Alejandra, a 34-year-old pregnant female at 39 weeks’ gestation, arrives at the emergency department of her local hospital accompanied by her husband. She is experiencing regular contractions and reports escalating pain intensity. Alejandra is a gravida 2, para 1, with a history of a previous cesarean section. Alejandra describes her pain as intense and continuous, radiating from her lower abdomen to her lower back. She reports a desire for pain relief to cope with the discomfort of labor contractions. The couple expresses concerns about the potential for a prolonged and painful labor process. Alejandra's first pregnancy resulted in a cesarean section due to breech presentation. She has had a generally uncomplicated prenatal course during this pregnancy, with no significant medical issues. Regular prenatal checkups have shown a healthy fetus with no identified complications. Her vital signs are as follows: blood pressure: 122/78 mm Hg, heart rate: 96 bpm, respiratory rate: 20 breaths per minute, temperature: 98.6° F (37° C), and fetal heart rate: 140 bpm, regular rhythm.
1 .
What nonpharmacologic and pharmacologic pain management solutions can be offered to Alejandra, considering her history and current pain level, and how might involving her husband in the decision-making process enhance the effectiveness of these solutions?
2 .
After implementing pain management strategies, what indicators should the nurse monitor to assess the effectiveness of the interventions, and how might the nurse adjust the plan based on Alejandra's feedback and progress in labor?


2: Geometric Optics and Image Formation
This chapter introduces the major ideas of geometric optics, which describe the formation of images due to reflection and refraction. It is called “geometric” optics because the images can be characterized using geometric constructions, such as ray diagrams. We have seen that visible light is an electromagnetic wave; however, its wave nature becomes evident only when light interacts with objects with dimensions comparable to the wavelength (about 500 nm for visible light). Therefore, the laws of geometric optics only apply to light interacting with objects much larger than the wavelength of the light.
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- 2.1: Prelude to Geometric Optics and Image Formation
- loud Gate is a public sculpture by Anish Kapoor located in Millennium Park in Chicago. Its stainless steel plates reflect and distort images around it, including the Chicago skyline. Dedicated in 2006, it has become a popular tourist attraction, illustrating how art can use the principles of physical optics to startle and entertain.
-
- 2.2: Images Formed by Plane Mirrors
- The law of reflection tells us that the angle of incidence is the same as the angle of reflection. A plane mirror always forms a virtual image (behind the mirror). The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright.
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- 2.3: Spherical Mirrors
- Spherical mirrors may be concave (converging) or convex (diverging). The focal length of a spherical mirror is one-half of its radius of curvature: \(f = \frac{R}{2}\).  Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors.
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- 2.4: Images Formed by Refraction
- When an object is observed through a plane interface between two media, then it appears at an apparent distance hi that differs from the actual distance \(h_0\): \(h_i = \left(\frac{n_2}{n_1}\right)h_0\). An image is formed by the refraction of light at a spherical interface between two media of indices of refraction n1 and \(n_2\). Image distance depends on the radius of curvature of the interface, location of the object, and the indices of refraction of the media.
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- 2.5: Thin Lenses
- Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens. By the end of this section, you will be able to use ray diagrams to locate and describe the image formed by a lens and employ the thin-lens equation to describe and locate the image formed by a lens.
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- 2.8: The Simple Magnifier
- A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens. The magnification of an image when observed by the eye is the angular magnification M, which is defined by the ratio of the angle \(θ_{image}\) subtended by the image to the angle \(θ_{object}\) subtended by the object.
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- 2.9: Microscopes and Telescopes
- Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element. The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece.
Thumbnail: Rays reflected by a convex spherical mirror: Incident rays of light parallel to the optical axis are reflected from a convex spherical mirror and seem to originate from a well-defined focal point at focal distance f on the opposite side of the mirror. The focal point is virtual because no real rays pass through it. (CC BY 4.0; OpenStax)


5.4: pH and pOH
Skills to Develop
- Explain the characterization of aqueous solutions as acidic, basic, or neutral
- Express hydronium and hydroxide ion concentrations on the pH and pOH scales
- Perform calculations relating pH and pOH
As discussed earlier, hydronium and hydroxide ions are present both in pure water and in all aqueous solutions, and their concentrations are inversely proportional as determined by the ion product of water ( K w ). The concentrations of these ions in a solution are often critical determinants of the solution’s properties and the chemical behaviors of its other solutes, and specific vocabulary has been developed to describe these concentrations in relative terms. A solution is neutral if it contains equal concentrations of hydronium and hydroxide ions; acidic if it contains a greater concentration of hydronium ions than hydroxide ions; and basic if it contains a lesser concentration of hydronium ions than hydroxide ions.
A common means of expressing quantities, the values of which may span many orders of magnitude, is to use a logarithmic scale. One such scale that is very popular for chemical concentrations and equilibrium constants is based on the p-function, defined as shown where “X” is the quantity of interest and “log” is the base-10 logarithm:
\[\mathrm{pX=−\log X} \label{1}\]
The pH of a solution is therefore defined as shown here, where [H 3 O + ] is the molar concentration of hydronium ion in the solution:
\[\mathrm{pH=-\log[H_3O^+]}\label{\(\PageIndex{2}\)}\]
Rearranging this equation to isolate the hydronium ion molarity yields the equivalent expression:
\[\mathrm{[H_3O^+]=10^{−pH}}\label{\(\PageIndex{3}\)}\]
Likewise, the hydroxide ion molarity may be expressed as a p-function, or pOH:
\[\mathrm{pOH=-\log [OH^−]}\label{\(\PageIndex{4}\)}\]
or
\[\mathrm{[OH^-]=10^{−pOH}} \label{\(\PageIndex{5}\)}\]
Finally, the relation between these two ion concentration expressed as p-functions is easily derived from the \(K_w\) expression:
\[K_\ce{w}=\ce{[H_3O^+][OH^- ]} \label{\(\PageIndex{6}\)}\]
\[-\log K_\ce{w}=\mathrm{-\log([H_3O^+][OH^−])=-\log[H_3O^+] + -\log[OH^-]}\label{\(\PageIndex{7}\)}\]
\[\mathrm{p\mathit{K}_w=pH + pOH} \label{\(\PageIndex{8}\)}\]
At 25 °C, the value of \(K_w\) is \(1.0 \times 10^{−14}\), and so:
\[\mathrm{14.00=pH + pOH} \label{\(\PageIndex{9}\)}\]
The hydronium ion molarity in pure water (or any neutral solution) is \( 1.0 \times 10^{-7}\; M\) at 25 °C. The pH and pOH of a neutral solution at this temperature are therefore:
\[\mathrm{pH=-\log[H_3O^+]=-\log(1.0\times 10^{−7}) = 7.00} \label{10}\]
\[\mathrm{pOH=-\log[OH^−]=-\log(1.0\times 10^{−7}) = 7.00} \label{11}\]
And so, at this temperature, acidic solutions are those with hydronium ion molarities greater than \( 1.0 \times 10^{-7}\; M\) and hydroxide ion molarities less than \( 1.0 \times 10^{-7}\; M\) (corresponding to pH values less than 7.00 and pOH values greater than 7.00). Basic solutions are those with hydronium ion molarities less than \( 1.0 \times 10^{-7}\; M\) and hydroxide ion molarities greater than \( 1.0 \times 10^{-7}\; M\) (corresponding to pH values greater than 7.00 and pOH values less than 7.00).
When \(pH=7\) Solutions are not Neutral
Since the autoionization constant \(K_w\) is temperature dependent, these correlations between pH values and the acidic/neutral/basic adjectives will be different at temperatures other than 25 °C. For example, the hydronium molarity of pure water at 80 °C is 4.9
\[\begin{align*} pH &=-\log[\ce{H_3O^+}] \\[5pt] &= -\log(4.9\times 10^{−7}) \\[5pt] &=6.31 \label{12} \end{align*}\]
\[\begin{align*} pOH &=-\log[\ce{OH^-}]\\[5pt] & =-\log(4.9\times 10^{−7}) \\[5pt] &=6.31 \label{13}\end{align*}\]
At this temperature, then, neutral solutions exhibit pH = pOH = 6.31, acidic solutions exhibit pH less than 6.31 and pOH greater than 6.31, whereas basic solutions exhibit pH greater than 6.31 and pOH less than 6.31. This distinction can be important when studying certain processes that occur at nonstandard temperatures, such as enzyme reactions in warm-blooded organisms. Unless otherwise noted, references to pH values are presumed to be those at standard temperature (25 °C) (Table \(\PageIndex{1}\)).
| Classification | Relative Ion Concentrations | pH at 25 °C |
|---|---|---|
| acidic | [H 3 O + ] > [OH − ] | pH < 7 |
| neutral | [H 3 O + ] = [OH − ] | pH = 7 |
| basic | [H 3 O + ] < [OH − ] | pH > 7 |
Figure \(\PageIndex{1}\) shows the relationships between [H 3 O + ], [OH − ], pH, and pOH, and gives values for these properties at standard temperatures for some common substances.
Figure \(\PageIndex{1}\) : The pH and pOH scales represent concentrations of [H 3 O + ] and OH − , respectively. The pH and pOH values of some common substances at standard temperature (25 °C) are shown in this chart.
Example \(\PageIndex{1}\): Calculation of pH from \(\ce{[H_3O^+]}\)
What is the pH of stomach acid, a solution of HCl with a hydronium ion concentration of \(1.2 \times 10^{−3}\; M\)?
Solution
\[\begin{align*} pH &=-\log [H_3O^+] \\[5pt] &= -\log(1.2 \times 10^{−3}) \\[5pt] &=−(−2.92) \\[5pt]&=2.92 \end{align*}\]
Exercise \(\PageIndex{1}\)
Water exposed to air contains carbonic acid, H 2 CO 3 , due to the reaction between carbon dioxide and water:
\[\ce{CO2(aq) + H2O (l) \rightleftharpoons H2CO3(aq)} \nonumber\]
Air-saturated water has a hydronium ion concentration caused by the dissolved \(\ce{CO_2}\) of \(2.0 \times 10^{−6}\; M\), about 20-times larger than that of pure water. Calculate the pH of the solution at 25 °C.
- Answer
-
5.70
Example \(\PageIndex{2}\): Calculation of Hydronium Ion Concentration from pH
Calculate the hydronium ion concentration of blood, the pH of which is 7.3 (slightly alkaline).
Solution
\[\mathrm{pH=-\log[H_3O^+]=7.3} \nonumber\]
\[\mathrm{\log[H_3O^+]=−7.3} \nonumber\]
\[\mathrm{[H_3O^+]=10^{−7.3}} \nonumber\]
or
\[[\ce{H_3O^+}]=\textrm{antilog of} −7.3 \nonumber\]
\[[\ce{H_3O^+}]=5\times 10^{−8}\;M \nonumber\]
(On a calculator take the antilog, or the “inverse” log, of −7.3, or calculate 10 −7.3 .)
Exercise \(\PageIndex{2}\)
Calculate the hydronium ion concentration of a solution with a pH of −1.07.
- Answer
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12 M
Environmental Science
Normal rainwater has a pH between 5 and 6 due to the presence of dissolved CO 2 which forms carbonic acid:
\[\ce{H2O (l) + CO2(g) ⟶ H2CO3(aq)} \label{14}\]
\[\ce{H2CO3(aq) \rightleftharpoons H^+(aq) + HCO3^- (aq)} \label{15}\]
Acid rain is rainwater that has a pH of less than 5, due to a variety of nonmetal oxides, including CO 2 , SO 2 , SO 3 , NO, and NO 2 being dissolved in the water and reacting with it to form not only carbonic acid, but sulfuric acid and nitric acid. The formation and subsequent ionization of sulfuric acid are shown here:
\[\ce{H2O (l) + SO3(g) ⟶ H2SO4(aq)} \label{16}\]
\[\ce{H2SO4(aq) ⟶ H^+(aq) + HSO4^- (aq)} \label{17}\]
Carbon dioxide is naturally present in the atmosphere because we and most other organisms produce it as a waste product of metabolism. Carbon dioxide is also formed when fires release carbon stored in vegetation or when we burn wood or fossil fuels. Sulfur trioxide in the atmosphere is naturally produced by volcanic activity, but it also stems from burning fossil fuels, which have traces of sulfur, and from the process of “roasting” ores of metal sulfides in metal-refining processes. Oxides of nitrogen are formed in internal combustion engines where the high temperatures make it possible for the nitrogen and oxygen in air to chemically combine.
Acid rain is a particular problem in industrial areas where the products of combustion and smelting are released into the air without being stripped of sulfur and nitrogen oxides. In North America and Europe until the 1980s, it was responsible for the destruction of forests and freshwater lakes, when the acidity of the rain actually killed trees, damaged soil, and made lakes uninhabitable for all but the most acid-tolerant species. Acid rain also corrodes statuary and building facades that are made of marble and limestone (Figure \(\PageIndex{2}\)). Regulations limiting the amount of sulfur and nitrogen oxides that can be released into the atmosphere by industry and automobiles have reduced the severity of acid damage to both natural and manmade environments in North America and Europe. It is now a growing problem in industrial areas of China and India.
Figure \(\PageIndex{2}\): (a) Acid rain makes trees more susceptible to drought and insect infestation, and depletes nutrients in the soil. (b) It also is corrodes statues that are carved from marble or limestone. (credit a: modification of work by Chris M Morris; credit b: modification of work by “Eden, Janine and Jim”/Flickr)
Example \(\PageIndex{3}\): Calculation of pOH
What are the pOH and the pH of a 0.0125-M solution of potassium hydroxide, KOH?
Solution
Potassium hydroxide is a highly soluble ionic compound and completely dissociates when dissolved in dilute solution, yielding [OH − ] = 0.0125 M:
\[\mathrm{pOH=-\log[OH^− ]=-\log 0.0125}\]
\[=−(−1.903)=1.903\]
The pH can be found from the \(\ce{pOH}\):
\[\mathrm{pH+pOH=14.00}\]
\[\mathrm{pH=14.00−pOH=14.00−1.903=12.10}\]
Exercise \(\PageIndex{3}\)
The hydronium ion concentration of vinegar is approximately \(4 \times 10^{−3}\; M\). What are the corresponding values of pOH and pH?
- Answer
-
pOH = 11.6,
pH = 14.00 - pOH = 2.4
The acidity of a solution is typically assessed experimentally by measurement of its pH. The pOH of a solution is not usually measured, as it is easily calculated from an experimentally determined pH value. The pH of a solution can be directly measured using a pH meter (Figure \(\PageIndex{3}\)).
Figure \(\PageIndex{3}\): (a) A research-grade pH meter used in a laboratory can have a resolution of 0.001 pH units, an accuracy of ± 0.002 pH units, and may cost in excess of $1000. (b) A portable pH meter has lower resolution (0.01 pH units), lower accuracy (± 0.2 pH units), and a far lower price tag. (credit b: modification of work by Jacopo Werther)
The pH of a solution may also be visually estimated using colored indicators (Figure \(\PageIndex{3}\)).
Figure \(\PageIndex{4}\): (a) A universal indicator assumes a different color in solutions of different pH values. Thus, it can be added to a solution to determine the pH of the solution. The eight vials each contain a universal indicator and 0.1-M solutions of progressively weaker acids: HCl (pH = l), CH 3 CO 2 H (pH = 3), and NH 4 Cl (pH = 5), deionized water, a neutral substance (pH = 7); and 0.1-M solutions of the progressively stronger bases: KCl (pH = 7), aniline, C 6 H 5 NH 2 (pH = 9), NH 3 (pH = 11), and NaOH (pH = 13). (b) pH paper contains a mixture of indicators that give different colors in solutions of differing pH values. (credit: modification of work by Sahar Atwa).
Summary
The concentration of hydronium ion in a solution of an acid in water is greater than \( 1.0 \times 10^{-7}\; M\) at 25 °C. The concentration of hydroxide ion in a solution of a base in water is greater than \( 1.0 \times 10^{-7}\; M\) at 25 °C. The concentration of
Key Equations
-
\(\ce{pH}=-\log[\ce{H3O+}]\) - \(\ce{pOH} = -\log[\ce{OH-}]\)
- [H 3 O + ] = 10 −pH
- [OH − ] = 10 −pOH
- pH + pOH = p K w = 14.00 at 25 °C
Glossary
- acidic
- describes a solution in which [H 3 O + ] > [OH − ]
- basic
- describes a solution in which [H 3 O + ] < [OH − ]
- neutral
- describes a solution in which [H 3 O + ] = [OH − ]
- pH
- logarithmic measure of the concentration of hydronium ions in a solution
- pOH
- logarithmic measure of the concentration of hydroxide ions in a solution
Contributors
-
Paul Flowers (University of North Carolina - Pembroke), Klaus Theopold (University of Delaware) and Richard Langley (Stephen F. Austin State University) with contributing authors. Textbook content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at<EMAIL_ADDRESS>).


4.1: Introduction
What is culture ? When some people speak of culture, they are thinking of high culture (e.g. ballet or opera). Others may think of current, prominent topics (i.e. pop culture). Academic settings, though, are referring to something else. Culture is a learned behavior and a human construct. Culture exists to answer questions. Some of the questions that are answered are philosophical or ideological, for example, “Where did we come from?” or “What is acceptable behavior?” Other questions revolve around daily life. “How do we secure shelter, clothe ourselves, produce food, and transmit information?” Culture provides us with guidance for our lives. It both asks and answers questions. Children, from an early age, start asking “What is my place in the world?” Culture helps to answer that.
The word culture itself comes the Latin word cultura , meaning cultivation or growing. This is precisely what humans do with both their material and abstract cultural components. Humans, since early childhood, learn to shape, create, share, and change their culture. Culture is the very vehicle we use to navigate through our environments. Culture is a form of communication and it evolves. And as a type of compass, it leads.
4.1.1 Components of Culture
At the most simplistic levels, culture can be either concrete and tangible, or abstract. Either way, culture is used to express identity for both individuals and groups.  People convey culture through various outlets such as festivals, food, and architecture. They are able to meet their worldwide fundamental needs while maintaining individual group qualities. Culture can be classified into three different categories: mentifacts (ideas or beliefs), artifacts (goods or technology), and sociofacts (forms of social organization).
All cultures have underlying beliefs and thought processes. These beliefs include religion (Chapter 6) and language (Chapter 5) but go far beyond that. Other important beliefs include things like nationalism (see Chapter 8), customs orprejudices. These beliefs can be expressed through various avenues, using a variety of auditory, visual, and tactile means. For example, nationalism can be expressed through song, cuisine, dress, and public events. You can hear nationalism in the form of an anthem, see it in the form of a flag, taste it when you eat a dish that represents a group of people, and feel it in the form of a piece of jewelry.
Technology is a human construct. From our earliest inventions (fire, weapons) to a supercomputer, the things that people build are products of their perceived needs, their technical abilities and their available resources. Technology includes clothing, foods and housing. Another name for technology is material culture . Think of material culture as the material that archaeologists study. The materials that we use are often left behind for later people to study, like the clay tablets the Sumerians used to record their writing or the remnants of an Iroquois longhouse used for shared living. Other components of culture (like ideas) leave fewer traces. We can find material culture related to burial practices that date back millennia but may not always have the material evidence to show how people grieve.
Lifestyle is a component of culture that can be overlooked, but it is vitally important. In many cultures, a family is a very large unit and people can tell in great detail their exact relationship to everyone else in a place. In the modern context, a family could consist of a single parent and a child and it is possible to live in a neighborhood filled with unrelated people and not know the name of a single neighbor.
Culture can be seen either through the lens of a microscope or through that of a telescope. Folk culture is local, small and tightly bound to the immediate landscape. Popular culture is large, dispersed, and globalizing. These two forms of culture are not totally separated. They are related and both currently exist in the world. Prior to about 2008, most people on Earth lived in rural communities, often practicing a folk culture. The world as a whole is moving toward popular culture.
4.1.2 Cultural Reproduction
As human beings, we reproduce in two ways: biologically and socially. Physically we reproduce ourselves through having children. However, culture consists solely of learned behavior. In order for culture to reproduce itself, it has to be taught. This is what makes culture a human creation. How is culture transmitted? Human beings are natural mimics. This is the way we learn to speak, and it is the way we learn the rest of our culture as well. We learn through observation and, subsequently, through practice. At another scale, mimicry is the mechanism that drives cultural diffusion. Human beings copy the things we like. The old line “Imitation is the sincerest form of flattery,” perfectly describes the human desire to incorporate successful adaptations.
How people have shared culture has changed drastically over time. This can partly be attributed to the channels in which we share culture. In the past, culture was shared orally and in person. Words eventually became written, the written became electronic, and we now have access to things from anywhere at any time.
The debate over authenticity has also become a topic of debate. If culture is created, recreated, and is fluid, how can we define authenticity? Has culture become placeless ? Placelessness or the irrelevance of place has become a central topic in the contemporary philosophy of geography. Can people have an All-American dining experience in the heart of Madrid, Spain? Can they experience Spanish street-food at a historic theme park in Copenhagen, Denmark? As the following pictures show, icons representing other places are now common in the landscape.
4.1.3 Culture Hearths
Human beings have always had learned behaviors, it’s one of the defining characteristics of human beings. Cultural evolution describes the increasing complexity of human societies over time. Our earliest cultures were simple. Welived in small groups, ranged across fairly large areas, and lived off the natural landscape.  Earlier peoples burned forests to clear land and flush game, and in some places hunted the megafauna to extinction.
Recognizable cultures have places of origin. The word culture refers to cultivation or growing. We care for something, we nurture an idea as it grows. All cultural elements have a place of origin. Some places have been responsible for a great deal of cultural development. We call these places culture hearths . Culture hearths provided many of the cultural elements (technologies, organizational structures, and ideologies) that would diffuse to other places and later times. Cultural hearths provide operational scripts for societies.
Culture hearths are closely associated with the foods that they domesticated. food is an important cultural element due to the fact that it is both a technology as well as form of expression. Although the preceding map shows areas of ancient civilization, these are not the only places that have contributed to contemporary cultures. Ideas can arise anywhere, but ancient ideas collected in these places.
Cultures incorporate pieces of other cultures. Some recognizable themes in creation myths are stories of great floods or other cataclysmic events, and these types of stories recycled through history. Languages without writing will often reuse another language’s writing system. Once again, desirable characteristics get copied.


3.3.3: Attributions - Interpreting the Causes of Behavior
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3. How do people attribute credit and blame for organizational events?
A major influence on how people behave is the way they interpret the events around them. People who feel they have control over what happens to them are more likely to accept responsibility for their actions than those who feel control of events is out of their hands. The cognitive process by which people interpret the reasons or causes for their behavior is described by attribution theory. 21 Specifically, "attribution theory concerns the process by which an individual interprets events as being caused by a particular part of a relatively stable environment." 22
Attribution theory is based largely on the work of Fritz Heider. Heider argues that behavior is determined by a combination of internal forces (e.g., abilities or effort) and external forces (e.g., task difficulty or luck). Following the cognitive approach of Lewin and Tolman, he emphasizes that it is perceived determinants, rather than actual ones, that influence behavior. Hence, if employees perceive that their success is a function of their own abilities and efforts, they can be expected to behave differently than they would if they believed job success was due to chance.
The Attribution Process
The underlying assumption of attribution theory is that people are motivated to understand their environment and the causes of particular events. If individuals can understand these causes, they will then be in a better position to influence or control the sequence of future events. This process is diagrammed in Exhibit 3.5 . Specifically, attribution theory suggests that particular behavioral events (e.g., the receipt of a promotion) are analyzed by individuals to determine their causes. This process may lead to the conclusion that the promotion resulted from the individual’s own effort or, alternatively, from some other cause, such as luck. Based on such cognitive interpretations of events, individuals revise their cognitive structures and rethink their assumptions about causal relationships. For instance, an individual may infer that performance does indeed lead to promotion. Based on this new structure, the individual makes choices about future behavior. In some cases, the individual may decide to continue exerting high levels of effort in the hope that it will lead to further promotions. On the other hand, if an individual concludes that the promotion resulted primarily from chance and was largely unrelated to performance, a different cognitive structure might be created, and there might be little reason to continue exerting high levels of effort. In other words, the way in which we perceive and interpret events around us significantly affects our future behaviors.
Internal and External Causes of Behavior
Building upon the work of Heider, Harold Kelley attempted to identify the major antecedents of internal and external attributions.23 He examined how people determine-or, rather, how they actually perceive-whether the behavior of another person results from internal or external causes. Internal causes included ability and effort, whereas external causes include luck and task ease or difficulty.24 Kelley's conclusion, illustrated in Exhibit 3.6 , is that people actually focus on three factors when making causal attributions:
- Consensus. The extent to which you believe that the person being observed is behaving in a manner that is consistent with the behavior of his or her peers. High consensus exists when the person’s actions reflect or are similar to the actions of the group; low consensus exists when the person’s actions do not.
- Consistency. The extent to which you believe that the person being observed behaves consistently—in a similar fashion—when confronted on other occasions with the same or similar situations. High consistency exists when the person repeatedly acts in the same way when faced with similar stimuli.
- Distinctiveness. The extent to which you believe that the person being observed would behave consistently when faced with different situations. Low distinctiveness exists when the person acts in a similar manner in response to different stimuli; high distinctiveness exists when the person varies his or her response to different situations.
How do these three factors interact to influence whether one’s attributions are internal or external? According to the exhibit, under conditions of high consensus, high consistency, and high distinctiveness, we would expect the observer to make external attributions about the causes of behavior. That is, the person would attribute the behavior of the observed (say, winning a golf tournament) to good fortune or some other external event. On the other hand, when consensus is low, consistency is high, and distinctiveness is low, we would expect the observer to attribute the observed behavior (winning the golf tournament) to internal causes (the winner’s skill).
In other words, we tend to attribute the reasons behind the success or failure of others to either internal or external causes according to how we interpret the underlying forces associated with the others’ behavior. Consider the example of the first female sales manager in a firm to be promoted to an executive rank. How do you explain her promotion—luck and connections or ability and performance? To find out, follow the model. If she, as a sales representative, had sold more than her (male) counterparts (low consensus in behavior), consistently sold the primary product line in different sales territories (high consistency), and was also able to sell different product lines (low distinctiveness), we would more than likely attribute her promotion to her own abilities. On the other hand, if her male counterparts were also good sales representatives (high consensus) and her sales record on secondary products was inconsistent (high distinctiveness), people would probably attribute her promotion to luck or connections, regardless of her sales performance on the primary product line (high consistency).
Attributional Bias
One final point should be made with respect to the attributional process. In making attributions concerning the causes of behavior, people tend to make certain errors of interpretation. Two such errors, or attribution biases , should be noted here. The first is called the fundamental attribution error . This error is a tendency to underestimate the effects of external or situational causes of behavior and to overestimate the effects of internal or personal causes. Hence, when a major problem occurs within a certain department, we tend to blame people rather than events or situations.
The second error in attribution processes is generally called the self-serving bias . There is a tendency, not surprisingly, for individuals to attribute success on an event or project to their own actions while attributing failure to others. Hence, we often hear sales representatives saying, “ I made the sale,” but “ They stole the sale from me” rather than “I lost it.” These two biases in interpreting how we see the events around us help us understand why employees looking at the same event often see substantially different things.
concept check
1. What is attribution theory? Describe the attribution process.
2. What are the internal and external causes of attribution?
21. H. H. Kelley, “The Process of Causal Attributions,” American Psychologist , February 1973, pp. 107–128; F. Forsterling, “Attributional Retraining: A Review,” Psychological Bulletin, November 1985, pp. 495–512; B. Weiner, Human Motivation (New York: Holt, Rinehart and Winston, 1980).
22. Kelley, op. cit., p. 193.
23. Ibid.
24. Ibid.
Exhibit 3.6 Causes of Internal and External Attributions Adapted from Nyla Branscombe and Robert A. Baron. Social Psychology . Fourteenth Edition, 2016, Pearson. (Attribution: Copyright Rice University, OpenStax, under CC BY-NC-SA 4.0 license)
Exhibit 3.7 Golf What internal and external attributions can you make about this golfer who is celebrating a hole in one? (Notice the untied shoe.) (Credit: John Fink/ flickr/ Attribution 2.0 Generic (CC BY 2.0))


16.4B: Platelet Formation
Platelets are membrane-bound cell fragments derived from megakaryocytes, which are produced during thrombopoiesis.
- Describe the process of platelet formation
Key Points
- Megakaryocytes are produced from stem cells in the bone marrow by a process called thrombopoiesis.
- Megaryocytes create platelets by releasing protoplatelets that break up into numerous smaller, functional platelets.
- Thrombopoiesis is stimulated and regulated by the hormone thrombopoietin.
- Platelets have an average life span of five to ten days.
- Old platelets are destroyed by phagocytosis. The spleen holds a reservoir of additional platelets.
- Abnormal numbers of platelets result from problems in thrombopoiesis. This is associated with various disorders and potential pathological complications.
Key Terms
- megakaryocyte : A large cell found in bone marrow that is responsible for the production of platelets.
- Thrombopotein : A hormone produced by the liver or kidneys that stimulates megakaryocyte differentiation and platelet release.
- bone marrow : The fatty vascular tissue that fills the cavities of bones; the place where new blood cells are produced.
Platelets are small, clear, irregularly-shaped cell fragments produced by larger precursor cells called megakaryocytes. Platelets are also called thrombocytes because they are involved in the blood clotting process, which is necessary for wound healing. Platelets are continuously produced as a component product of hematopoiesis (blood cell formation).
Thrombopoiesis
Platelets are produced during hematopoiesis in a sub-process called thromopoiesis, or production of thrombocytes. Thrombopoiesis occurs from common myeloid progenitor cells in the bone marrow, which differentiate into promegakaryocytes and then into megakaryocytes. Megakaryocytes stay in the bone marrow and are thought to produce protoplatelets within their cytoplasm, which are released in cytoplasmic extensions upon cytokine stimulus. The protoplatelets then break up into hundreds of platelets that circulate throughout the bloodstream, while the remaining nucleus of the ruptured megakaryocyte is consumed by macrophages.
Megakaryocyte and platelet production is regulated by thrombopoietin, a hormone produced by the liver and kidneys. Thrombopoietin stimulates differentiation of myeloid progenitor cells into megakaryocytes and causes the release of platelets. Thrombopoietin is regulated by a negative feedback mechanism based on platelet levels in the body so that high levels of platelets result in lower levels of thrombopoietin, while low levels of platelets result in higher levels of
thrombopoietin.
Each megakaryocyte produces between 5,000 and 10,000 platelets before its cellular components are fully depleted. Altogether, around 10^11 platelets are produced each day in a healthy adult. The average lifespan of a platelet is just 5 to 10 days. Old platelets are destroyed by macrophage phagocytosis in the spleen and by Kupffer cells in the liver. Up to 40% of platelets are stored in the spleen as a reserve, released when needed by sympathetically-induced splenic muscle contractions during severe injury.
Hematopoiesis : Myeloid progenitor cells differentiate into promegakaryocytes, and megakaryocytes, which release platelets.
Implications of Platelet Formation
Balanced thrombopoiesis is important because it directly influences the amount of platelets in the body and their associated complications. If the number of platelets is too low, excessive bleeding can occur, even from minor or superficial injuries. If the number of platelets is too high, blood clots can form (thrombosis) and travel through the bloodstream, which may obstruct blood vessels and result in ischemic events. These include stroke, myocardial infarction, pulmonary embolism, or infarction of other tissues.
An abnormality or disease of the platelets is called a thrombocytopathy, which could be either a low number of platelets (thrombocytopenia), a decrease in function of platelets (thrombasthenia), or an increase in the number of platelets (thrombocytosis). In any case, issues with the number of circulating platelets is often due to issues in thrombopoietin feedback regulation, but may also be associated with genetic characteristics and certain medications and diseases. For example, thrombocytopenia often occurs in leukemia patents. Cancerous myeloid cells crowd out healthy ones in the bone marrow, causing impaired thrombopoiesis.
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4.8: Live Regions
Live regions are used to present changes in web content that occur after a web page has loaded. Typical uses include presenting news feeds, feedback and error messages, or live chat output to screen readers, which would otherwise not know about this content changing or being added to a web page already rendered. Live regions can also be used to announce feedback and error messages when a page loads, so screen reader users do not need to search through a web page to find feedback. It reads automatically when a page finishes loading.
Types of Live Regions
A typical live region can be created by adding
aria-live="polite"
to any element in which content is updated after a web page has loaded. The “polite” value indicates the priority of the content being updated. In this case, a screen reader will wait for a break in its audio output before announcing the change that occurred. You may also use
aria-live="assertive"
to interrupt whatever the screen reader is reading, and instead read the changed content before continuing. Typically, “assertive” should be avoided. Only use it in cases where critical information is being updated, such as an error message or critical feedback.
Normally,
aria-live
would not be used to present feedback or error messages, though it is possible. Instead
role="alert"
, introduced earlier, would be used. Using
role="alert"
creates an assertive live region that interrupts a screen reader to present its content. They can be used within rendered content to present messages without reloading the page, or they can be used after a page loads, to present the message before any of the other content on the page is read.
In addition to the commonly used
role="alert"
, there are other less commonly used roles that also act as live regions. These are:
- role=”log”
- role=”marquee”
- role=”timer”
- role=”status”
Here is the full list of live region attributes:
- aria-live: polite, assertive, off
- aria-relevant: additions, removals, text, all
- aria-atomic: true, false
- aria-busy: true, false
- role=”alert”
- role=”log”
- role=”marquee”
- role=”timer”
- role=”status”
Care When Using Live Regions
There are a few cases where using a live region (
aria-live
) to read changing content can create a barrier. Take, for instance, a carousel that presents a series of panels that rotate at a particular frequency. It can be helpful to set up a carousel as a live region, so as each panel slides into view, a screen reader reads the content. However, this behaviour could present a barrier, interfering with the screen reader when it is focused elsewhere, reading other content on the page. If a live region is used with a carousel, it should only be active when the carousel has focus. While typically a live region is created as a static WAI-ARIA attribute, in this case, it should be dynamically added on focus and dynamically removed on blur.
For carousels, it is also important to consider the rate at which panels rotate, ensuring that screen readers have enough time to read the content of the panel before rotating on to the next. This timing can be difficult to predict. It depends on the amount of content on each panel, which can vary significantly, and the rate at which users have their reading rate set on their screen reader. One solution to this issue may be to make the carousel manually rotate when it has focus so users can proceed to the next panel only when they are ready.
Another case where live regions can be problematic is with timers. Timers counting by seconds can essentially render the rest of the content on a page unusable for a screen reader user. As the screen reader announces every second, it interrupts the reading of the other content on a page. Timers that increment each minute, for instance, would not have this problem.
Other places where live regions may be problematic are with very active news or Twitter feeds. Though live regions can be useful for this type of updating content, if there is a constant stream of updates or updates occur frequently, screen reader users may have difficulty comprehending other page content with the frequent interruptions.
Try This: To experience the aggravation of a constantly updating live region, open ChromeVox and give focus to the timer below. In this case, the timer is in an iframe, so you can simply set focus outside the iframe to stop it from reading. If the timer were embedded in the content of the page itself, you would not have this option, and the rest of the page would become unusable with a screen reader. The only option would be to leave the page.


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Conservation biology has three goals: (a) to document Earth’s biological diversity; (b) to investigate how humans influence species, evolution, and ecosystem processes; and (c) to investigate approaches to protect and restore biological communities, maintain genetic diversity, and prevent the extinction of species.
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Because conservation is multidisciplinary and requires a deep understanding of natural processes and human society, conservation biologists must take on multiple roles. Specifically, conservation biologists, as a group, must be curious, good communicators, effective educators, law-abiding citizens, and effective managers and practitioners of conservation projects.
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Conservation biology relies on scientific evidence and ethical principles that underpins the preservation of biodiversity. Conservation biologists generally agree that biodiversity should be preserved, untimely extinctions should be prevented, ecological complexity should be maintained, evolution should continue, and biodiversity has intrinsic value.
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Science provides conservation biologists with useful tools that guide the setting of clear, achievable, and measurable goals, to monitor conservation actions to assess whether goals have been met, and to communicate in a clear and unbiased manner.
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Environmental ethics appeals to people of different walks to life to preserve biodiversity. It holds that biodiversity must also be protected because human well-being and economic opportunities are linked to a healthy environment.


6: Neutral Diversity and Population Structure
How does genetic differentiation build up between closely related populations? How does migration act to reduce differentiation? These questions are key to understand the conditions under which populations (and species) can start to genetically diverge from each other. To answer these questions, we’ll first consider this in the context of neutral alleles, and then return to think about selection and differentiation in later chapters. We’ve considered neutral alleles drawn from a randomly-mating population, and divergence among alleles drawn from two distantly-related populations. We’ll now turn to consider divergence among more closely related populations. In thinking about the coalescent within populations we made the assumption that any pair of lineages is equally likely to coalesce with each other. However, when there is population structure this assumption is violated, as the parent for an allele is likely to be found in the same population as it’s child and so lineages in different populations are less likely to coalesce.
To develop models of about population structure we’ll use the statistic \(F_{\mathrm{ST}}\), which we introduced in Section [section:F_stats] of discussion of summarizing population structure in allele frequencies. We have previously written the measure of population structure \(F_{\mathrm{ST}}\) as
\[F_{\mathrm{ST}} = \dfrac{H_T-H_S}{H_T}\]
where \(H_S\) is the probability that two alleles sampled at random from a subpopulation differ, and \(H_T\) is the probability that two alleles sampled at random from the total population differ.
A simple population split model
Imagine a population of constant size of \(N_e\) diploid individuals that \(T\) generations in the past split into two daughter populations (sub-populations) each of size \(N_e\) individuals, which do not subsequently exchange migrants. In the current day we sample an equal number of alleles from both subpopulations.
Consider a pair of alleles sampled within one of our sub-populations and think about their per site heterozygosity. These alleles have experienced a population of size \(N_e\) and so the probability that they differ is \(H_S \approx 4N_e \mu\) (assuming that \(N_e \mu \ll 1\), using our Equation \ref{eqn:hetero} for heterozygosity within a population ).
The heterozygosity in our total population is a little more tricky to calculate. Assuming that we equally sample both sub-populations, when we draw two alleles from our total sample, \(50\%\) of the time they are drawn from the same subpopulation and \(50\%\) of the time they are drawn from different subpopulations. Therefore, our total heterozygosity is given by
\[H_T = \half H_S + \half H_B\]
where \(H_B\) is the probability that a pair of alleles drawn from our two different sub-populations differ from each other. A pair of alleles from different sub-populations cannot find a common ancestor with each other for at least \(T\) generations into the past as they are in distinct populations (not connected by migration). Once our alleles find themselves back in the combined ancestral population it takes them on average \(2N\) generations to coalesce. So the total opportunity for mutation between our pair of alleles sampled from different populations is \(2 (T + 2N )\) generations of meioses, such that the probability that our pairs of alleles is different is
\[H_B \approx 2\mu ( T + 2 N) %\left( 1-(1-\mu)^{2T} \right) + (1-\mu)^{2T} %\dfrac{\theta}{\theta+1}\]
We can plug this into our expression for \(H_T\), and then that in turn into \(F_{\mathrm{ST}}\). Doing so we find that
\[F_{\mathrm{ST}} \approx \dfrac{ \mu T}{\mu T + 4N_e\mu } = \dfrac{ T}{ T + 4N_e } \label{eqn:FST_split}\]
Note that \(\mu\) cancels out of this equation. In this simple toy model, \(F_{\mathrm{ST}}\) is increasing because the amount of between-population diversity increases with the divergence time of the two populations (initially linearly with \(T\)). \(F_{\mathrm{ST}}\) grows at a rate give by \(\dfrac{T}{(4N_e)}\) so that differentiation will be higher between populations separated by long divergence times or with small effective population sizes.
The genome-wide \(F_{ST}\) between Bornean and Sumatran orangutan species samples ( Pongo pygmaeus and Pongo abelii ) is \(\approx 0.37\) , (Locke et al., 2011) representing a deep population split between the species (potentially with little subsequent gene flow). Within the populations the genome-wide average Watterson’s \(\theta\) is \(\theta_W=1.4\)kb \(^{-1}\), estimated from the number of segregating sites. Assume a generation time of 20 years, and a mutation rate of \(2 \times 10^{-8}\) per base per generation. How far in the past did the two populations diverge?
A simple model of migration between an island and the mainland.
We can also use the coalescent to think about patterns of differentiation under a simple model of migration-drift equilibrium. Let’s consider a small island population that is relatively isolated from a large mainland population, where both of these populations are constant in size. We’ll assume that the expected heterozygosity for a pair of alleles sampled on the mainland is \(H_M\).
Our island has a population size \(N_{I}\) that is very small compared to our mainland population. Each generation some low fraction \(m\) of our individuals on the island have migrant parents from the mainland the generation before. Our island may also send migrants back to the mainland, but these are a drop in the ocean compared to the large population size on the mainland and their effect can be ignored.
If we sample an allele on the island and trace its ancestral lineage backward in time, each generation our ancestral allele has a low probability \(m\) of being descended from the mainland in the preceding generation (if we go back far enough the allele eventually has to be descended from an allele on the mainland). The probability that a pair of alleles sampled on the island are descended from a shared recent common ancestral allele on the island is the probability that our pair of alleles coalesces before either lineage migrates. Well our pair of lineages coalesce with probability \(\dfrac{1}{2N_I}\) in a given generation and, assuming that the rate of migration is not too high ( \(m \ll 1\)), the probability that one or other lineage migrates in a given generation is \(2m\). So the probability that our lineages coalesce before they migrate is
\[\dfrac{\dfrac{1}{(2N_I)}}{\dfrac{1}{(2N_I)} + 2m},\]
which follows as an exactly analogous argument to our probability that a pair of lineages coalesce before a mutation, [eqn:coal_no_mut] , that we used in deriving the expected heterozygosity.
Conditional on one or other of our alleles migrating to the mainland, both of our alleles represent independent draws from the mainland and so differ from each other with probability \(H_M\). Therefore, the level of heterozygosity on the island is given by
\[H_I = \left(1 - \dfrac{\dfrac{1}{(2N_I)}}{\dfrac{1}{(2N_I)} + 2m} \right)H_M\]
So the reduction of heterozygosity on the island compared to the mainland is
\[F_{IM} = 1- \dfrac{H_I}{H_M} = \dfrac{\dfrac{ 1}{(2N_I)}}{\dfrac{1}{(2N_I)} + 2m} = \dfrac{ 1 }{1 + 4N_Im}. \label{eqn:FIM}\]
The level of inbreeding on the island compared to the mainland will be high if the migration rate is low and the effective population size of the island is low, as allele frequencies on the island are drifting and diversity on the island is not being replenished by migration. The key parameter here is the number individuals on the island replaced by immigrants from the mainland each generation ( \(N_I m\)), even a few migrants arriving on the island a generation is enough to prevent much allele frequency differentiation building up.
We have framed this problem as being about the reduction in genetic diversity on the island compared to the mainland. However, if we consider collecting individuals on the island and mainland in proportion to their population sizes, the total level of heterozygosity would be \(H_T=H_M\), as samples from our mainland would greatly outnumber those from our island. Therefore, considering the island as our sub-population, we have derived another simple model of \(F_{ST}\).
You are investigating a small river population of sticklebacks, which receives infrequent migrants from a very large marine population. At a set of putatively neutral biallelic markers the freshwater population has frequencies:
0.2, 0.7, 0.8
at the same markers the marine population has frequencies:
0.4, 0.5 and 0.7.
From studying patterns of heterozygosity at a large collection of markers, you have estimated the long term effective size of your freshwater population is 2000 individuals.
What is your estimate of the migration rate from the marine populations into the river?
Incomplete Lineage Sorting
Often when we’re studying multiple populations, e.g. species, we’re interested in the underlying order in which populations split off from each other, and the timing of these events. In the case where populations split off from each other with no subsequent gene flow, we can represent this pattern of splitting by a population tree. Because it can take a long time for a polymorphism to drift up or down in frequency, multiple population splits may occur during the time an allele is still segregating. This can lead to incongruence between the overall population tree and the information about relationships present at individual loci. As we have seen in the previous chapters the relationships between sampled alleles at a locus are represented by coalescent tree, sometimes call gene trees in the context of incomplete lineage and more generally in phylogenetics. In Figure \(\PageIndex{4}\) and Figure \(\PageIndex{5}\) we show a simulation of three populations where the bottom population splits off from the other two first, followed by the subsequent splitting of the the top and the middle populations. We start both simulations with a newly introduced red allele being polymorphic in the combined ancestral population. The most likely fate of this allele is that it is quickly lost from the population, but sometimes the allele can drift up in frequency and be polymorphic when the populations split, as the allele in our two figures has done. If the allele is lost/fixed in the descendant populations before the next population split, our allele configuration will agree with the population tree, as it does in Figure \(\PageIndex{4}\), and so too the gene tree will agree with population tree (as shown in the left side of Figure \(\PageIndex{6}\)). However, if the allele persists as a polymorphism in the ancestral population until the top and the middle populations split, then the allele could fix in one of these populations and not the other. Such an event leads to a substitution pattern that disagrees with the population tree, as in Figure \(\PageIndex{5}\). If we were to construct a phylogeny using the variation at this site we would see a disagreement between the gene tree and population tree. In Figure \(\PageIndex{5}\) an allele drawn from the top and the bottom populations are necessarily more closely related to each other than either is to an allele drawn from population 2; tracing our allelic lineages from the top and bottom populations back through time, they must coalesce with each other before we reach the point where the red mutation arose; in contrast, a lineage from the middle population cannot have coalesced with either other lineage until past the time the red mutation arose. An example of this ‘incomplete lineage sorting’ in terms of the underlying tree is shown on the right side of Figure \(\PageIndex{6}\).
A natural pedigree analogy to incomplete lineage sorting is the fact that while two biological siblings are more closely related to each other genealogically than either is to their cousin, at any given locus one of the siblings can share an allele IBD with their cousin that they do not share with their own sibling, due to the randomness of Mendelian segregation down their pedigree. In these cases, the average relatedness of the individuals/populations disagrees with the patterns of relatedness at a particular locus.
As an empirical example of incomplete lineage sorting, let’s consider the work of Jennings and Edwards (2005) who sequenced a single allele from three different species of Australian grass finches ( Poephila ): two sister species of long-tailed finches ( Poephila acuticauda and P. hecki ) and the black-throated finch ( Poephila cincta , see Figure \(\PageIndex{7}\)). They collected sequence data for 30 genes and constructed phylogenetic gene trees at each of these loci, resulting in 28 well-resolved gene trees. Sixteen of the gene trees showed P. acuticauda and P. hecki as sisters with P. cincta ) (the tree ((A,H),C) ), while for twelve genes the gene tree was discordant with the population tree: for seven of their genes P. hecki fell as an outgroup to the other two and at five P. acuticauda fell as an outgroup (the trees ((A,C),H) and ((H,C),A) respectively).
Let’s use the coalescent to understand this discordance between gene trees and species trees. Let’s assume that two sister populations (A & B) split \(t_1\) generations in the past, with a deeper split from a third outgroup population (C) \(t_2\) generations in the past. We’ll assume that there’s no gene flow among our populations after each split. We can trace back the ancestral lineages of our three alleles. The first opportunity for the A & B lineages to coalesce is \(t_1\) generations ago. If they coalesce with each other in their shared ancestral population before \(t_2\) in the past (left side of Figure \(\PageIndex{6}\)) their gene tree will definitely agree with the population tree. So the only way for the gene tree to disagree with the population tree is for the A & B lineages to fail to coalesce in their shared ancestral population between \(t_1\) and \(t_2\); this happens with probability \(\left(1 - \dfrac{1}{2N}\right)^{t_2-t_1}\). We’ll get a discordant gene tree if A & B make it back to the shared ancestral population with C without coalescing, and then one or the other of them coalesces with the C lineage before they coalesce with each other. This happens with probability \(2/3\), as at the first pairwise-coalescent event there are are three possible pairs of lineages that could coalesce, two of which (A & C and B & C ) result in a discordant tree. So the probability that we get a coalescent tree that is discordant with the population tree is
\[\dfrac{2}{3} \left(1 - \dfrac{1}{2N}\right)^{t_2-t_1}. \label{eqn:ILS_coal}\]
This equation allows us to relate the fraction of loci showing incomplete lineage sorting to the population genetics parameters of the ancestral population.
Let’s return to Jennings and Edwards’s Australian grass finches example. They estimated that the ancestral population size of our two long-tailed finches was four hundred thousand. What is your best estimate of the inter-speciation time, i.e. \(t_2-t_1\)?
The fraction of loci showing ILS, eqn [eqn:ILS_coal] , depends on the times between population splits ( \(t_2-t_1\)) Thus we should expect gene-tree population-tree discordance when populations split in rapid succession and/or population sizes are large.
Testing for gene flow
We often want to test whether gene flow has occurred between populations. For example, we might want to establish a case that interbreeding between humans and Neanderthals occurred or demonstrate that gene flow occurred after two populations began to speciate. A broad range of methods have been designed to test for gene flow and to estimate gene flow rates based on neutral expectations. Here we’ll briefly just discuss one method based on some simple coalescent ideas. Above we assumed that gene-tree population-tree discordance was due to incomplete lineage sorting due to populations rapidly splitting. However, gene flow among populations can also lead to gene-tree discordance. While both ILS and gene flow can lead to discordance, under simplifying assumptions, ILS implies more symmetry in how these discordances manifest themselves.
Take a look at Figure \(\PageIndex{8}\). In both cases the lineages from 1 and 2 fail to coalesce in their initial shared ancestral population, and one or the other of them coalesces with the lineage from 3 before they coalesce with each other. Each option is equally likely; therefore the mutational patterns ABBA and BABA are equally likely to occur under ILS, but differential gene flow will break the symmetry.
To test for this effect of gene flow, we can sample a sequence from each of our 4 populations and count up the number of sites that show the two mutational patterns consistent with the gene-tree discordance \(n_{ABBA}\) and \(n_{BABA}\) and calculate
\[\dfrac{n_{ABBA}-n_{BABA}}{n_{ABBA}+n_{BABA}} \label{eqn:ABBA_BABA}\]
This statistic will have expectation zero if the gene-tree discordance is due to ILS. If there is gene flow between between 2 and 3, that excludes 1, see Figure [fig:ABBA_BABA_introgression] , there will be an excess ABBAs and so the ABBA-BABA statistic will be skewed positively (and conversely it’ll skew negatively if gene flow occurred between 3 into 1). In practice, whether this is significantly different from zero is judged by constructing a Z statistic with a standard error found by recalculating the statistic on computationally resampled dataset of large genomic windows.
The big cats ( Panthera ) clade is a recent radiation, with a considerable amount of shared genetic variation still segregating across the group. Figueiró et al. (2017) examined patterns of genomic divergence, incomplete lineage sorting, and gene flow across this clade using ABBA-BABA tests with a Domestic cat sequence as the outgroup. One example, for snow leopard, tiger, and lion is shown below. Snow leopards and tigers are known more closely related to each other than either is to lions. Figueiró et al. counted SNPs where snow leopard and lion sequences shared a derived allele to the exclusion of tiger (ABBA) and those where where the tiger and lion sequences shared a derived allele to the exclusion of snow leopard (BABA) and found:
| Snow leopard | Tiger | Lion | Domestic cat | Counts |
|---|---|---|---|---|
| A | B | B | A | 1,434,106 |
| B | A | B | A | 1,250,134 |
The calculated ABBA-BABA statistic, [eqn:ABBA_BABA] , is \(0.07 \pm 0.0026~s.e.\), which is highly significantly different from zero. The direction of this statistics with a strong excess of derived SNPs where the tiger sequence is closer to the lion sequence than snow leopard, is consistent with gene flow between tigers and lions after tigers split off from snow leopards (Figure \(\PageIndex{10}\)). Historically, lions had a large geographic range, and so this interbreeding deep in the past is plausible.
Summary
- We developed simple models of neutral population structure and developed expectations of allele frequency differentiation as measured by \(F_{\mathrm{ST}}\) under these models.
- Under a simple model of population isolation, allele frequency differentiation builds up due to genetic drift in proportion to the split time divided by the population size.
- Only a small number of migrants between populations per generation is sufficient to prevent the build up of neutral allele frequency differentiation.
- Incomplete lineage sorting of ancestral variation is one source of disagreement between population/species-trees and gene trees. It occurs when the split times between populations are in quick enough succession that lineages do not have time coalesce between more closely related populations.
- Gene flow can also lead to patterns similar to incomplete lineage sorting. We can test between a model of incomplete lineage sorting and gene flow using tests such as ABBA-BABA.
You are studying a two species of fish (red fish & blue fish), and sequencing a set of pseudogenes. Here are some facts you’ve collected:
- A third species of fish (black fish) diverged from the common ancestor of red/blue fish 3 million years ago. Assume 1 fish generation per year. Between red fish and black fish there is on average 1 substitution every 100 basepairs.
- In these pseudogenes, within red fish, you estimate that heterozygosity within red fish is \(10^{-4}\) per basepair.
- \(F_{ST}\) between red fish and blue fish is 0.1.
- There has been no gene flow among any of these species after they split.
- What is the per base mutation rate?
- What is the effective population size of red fish?
- When did the red and blue fish populations split? Assume they have equal population sizes.
With reference to the population tree shown in Figure [fig:ABBA_Neanderthal] :
- On the population tree the dashed lines show an incomplete gene phylogeny (for a single allele drawn from each population). At a locus, the Chimp lineage has the A allele. Complete a gene genealogy in a way that would be consistent with Neanderthal and European lineages sharing a derived B allele, to the exclusion of the African lineage (ABBA). Mark the branch that a mutation from \(A \rightarrow B\) must occur on in order to generate this pattern (assuming a single mutation).
- What is the probability of observing a gene tree consistent with the one you drew in part A under the coalescent model? Hint: Remember that incomplete lineage sorting is due to failing to coalesce within an ancestral population. Assume a generation time of 30 years, and an effective population size of 10,000 in all populations. Further, assume that lineages sampled from the Neanderthal and modern human populations will definitely coalesce with each other before the common ancestral population with chimp.


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active electrode
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electrode that participates as a reactant or product in the oxidation-reduction reaction of an electrochemical cell; the mass of an active electrode changes during the oxidation-reduction reaction
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alkaline battery
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primary battery similar to a
dry cell
that uses an alkaline (often potassium hydroxide) electrolyte; designed to be an improved replacement for the dry cell, but with more energy storage and less electrolyte leakage than typical dry cell
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anode
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electrode in an electrochemical cell at which oxidation occurs
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battery
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single or series of galvanic cells designed for use as a source of electrical power
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cathode
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electrode in an electrochemical cell at which reduction occurs
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cathodic protection
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approach to preventing corrosion of a metal object by connecting it to a
sacrificial anode
composed of a more readily oxidized metal
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cell notation (schematic)
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symbolic representation of the components and reactions in an electrochemical cell
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cell potential (
E
cell
)
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difference in potential of the cathode and anode half-cells
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concentration cell
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galvanic cell comprising half-cells of identical composition but for the concentration of one redox reactant or product
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corrosion
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degradation of metal via a natural electrochemical process
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dry cell
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primary battery, also called a zinc-carbon battery, based on the spontaneous oxidation of zinc by manganese(IV)
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electrode potential (
E
X
)
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the potential of a cell in which the half-cell of interest acts as a cathode when connected to the standard hydrogen electrode
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electrolysis
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process using electrical energy to cause a nonspontaneous process to occur
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electrolytic cell
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electrochemical cell in which an external source of electrical power is used to drive an otherwise nonspontaneous process
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Faraday’s constant (F)
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charge on 1 mol of electrons;
F
= 96,485 C/mol e
−
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fuel cell
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devices similar to galvanic cells that require a continuous feed of redox reactants; also called a
flow battery
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galvanic (voltaic) cell
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electrochemical cell in which a spontaneous redox reaction takes place; also called a
voltaic cell
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galvanization
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method of protecting iron or similar metals from corrosion by coating with a thin layer of more easily oxidized zinc.
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half cell
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component of a cell that contains the redox conjugate pair (“couple”) of a single reactant
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inert electrode
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electrode that conducts electrons to and from the reactants in a half-cell but that is not itself oxidized or reduced
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lead acid battery
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rechargeable battery commonly used in automobiles; it typically comprises six galvanic cells based on Pb half-reactions in acidic solution
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lithium ion battery
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widely used rechargeable battery commonly used in portable electronic devices, based on lithium ion transfer between the anode and cathode
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Nernst equation
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relating the potential of a redox system to its composition
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nickel-cadmium battery
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rechargeable battery based on Ni/Cd half-cells with applications similar to those of lithium ion batteries
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primary cell
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nonrechargeable battery, suitable for single use only
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sacrificial anode
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electrode constructed from an easily oxidized metal, often magnesium or zinc, used to prevent corrosion of metal objects via cathodic protection
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salt bridge
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tube filled with inert electrolyte solution
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secondary cell
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battery designed to allow recharging
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standard cell potential
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the cell potential when all reactants and products are in their standard states (1 bar or 1 atm or gases; 1
M
for solutes), usually at 298.15 K
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standard electrode potential ()
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electrode potential measured under standard conditions (1 bar or 1 atm for gases; 1
M
for solutes) usually at 298.15 K
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standard hydrogen electrode (SHE)
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half-cell based on hydrogen ion production, assigned a potential of exactly 0 V under standard state conditions, used as the universal reference for measuring electrode potential
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