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Dispersion describes the spread of the data or how it varies from its mean.The chapter begins with the calculation of the variance and then the more important standard deviation, along with their interpretation.Students learn how to calculate these measures by hand and in the R Commander.Other measures of dispersion like skewness and kurtosis are described.The range and interquartile range are also calculated using the R Commander software for ordinal variables.
Paleoecological studies can provide some insight into factors influencing a species’ present-day distribution, and its present-day distribution can, in turn, provide some insight into its future distribution. Being able to predict future distributions is very important because climate, an important influence on species distribution, is now changing at a rapid rate. Within a population, individuals may have a random, uniform, or clumped dispersion, though a clumped dispersion is most common because essential resources such as food, light, and undisturbed habitat are often spatially clumped. Distribution patterns change over the short term, as a result of dispersal, and over the long term from factors that influence range expansion and contraction. Abiotic factors, such as climate, soils, light availability and disturbance, and biotic factors, such as behavior, life histories and interactions with other species, can influence the distribution of species. Changes in these factors can lead to changes in distribution, including range expansion, range contraction and extinction. By quantitatively describing a species’ ecological niche, ecologists can understand a species’ present distribution, and may be able to make predictions about its future distribution.
This chapter explores the voice as a complex, expressive instrument. It begins by outlining voice types, techniques, and styles – ranging from opera to musical theatre and popular music – before looking at the relationship between language and music, and finally exploring the nature of idiomatic vocal writing and so-called extended techniques. The chapter finishes with a nod to the future of vocal music by briefly thinking about the voice in conjunction with electronics.
An important operation in signal processing and machine learning is dimensionality reduction. There are many such methods, but the starting point is usually linear methods that map data to a lower-dimensional set called a subspace. When working with matrices, the notion of dimension is quantified by rank. This chapter reviews subspaces, span, dimension, rank, and nullspace. These linear algebra concepts are crucial to thoroughly understanding the SVD, a primary tool for the rest of the book (and beyond). The chapter concludes with a machine learning application, signal classification by nearest subspace, that builds on all the concepts of the chapter.
Grey seals from both the Atlantic and Baltic Sea subspecies are recovering from dramatic declines and recolonising former ranges, potentially leading to overlapping distributions and an emerging subspecies transition zone in Kattegat between Denmark and Sweden. The two subspecies have asynchronous moulting and pupping seasons. We present aerial survey data from 2011 to 2023 in Danish Kattegat during the Atlantic subspecies' moulting (March–April) and pupping (December–January) seasons, as well as the Baltic subspecies' moulting season (May–June). During the Atlantic subspecies' peak moulting season, 82% of the grey seals were recorded north of the island of Læsø (N57°18′, E11°00′). In contrast, during the Baltic moulting season in those years, only 9% of the grey seals were recorded here. This indicates a predominance of Atlantic grey seals in the north and Baltic grey seals in central and southern Kattegat. In 2022 and 2023, three pups were recorded around Læsø during early January, which coincides with the pupping season of northern Wadden Sea grey seals. Previously, pups have been recorded in the same locations during the Baltic pupping season, which demonstrates overlapping breeding ranges. Grey seals are known to have plasticity in the timing of pupping indicated by a west to east cline of progressively later pupping in the eastern North Atlantic. Historical sources document that the Baltic pupping season in Kattegat was earlier than it has been in recent years. Thus, the expanding ranges may be associated with convergence of Atlantic and Baltic subspecies' pupping seasons and potential hybridisation in this emerging transition zone.
Chapter 3 covers MEASURES OF LOCATION, SPREAD, AND SKEWNESS and includes the following specific topics, among others:Mode, Median, Mean, Weighted Mean,Range, Interquartile Range, Variance, Standard Deviation, and Skewness.
Chapter 3 covers measures of location, spread and skewness and includes the following specific topics, among others: mode, median, mean, weighted mean, range, interquartile range, variance, standard deviation, and skewness.
The outdoor range in free-range, egg-production systems contains features that aim to promote the performance of natural behaviours. It is unclear what features of the range laying hens prefer and how these influence hen behaviour. We hypothesised that hens would demonstrate a preference for features of the environment in which their ancestor evolved, such as relatively dense vegetation, within the outdoor range and that the behavioural time budget of hens will differ between distinct environments. Characteristics of the outdoor range in one free-range commercial egg farm were mapped and four distinct environments (‘locations’) were identified based on ground substrate and cover (Wattle Tree, Gum Tree, Bare Earth and Sapling). The number of hens accessing each location and behavioural time budget of these hens was recorded over a three-week period during the southern hemisphere summer (January-February). Hens showed a clear preference for the Wattle Tree and Gum Tree locations; however, a significant interaction between location and time of day suggested that the hens’ preference for different locations changed throughout the day. The most common behaviours displayed by hens were foraging, preening, locomotion, resting and vigilance, and most behaviours were influenced by the interaction between location and time of day. Overall, a wider variety of behaviours were performed in the highly preferred environments, but not all behaviours were performed equally within each environment throughout the day. Understanding what features hens prefer in the outdoor range and how this influences the performance of natural behaviours is important in promoting the welfare of hens in free-range production.
This chapter completes our critical exploration of Popper’s key work, the Logic of Scientific Discovery and how it applies to corpus linguistics. In this chapter we address the question of how easily linguistics may be viewed as a science, in Popper’s terms. We also consider important critiques of Popper’s work and use those to both clarify and, where necessary, adapt the framework.
This chapter looks at what vocabulary and how much vocabulary needs to be learned. It is useful to use frequency and range of occurrence to distinguish several levels of vocabulary. Distinguishing these levels helps ensure that learners learn vocabulary in the most useful sequence and thus gain the most benefit from the vocabulary they learn. Making the high-frequency/mid-frequency/low-frequency distinctions ensures that the teacher and learners deal with vocabulary in the most efficient ways. High-frequency words are the most useful words of the language and should be learned first. There are 3,000 high-frequency words. These should be followed by mid-frequency words or specialised vocabulary. The mid-frequency and low-frequency words should not be taught but should be learned through extensive listening and extensive reading, along with the use of vocabulary learning strategies such as flash cards, word part analysis. and dictionary use.
When learners have mastered the 2,000–3,000 high frequency words of general usefulness in English, it is often efficient to direct vocabulary learning to more specialised areas depending on the aims of the learners. It is possible to specialise by learning the shared vocabulary of several fields of study, for example, academic vocabulary, or the vocabulary of the hard sciences or soft sciences. It is also possible to specialise by focusing on the specialised vocabulary of one particular field or part of that field, that is, technical vocabulary. There are several lists of academic vocabulary including the Academic Word List, the Academic Vocabulary List, the Academic Spoken Word List, the Hard Science Spoken Word, List and the Soft Science Spoken Word List. Technical word lists usually consist of one or two thousand words, but some specialist areas like medicine, botany, or zoology have very large technical vocabularies. The chapter looks at how academic and technical vocabulary can be learned. It also looks at the various roles that vocabulary plays in texts.
This chapter discusses two types of descriptive statistics: models of central tendency and models of variability. Models of central tendency describe the location of the middle of the distribution, and models of variability describe the degree that scores are spread out from one another. There are four models of central tendency in this chapter. Listed in ascending order of the complexity of their calculations, these are the mode, median, mean, and trimmed mean. There are also four principal models of variability discussed in this chapter: the range, interquartile range, standard deviation, and variance. For the latter two statistics, students are shown three possible formulas (sample standard deviation and variance, population standard deviation and variance, and population standard deviation and variance estimated from sample data), along with an explanation of when it is appropriate to use each formula. No statistical model of central tendency or variability tells you everything you may need to know about your data. Only by using multiple models in conjunction with each other can you have a thorough understanding of your data.
The coast of Aragua is a home of bottlenose dolphins (BND), Atlantic spotted dolphins (ASD) and fishermen (FIS) from four towns. A photo-identification study was carried out on BND to estimate their home ranges. From 2004 to 2008, 100 field surveys were carried out along 30 km of coastline (92.12 km2). In each sighting of BND, information regarding date, time, latitude/longitude and photographs were registered (ASD and FIS were registered without photography). The data were analysed using a Geographic Information System to estimate Minimum Convex Polygon (MCP) and Fixed Kernel (FK) at 95%. The home ranges of BND were estimated for seven individuals. This included three females (29–31 sightings) with estimated areas ranging from 33.90–39.90 km2 with MCP (36.79–43.31% of the study area) and from 80.47–101.31 km2 with FK (109.97–104.26%). For the remaining four dolphins (14–20 sightings) the estimated areas ranged from 9.67–22.34 km2 (MCP), the predominant depth of these home ranges varied from 51–100 m (χ2 = 24.5, df = 2, P = 4.785 × 10−6). For the pods of ASD the estimated area ranged 75.23 km2 with MCP (81.66%) and 119.86 km2 with FK (130.11%) with predominant depths of 101–200 m (χ2 = 24.5, df = 2, P = 4.785 × 10−6). The area used by FIS ranged 93.27 km2 by MCP and 228.49 km2 by FK. Finally, the overlap area of BND, ASD and FIS ranged 24.75 km2 (26.86%). We point out this locality presents important oceanographic and ecological aspects which deserve to be the subject of application of management plans for the conservation of its habitat and species.
We consider linear maps between normed spaces. We define what it means for a linear map to be bounded and show that this is equivalent to continuity. We define the norm of a linear operator and show that the space of all linear maps from X to Y is a vector space, which is complete if Y is complete. We give a number of examples and then discuss inverses and invertibility in some detail.
Downy brome (Bromus tectorum L., syn. cheatgrass) is a winter annual grass that invades North American cropping, forage, and rangeland systems. Control is often difficult to achieve, because B. tectorum has a large seedbank, which results in continuous propagule pressure. Pyrenophora semeniperda (Brittlebank and Adam) Shoemaker, a soilborne fungal pathogen, has been investigated as a biological control for B. tectorum, because it can kill seeds that remain in the seedbank, thereby reducing propagule pressure. Temperature influences P. semeniperda and has not been investigated in the context of seeds collected from different B. tectorum locations, that may vary in susceptibility to infection. We compared the effects of temperature (13, 17, 21, 25 C) and B. tectorum seed locations (range, crop, subalpine) with different mean seed weights on infection rates of P. semeniperda using a temperature-gradient table. Infection differed by seed location (P < 0.001) and temperature (P < 0.001), with lighter-weight seeds (i.e., range and subalpine) more susceptible to P. semeniperda infection. Infection increased as temperature increased and was higher at 21 C (66.7 ± 6.7%) and 25 C (73.3 ± 6.0%). Germination was affected by seed location (P < 0.001) and temperature (P = 0.019). Germination was highest for the crop seed location (45.4 ± 4.2%) and overall decreased at higher temperatures (21 and 25 C). Our results suggest that B. tectorum seeds from a crop location are less affected by P. semeniperda than those from range and subalpine locations. Moreover, this demonstrates a temperature-dependent effect on all populations.
Iteration allows code to be repeated and this chapter shows the reader how to create count-controlled loops (using for loops) that implement the range expression. They complete ten challenges ensuring they are familiar with using iteration in their coding.
Drawing shapes and patterns with the Python turtle allows readers to practise using loops and helps them learn computational thinking skills where they have to spot repeating patterns. The nine challenges allow them to put these skills into practice.
Many seed quality tests are conducted by first randomly assigning seeds into replicates of a given size. The replicate results are then used to check whether or not any problems occur in the realization of the test. The two main tools developed for this verification are the ratio of the observed variance of the replicate results to a theoretical variance and the tolerance for the range of the results. In this paper, we derive the theoretical distribution and its related properties of the sequence of numbers of seeds with a given quality attribute present in the replicates. From these theoretical results, we revisit the two quality checking tools widely used for the germination test. We show a precaution to be taken when relying on the variance ratio to check for under- or over-dispersion of the replicate results. This has led to the development of tables providing credible intervals of the variance ratio. The International Seed Testing Association tolerance tables for the range of the results are also compared with tolerances computed from the exact theoretical distribution of the range, leading us to recommend a revision of these tables.
Weed maps are typically produced from data sampled at discrete intervals on a regular grid. Errors are expected to occur as data are sampled at increasingly coarse scales. To demonstrate the potential effect of sampling strategy on the quality of weed maps, we analyzed a data set comprising the counts of capeweed in 225,000 quadrats completely covering a 0.9-ha area. The data were subsampled at different grid spacings, quadrat sizes, and starting points and were then used to produce maps by kriging. Spacings of 10 m were found to overestimate the geostatistical range by 100% and missed details apparently resulting from the spraying equipment. Some evidence was found supporting the rule of thumb that surveys should be conducted at a spacing of about half the scale of interest. Quadrat size had less effect than spacing on the map quality. At wider spacings the starting position of the sample grid had a considerable effect on the qualities of the maps but not on the estimated geostatistical range. Continued use of arbitrary survey designs is likely to miss the information of interest to biologists and may possibly produce maps inappropriate to spray application technology.
We provide asymptotics for the range $R_{n}$ of a random walk on the $d$-dimensional lattice indexed by a random tree with $n$ vertices. Using Kingman’s subadditive ergodic theorem, we prove under general assumptions that $n^{-1}R_{n}$ converges to a constant, and we give conditions ensuring that the limiting constant is strictly positive. On the other hand, in dimension $4$, and in the case of a symmetric random walk with exponential moments, we prove that $R_{n}$ grows like $n/\!\log n$. We apply our results to asymptotics for the range of a branching random walk when the initial size of the population tends to infinity.