on at-sea movements of marine mammals around wind farms limits our understanding of the nature of their potential impacts. 2. Here, we present the results of a telemetry study on harbour seals Phoca vitulina in The Wash, south-east England, an area where wind farms are being constructed using impact pile driving. We investigated whether seals avoid wind farms during operation, construction in its entirety, or during piling activity. The study was carried out using historical telemetry data collected prior to any wind farm development and telemetry data collected in 2012 during the construction of one wind farm and the operation of another. 3. Within an operational wind farm, there was a close-to-significant increase in seal usage compared to prior to wind farm development. However, the wind farm was at the edge of a large area of increased usage, so the presence of the wind farm was unlikely to be the cause. 4. There was no significant displacement during construction as a whole. However, during piling, seal usage (abundance) was significantly reduced up to 25 km from the piling activity; within 25 km of the centre of the wind farm, there was a 19 to 83% (95% confidence intervals) decrease in usage compared to during breaks in piling, equating to a mean estimated displacement of 440 individuals. This amounts to significant displacement starting from predicted received levels of between 166 and 178 dB re 1 μPa(p·p). Displacement was limited to piling activity; within 2 h of cessation of pile driving, seals were distributed as per the non-piling scenario. 5. Synthesis and applications. Our spatial and temporal quantification of avoidance of wind farms by harbour seals is critical to reduce uncertainty and increase robustness in environmental impact assessments of future developments. Specifically, the results will allow policymakers to produce industry guidance on the likelihood of displacement of seals in response to pile driving; the relationship between sound levels and avoidance rates; and the duration of any avoidance, thus allowing far more accurate environmental assessments to be carried out during the consenting process. Further, our results can be used to inform mitigation strategies in terms of both the sound levels likely to cause displacement and what temporal patterns of piling would minimize the magnitude of the energetic impacts of displacement. ; Publisher PDF ; Peer reviewed

FUNDING Analysis was funded by the UK Government Department for Business, Energy and Industrial Strategy (BEIS; OESEA-16-76/OESEA-17-78) with support from the Natural Environment Research Council (NERC; INSITE Phase II NE/T010614/1 EcoSTAR), EU INTERREG (MarPAMM), and the Scottish Government (MMSS/002/15). DJFR's contribution was funded by NERC National Capability Funding (NE/R015007/1). WJG was supported by INSITE Phase I (MAPS). Telemetry tags and their deployment were funded in the UK by BEIS (and previous incarnations), NERC, Marine Scotland, Scottish Government, NatureScot, SMRU, SMRU Instrumentation Group, Marine Current Turbines, Ørsted, the Met Office, the Zoological Society of London (ZSL), the Crown Estate, Highlands & Islands Enterprise, Moray Firth Renewables Limited (MORL), Beatrice Offshore Windfarm Limited (BOWL), SITA Trust, BBC Wildlife Fund and the Hampshire & Isle of Wight Wildlife Trust. Tags and their deployment in Ireland were funded by Inland Fisheries Ireland, the Department of Communications, Marine and Natural Resources, the Higher Education Authority of Ireland, the National Geographic Society, the Department of Agriculture, Food and the Marine, and the National Parks and Wildlife Service. UK aerial surveys conducted by SMRU were funded by NERC (NE/R015007/1), NatureScot, the Department for Agriculture, Environment and Rural Affairs (Northern Ireland), Marine Current Turbines, Marine Scotland, Natural England, and Scottish Power. Aerial surveys in Ireland were funded by the Department for Tourism, Culture, Arts, Gaeltacht, Sport and Media. ACKNOWLEDGMENTS We thank Matt Bivins (SMRU), Phil Lovell (SMRU Instrumentation Group), and the many people who were involved in or facilitated fieldwork, including landowners and reserve managers. We are grateful to Dr Carol Sparling (SMRU), Dr Sophie Smout (SMRU) and Prof. Philip Hammond (SMRU) for useful discussions. We thank Hartley Anderson Ltd. for their support and guidance. This study is dedicated to the memory of Dr Bernie McConnell; ...

Analysis was funded by the UK Government Department for Business, Energy and Industrial Strategy (BEIS; OESEA-16-76/OESEA-17-78) with support from the Natural Environment Research Council (NERC; INSITE Phase II NE/T010614/1 EcoSTAR), EU INTERREG (MarPAMM), and the Scottish Government (MMSS/002/15). DJFR's contribution was funded by NERC National Capability Funding (NE/R015007/1). WJG was supported by INSITE Phase I (MAPS). Telemetry tags and their deployment were funded in the UK by BEIS (and previous incarnations), NERC, Marine Scotland, Scottish Government, NatureScot, SMRU, SMRU Instrumentation Group, Marine Current Turbines, Ørsted, the Met Office, the Zoological Society of London (ZSL), the Crown Estate, Highlands & Islands Enterprise, Moray Firth Renewables Limited (MORL), Beatrice Offshore Windfarm Limited (BOWL), SITA Trust, BBC Wildlife Fund and the Hampshire & Isle of Wight Wildlife Trust. Tags and their deployment in Ireland were funded by Inland Fisheries Ireland, the Department of Communications, Marine and Natural Resources, the Higher Education Authority of Ireland, the National Geographic Society, the Department of Agriculture, Food and the Marine, and the National Parks and Wildlife Service. UK aerial surveys conducted by SMRU were funded by NERC (NE/R015007/1), NatureScot, the Department for Agriculture, Environment and Rural Affairs (Northern Ireland), Marine Current Turbines, Marine Scotland, Natural England, and Scottish Power. Aerial surveys in Ireland were funded by the Department for Tourism, Culture, Arts, Gaeltacht, Sport and Media. ; Marine predator populations are crucial to the structure and functioning of ecosystems. Like many predator taxa, pinnipeds face an increasingly complex array of natural and anthropogenic threats. Understanding the relationship between at-sea processes and trends in abundance at land-based monitoring sites requires robust estimates of at-sea distribution, often on multi-region scales. Such an understanding is critical for effective conservation ...

Acknowledgements Funding was provided by the UK Natural Environmental Research Council (NERC) [grant number NE/M017990/1] and Fundação para a Ciência e a Tecnologia (FCT) [grant numbers MARE -UIDB/04292/2020 and UIDP/04292/2020]. Remotely-sensed data were supplied by the NERC Earth Observation Data Acquisition and Analysis Service (NEODAAS) and the Copernicus Marine Service. Permission to track birds was provided by the Tristan da Cunha Government (Gough Island), the Falkland Islands Government (permit R09/2016, Kidney Island), the Região Autónoma dos Açores (permit 84/2016/DRA, Corvo), and Orkney Islands Council and BTO (Eynhallow). Logistical support was provided by the RSPB, FitzPatrick Institute of African Ornithology and South African National Antarctic Programme (Gough Island), the South Atlantic Environmental Research Institute (Kidney Island), and Sociedade Portuguesa para o Estudo das Aves (Corvo). Stefan Schoombie, José Pedro Granadeiro and Ewan Edwards provided raw GPS data to inform movement parameters used in the shearwater GLS data analysis and Rob Ronconi, Alex Bond and Gail Davoren provided advice on the study design. Support for NOFU loggers and analysis was provided through the SEATRACK project http://www.seapop.no/en/seatrack/, funded by the Norwegian Ministries of Climate and Environment, and Foreign Affairs and the Norwegian Oil and Gas Association. We are very grateful to Captain Antonio Gatti and the crew of the RRS Discovery, the many fieldworkers who deployed/recovered the GLS tags and Igor Belkin, who generously provided constructive advice on the study design and manuscript. ; Peer reviewed ; Publisher PDF