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Multiple predictors can all be continuous, or they can be mixtures of continuous and categorical. A common biological situation is a substantial number of continuous predictors, and fitting these models is commonly labeled multiple regression. We might also mix continuous and categorical predictors, and these have been called analyses of covariance. We show how these two analyses are closely related and how to fit and interpret these models. This chapter introduces the complication of correlated predictors (collinearity) and describes ways of detecting and dealing with the problem. This chapter also introduces measures of influence and leverage as part of checking assumptions.
Making repeated observations through time adds complications, but it’s a common way to deal with limited research resources and reduce the use of experimental animals. A consequence of this design is that observations fall into clusters, often corresponding to individual organisms or “subjects.” We need to incorporate these relationships into statistical models and consider the additional complication where observations closer together in time may be more similar than those further apart. These designs were traditionally analyzed with repeated measures ANOVA, fitted by OLS. We illustrate this traditional approach but recommend the alternative linear mixed models approach. Mixed models offer better ways to deal with correlations within the data by specifying the clusters as random effects and modeling the correlations explicitly. When the repeated measures form a sequence (e.g. time), mixed models also offer a way to deal with occasional missing observations without omitting the whole subject from the model.
The components or functions derived from an eigenanalysis are linear combinations of the original variables. Principal components analysis (PCA) is a very common method that uses these components to examine patterns among the objects, often in a plot termed an ordination, and identify which variables are driving those patterns. Correspondence analysis (CA) is a related method used when the variables represent counts or abundances. Redundancy analysis and canonical CA are constrained versions of PCA and CA, respectively, where the components are derived after taking into account the relationships with additional explanatory variables. Finally, we introduce linear discriminant function analysis as a way of identifying and predicting membership of objects to predefined groups.
By this last chapter, you should have a clear biological and statistical model, well-designed data collection, and careful interpretation of models fitted to your data. The challenge now is to communicate what may be some complex analyses to a range of audiences. This aspect of data analysis has been relatively neglected, but we now have audiences less tolerant of unclear or unengaging communication, coupled with the challenge of describing complex analyses. We advocate bringing a storytelling approach to presenting results and being very clear how the data support our larger biological story. We also introduce basic ideas about how to report complex analyses and offer suggestions for improving the clarity of supporting graphics. Two important recommendations are that biologists learn more about how to communicate quantitative information and alter our data communication dramatically to match the mode of delivery and the target audience.
There is a daunting array of statistical “methods” out there – regression, ANOVA, loglinear models, GLMMS, ANCOVA, etc. They often are treated as different data analysis approaches. We take a more holistic view. Most methods biologists use are variations on a central theme of generalized linear models – relating a biological response to a linear combination of predictor variables. We show how several common “named” methods are related, based on classifying biological response and predictor variables as continuous or categorical. We use simple regression, single-factor ANOVA, logistic regression, and two-dimensional contingency tables to show how these methods all represent generalized linear models with a single predictor. We describe how we fit these models and outline their assumptions.
For the bioassessment of tropical marine ecosystem, a survey of protozoa colonizing artificial substrate was conducted in the coastal waters of northern Bay of Bengal, Bangladesh. Protozoan samples were collected using glass slides from 1 and 2 m water depths at time intervals of 3, 7, 10, 14, 21, and 28 days during winter and monsoon seasons. Thus, the colonization processes of protozoa were assigned into three stages namely the initial (3 days), transitional (7 days), and equilibrium stages (10–28 days) at two depths in two seasons. Regression analyses demonstrated that the colonization dynamics of protozoa were well fitted to the MacArthur-Wilson model and logistic equation. Species richness reached equilibrium after 10–14 days and species abundance was maximum at a depth of 1 m. These results suggest that samples of protozoa can be collected at 1 m depth in winter season for monitoring the ecological health of tropical marine ecosystems.
The model fitting and estimation approach is laid out using two simple linear models, one for a continuous biological predictor variable and one for a categorical predictor. These two models are the familiar simple linear regression and the single-factor ANOVA. We show how these two models are variations on a theme and describe how to fit them to data. The model fitting is treated in detail, laying the foundation for more complex models in the following chapters. We emphasize what the model parameters mean, how to estimate them, calculate standard errors and confidence intervals, and test hypotheses about them. For categorical predictors, we introduce and recommend planned comparisons (contrasts) to examine patterns across categories. Checking assumptions and identifying unusual and influential data is detailed, as is the use of power analysis to determine necessary sample sizes.
Predictors can be fixed or random, and their classification affects how we fit and interpret statistical models. A mismatch between their treatment in the model and their interpretation is a common problem. This chapter focuses on categorical predictors and introduces nested or hierarchical designs that combine fixed and random effects. For these designs, we distinguish between those where the random effects correspond to replicate experimental and sampling units and those that also include multiple observational units within each replicate. We also consider factorial mixed models and introduce hybrid designs that combine factorial and nested components. We describe the fitting of these models using traditional “ANOVA” approaches using OLS and present an alternative approach used in the following chapters – linear mixed models or multilevel models. These modeling approaches are illustrated for multilevel nested designs and factorial designs with and without replication.
The alvinocaridid shrimp Shinkaicaris leurokolos Kikuchi and Hashimoto, 2000, is an evolutionarily important deep-sea species in hydrothermal vents of north-western Pacific. A genome survey of S. leurokolos was carried out in order to provide a foundation for its whole-genome sequencing. A total of 599 Gb high-quality sequence data were obtained in the study, representing approximately 118× coverage of the S. leurokolos genome. According to the 17-mer distribution frequency, the estimated genome size was 5.08 Gb, and its heterozygosity ratio and percentage of repeated sequences were 2.85 and 87.03%, respectively, showing a complex genome. The final scaffold assembly accounted for a total size of 9.53 Gb (32,796,062 scaffolds, N50 = 597 bp). Repetitive elements nearly constituted 45% of the nuclear genome, among which the most ubiquitous were long interspersed nuclear elements, DNA transposons and long-terminal repeat elements. A total of 12,121,553 genomic simple sequence repeats were identified, with the most frequent repeat motif being di-nucleotide (70.27%), followed by tri-nucleotide and tetra-nucleotide. From the genome survey sequences, the mitochondrial genome of S. leurokolos was also constructed and 71 single nucleotide polymorphisms were identified by comparison with previous published reference. This is the first report of de novo whole-genome sequencing and assembly of S. leurokolos. These newly developed genomic data contribute to a better understanding of genomic characteristics of shrimps from deep-sea chemosynthetic ecosystems, and provides valuable resources for further molecular marker development.
Water is a vital resource essential for both sustaining life and a healthy environment as well as being a critical hazard in the form of floods or droughts which can destroy people’s livelihoods and property. This gives rise to a multi-faceted set of concerns and issues that affect everybody. For example, when contaminated with pathogens, wastewater can carry and rapidly transmit disease. The global distribution of freshwater is uneven and the problems this creates are likely to get worse due to climate change and the uncertainties associated with changing rainfall patterns and the emergence of more extreme weather events. Water has been described as the “new oil,” with potential conflicts arising out of disputed access to scarce water resources in the rest of this century. Billions of people around the world still do not have access to adequate safe water supplies or basic sanitation facilities, so in bringing basic water services to all there is much still to be done.
Despite holding the accolade as the largest animal ever to live on planet earth and ubiquitously inhabiting the world's major oceans, an acute paucity of information surrounds the geographical distribution and migration phenology of the endangered blue whale (Balaenoptera musculus) in the northeast Atlantic. Current migration and distribution information derived from robust scientific studies is required to ensure the formulation and implementation of successful conservation measures with a vision to support the ongoing recovery of the northeast Atlantic population. At 10:21 (UTC) on the 9th of November 2020, two blue whales were observed at position 55°13.99′N, 01°13.62′W, 18 km off the coast of the UK in the central North Sea just north of Newcastle at a water depth of 76 m. This is the first paper that has confirmed an account of live blue whales frequenting shallow waters of the central North Sea and represents a new area of occurrence within the accepted range of the northeast Atlantic population, an area in which sightings are extremely rare and may provide insight into the intricacies of migration routes and behaviour.
Applying statistical concepts to biological scenarios, this established textbook continues to be the go-to tool for advanced undergraduates and postgraduates studying biostatistics or experimental design in biology-related areas. Chapters cover linear models, common regression and ANOVA methods, mixed effects models, model selection, and multivariate methods used by biologists, requiring only introductory statistics and basic mathematics. Demystifying statistical concepts with clear, jargon-free explanations, this new edition takes a holistic approach to help students understand the relationship between statistics and experimental design. Each chapter contains further-reading recommendations, and worked examples from today's biological literature. All examples reflect modern settings, methodology and equipment, representing a wide range of biological research areas. These are supported by hands-on online resources including real-world data sets, full R code to help repeat analyses for all worked examples, and additional review questions and exercises for each chapter.
The tragic Andrée balloon expedition of 1897 serves as a haunting reminder of the dangers posed by ice drift during polar exploration. This paper examines Andrée’s initial decision after his balloon flight to march towards Cape Flora in Franz Josef Land, despite its much greater distance compared to the Sjuøyane archipelago. The rationale behind this choice remains unclear, but potential factors include stored supplies, the demonstrated winter survival in Franz Josef Land and the scientific interest in unexplored regions. By analysing historical accounts and employing scenario analyses, this study contributes to a better understanding of Andrée’s perception of ice drift and its impact on their ill-fated journey. The paper explores major forces affecting ice drift, reviews the historical development of understanding ice drift in the area, and presents an analysis of Andrée’s understanding and decision-making. The overall conclusion is that Andrée probably was unaware of the substantial deflection to the right of the direction of the wind that ice drift in the Arctic on average is characterised of due to the Earth’s rotation (the Coriolis effect). Without this deflection, the decision to march towards Cape Flora would have made sense under the assumption of continued northerly winds.
The frigid geographical environment in the Arctic has shaped the exploration attribute of the polar cruise shipping network. In this study, the typical characteristics and special structure of the Arctic adventure cruise shipping network are investigated by using the network analysis method based on the data of 172 adventure cruise itineraries in the Arctic. It is found that the Arctic adventure cruise itineraries are dominated by 8–17 days of medium itineraries, and the ratio of one-way itineraries to round-trip itineraries is about 1:1. There are differences in the centrality of different ports, forming two core ports Reykjavík and Longyearbyen and a sub-core port Kangerlussuaq. The overall contact strength of the Arctic adventure cruise shipping network is low. Under the joint influence of such factors as centrality and contact strength, the Arctic constitutes the dual-core clusters of Iceland and Svalbard Islands and a sub-core cluster of Greenland.
The Arctic region is commonly seen as a territory of international dialogue and cooperation. This perception is largely due to the science diplomacy efforts that are largely being contributed by universities, scientific centres, research teams and individual scholars. This paper discusses the Arctic science diplomacy initiatives proposed by Russia’s northernmost federal university. Of particular interest is the case of establishing in the Arctic Zone of the Russian Federation of national biological monitoring network – the initiative supported by the government-funded mega-grant programme. Our analysis suggests that two pillars of science diplomacy – “science for diplomacy” and “diplomacy for science” – can be successfully combined within the framework of one project. Evidence is provided of the pursuit of national interests being not a limiting factor but rather a driver in the process of promoting diplomatic collaborations in science, serving as a third science diplomacy pillar. Significant progress towards ensuring peace and harmony in the Arctic and sustaining international dialogue on science-based responses to global challenges has been achieved through science diplomacy initiatives proposed by Northern (Arctic) Federal University (NArFU). The authors confirm that most effective tools for establishing good neighbourly relations in the Arctic and promoting international cooperation are offered by scientific discussion.
The move towards unlimited financial penalties in the UK for sewerage systems that do not operate in line with their discharge permits (and the even more extreme suggestion that there should be a financial penalty every time an overflow spills) sets a challenge to whether our existing sewerage models are accurate enough to provide certainty of avoiding those penalties. This article sets out proposed improved practice in the preparation of urban drainage models to improve their accuracy and usefulness and identifies areas where research, particularly into machine learning techniques, could deliver further improvements.