4.1: Paths through This Book
2
With a digital/online text, it is even easier than with a print book to do what professors regularly do with textbooks—namely, mix up the order in which students are expected to read chapters/sections. In fact, although the book is structured in three main parts, that is not the order the author asks students to read materials in. It makes sense to jump from Bach as composer to the theme of Passions, for instance. But at several points, chapters earlier in the book offer you a chance to jump to the chapter about a specific composer who created a work that is an example of what that chapter is discussing. There is no need to follow a linear path through the book, whether you are reading it for your own interest or using it as a textbook in a course.
In this appendix you will find the author’s own outline in case it provides a convenient structure for a course that you will use it in as a textbook. If this order doesn’t work for you, try a different one, and if it works well for you and your students, please tell the author, as he may want to adopt your organization for his course as well!
Provisional Topic and Meeting Outline (Based on a Schedule of Two Meetings per Week)
First Meeting
Introduction to the class: What is music? What is the Bible? Reading: Introduction
Clarifying the syllabus: Class meetings, activities, grading, earning points
Week 1
Topic 1: Music behind and in the Bible. Reading: 1. Ancient Music Behind and in the Bible
Topic 2: Chanting Scripture in the temple, synagogues, and churches. Reading: 2. Chanting in Synagogues ; 3. Chanting in Churches
Week 2
Topic 1: Impact of the Protestant Reformation; metrical psalms. Reading: 4. The Protestant Reformation and Metrical Psalms
Topic 2: More on translation, paraphrase, retelling, and meaning
Week 3 : Creation in Music and Creativity
Topic 1: Creation: Haydn to Copland and Beyond. Reading: 7. Creation
Topic 2: Creation in Genesis and musical creation continued. Reading: Appendix 2: Making Music with Apps, Websites, and Software
Week 4 : Combining Texts
Topic 1: Handel as entrepreneur and biblical Stories as entertainment. Reading: 27. The Bible as Musical, Oratorio, and Opera
Topic 2: Bringing texts together: Messiah , requiems, and more. Reading: 28. Handel’s Messiah
Week 5 : The Story of Jesus in Music and Film
Topic 1: Bach as theologian. Reading: 25. Johann Sebastian Bach
Topic 2: Passions: From Bach to Mel Gibson and beyond. Reading: 26. Passions: Bach and Beyond
Week 6
Topic 1: Saul, David, and Bathsheba. Reading: 11. King David (and His Family, Friends, and Enemies)
Topic 2: Music as Prayer? Reading: 8. Psalms ; 18. Our Father
Week 7
No class meeting: Projects / spring or fall break
Week 8
Topic 1: Children’s songs (student show and tell)
Topic 2: Children’s songs (continued)
Week 9 Moses and the Exodus
Topic 1: Spirituals and slavery. Reading: 5. Spirituals ; 10. Exodus
Topic 2: Schoenberg and liberation from tonality. Reading: 30. Arnold Schoenberg
Week 10
Topic 1: Magnificat and Nunc Dimittis: Setting the same text more than once. Reading: 17. Magnificat and Nunc Dimittis
Topic 2: Romance in the Bible? Ruth, Song of Songs, Delilah, and Esther. Reading: 14. Song of Songs ; 13. Romance in the Bible? Ruth and Boaz, Samson and Delilah ; 16. Salome
Week 11
Topic 1: Secular biblical music and “holy minimalism” Reading: 31. John Rutter ; 33. Arvo Pärt
Topic 2: Popular music. Reading: 20. Alleluias and Allusions ; 9. Isaac and Family
Week 12 : Scavenger Hunt and Allusions
Topic: Students earn one point per example of a pop (not “classical” or “worship”) song with the relevant biblical reference, plus one additional point for explanation of meaning.
Week 13 : Work on Final Projects
Topic: If time permits, include reading: 21. Biblical Music without Words
Week 14 : Student Presentation of Final Projects


1.34: Direct space
The direct space (or crystal space ) is the point space , E n , in which the structures of finite real crystals are idealized as infinite perfect three-dimensional structures. To this space one associates the vector space , V n , of which lattice and translation vectors are elements. It is a Euclidean space where the scalar product of two vectors is defined. The two spaces are connected through the following relations:
(i) To any two points P and Q of the point space E n a vector PQ = r of the vector space V n is attached
(ii) For each point P of E n and for each vector r of V n there is exactly one point Q of E n for which PQ = r holds
(iii) If R is a third point of the point space, PQ + QR = PR


47.1: The Biodiversity Crisis
Skills to Develop
- Define biodiversity
- Describe biodiversity as the equilibrium of naturally fluctuating rates of extinction and speciation
- Identify historical causes of high extinction rates in Earth’s history
Traditionally, ecologists have measured biodiversity , a general term for the variety present in the biosphere, by taking into account both the number of species and their commonness. Biodiversity can be estimated at a number of levels of organization of living things. These estimation indexes, which came from information theory, are most useful as a first step in quantifying biodiversity between and within ecosystems; they are less useful when the main concern among conservation biologists is simply the loss of biodiversity. However, biologists recognize that measures of biodiversity, in terms of species diversity, may help focus efforts to preserve the biologically or technologically important elements of biodiversity.
The Lake Victoria cichlids provide an example through which we can begin to understand biodiversity. The biologists studying cichlids in the 1980s discovered hundreds of cichlid species representing a variety of specializations to particular habitat types and specific feeding strategies: eating plankton floating in the water, scraping and then eating algae from rocks, eating insect larvae from the bottom, and eating the eggs of other species of cichlid. The cichlids of Lake Victoria are the product of an adaptive radiation . An adaptive radiation is a rapid (less than three million years in the case of the Lake Victoria cichlids) branching through speciation of a phylogenetic tree into many closely related species; typically, the species “radiate” into different habitats and niches. The Galápagos finches are an example of a modest adaptive radiation with 15 species. The cichlids of Lake Victoria are an example of a spectacular adaptive radiation that includes about 500 species.
At the time biologists were making this discovery, some species began to quickly disappear. A culprit in these declines was a species of large fish that was introduced to Lake Victoria by fisheries to feed the people living around the lake. The Nile perch was introduced in 1963, but lay low until the 1980s when its populations began to surge. The Nile perch population grew by consuming cichlids, driving species after species to the point of extinction (the disappearance of a species). In fact, there were several factors that played a role in the extinction of perhaps 200 cichlid species in Lake Victoria: the Nile perch, declining lake water quality due to agriculture and land clearing on the shores of Lake Victoria, and increased fishing pressure. Scientists had not even catalogued all of the species present—so many were lost that were never named. The diversity is now a shadow of what it once was.
The cichlids of Lake Victoria are a thumbnail sketch of contemporary rapid species loss that occurs all over Earth and is caused by human activity. Extinction is a natural process of macroevolution that occurs at the rate of about one out of 1 million species becoming extinct per year. The fossil record reveals that there have been five periods of mass extinction in history with much higher rates of species loss, and the rate of species loss today is comparable to those periods of mass extinction. However, there is a major difference between the previous mass extinctions and the current extinction we are experiencing: human activity. Specifically, three human activities have a major impact: destruction of habitat, introduction of exotic species, and over-harvesting. Predictions of species loss within the next century, a tiny amount of time on geological timescales, range from 10 percent to 50 percent. Extinctions on this scale have only happened five other times in the history of the planet, and they have been caused by cataclysmic events that changed the course of the history of life in each instance. Earth is now in one of those times.
Types of Biodiversity
Scientists generally accept that the term biodiversity describes the number and kinds of species in a location or on the planet. Species can be difficult to define, but most biologists still feel comfortable with the concept and are able to identify and count eukaryotic species in most contexts. Biologists have also identified alternate measures of biodiversity, some of which are important for planning how to preserve biodiversity.
Genetic diversity is one of those alternate concepts. Genetic diversity or variation is the raw material for adaptation in a species. A species’ future potential for adaptation depends on the genetic diversity held in the genomes of the individuals in populations that make up the species. The same is true for higher taxonomic categories. A genus with very different types of species will have more genetic diversity than a genus with species that look alike and have similar ecologies. If there were a choice between one of these genera of species being preserved, the one with the greatest potential for subsequent evolution is the most genetically diverse one. It would be ideal not to have to make such choices, but increasingly this may be the norm.
Many genes code for proteins, which in turn carry out the metabolic processes that keep organisms alive and reproducing. Genetic diversity can be measured as chemical diversity in that different species produce a variety of chemicals in their cells, both the proteins as well as the products and byproducts of metabolism. This chemical diversity has potential benefit for humans as a source of pharmaceuticals, so it provides one way to measure diversity that is important to human health and welfare.
Humans have generated diversity in domestic animals, plants, and fungi. This diversity is also suffering losses because of migration, market forces, and increasing globalism in agriculture, especially in heavily populated regions such as China, India, and Japan. The human population directly depends on this diversity as a stable food source, and its decline is troubling biologists and agricultural scientists.
It is also useful to define ecosystem diversity , meaning the number of different ecosystems on the planet or in a given geographic area (Figure \(\PageIndex{1}\)). Whole ecosystems can disappear even if some of the species might survive by adapting to other ecosystems. The loss of an ecosystem means the loss of interactions between species, the loss of unique features of coadaptation, and the loss of biological productivity that an ecosystem is able to create. An example of a largely extinct ecosystem in North America is the prairie ecosystem. Prairies once spanned central North America from the boreal forest in northern Canada down into Mexico. They are now all but gone, replaced by crop fields, pasture lands, and suburban sprawl. Many of the species survive, but the hugely productive ecosystem that was responsible for creating the most productive agricultural soils is now gone. As a consequence, soils are disappearing or must be maintained at greater expense.
Current Species Diversity
Despite considerable effort, knowledge of the species that inhabit the planet is limited. A recent estimate suggests that the eukaryote species for which science has names, about 1.5 million species, account for less than 20 percent of the total number of eukaryote species present on the planet (8.7 million species, by one estimate). Estimates of numbers of prokaryotic species are largely guesses, but biologists agree that science has only begun to catalog their diversity. Even with what is known, there is no central repository of names or samples of the described species; therefore, there is no way to be sure that the 1.5 million descriptions is an accurate number. It is a best guess based on the opinions of experts in different taxonomic groups. Given that Earth is losing species at an accelerating pace, science is very much in the place it was with the Lake Victoria cichlids: knowing little about what is being lost. Table \(\PageIndex{1}\) presents recent estimates of biodiversity in different groups.
Table \(\PageIndex{1}\): Estimates of the described and predicted species by Taxonomic group
| Mora et al. 2011 1 | Chapman 2009 2 | Groombridge & Jenkins 2002 3 | ||||
|---|---|---|---|---|---|---|
| Described | Predicted | Described | Predicted | Described | Predicted | |
| Animalia | 1,124,516 | 9,920,000 | 1,424,153 | 6,836,330 | 1,225,500 | 10,820,000 |
| Chromista | 17,892 | 34,900 | 25,044 | 200,500 | — | — |
| Fungi | 44,368 | 616,320 | 98,998 | 1,500,000 | 72,000 | 1,500,000 |
| Plantae | 224,244 | 314,600 | 310,129 | 390,800 | 270,000 | 320,000 |
| Protozoa | 16,236 | 72,800 | 28,871 | 1,000,000 | 80,000 | 600,000 |
| Prokaryotes | — | — | 10,307 | 1,000,000 | 10,175 | — |
| Total | 1,438,769 | 10,960,000 | 1,897,502 | 10,897,630 | 1,657,675 | 13,240,000 |
There are various initiatives to catalog described species in accessible ways, and the internet is facilitating that effort. Nevertheless, it has been pointed out that at the current rate of species description, which according to the State of Observed Species Report is 17,000 to 20,000 new species per year, it will take close to 500 years to finish describing life on this planet. 4 Over time, the task becomes both increasingly impossible and increasingly easier as extinction removes species from the planet.
Naming and counting species may seem an unimportant pursuit given the other needs of humanity, but it is not simply an accounting. Describing species is a complex process by which biologists determine an organism’s unique characteristics and whether or not that organism belongs to any other described species. It allows biologists to find and recognize the species after the initial discovery, and allows them to follow up on questions about its biology. In addition, the unique characteristics of each species make it potentially valuable to humans or other species on which humans depend. Understanding these characteristics is the value of finding and naming species.
Patterns of Biodiversity
Biodiversity is not evenly distributed on Earth. Lake Victoria contained almost 500 species of cichlids alone, ignoring the other fish families present in the lake. All of these species were found only in Lake Victoria; therefore, the 500 species of cichlids were endemic. Endemic species are found in only one location. Endemics with highly restricted distributions are particularly vulnerable to extinction. Higher taxonomic levels, such as genera and families, can also be endemic. Lake Huron contains about 79 species of fish, all of which are found in many other lakes in North America. What accounts for the difference in fish diversity in these two lakes? Lake Victoria is a tropical lake, while Lake Huron is a temperate lake. Lake Huron in its present form is only about 7,000 years old, while Lake Victoria in its present form is about 15,000 years old. Biogeographers have suggested these two factors, latitude and age, are two of several hypotheses to explain biodiversity patterns on the planet.
Career Connection: Biogeographer
Biogeography is the study of the distribution of the world’s species—both in the past and in the present. The work of biogeographers is critical to understanding our physical environment, how the environment affects species, and how environmental changes impact the distribution of a species; it has also been critical to developing evolutionary theory. Biogeographers need to understand both biology and ecology. They also need to be well-versed in evolutionary studies, soil science, and climatology.
There are three main fields of study under the heading of biogeography: ecological biogeography, historical biogeography (called paleobiogeography), and conservation biogeography. Ecological biogeography studies the current factors affecting the distribution of plants and animals. Historical biogeography, as the name implies, studies the past distribution of species. Conservation biogeography, on the other hand, is focused on the protection and restoration of species based upon known historical and current ecological information. Each of these fields considers both zoogeography and phytogeography—the past and present distribution of animals and plants.
One of the oldest observed patterns in ecology is that species biodiversity in almost every taxonomic group increases as latitude declines. In other words, biodiversity increases closer to the equator (Figure \(\PageIndex{2}\)).
It is not yet clear why biodiversity increases closer to the equator, but hypotheses include the greater age of the ecosystems in the tropics versus temperate regions that were largely devoid of life or drastically impoverished during the last glaciation. The idea is that greater age provides more time for speciation. Another possible explanation is the increased energy the tropics receive from the sun versus the decreased energy that temperate and polar regions receive. It is not entirely clear how greater energy input could translate into more species. The complexity of tropical ecosystems may promote speciation by increasing the heterogeneity , or number of ecological niches, in the tropics relative to higher latitudes. The greater heterogeneity provides more opportunities for coevolution, specialization, and perhaps greater selection pressures leading to population differentiation. However, this hypothesis suffers from some circularity—ecosystems with more species encourage speciation, but how did they get more species to begin with? The tropics have been perceived as being more stable than temperate regions, which have a pronounced climate and day-length seasonality. The tropics have their own forms of seasonality, such as rainfall, but they are generally assumed to be more stable environments and this stability might promote speciation.
Regardless of the mechanisms, it is certainly true that all levels of biodiversity are greatest in the tropics. Additionally, the rate of endemism is highest, and there are more biodiversity hotspots. However, this richness of diversity also means that knowledge of species is lowest, and there is a high potential for biodiversity loss.
Conservation of Biodiversity
In 1988, British environmentalist Norman Myers developed a conservation concept to identify areas rich in species and at significant risk for species loss: biodiversity hotspots. Biodiversity hotspots are geographical areas that contain high numbers of endemic species. The purpose of the concept was to identify important locations on the planet for conservation efforts, a kind of conservation triage. By protecting hotspots, governments are able to protect a larger number of species. The original criteria for a hotspot included the presence of 1500 or more endemic plant species and 70 percent of the area disturbed by human activity. There are now 34 biodiversity hotspots (Figure \(\PageIndex{3}\)) containing large numbers of endemic species, which include half of Earth’s endemic plants.
Biodiversity Change through Geological Time
The number of species on the planet, or in any geographical area, is the result of an equilibrium of two evolutionary processes that are ongoing: speciation and extinction. Both are natural “birth” and “death” processes of macroevolution. When speciation rates begin to outstrip extinction rates, the number of species will increase; likewise, the number of species will decrease when extinction rates begin to overtake speciation rates. Throughout Earth’s history, these two processes have fluctuated—sometimes leading to dramatic changes in the number of species on Earth as reflected in the fossil record (Figure \(\PageIndex{4}\)).
Paleontologists have identified five strata in the fossil record that appear to show sudden and dramatic (greater than half of all extant species disappearing from the fossil record) losses in biodiversity. These are called mass extinctions. There are many lesser, yet still dramatic, extinction events, but the five mass extinctions have attracted the most research. An argument can be made that the five mass extinctions are only the five most extreme events in a continuous series of large extinction events throughout the Phanerozoic (since 542 million years ago). In most cases, the hypothesized causes are still controversial; however, the most recent event seems clear.
The Five Mass Extinctions
The fossil record of the mass extinctions was the basis for defining periods of geological history, so they typically occur at the transition point between geological periods. The transition in fossils from one period to another reflects the dramatic loss of species and the gradual origin of new species. These transitions can be seen in the rock strata. Table \(\PageIndex{2}\) provides data on the five mass extinctions.
| Geological Period | Mass Extinction Name | Time (millions of years ago) |
|---|---|---|
| Ordovician–Silurian | end-Ordovician O–S | 450–440 |
| Late Devonian | end-Devonian | 375–360 |
| Permian–Triassic | end-Permian | 251 |
| Triassic–Jurassic | end-Triassic | 205 |
| Cretaceous–Paleogene | end-Cretaceous K–Pg (K–T) | 65.5 |
The Ordovician-Silurian extinction event is the first recorded mass extinction and the second largest. During this period, about 85 percent of marine species (few species lived outside the oceans) became extinct. The main hypothesis for its cause is a period of glaciation and then warming. The extinction event actually consists of two extinction events separated by about 1 million years. The first event was caused by cooling, and the second event was due to the subsequent warming. The climate changes affected temperatures and sea levels. Some researchers have suggested that a gamma-ray burst, caused by a nearby supernova, is a possible cause of the Ordovician-Silurian extinction. The gamma-ray burst would have stripped away the Earth’s ozone layer causing intense ultraviolet radiation from the sun and may account for climate changes observed at the time. The hypothesis is speculative, but extraterrestrial influences on Earth’s history are an active line of research. Recovery of biodiversity after the mass extinction took from 5 to 20 million years, depending on the location.
The late Devonian extinction may have occurred over a relatively long period of time. It appears to have affected marine species and not the plants or animals inhabiting terrestrial habitats. The causes of this extinction are poorly understood.
The end-Permian extinction was the largest in the history of life. Indeed, an argument could be made that Earth nearly became devoid of life during this extinction event. The planet looked very different before and after this event. Estimates are that 96 percent of all marine species and 70 percent of all terrestrial species were lost. It was at this time, for example, that the trilobites, a group that survived the Ordovician–Silurian extinction, became extinct. The causes for this mass extinction are not clear, but the leading suspect is extended and widespread volcanic activity that led to a runaway global-warming event. The oceans became largely anoxic, suffocating marine life. Terrestrial tetrapod diversity took 30 million years to recover after the end-Permian extinction. The Permian extinction dramatically altered Earth’s biodiversity makeup and the course of evolution.
The causes of the Triassic–Jurassic extinction event are not clear and hypotheses of climate change, asteroid impact, and volcanic eruptions have been argued. The extinction event occurred just before the breakup of the supercontinent Pangaea, although recent scholarship suggests that the extinctions may have occurred more gradually throughout the Triassic.
The causes of the end-Cretaceous extinction event are the ones that are best understood. It was during this extinction event about 65 million years ago that the dinosaurs, the dominant vertebrate group for millions of years, disappeared from the planet (with the exception of a theropod clade that gave rise to birds). Indeed, every land animal that weighed more then 25 kg became extinct. The cause of this extinction is now understood to be the result of a cataclysmic impact of a large meteorite, or asteroid, off the coast of what is now the Yucatán Peninsula. This hypothesis, proposed first in 1980, was a radical explanation based on a sharp spike in the levels of iridium (which rains down from space in meteors at a fairly constant rate but is otherwise absent on Earth’s surface) at the rock stratum that marks the boundary between the Cretaceous and Paleogene periods (Figure \(\PageIndex{5}\)). This boundary marked the disappearance of the dinosaurs in fossils as well as many other taxa. The researchers who discovered the iridium spike interpreted it as a rapid influx of iridium from space to the atmosphere (in the form of a large asteroid) rather than a slowing in the deposition of sediments during that period. It was a radical explanation, but the report of an appropriately aged and sized impact crater in 1991 made the hypothesis more believable. Now an abundance of geological evidence supports the theory. Recovery times for biodiversity after the end-Cretaceous extinction are shorter, in geological time, than for the end-Permian extinction, on the order of 10 million years.
Art Connection
Scientists measured the relative abundance of fern spores above and below the K–Pg boundary in this rock sample. Which of the following statements most likely represents their findings?
- An abundance of fern spores from several species was found below the K–Pg boundary, but none was found above.
- An abundance of fern spores from several species was found above the K–Pg boundary, but none was found below.
- An abundance of fern spores was found both above and below the K–Pg boundary, but only one species was found below the boundary, and many species were found above the boundary.
- Many species of fern spores were found both above and below the boundary, but the total number of spores was greater below the boundary.
The Pleistocene Extinction
The Pleistocene Extinction is one of the lesser extinctions, and a recent one. It is well known that the North American, and to some degree Eurasian, megafauna , or large animals, disappeared toward the end of the last glaciation period. The extinction appears to have happened in a relatively restricted time period of 10,000–12,000 years ago. In North America, the losses were quite dramatic and included the woolly mammoths (last dated about 4,000 years ago in an isolated population), mastodon, giant beavers, giant ground sloths, saber-toothed cats, and the North American camel, just to name a few. The possibility that the rapid extinction of these large animals was caused by over-hunting was first suggested in the 1900s. Research into this hypothesis continues today. It seems likely that over-hunting caused many pre-written history extinctions in many regions of the world.
In general, the timing of the Pleistocene extinctions correlated with the arrival of humans and not with climate-change events, which is the main competing hypothesis for these extinctions. The extinctions began in Australia about 40,000 to 50,000 years ago, just after the arrival of humans in the area: a marsupial lion, a giant one-ton wombat, and several giant kangaroo species disappeared. In North America, the extinctions of almost all of the large mammals occurred 10,000–12,000 years ago. All that are left are the smaller mammals such as bears, elk, moose, and cougars. Finally, on many remote oceanic islands, the extinctions of many species occurred coincident with human arrivals. Not all of the islands had large animals, but when there were large animals, they were lost. Madagascar was colonized about 2,000 years ago and the large mammals that lived there became extinct. Eurasia and Africa do not show this pattern, but they also did not experience a recent arrival of humans. Humans arrived in Eurasia hundreds of thousands of years ago after the origin of the species in Africa. This topic remains an area of active research and hypothesizing. It seems clear that even if climate played a role, in most cases human hunting precipitated the extinctions.
Present-Time Extinctions
The sixth, or Holocene, mass extinction appears to have begun earlier than previously believed and has mostly to do with the activities of Homo sapiens . Since the beginning of the Holocene period, there are numerous recent extinctions of individual species that are recorded in human writings. Most of these are coincident with the expansion of the European colonies since the 1500s.
One of the earlier and popularly known examples is the dodo bird. The dodo bird lived in the forests of Mauritius, an island in the Indian Ocean. The dodo bird became extinct around 1662. It was hunted for its meat by sailors and was easy prey because the dodo, which did not evolve with humans, would approach people without fear. Introduced pigs, rats, and dogs brought to the island by European ships also killed dodo young and eggs.
Steller's sea cow became extinct in 1768; it was related to the manatee and probably once lived along the northwest coast of North America. Steller's sea cow was first discovered by Europeans in 1741 and was hunted for meat and oil. The last sea cow was killed in 1768. That amounts to 27 years between the sea cow’s first contact with Europeans and extinction of the species.
In 1914, the last living passenger pigeon died in a zoo in Cincinnati, Ohio. This species had once darkened the skies of North America during its migrations, but it was hunted and suffered from habitat loss through the clearing of forests for farmland. In 1918, the last living Carolina parakeet died in captivity. This species was once common in the eastern United States, but it suffered from habitat loss. The species was also hunted because it ate orchard fruit when its native foods were destroyed to make way for farmland. The Japanese sea lion, which inhabited a broad area around Japan and the coast of Korea, became extinct in the 1950s due to fishermen. The Caribbean monk seal was distributed throughout the Caribbean Sea but was driven to extinction via hunting by 1952.
These are only a few of the recorded extinctions in the past 500 years. The International Union for Conservation of Nature (IUCN) keeps a list of extinct and endangered species called the Red List. The list is not complete, but it describes 380 extinct species of vertebrates after 1500 AD, 86 of which were driven extinct by overhunting or overfishing.
Estimates of Present-Time Extinction Rates
Estimates of extinction rates are hampered by the fact that most extinctions are probably happening without observation. The extinction of a bird or mammal is likely to be noticed by humans, especially if it has been hunted or used in some other way. But there are many organisms that are of less interest to humans (not necessarily of less value) and many that are undescribed.
The background extinction rate is estimated to be about one per million species per year (E/MSY). For example, assuming there are about ten million species in existence, the expectation is that ten species would become extinct each year (each year represents ten million species per year).
One contemporary extinction rate estimate uses the extinctions in the written record since the year 1500. For birds alone this method yields an estimate of 26 E/MSY. However, this value may be underestimated for three reasons. First, many species would not have been described until much later in the time period, so their loss would have gone unnoticed. Second, the number of recently extinct species is increasing because extinct species now are being described from skeletal remains. And third, some species are probably already extinct even though conservationists are reluctant to name them as such. Taking these factors into account raises the estimated extinction rate closer to 100 E/MSY. The predicted rate by the end of the century is 1500 E/MSY.
A second approach to estimating present-time extinction rates is to correlate species loss with habitat loss by measuring forest-area loss and understanding species-area relationships. The species-area relationship is the rate at which new species are seen when the area surveyed is increased. Studies have shown that the number of species present increases as the size of the island increases. This phenomenon has also been shown to hold true in other habitats as well. Turning this relationship around, if the habitat area is reduced, the number of species living there will also decline. Estimates of extinction rates based on habitat loss and species-area relationships have suggested that with about 90 percent habitat loss an expected 50 percent of species would become extinct. Species-area estimates have led to species extinction rate calculations of about 1000 E/MSY and higher. In general, actual observations do not show this amount of loss and suggestions have been made that there is a delay in extinction. Recent work has also called into question the applicability of the species-area relationship when estimating the loss of species. This work argues that the species-area relationship leads to an overestimate of extinction rates. A better relationship to use may be the endemics-area relationship. Using this method would bring estimates down to around 500 E/MSY in the coming century. Note that this value is still 500 times the background rate.
Link to Learning
Check out this interactive exploration of endangered and extinct species, their ecosystems, and the causes of the endangerment or extinction.
Summary
Biodiversity exists at multiple levels of organization and is measured in different ways depending on the goals of those taking the measurements. These measurements include numbers of species, genetic diversity, chemical diversity, and ecosystem diversity. The number of described species is estimated to be 1.5 million with about 17,000 new species being described each year. Estimates for the total number of species on Earth vary but are on the order of 10 million. Biodiversity is negatively correlated with latitude for most taxa, meaning that biodiversity is higher in the tropics. The mechanism for this pattern is not known with certainty, but several plausible hypotheses have been advanced.
Five mass extinctions with losses of more than 50 percent of extant species are observable in the fossil record. Biodiversity recovery times after mass extinctions vary, but have been up to 30 million years. Recent extinctions are recorded in written history and are the basis for one method of estimating contemporary extinction rates. The other method uses measures of habitat loss and species-area relationships. Estimates of contemporary extinction rates vary, but some rates are as high as 500 times the background rate, as determined from the fossil record, and are predicted to rise.
Art Connections
Figure \(\PageIndex{5}\): Scientists measured the relative abundance of fern spores above and below the K-Pg boundary in this rock sample. Which of the following statements most likely represents their findings?
- An abundance of fern spores from several species was found below the K-Pg boundary, but none was found above.
- An abundance of fern spores from several species was found above the K-Pg boundary, but none was found below.
- An abundance of fern spores was found both above and below the K-Pg boundary, but only one species was found below the boundary , and many species were found above the boundary.
- Many species of fern spores were found both above and below the boundary, but the total number of spores was greater below the boundary.
- Answer
-
A. An abundance of fern spores from several species was found below the K-Pg boundary, but none was found above.
Footnotes
- 1 Mora Camilo et al., “How Many Species Are There on Earth and in the Ocean?” PLoS Biology (2011), doi:10.1371/journal.pbio.1001127.
- 2 Arthur D. Chapman, Numbers of Living Species in Australia and the World , 2nd ed. (Canberra, AU: Australian Biological Resources Study, 2009). www.environment.gov.au/biodiv...d-complete.pdf.
- 3 Brian Groombridge and Martin D. Jenkins. World Atlas of Biodiversity: Earth’s Living Resources in the 21 st Century . Berkeley: University of California Press, 2002.
- 4 International Institute for Species Exploration (IISE), 2011 State of Observed Species (SOS) . Tempe, AZ: IISE, 2011. Accessed May, 20, 2012. species.asu.edu/SOS.
Glossary
- adaptive radiation
- rapid branching through speciation of a phylogenetic tree into many closely related species
- biodiversity
- variety of a biological system, typically conceived as the number of species, but also applying to genes, biochemistry, and ecosystems
- biodiversity hotspot
- concept originated by Norman Myers to describe a geographical region with a large number of endemic species and a large percentage of degraded habitat
- chemical diversity
- variety of metabolic compounds in an ecosystem
- ecosystem diversity
- variety of ecosystems
- endemic species
- species native to one place
- extinction
- disappearance of a species from Earth; local extinction is the disappearance of a species from a region
- extinction rate
- number of species becoming extinct over time, sometimes defined as extinctions per million species–years to make numbers manageable (E/MSY)
- genetic diversity
- variety of genes in a species or other taxonomic group or ecosystem, the term can refer to allelic diversity or genome-wide diversity
- heterogeneity
- number of ecological niches
- megafauna
- large animals
- species-area relationship
- relationship between area surveyed and number of species encountered; typically measured by incrementally increasing the area of a survey and determining the cumulative numbers of species


2.3A: pH, Buffers, Acids, and Bases
Acids dissociate into H + and lower pH, while bases dissociate into OH − and raise pH; buffers can absorb these excess ions to maintain pH.
- Explain the composition of buffer solutions and how they maintain a steady pH
Key Points
- A basic solution will have a pH above 7.0, while an acidic solution will have a pH below 7.0.
- Buffers are solutions that contain a weak acid and its a conjugate base; as such, they can absorb excess H + ions or OH − ions, thereby maintaining an overall steady pH in the solution.
- pH is equal to the negative logarithm of the concentration of H + ions in solution: pH = −log[H + ].
Key Terms
- alkaline : having a pH greater than 7; basic
- acidic : having a pH less than 7
- buffer : a solution composed of a weak acid and its conjugate base that can be used to stabilize the pH of a solution
Self-Ionization of Water
Hydrogen ions are spontaneously generated in pure water by the dissociation (ionization) of a small percentage of water molecules into equal numbers of hydrogen (H + ) ions and hydroxide (OH – ) ions. The hydroxide ions remain in solution because of their hydrogen bonds with other water molecules; the hydrogen ions, consisting of naked protons, are immediately attracted to un-ionized water molecules and form hydronium ions (H 3 0 + ). By convention, scientists refer to hydrogen ions and their concentration as if they were free in this state in liquid water.
2H2O⇋H3O++OH−2H2O⇋H3O++OH−
The concentration of hydrogen ions dissociating from pure water is 1 × 10 −7 moles H + ions per liter of water. The pH is calculated as the negative of the base 10 logarithm of this concentration:
pH = −log[H + ]
The negative log of 1 × 10 −7 is equal to 7.0, which is also known as neutral pH. Human cells and blood each maintain near-neutral pH.
pH Scale
The pH of a solution indicates its acidity or basicity (alkalinity). The pH scale is an inverse logarithm that ranges from 0 to 14: anything below 7.0 (ranging from 0.0 to 6.9) is acidic, and anything above 7.0 (from 7.1 to 14.0) is basic (or alkaline ). Extremes in pH in either direction from 7.0 are usually considered inhospitable to life. The pH in cells (6.8) and the blood (7.4) are both very close to neutral, whereas the environment in the stomach is highly acidic, with a pH of 1 to 2.
The pH scale : The pH scale measures the concentration of hydrogen ions (H + ) in a solution.
Non-neutral pH readings result from dissolving acids or bases in water. Using the negative logarithm to generate positive integers, high concentrations of hydrogen ions yield a low pH, and low concentrations a high pH.
An acid is a substance that increases the concentration of hydrogen ions (H + ) in a solution, usually by dissociating one of its hydrogen atoms. A base provides either hydroxide ions (OH – ) or other negatively-charged ions that react with hydrogen ions in solution, thereby reducing the concentration of H + and raising the pH.
Strong Acids and Strong Bases
The stronger the acid, the more readily it donates H + . For example, hydrochloric acid (HCl) is highly acidic and completely dissociates into hydrogen and chloride ions, whereas the acids in tomato juice or vinegar do not completely dissociate and are considered weak acids; conversely, strong bases readily donate OH – and/or react with hydrogen ions. Sodium hydroxide (NaOH) and many household cleaners are highly basic and give up OH – rapidly when placed in water; the OH − ions react with H + in solution, creating new water molecules and lowering the amount of free H + in the system, thereby raising the overall pH. An example of a weak basic solution is seawater, which has a pH near 8.0, close enough to neutral that well-adapted marine organisms thrive in this alkaline environment.
Buffers
How can organisms whose bodies require a near-neutral pH ingest acidic and basic substances (a human drinking orange juice, for example) and survive? Buffers are the key. Buffers usually consist of a weak acid and its conjugate base; this enables them to readily absorb excess H + or OH – , keeping the system’s pH within a narrow range.
Maintaining a constant blood pH is critical to a person’s well-being. The buffer that maintains the pH of human blood involves carbonic acid (H 2 CO 3 ), bicarbonate ion (HCO 3 – ), and carbon dioxide (CO 2 ). When bicarbonate ions combine with free hydrogen ions and become carbonic acid, hydrogen ions are removed, moderating pH changes. Similarly, excess carbonic acid can be converted into carbon dioxide gas and exhaled through the lungs; this prevents too many free hydrogen ions from building up in the blood and dangerously reducing its pH; likewise, if too much OH – is introduced into the system, carbonic acid will combine with it to create bicarbonate, lowering the pH. Without this buffer system, the body’s pH would fluctuate enough to jeopardize survival.
Buffers in the body : This diagram shows the body’s buffering of blood pH levels: the blue arrows show the process of raising pH as more CO2 is made; the purple arrows indicate the reverse process, lowering pH as more bicarbonate is created.
Antacids, which combat excess stomach acid, are another example of buffers. Many over-the-counter medications work similarly to blood buffers, often with at least one ion (usually carbonate) capable of absorbing hydrogen and moderating pH, bringing relief to those that suffer “heartburn” from stomach acid after eating.


41.3.2: Chapter 3
Review Questions
1.
c.
HIPAA set forth standards to protect sensitive health information from being disclosed without the consent or knowledge of the individual.
2.
d.
Beneficence is the ethical principle that requires a nurse to “do good” and to act in ways that promote the health and well-being of their clients.
3.
c.
Autonomy means having the right to make one’s own health care decisions.
4.
a.
Potential benefits of autonomy include improved outcomes, safety, decreased costs, improved self-confidence, and improved adherence to the care plan.
5.
b.
The nurse should own the duty of caring for self. This, in turn, will improve client safety when allowing oneself the self-care of time off.
6.
c.
An adverse drug reaction is an undesired effect that occurs at normal doses of the drug.
7.
d.
An adverse drug event is client harm resulting from exposure to a drug. This is injury from a medication, a missed medication, or an inappropriately dosed medication.
8.
c.
CPOE is the acronym for computerized prescriber order entry, also known as e-prescriber.
9.
a.
Alerts (both soft alerts and hard alerts) are there to improve client safety.
10.
b.
The correct order has a leading zero before the decimal point. A trailing zero should not be used.


6.1: International Governmental Organisations
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An international governmental organisation (IGO), also referred to as an intergovernmental organisation, is an organisation with a membership of only states. The organisation is usually founded upon a treaty, or a multilateral agreement, and consists of more than two states. Member states determine the way in which the organisation is run, vote within the organisation and provide its funding.
Established in 1945 following the end of the Second World War, the United Nations (UN) is a prime example of an international governmental organisation with almost universal membership. Only states can be members of the United Nations and membership is valued because it confers upon the member state international recognition of its sovereignty. As of 2017 there are 193 UN member states – but it is important to note that a small number of states are not members. Taiwan, for example, has repeatedly requested membership but has had its request blocked by China. This is because China regards Taiwan as a part of its sovereign territory and does not recognise it as an independent nation. Taiwan, of course, wants United Nations membership because this will mean that the international community fully accepts its sovereignty. The Taiwan example has gone unresolved for decades due to the major role that China plays within the United Nations as one of its most powerful members.
There are six main organs of the United Nations. Once a state is a member, it is automatically a member of the General Assembly. This is the most democratic organ where each state gets one vote, no matter how big or small, rich or poor the country. It is also the place where, every September, world leaders give their address to the international community from behind a dark green podium with the UN crest clearly visible. The other organs are the Security Council, the Economic and Social Council (ECOSOC), the Trusteeship Council, the Secretariat and the International Court of Justice. By far the most powerful organ is the Security Council, which has 15 members. Five states – China, France, Russia, the United Kingdom, and the United States – are permanent members of the Security Council. The other ten are voted in by the General Assembly for two-year tenures. The Security Council is the only organ that can impose sanctions on states or deploy military forces on behalf of the international community to keep the peace in a certain area, region or country. The United Nations itself does not have its own military force, but it can muster military and police personnel through contributions by its members. These UN peacekeepers are distinguished by their trademark blue helmets, giving rise to the nickname ‘Blue Berets’.
In order to be inclusive the United Nations has welcomed the participation (note participation, not membership) of civil society groups during some of its meetings, but never at the sessions of the all-important Security Council. Organisations may speak as observers to the General Assembly, or as organisations with ‘consultative status’ with the UN Economic and Social Council for example. There are civil society organisations on all issues, ranging from disarmament to oceanic noise pollution, and from mental health to refugees. There are also private individuals who are invited to speak at special United Nations meetings. It is therefore common to witness heart wrenching first-hand accounts of sexual abuses, torture, or discrimination. Such testimonies have the power to galvanise the international community. Yet, no matter how powerful these testimonies are, it is ultimately up to the member states to determine the course of action. The Secretariat, including the Secretary-General who leads the United Nations, cannot take action on its own and can only appeal to member states to ‘do something’. Because of this, the United Nations remains undeniably and irrevocably an international governmental organisation and not a level of authority above the states.
Here, the other designation sometimes used to describe IGOs – ‘intergovernmental organisation’ – is helpful in appreciating the difference in ‘global governance’ (which IGOs bring to our international system) and ‘global government’ (which does not currently exist). Virtually all IGOs are intergovernmental. This means that their power rests with governments (the member states) not with the organisation. States are free to leave the organisations, or even in some cases to ignore them. There are usually consequences for both actions, but the fact remains that even in extreme cases – when an organisation like the United Nations imposes sanctions, or authorises war, on a state – international governmental organisations do not rule over states. Such punitive measures are only possible when the members of the UN Security Council are in accord, agree with such proposals, and a coalition of states agrees to finance and partake in the operation. Therefore, the power rests with the states themselves, especially the more powerful states, and there are regular examples of states rejecting a certain course of action because it was not in their national interest. Here, the failures of the United Nations to establish a coordinated response to the Syrian war comes to mind, despite hundreds of thousands killed and millions displaced since 2011.
If an IGO was not intergovernmental, as explained above, it would be in the rare category of ‘supranational’. To have supranational powers means that an organisation is actually able to govern its members and have a degree of independence from its member states. The only clear example of a major organisation such as this is the European Union (EU). For that reason, it is often described as sui generis, or ‘unique’ in its own right. The European Union is unique because, unlike the United Nations and other international governmental organisations, it can actually be said to exercise a degree of sovereignty over its members via law-making powers in certain areas that its members agreed to relocate to the supranational level. It also has its own currency which, together with other capabilities, gives it some of the powers otherwise only seen in states. This is not without controversy in Europe and there is a rising tide of discontent with the growing power of the European Union and a desire in some political circles to weaken, or even dissolve, the organisation so that more of the power returns to the states. The ‘Brexit’ debate, when the British public voted in a 2016 referendum to leave the European Union, raised many of these issues and is an interesting instance of the idea of supranationalism being challenged.
Leaving aside bigger organisations like the European Union and the United Nations, international governmental organisations are typically more specific in nature – often dealing with just one particular issue or a specific geographical area. The work that they do is often clear from their names – for example, the International Whaling Commission (IWC) or the International Criminal Police Organization (INTERPOL). These are issue-based organisations and their members are worldwide. Then there are organisations of states in specific regions, such as the Association of Southeast Asian Nations (ASEAN) and the African Union (AU). These often emulate elements of the European Union, but none (as yet) feature supranational powers. Other organisations are neither geographically limited nor limited to a single issue. The Commonwealth of Nations, for example, is an organisation whose membership is restricted to former colonies of the United Kingdom. Having been around since 1949, the Commonwealth also has its own permanent secretariat. An international governmental organisation that does not have its own fixed secretariat is the BRICS – an intergovernmental organisation of only five countries (Brazil, Russia, India, China and South Africa) focusing on economic and financial issues of interest to its members. The point to remember is that as long as an organisation is composed exclusively of states, or governments (including government agencies), it is an international governmental organisation operating according to international norms.
These international governmental organisations are outside the United Nations but are almost always tied to the UN in some way or another. For some, these ties are explicitly spelled out in the document that establishes them. For others, the simple goal of ensuring that their work is relevant ties them to the United Nations at least tangentially. Take the International Atomic Energy Agency (IAEA), for example. The founding statute of the Agency dictates that its reports should go to the United Nations so that the Security Council may take action against any countries that fail to meet their obligations. This works out well for the international community – as the International Atomic Energy Agency monitors the use of nuclear technology while the UN Security Council enforces measures to ensure state compliance over nuclear safety and security.


6.3: Nominal data- The chi-square test
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As mentioned in the preceding chapter, nominal data (or data that are best treated like nominal data) are the type of data most frequently encountered in corpus linguistics. I will therefore treat them in slightly more detail than the other two types, introducing different versions and (in the next chapter) extensions of the most widely used statistical test for nominal data, the chi-square (χ 2 ) test. This test in all its variants is extremely flexible; it is thus more useful across different research designs than many of the more specific and more sophisticated procedures (much like a Swiss army knife is an excellent all-purpose tool despite the fact that there is usually a better tool dedicated to a specific task at hand).
Despite its flexibility, there are two requirements that must be met in order for the χ 2 test to be applicable: first, no intersection of variables must have a frequency of zero in the data, and second, no more than twenty-five percent of the intersections must have frequencies lower than five. When these conditions are not met, an alternative test must be used instead (or we need to collect additional data).
6.3.1 Two-by-two designs
Let us begin with a two-by-two design and return to the case of discourse-old and discourse-new modifiers in the two English possessive constructions. Here is the research hypothesis again, paraphrased from (9) and (11) in Chapter 5:
(3) H1 : There is a relationship between DISCOURSE STATUS and TYPE OF POSSESSIVE such that the S -POSSESSIVE is preferred when the modifier is DISCOURSE-OLD, the OF -POSSESSIVE is preferred when the modifier is DISCOURSE-NEW.
Prediction: There will be more cases of the S -POSSESSIVE with DISCOURSE-OLD modifiers than with discourse-new modifiers, and more cases of the OF -POSSESSIVE with discourse-new modifiers than with DISCOURSE-OLD modifiers.
The corresponding null hypothesis is stated in (4):
(4) H0 : There is no relationship between DISCOURSE STATUS and TYPE OF POSSESSIVE.
Prediction: Discourse-old and discourse-new modifiers will be distributed randomly across the two Possessive constructions.
We already reported the observed and expected frequencies in Table 5.4, but let us repeat them here as Table 6.3 for convenience in a slightly simplified form that we will be using from now on, with the expected frequencies shown in parentheses below the observed ones.
Table 6.3: Observed and expected frequencies of old and new modifiers in the s - and the of -possessive (= Table 5.4)
In order to test our research hypothesis, we must show that the observed frequencies differ from the null hypothesis in the direction of our prediction. We already saw in Chapter 5 that this is the case: The null hypothesis predicts the expected frequencies, but there are more cases of s -possessives with old modifiers and of -possessives with new modifiers than expected. Next, we must apply the coin-flip logic and ask the question: “Given the sample size, how surprising is the difference between the expected frequencies (i.e., a perfectly random distribution) and the observed frequencies (i.e., the distribution we actually find in our data)?”
As mentioned above, the conceptually simplest way of doing this would be to compute all possible ways in which the marginal frequencies (the sums of the columns and rows) could be distributed across the four cells of our table and then check what proportion of these tables deviates from a perfectly random distribution at least as much as the table we have actually observed. For two-by-two tables, there is, in fact, a test that does this, the exact test (also called Fisher’s exact test or, occasionally, Fisher-Yates exact test), and where the conditions for using the χ2 test are not met, we should use it. But, as mentioned above, this test is difficult to perform without statistical software, and it is not available for tables larger than 2-by-2 anyway, so instead we will derive the χ2 test statistic from the table.
First, we need to assess the magnitude of the differences between observed and expected frequencies. The simplest way of doing this would be to subtract the expected differences from the observed ones, giving us numbers that show for each cell the size of the deviation as well as its direction (i.e., are the observed frequencies higher or lower than the expected ones). For example, the values for Table 6.3 would be 77.19 for cell C11 ( S -POSSESSIVE ∩ OLD), −77.19 for C21 ( OF -POSSESSIVE ∩ OLD), −77.19 for C12 ( S -POSSESSIVE ∩ NEW) and 77.19 for C22 ( OF -POSSESSIVE ∩ NEW)
However, we want to derive a single measure from the table, so we need a measure of the overall deviation of the observed frequencies from the expected, not just a measure for the individual intersections. Obviously, adding up the differences of all intersections does not give us such a measure, as it would always be zero (since the marginal frequencies are fixed, any positive deviance in one cell will have a corresponding negative deviance in its neighboring cells). Second, subtracting the observed from the expected frequencies gives us the same number for each cell, when it is obvious that the actual magnitude of the deviation depends on the expected frequency. For example, a deviation of 77.19 is more substantial if the expected frequency is 75.81 than if the expected frequency is 102.81. In the first case, the observed frequency is more than a hundred percent higher than expected, in the second case, it is only 75 percent higher.
The first problem is solved by squaring the differences. This converts all deviations into positive numbers, and thus their sum will no longer be zero, and it has the additional effect of weighing larger deviations more strongly than smaller ones. The second problem is solved by dividing the squared difference by the expected frequencies. This will ensure that a deviation of a particular size will be weighed more heavily for a small expected frequency than for a large expected frequency. The values arrived at in this way are referred to as the cell components of χ 2 (or simply χ 2 components); the formulas for calculating the cell components in this way are shown in Table 6.4.
Table 6.4: Calculating χ 2 components for individual cells
If we apply this procedure to Table 6.3, we get the components shown in Table 6.5.
Table 6.5: χ 2 components for Table 6.3
The degree of deviance from the expected frequencies for the entire table can then be calculated by adding up the χ 2 components. For Table 7.3, the χ 2 value (χ 2 ) is 272.16. This value can now be used to determine the probability of error by checking it against a table like that in Section 14.1 in the Statistical Tables at the end of this book.
Before we can do so, there is a final technical point to make. Note that the degree of variation in a given table that is expected to occur by chance depends quite heavily on the size of the table. The bigger the table, the higher the number of cells that can vary independently of other cells without changing the marginal sums (i.e., without changing the overall distribution). The number of such cells that a table contains is referred to as the number of degrees of freedom of the table. In the case of a two-by-two table, there is just one such cell: if we change any single cell, we must automatically adjust the other three cells in order to keep the marginal sums constant. Thus, a two-by-two table has one degree of freedom.
The general formula for determining the degrees of freedom of a table is the following, where N rows is the number of rows and N column is the number of columns:
(5) df = (N rows − 1) × (N columns − 1)
Significance levels of χ 2 values differ depending on how many degrees of freedom a table has, so we always need to determine the degrees of freedom before we can determine the p -value. Turning to the table of χ 2 values in Section 14.1, we first find the row for one degree of freedom (this is the first row); we then check whether our χ 2 -value is larger than that required for the level of significance that we are after. In our case, the value of 272.16 is much higher than the χ 2 value required for a significance level of 0.001 at one degree of freedom, which is 10.83. Thus, we can say that the differences in Table 6.3 are statistically highly significant . The results of a χ 2 test are conventionally reported in the following format:
(6) Format for reporting the results of a χ 2 test (χ 2 = [chi-square value], df = [deg. of freedom], p < (or >) [sig. level])
In the present case, the analysis might be summarized along the following lines: “This study has shown that s -possessives are preferred when the modifier is discourse-old while of -possessives are preferred when the modifier is discourse-new. The differences between the constructions are highly significant (χ 2 = 272.16, df = 1, p < 0.001)”.
A potential danger to this way of formulating the results is the meaning of the word significant . In statistical terminology, this word simply means that the results obtained in a study based on one particular sample are unlikely to be due to chance and can therefore be generalized, with some degree of certainty, to the entire population. In contrast, in every-day usage the word means something along the lines of ‘having an important effect or influence’ (LDCE, s.v. significant ). Because of this every-day use, it is easy to equate statistical significance with theoretical importance. However, there are at least three reasons why this equation must be avoided.
First, and perhaps most obviously, statistical significance has nothing to do with the validity of the operational definitions used in our research design. In our case, this validity is reasonably high, provided that we limit our conclusions to written English. As a related point, statistical significance has nothing to do with the quality of our data. If we have chosen unrepresentative data or if we have extracted or annotated our data sloppily, the statistical significance of the results is meaningless.
Second, statistical significance has nothing to do with theoretical relevance. Put simply, if we have no theoretical model in which the results can be interpreted meaningfully, statistical significance does not add to our understanding of the object of research. If, for example, we had shown that the preference for the two possessives differed significantly depending on the font in which a modifier is printed, rather than on the discourse status of the modifier, there is not much that we conclude from our findings. 3
Third, and perhaps least obviously but most importantly, statistical significance does not actually tell us anything about the importance of the relationship we have observed. A relationship may be highly significant (i.e., generalizable with a high degree of certainty) and still be extremely weak. Put differently, statistical significance is not typically an indicator of the strength of the association. 4
To solve the last problem, we can calculate a so-called measure of effect size , which, as its name suggests, indicates the size of the effect that our independent variable has on the dependent variable. For two-by-two contingency tables with categorical data, there is a widely-used measure referred to as ϕ ( phi ) that is calculated as follows:
(7)
In our example, this formula gives us
The ϕ -value is a so-called correlation coefficient, whose interpretation can be very subtle (especially when it comes to comparing two or more of them), but we will content ourselves with two relatively simple ways of interpreting them.
First, there are generally agreed-upon verbal descriptions for different ranges that the value of a correlation coefficient may have (similarly to the verbal descriptions of p -values discussed above. These descriptions are shown in Table 6.6.
Table 6.6: Conventional interpretation of correlation coefficients
Our ϕ -value of 0.8744 falls into the very strong category, which is unusual in uncontrolled observational research, and which suggests that DISCOURSE STATUS is indeed a very important factor in the choice of POSSESSIVE constructions in English.
Exactly how much of the variance in the use of the two possessives is accounted for by the discourse status of the modifier can be determined by looking at the square of the ϕ coefficient: the square of a correlation coefficient generally tells us what proportion of the distribution of the dependent variable we can account for on the basis of the independent variable (or, more generally, what proportion of the variance our design has captured). In our case, ϕ 2 = (0.8744 × 0.8744) = 0.7645. In other words, the variable DISCOURSE STATUS explains roughly three quarters of the variance in the use of the POSSESSIVE constructions – if, that is, our operational definition actually captures the discourse status of the modifier, and nothing else. A more precise way of reporting the results from our study would be something like the following “This study has shown a strong and statistically highly significant influence of DISCOURSE STATUS on the choice of possessive construction: s -possessives are preferred when the modifier is discourse-old (defined in this study as being realized by a pronoun) while of -possessives are preferred when the modifier is discourse-new (defined in this study as being realized by a lexical NP) (χ 2 = 272.16, df = 1, p < 0.001, ϕ 2 = 0.7645)”.
Unfortunately, studies in corpus linguistics (and in the social sciences in general) often fail to report effect sizes, but we can usually calculate them from the data provided, and one should make a habit of doing so. Many effects reported in the literature are actually somewhat weaker than the significance levels might lead us to believe.
6.3.2 One-by- n designs
In the vast majority of corpus linguistic research issues, we will be dealing with designs that are at least bivariate (i.e., that involve the intersection of at least two variables), like the one discussed in the preceding section. However, once in a while we may need to test a univariate distribution for significance (i.e., a distribution of values of a single variable regardless of any specific condition). We may, for instance, have annotated an entire corpus for a particular speaker variable (such as sex), and we may now want to know whether the corpus is actually balanced with respect to this variable.
 In order to determine whether the BNC can be considered a balanced corpus with respect to SPEAKER SEX, we can compare this observed distribution of speakers to the expected one more or less exactly in the way described in the previous sections except that we have two alternative ways of calculating the expected frequencies.
First, we could simply take the total number of elements and divide it by the number of categories (values), on the assumption that “random” distribution means that every category should occur with the same frequency. In this case, the expected number of MALE and FEMALE speakers would be [Total Number of Speakers / Sex Categories], i.e. 3628 / 2 = 1814. We can now calculate the X 2 components just as we did in the preceding sections, using the formula (( O − E ) 2 )/ E . Table 6.7 shows the results.
Adding up the components gives us a χ 2 value of 272.34. A one-by-two table has one degree of freedom (if we vary one cell, we have to adjust the other one automatically to keep the marginal sum constant). Checking the appropriate row in the table in Section 14.1, we can see that this value is much higher than the 10.83 required for a significance level of 0.01. Thus, we can say that “the BNC corpus contains a significantly higher proportion of male speakers than expected by chance (χ 2 = 272.34, df = 1, p < 0.001)” – in other words, the corpus is not balanced well with respect to the variable Speaker Sex (note that since this is a test of proportions rather than correlations, we cannot calculate a phi value here).
Table 6.7: Observed and expected frequencies of Speaker Sex in the BNC (based on the assumption of equal proportions)
The second way of deriving expected frequencies for a univariate distribution is from prior knowledge concerning the distribution of the values in general. In our case, we could find out the proportion of men and women in the relevant population and then derive the expected frequencies for our table by assuming that they follow this proportion. The relevant population in this case is that of the United Kingdom between 1991 and 1994, when the BNC was assembled. According to the World Bank, the women made up 51.4 percent and men 48.6 percent of the total population at that time, so the expected frequencies of male and female speakers in the corpus are as shown in Table 6.8.
Table 6.8: Observed and expected frequencies of Speaker Sex in the BNC (based on the proportions in the general population)
Clearly, the empirical distribution in this case closely resembles our hypothesized equal distribution, and thus the results are very similar – since there are slightly more women than men in the population, their underrepresentation in the corpus is even more significant.
Incidentally, the BNC not only contains speech by more male speakers than female speakers, it also includes more speech by male than by female speakers: men contribute 5 654 348 words, women contribute 3 825 804. I will leave it as an exercise to the reader to determine whether and in what direction these frequencies differ from what would be expected either under an assumption of equal proportions or given the proportion of female and male speakers in the corpus.
In the case of speaker sex it does not make much of a difference how we derive the expected frequencies, as men and women make up roughly half of the population each. For variables where such an even distribution of values does not exist, the differences between these two procedures can be quite drastic. As an example, consider Table 6.9, which lists the observed distribution of the speakers in the spoken part of the BNC across age groups (excluding speakers whose age is not recorded), together with the expected frequencies on the assumption of equal proportions, and the expected frequencies based on the distribution of speakers across age groups in the real world. The distribution of age groups in the population of the UK between 1991 and 1994 is taken from the website of the Office for National Statistics, averaged across the four years and cumulated to correspond to the age groups recorded in the BNC.
Table 6.9: Observed and expected frequencies of Speaker Age in the BNC
Adding up the χ 2 components gives us an overall χ 2 value of 53.63 in the first case and 115.07 in the second case. For univariate tables, df = (Number of Values – 1), so Table 6.9 has four degrees of freedom (we can vary four cells independently and then simply adjust the fifth to keep the marginal sum constant). The required χ 2 value for a 0.001-level of significance at four degrees of freedom is 18.47: clearly, whichever way we calculate the expected frequencies, the differences between observed and expected are highly significant. However, the distribution of age groups in the corpus is much closer to the assumption of equal proportions than to the actual proportions in the population; also, the conclusions we will draw concerning the over- or underrepresentation of individual categories will be very different. In the first case, for example, we might be led to believe that the age group 34–44 is fairly represented while the age group 15–24 is underrepresented. In the second case, we see that in fact both age groups are overrepresented. In this case, there is a clear argument for using empirically derived expected frequencies: the categories differ in terms of the age span each of them covers, so even if we thought that the distribution of ages in the population is homogeneous, we would not expect all categories to have the same size.
The exact alternative to the univariate χ 2 test with a two-level variable is the binomial test, which we used (without calling it that), in our coin-flip example in Section 6.2 above and which is included as a predefined function in many major spreadsheet applications and in R; for one-by-n tables, there is a multinomial test also available in R and other statistics packages.
3 This problem cannot be dismissed as lightly as this example may suggest: it points to a fundamental difficulty in doing science. Note that if we did find that the font has an influence on the choice of possessive, we would most likely dismiss this finding as a random fluke despite its statistical significance. And we may well be right, since even a level of significance of p < 0.001 does not preclude the possibility that the observed frequencies are due to chance. In contrast, an influence of the discourse status of the modifier makes sense because discourse status has been shown to have effects in many areas of grammar, and thus we are unlikely to question such an influence. In other words, our judgment of what is and is not plausible will influence our interpretation of our empirical results even if they are statistically significant. Alternatively, we could take every result seriously and look for a possible explanation, which will then typically require further investigation. For example, we might hypothesize that there is a relationship between font and level of formality, and the latter has been shown to have an influence on the choice of possessive constructions (Jucker 1993).
4 This statement must be qualified to a certain degree: given the right research design, statistical significance may actually be a very reasonable indicator of association strength (cf. e.g. Stefanowitsch & Gries 2003, Gries & Stefanowitsch 2004 for discussion). However, in most contexts we are well advised to keep statistical significance and association strength conceptually separate.


9.1: Module Introduction
This module explores the minor bodies of the solar system: asteroids, comets, and dwarf planets, as well as meteors and meteorites.
Objectives
Upon completion of this module, the student will be able to:Upon completion of this module, the student will be able to:
- Differentiate between the types of minor bodies found in our solar system
- List the characteristics of asteroids, including Near-Earth Asteroids (NEOs) and Potentially-Hazardous Asteroids (PHAs)
- Differentiate among meteoroids, meteors, and meteorites
- List the characteristics of three types of meteorites
- List the characteristics of comets
- List the characteristics of centaurs
- Explain the discoveries of Pluto and Eris
- List the characteristics of the Trans-Neptunian objects, Kuiper Belt and the Oort Cloud


1.6: Putting it Together
SUMMARY
In this section, you learned the following:
- The extensive definition of geology
- The various fields within geology and what they study
- How scientists use the scientific method to answer questions
SYNTHESIS
While we have not thoroughly answered our questions from the beginning of the outcome, we should be able to understand the connection these questions have to geology. We now know that geology is more than rocks—it deals with the resources we use in our everyday life, and it explains why some areas are more tectonically active than others. As we move through the course, keep these questions in mind.
So let’s get started on this course and see why geology rocks .
Contributors and Attributions
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Original content from Kimberly Schulte (Columbia Basin College) and supplemented by Lumen Learning . The content on this page is copyrighted under a Creative Commons Attribution 4.0 International license.


4.3: Field Technique Tips for Counting Whorls:
4.3 Field Technique Tips for Counting Whorls:
Because each whorl represents one year of growth, one can estimate age on young trees with determinate height growth by counting the whorls.
1. On most trees, the lowest tree branches are systematically dropped as the tree grows and the sun no longer hits the base of the tree. Therefore, when estimating age using this method, it is important to include the bottom-most stubs and/or knots where it is evident branches once existed.
2. Two to four years should be added to most species to allow for the time between seedling germination and evidence of branch whorls on the trunk (Figure 4.4).
3. Small single branches between major branch whorls do not constitute a true whorl or year of growth. Do not count these false whorls.
4. A very short increase in length between whorls that seems unlike the other years’ growth may indicate a “lammas” year, in which the tree flushed twice, often in response to extraordinary growing conditions. Ignore those years unless it is evident that some injury is responsible for the very short internode (Figure 4.4).
This method of “counting the whorls” usually works very well up to fifteen years of age or so for conifers such as Douglas-fir, spruces ( Picea spp.), pines ( Pinus spp.) and true firs ( Abies spp.). It is more challenging for cedars ( Thuja spp., Chamaecyparis spp.), hemlocks ( Tsuga spp.), and some hardwoods. One really has to get close to the tree, look carefully for evidence of bud scars, and know the growth habits of the species.


20.6A: Clonal Selection and B-Cell Differentiation
B cells mature in the bone marrow, where they undergo VDJ recombination to produce unique receptors that do not react to self-antigens.
- Describe clonal selection and B cell differentiation
Key Points
- In the bone marrow, central tolerance of B cells is produced through negative selection. Immature B cells are tested for auto-reactivity before leaving the bone marrow. The immature B cells whose receptors (BCRs) bind too strongly to self antigens will not be killed.
- When the B cell receptor on the cell surface matches its cognate antigen in the body, the B cell proliferates and secretes a free form of those receptors ( antibodies ), with identical binding sites as on the original cell surface.
- B cells that have not been exposed to antigen, also known as naïve B cells, can be activated in a T cell-dependent or independent manner.
- There are two types of T cell independent activation: Type 1 T cell-independent (polyclonal) activation, and type 2 T cell-independent activation.
- During clonal selection, random mutations during clonal expansion cause the production of B cells with increased antibody-binding affinity for their antigens.
- The clonal selection hypothesis may explain why secondary immune responses are so effective at preventing reinfection by the same pathogen.
Key Terms
- Clonal selection : The theory that lymphocytes bear antigen receptors before activation and that random mutations during clonal expansion cause the development of lymphocytes with high binding affinities for their antigens.
- humoral : Of or relating to the body fluids or humors.
- memory B cell : A B cell subtype formed following primary infection in which the cell recognizes a specific epitope.
B cells are lymphocytes that play a large role in the humoral immune response (as opposed to the cell-mediated immune response, which is governed by T cells). B cells primarily function to make antibodies against antigens, act as antigen-presenting cells (APCs), and eventually develop into memory B cells to provide long-term immunity. B cells undergo clonal selection and develop similarly to T cells with some notable differences.
B Cell Development
Immature B cells are produced in the bone marrow of most mammals. Their development occurs through several stages, each representing a change in the genome content at the antibody loci. An antibody is composed of two identical light (L) and two identical heavy (H) chains, and the genes specifying them are found in the V (variable) region and C (constant) region. The heavy-chain V region has three segments, V, D and J. These segments recombine randomly in a process called VDJ recombination to produce a unique variable domain in the immunoglobulin of each individual B cell.
Similar rearrangements occur for the light-chain V region but with only two segments involved: V and J. When the B cell fails in any step of the maturation process, it will die by apoptosis, here called clonal deletion. This is a form of positive selection. B cells are also tested for autoreactivity through negative selection. If these B cells have high affinity for binding to self-antigens, they will die by clonal deletion or another pathway such as anergy.
B Cell Activation
B cell activation refers to the differentiation and clonal expansion of B cells.When the B cell receptor on the cell surface matches its cognate antigen in the body, the B cell proliferates and secretes a free form of those receptors (antibodies) in the body, with binding sites identical to those on the original cell surface. However, B cell recognition of antigens is not the only element necessary for B cell activation. B cells that have not been exposed to antigen, also known as naïve B cells, can be activated in a T cell-dependent or independent manner.
- T cell dependent activation is activation of B cells by type 2 helper T cells in the lymph nodes.
- T cell independent activation occurs when antigens directly bind to B cell themselves, usually through cross-linking the antigen to the B cell receptor or receiving the antigen with a toll-like receptor.
T-dependent B cell activation : T cell-dependent B cell activation, showing a TH2-cell (left), B cell (right), and several interaction molecules.
B Cell Differentiation and Clonal Expansion
After activation, the B cell undergoes differentiation and clonal expansion, which usually involves migration to germinal centers if the activation takes place in a lymph node. B cell differentiation is the process by which B cells change into different types, such as plasma cells and plasma blasts. Clonal expansion is the process by which daughter cells arise from a parent cell. During B cell clonal expansion, many copies of that B cell are produced that share affinity with and specificity of the same antigen.
Clonal Selection
Clonal selection is a theory stating that B cells express antigen-specific receptors before antigens are ever encountered in the body. After B cell activation, the B cells clone themselves through clonal expansion, but during each cellular division, random mutations occur that gradually increase the binding affinity for B cell-produced antibodies to antigens.
For example, memory B cells that differentiate after an adaptive immune response are thought to undergo clonal selection so that antibodies produced by newer memory B cells have considerably higher binding affinities to their antigens. This theory may explain why secondary immune responses from memory cells are so effective that repeated infections by the same pathogen are stopped before symptoms even develop. Following the initial infection, random mutations during clonal selection could produce memory B cells that can more easily bind to antigens than can the original B cells.


3.4: Distinguishing Between The Three Types of Muscle Tissue
Information
Muscular tissue is the third of the four major categories of animal tissue. Muscle tissue is subdivided into three broad categories: skeletal muscle, cardiac muscle, and smooth muscle. The three types of muscle can be distinguished by both their locations and their microscopic features.
Skeletal muscle is found attached to bones. It consists of long multinucleate fibers. The fibers run the entire length of the muscle they come from and so are usually too long to have their ends visible when viewed under the microscope. The fibers are relatively wide and very long, but unbranched . Fibers are not individual cells, but are formed from the fusion of thousands of precursor cells. This is why they are so long and why individual fibers are multinucleate (a single fiber has many nuclei). The nuclei are usually up against the edge of the fiber. There are striations in skeletal muscle. These are alternating dark and light bands perpendicular to the edge of the fiber that are present all along the fiber.
Cardiac muscle is only found in the heart. Its fibers are longer than they are wide, and they are striated , like skeletal muscle fibers. But, unlike skeletal muscle fibers, cardiac muscle
fibers have distinct ends to them, called intercalated discs . These are dark lines that run from one side of the fiber to the other. The intercalated discs are not much thicker than the striations, but they are usually darker and so distinct for that reason. One cardiac muscle fiber is the material between two intercalated discs. Cardiac muscle fibers are mononucleate , with only one nucleus per fiber, and they can sometimes be branched .
Smooth muscle is found in the walls of internal organs, such as the organs of the digestive tract, blood vessels, and others. It consists of mononucleate fibers with tapered edges . No striations are visible in smooth muscle under the microscope. Because smooth muscle often is wrapping around the organ it is associated with, it can be hard to find an entire smooth muscle fiber in profile in a tissue slice on a microscope slide. Most of the fibers will be sectioned at angles or will be difficult to get into a single plane of focus, but a little bit of searching can usually turn up some with all of the defining characteristics visible.
LAB 3 EXERCISE \(\ PageIndex {1}\)
In each of the three photomicrographs below, identify which type of muscle is present. List the defining visual characteristics of that type of muscle, and draw arrows to features on the photograph that illustrate each characteristic.
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Muscle type: _________________ Visual characteristics 1. 2. 3. 4. |
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Muscle type: _________________ Visual characteristics 1. 2. 3. 4. |
|
Muscle type: _________________ Visual characteristics 1. 2. 3. 4. |
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- Obtain a slide of cardiac muscle tissue from the slide box.
- View the slide on an appropriate objective.
- Fill out the blanks next to your drawing.
- In the circle below, draw a representative sample of key features you identified, taking care to correctly and clearly draw their true shapes and directions. Draw your structures proportionately to their size in your microscope’s field of view.
- Obtain a slide of skeletal muscle tissue from the slide box.
- View the slide on an appropriate objective.
- Fill out the blanks next to your drawing.
- In the circle below, draw a representative sample of key features you identified, taking care to correctly and clearly draw their true shapes and directions. Draw your structures proportionately to their size in your microscope’s field of view.
- Obtain a slide of smooth muscle tissue from the slide box.
- View the slide on an appropriate objective.
- Fill out the blanks next to your drawing.
- In the circle below, draw a representative sample of key features you identified, taking care to correctly and clearly draw their true shapes and directions. Draw your structures proportionately to their size in your microscope’s field of view.
LICENSES AND ATTRIBUTIONS
A&P Labs. Authored by : Ross Whitwam. Provided by : Mississippi University for Women. Located at : http://www.muw.edu . License : CC BY-SA: Attribution-ShareAlike
CC LICENSED CONTENT, SPECIFIC ATTRIBUTION
Exercise \(\ PageIndex {1}\)A . Authored by : Kent Christensen, Ph.D., J. Matthew Velkey, Ph.D., Lloyd M. Stoolman, M.D., Laura Hessler, and Diedra Mosley-Brower. Provided by : University of Michigan Histology and Virtual Microscopy Learning Resources. Located at: <IP_ADDRESS>/Histology/Cardiovascular%20System/098HE_HISTO_40X.svs/view.apml . License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
Exercise \(\ PageIndex {1}\) B. Authored by : Kent Christensen, Ph.D., J. Matthew Velkey, Ph.D., Lloyd M. Stoolman, M.D., Laura Hessler, and Diedra Mosley-Brower. Provided by : University of Michigan Histology and Virtual Microscopy Learning Resources. Located at: <IP_ADDRESS>/Histology/Basic%20Tissues/Muscle/058L_HISTO_40X.svs/view.apml . License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
Exercise \(\ PageIndex {1}\) C. Authored by : Kent Christensen, Ph.D., J. Matthew Velkey, Ph.D., Lloyd M. Stoolman, M.D., Laura Hessler, and Diedra Mosley-Brower. Provided by : University of Michigan Histology and Virtual Microscopy Learning Resources. Located at: <IP_ADDRESS>/Histology/Basic%20Tissues/Muscle/169_HISTO_40X.svs/view.apml . License: CC BY-NC-SA: Attribution-NonCommercial-ShareAlike


4.9: Stokes' Theorem
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Stokes’ Theorem relates an integral over an open surface to an integral over the curve bounding that surface. This relationship has a number of applications in electromagnetic theory. Here is the theorem:
\[\boxed{ \int_{\mathcal S} \left( \nabla \times {\bf A} \right) \cdot d{\bf s} = \oint_{\mathcal C} {\bf A}\cdot d{\bf l} } \nonumber \]
where \(\mathcal{S}\) is the open surface bounded by the closed path \(\mathcal{C}\). The direction of the surface normal \(d{\bf s}=\hat{\bf n}ds\) is related to the direction of integration along \({\mathcal C}\) by the right-hand rule , illustrated in Figure \(\PageIndex{1}\). In this case, the right-hand rule states that the correct normal is the one that points through the surface in the same direction as the fingers of the right hand when the thumb of your right hand is aligned along \({\mathcal C}\) in the direction of integration.
Figure \(\PageIndex{1}\): The relative orientations of the direction of integration \(\mathcal C\) and surface normal \(\vec{\mathbf{n}}\) in Stokes’ Theorem. ( CC BY SA 3.0 ; Cronholm144).Stokes’ Theorem is a purely mathematical result and not a principle of electromagnetics per se . The relevance of the theorem to electromagnetic theory is primarily as a tool in the associated mathematical analysis. Usually the theorem is employed to transform a problem expressed in terms of an integration over a surface into an integration over a closed path or vice-versa. For more information on the theorem and its derivation, see “Additional Reading” at the end of this section.


2.13: Using Comments
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Before discussing any of the more complicated stuff, I want to introduce the
comment
character,
#
. It has a simple meaning: it tells R to ignore everything else you’ve written on this line. You won’t have much need of the
#
character immediately, but it’s very useful later on when writing scripts (see Chapter 8). However, while you don’t need to use it, I want to be able to include comments in my R extracts. For instance, if you read this:
41
seeker <- 3.1415 # create the first variable
lover <- 2.7183 # create the second variable
keeper <- seeker * lover # now multiply them to create a third one
print( keeper ) # print out the value of 'keeper'
## [1] 8.539539
it’s a lot easier to understand what I’m doing than if I just write this:
seeker <- 3.1415
lover <- 2.7183
keeper <- seeker * lover
print( keeper )
## [1] 8.539539
You might have already noticed that the code extracts in Chapter 3 included the
#
character, but from now on, you’ll start seeing
#
characters appearing in the extracts, with some human-readable explanatory remarks next to them. These are still perfectly legitimate commands, since R knows that it should ignore the
#
character and everything after it. But hopefully they’ll help make things a little easier to understand.


9.12: Statistical Literacy
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Learning Objectives
Research in March, 2012 reported here found evidence for the existence of the Higgs Boson particle. However, the evidence for the existence of the particle was not statistically significant.
Example \(\PageIndex{1}\):what do you think?
Did the researchers conclude that their investigation had been a failure or did they conclude they have evidence of the particle, just not strong enough evidence to draw a confident conclusion?
Solution
One of the investigators stated, "We see some tantalizing evidence but not significant enough to make a stronger statement." Therefore, they were encouraged by the result. In a subsequent study, the evidence was significant.