8.5.7: Degradation of amino acids
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Learning Objectives
- Understand the catabolism of amino acids, including transamination, oxidative amination, and urea cycle that takes care of the \(\ce{N}\) and processing of the \(\ce{C}\) skeleton of the amino acid to intermediates that enter into citric acid cycle for energy production.
Amino acids are the products of stage 1 of protein catabolism. Usually, amino acids are used to synthesize proteins and other substances that need nitrogen, e.g., nucleotides. Only about 10% of our energy is usually derived from amino acids. Still, when there is a shortage of carbohydrates and fats, e.g., during fasting or starvation, amino acids are used as an alternate energy source. Prolonged use of amino acids as an energy source may lead to the destruction of essential tissues.
Degradation of amino acids has two sets of catabolic pathways: one that deals with the processing of \(\ce{N}\) and the other that deals with the processing of the remaining \(\ce{C}\) skeleton of the amino acids.
Processing of \(\ce{N}\) of amino acids
Processing of \(\ce{N}\) usually happens in the liver and has three major stages: i) transamination, ii) oxidative deamination, and iii) urea cycle, as illustrated with some examples in Figure \(\PageIndex{1}\).
Transamination
Transamination is the process of exchange of an ammonium (\(\ce{-NH3^{+}}\)) group of amino acids with ketone (\(\ce{C=O}\)) group of an \(\alpha\)-ketoacid. Usually \(\alpha\)-amino acids exchange \(\ce{-NH3^{+}}\) group with ketone (\(\ce{C=O}\)) group of an \(\alpha\)-ketoglutarate. For example, alanine exchanges its \(\ce{-NH3^{+}}\) group with a \(\ce{C=O}\) of an \(\alpha\)-ketoglutarate producing a new \(\alpha\)-keto acid (pyruvate in this example) and a new \(\alpha\)-amino acids (L-glutamate in this example), as shown in reaction 1 in Figure \(\PageIndex{1}\). Other \(\alpha\)-keto acids can also receive \(\ce{-NH3^{+}}\) of amino acids also. For example, L-glutamate can transfer its \(\ce{-NH3^{+}}\) to oxaloacetate that regenerates \(\alpha\)-ketoglutarate and produces aspartate, as shown in reaction 3 in Figure \(\PageIndex{1}\).
Oxidative deamination
Oxidative deamination reaction replaces \(\ce{-NH3^{+}}\) with a \(\ce{C=O}\), producing an \(\alpha\)-keto acid and an ammonium (\(\ce{NH4^{+}}\)) ion, as shown in reaction 2 in Figure \(\PageIndex{1}\). This is an oxidation reaction that is coupled with the reduction of \(\ce{NAD^{+}}\) to \(\ce{NADH}\). It happens in mitochondria where \(\ce{NADH}\) enters oxidative phosphorylation pathway to produce \(\ce{ATP's}\). The other product, i.e., \(\ce{NH4^{+}}\), is a toxic substance that needs to be disposed off. Some of \(\ce{NH4^{+}}\) may be used in anabolic reactions, e.g., reactions 4 and 5 in Figure \(\PageIndex{1}\), but most of it enters the urea cycle.
Urea cycle
Ammonium ion \(\ce{NH4^{+}}\) is a toxic substance that is converted to less toxic urea in the urea cycle by the following overall reaction.
\(\ce{2NH4^{+} + CO2 -> \underbrace{H2N-\!\!{\overset{\overset{\huge\enspace\!{O}}|\!\!|\enspace}{C}}\!\!-NH2}_{Urea} + 2H^{+} + H2O}\).
Before entry into the urea cycle, \(\ce{NH4^{+}}\) reacts with two \(\ce{ATP's}\) and bicarbonate (\(\ce{HCO3^{-}}\)), producing carbamoyl phosphate, two \(\ce{ADP's}\) and phosphate (\(\ce{P_i}\), as shown below.
This reaction is catalyzed by an enzyme carbamoyl phosphate synthetase I. Blood contains \(\ce{HCO3^{-}}\) which is the product of dissolution of \(\ce{CO2}\). The product of the above reaction, i.e., Carbamoyl phosphate, goes through four reactions called the urea cycle illustrated in Figure \(\PageIndex{2}\).
- The first reaction of the urea cycle is catalyzed by ornithine transcarbamylase. The \(\ce{-COO^{-}}\) group of ornithine substitutes phosphate (\(\ce{P_{i}}\) from carbamoyl phosphate producing citrulline in mitochondria. Citrulline moves out from the matrix into the cytoplasm.
- The second reaction is a condensation reaction between the carbonyl (\(\ce{C=O}\)) group of citrulline and \(\ce{-NH3^{+}}\) group of aspartate that produces argininosuccinate. This reaction takes place in the cytosol and is catalyzed by argininosuccinate synthetase.
- In the third reaction, argininosuccinate is cleaved by the enzyme argininosuccinase to form arginine, which stays in the cycle, and fumarate, which leaves the cycle.
- In the fourth reaction, arginase cleaves arginine to form urea and ornithine. Ornithine is transported back to the matrix in mitochondria to start the next urea cycle, and urea is released into the blood.
Since \(\ce{HCO3^{-}}\) is produced by the dissolution of \(\ce{CO2}\) in water, the \(\ce{NH4^{+}}\) + \(\ce{HCO3^{-}}\) are equivalent to \(\ce{NH3}\) + \(\ce{CO2}\) + \(\ce{H2O}\). So, the overall equation of the urea cycle becomes:
\(\ce{NH3 + CO2 + H2O + aspartate + 3ATP + 3H2O -> urea + fumarate + 2ADP + 2P_{i} + AMP + PP_{i} + H2O}\)
Since \(\ce{NH3}\) is removed to convert aspartate into fumarate along with \(\ce{PP_{i} + H2O -> 2P_{i}}\), substituting these for aspartate and fumarate simplifies the above equation into:
\(\ce{2NH3 + CO2 + 3ATP + 3H2O -> urea + 2ADP + 4P_{i} + AMP}\)
One \(\ce{NADH}\) is produced during oxidative deamination of L-glutamate (reaction 2 in Figure \(\PageIndex{1}\)). Another \(\ce{NADH}\) is produced when fumarate from reaction 3 of the urea cycle is processed in the citric acid cycle, i.e., fumarate is converted into malate by enzyme fumarase and then malate is oxidized to oxaloacetate at the expense of reduction of \(\ce{NAD^{+}}\) to \(\ce{NADH}\) by enzyme malate dehydrogenase. Adding these reactions to the above reaction of the urea cycle results in the following overall reaction.
\(\ce{CO2 + glutamate + aspartate + 3ATP + 2NAD^{+} + 3H2O -> urea + \alpha{-ketoglutarate} + oxaloacetate + 2ADP + 2P_{i} + AMP + 2PP_{i} + 2NADH}\)
Three \(\ce{ATP}\) are consumed, one of them to \(\ce{AMP}\) that makes total equivalent to four \(\ce{ATP's}\) consumed but two \(\ce{NADH}\) enter oxidative phosphorylation and yield ~5\(\ce{ATP}\), i.e., there is net production of an \(\ce{ATP}\) in the process of \(\ce{N}\) of an amino acid.
The urea released into the blood is later filtered out by the kidneys and excreted with urine. An adult passes about 25 to 30 g of urea in urine per day. If urea is not eliminated properly, it builds to toxic levels and needs medical treatment, like dialysis. Reducing protein intake also lowers urea output.
The link between the urea cycle and the citric acid cycle
The urea cycle and citric acid cycle are two separate cycles but are linked with each other. Aspartate that provides one \(\ce{N}\) in the urea cycle is produced by oxaloacetate transamination, which is an intermediate in the citric acid cycle. Fumarate is a product of the urea cycle that is an intermediate of the citric acid cycle and returns to it.
processing of \(\ce{C}\) skeleton of amino acids
\(\alpha\)-Ketoacids are left as \(\ce{C}\) skeleton of amino acid after transamination or oxidative deamination. For example, pyruvate is left after transamination of alanine and \(\alpha\)-ketoglutarate is left after oxidative deamination of glutamate, as shown in reactions 1 and 2, respectively, in Figure \(\PageIndex{1}\). \(\alpha\)-Ketoacids are either used as precursors for the synthesis of other compounds, or they enter the citric acid cycle to produce \(\ce{CO2}\), \(\ce{H2O}\), and energy. \(\alpha\)-Ketoglutarate and oxaloacetate are \(\alpha\)-keto acids that are intermediates in the citric acid cycle and directly enter the cycle. Other \(\alpha\)-keto acids go through a series of reactions to convert into one of the intermediates in the citric acid cycle, or they convert to pyruvate or acetyl-(\ce{CoA}\) that enter the citric acid cycle, as illustrated in Figure \(\PageIndex{3}\). Details of the conversation of \(\alpha\)-keto acids into intermediates of the citric acid cycle or pyruvate or acetyl-(\ce{CoA}\) are not described here.
Amino acids that can degrade to pyruvate or oxaloacetate are called glucogenic because these products can form glucose through the glucogenesis pathway. For example, alanine yields pyruvate, and aspartate yield oxaloacetate, as shown in reactions 1 and 3 in Figure \(\PageIndex{1}\). Amino acids that degrade to acetyl-(\ce{CoA}\) or acetoacetic acid, which can not form glucose but can be converted into ketone bodies, are called ketogenic . Lysine and leucine are ketogenic amino acids. Several amino acids can catabolize to produce both glucogenic and ketogenic intermediates, and they fall into both classes, as shown in Figure \(\PageIndex{3}\).


9.12: Reading- Pyroclastic Deposits
Pyroclastic rocks or pyroclastics are clastic rocks composed solely or primarily of volcanic materials. Where the volcanic material has been transported and reworked through mechanical action, such as by wind or water, these rocks are termed volcaniclastic . Commonly associated with unsieved volcanic activity—such as Plinian or krakatoan eruption styles, or phreatomagmatic eruptions—pyroclastic deposits are commonly formed from airborne ash, lapilli and bombs or blocks ejected from the volcano itself, mixed in with shatteredcountry rock.
Pyroclastic rocks may be a range of clast sizes, from the largest agglomerates, to very fine ashes and tuffs. Pyroclasts of different sizes are classified as volcanic bombs, lapilli, and volcanic ash. Ash is considered to be pyroclastic because it is a fine dust made up of volcanic rock. One of the most spectacular forms of pyroclastic deposit are the ignimbrites, deposits formed by the high-temperature gas-and-ash mix of a pyroclastic flow event.
Classification
| Types of Pyroclasts [1] | |||
|---|---|---|---|
| Clast size | Pyroclast | Mainly unconsolidated: Tephra | Mainly consolidated: Pyroclastic rock |
| > 64 mm | Block, bomb | Agglomerate | Agglomerate, pyroclastic breccia |
| < 64 mm | Lapillus | Layer, lapilli tephra | Lapilli tuff, lapillistone |
| < 2 mm | Coarse ash | Coarse ash | Coarse (ash) tuff |
| < 0.063 mm | Fine ash | Fine ash | Fine (ash) tuff |
Three modes of transport can be distinguished: pyroclastic flow, pyroclastic surge, and pyroclastic fall. During Plinian eruptions, pumice and ash are formed when silicic magma is fragmented in the volcanic conduit, because of decompression and the growth of bubbles. Pyroclasts are then entrained in a buoyant eruption plume which can rise several kilometers into the air and cause aviation hazards. Particles falling from the eruption clouds form layers on the ground (this is pyroclastic fall or tephra). Pyroclastic density currents, which are referred to as “flows” or “surges” depending on particle concentration and the level turbulence, are sometimes called glowing avalanches . The deposits of pumice-rich pyroclastic flows can be called ignimbrites.
A pyroclastic eruption entails spitting or “fountaining” lava, where the lava will be thrown into the air along with ash, pyroclastic materials, and other volcanic byproducts. Hawaiian eruptions such as those at Kīlauea can eject clots of magma suspended into gas; this is called a “fire fountain”. The magma clots, if hot enough may coalesce upon landing to form a lava flow.
Pyroclastic deposits consist of pyroclasts which are not cemented together. Pyroclastic rocks (tuff) are pyroclastic deposits which have been lithified.
References
Blatt, Harvey and Robert J. Tracy (1996) Petrology: Igneous, Sedimentary, and Metamorphic , W.H.W. Freeman & Company; 2nd ed., pp. 26–29.
- Heiken, G. and Wohletz, K., 1985 Volcanic Ash , University of California Press;, pp. 246. ↵
Contributors and Attributions
- Pyroclastic rock. Provided by : Wikipedia. Located at : https://en.Wikipedia.org/wiki/Pyroclastic_rock#cite_ref-1 . License : CC BY-SA: Attribution-ShareAlike


8.1.5A: Consequences of Social Class
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One’s position in the the social class hierarchy has far-reaching effects on their health, family life, education, etc.
Learning Objectives
- Describe how socioeconomic status (SES) relates to the distributiuon of social opportunities and resources
Key Points
- While sociologists debate exactly how social classes are divided, there is substantial evidence that socioeconomic status is tied to tangible advantages and outcomes.
- Social class in the United States is a controversial issue, with social scientists disagreeing over models, definitions, and even the basic question of whether or not distinct classes exist.
- Many Americans believe in a simple three-class model that includes the rich or upper class, the middle class, and the poor or working class.
Key Terms
- hierarchy : Any group of objects ranked so that everyone but the topmost is subordinate to a specified group above it.
- socioeconomic : Of or pertaining to social and economic factors.
In the United States, a person’s social class has far-reaching consequences. Social class refers to the the grouping of individuals in a stratified hierarchy based on wealth, income, education, occupation, and social network (though other factors are sometimes considered). One’s position in the social class hierarchy may impact, for example, health, family life, education, religious affiliation, political participation, and experience with the criminal justice system.
Social class in the United States is a controversial issue, with social scientists disagreeing over models, definitions, and even the basic question of whether or not distinct classes exist. Many Americans believe in a simple three-class model that includes the rich or upper class, the middle class, and the poor or working class. More complex models that have been proposed by social scientists describe as many as a dozen class levels. Regardless of which model of social classes used, it is clear that socioeconomic status (SES) is tied to particular opportunities and resources. Socioeconomic status refers to a person’s position in the social hierarchy and is determined by their income, wealth, occupational prestige, and educational attainment.
While social class may be an amorphous and diffuse concept, with scholars disagreeing over its definition, tangible advantages are associated with high socioeconomic status. People in the highest SES bracket, generally referred to as the upper class, likely have better access to healthcare, marry people of higher social status, attend more prestigious schools, and are more influential in politics than people in the middle class or working class. People in the upper class are members of elite social networks, effectively meaning that they have access to people in powerful positions who have specialized knowledge. These social networks confer benefits ranging from advantages in seeking education and employment to leniency by police and the courts. Sociologists may dispute exactly how to model the distinctions between socioeconomic statuses, but the higher up the class hierarchy one is in America, the better health, educational, and professional outcomes one is likely to have.


Questions to consider:
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How can determining the situation help you think critically?
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How do you present informed, unbiased thinking?
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What is the difference between factual arguments and opinions?
Critical thinking has become a buzz phrase in education and corporate environments in recent years. The definitions vary slightly, but most agree that thinking critically includes some form of judgement that thinkers generate after careful analysis of the perspectives, opinions, or experimental results present for a particular problem or situation. Before you wonder if you’re even capable of critical thinking, consider that you think critically every day. When you grab an unwashed T-shirt off the top of the pile on the floor of your bedroom to wear into class but then suddenly remember that you may see the person of your dreams on that route, you may change into something a bit less disheveled. That’s thinking critically—you used data (the memory that your potential soul mate walks the same route you use on that day on campus) to change a sartorial decision (dirty shirt for clean shirt), and you will validate your thinking if and when you do have a successful encounter with said soul mate.
 You have to plan ahead, buy the food, possibly prepare it, arrange to and carry the lunch with you, and you may have various reasons for doing that—making healthier eating choices, saving money for an upcoming trip, or wanting more quiet time to unwind instead of waiting in a crowded lunch line. You are constantly weighing options, consulting data, gathering opinions, making choices, and then evaluating those decisions, which is a general definition of critical thinking.
Consider the following situations and how each one demands your thinking attention. Which do you find most demanding of critical thinking? Why?
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Participating in competitive athletic events
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Watching competitive athletic events
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Reading a novel for pleasure
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Reading a textbook passage in science
Critical thinking forces you to determine the actual situation under question and to determine your thoughts and actions around that situation.
Determining the Problem
One component to keep in mind to guide your critical thinking is to determine the situation. What problem are you solving? When problems become complex and multifaceted, it is easy to be distracted by the simple parts that may not need as much thinking to resolve but also may not contribute as much to the ultimate problem resolution. What aspect of the situation truly needs your attention and your critical thinking?
Imagine you’re planning a fantasy vacation as a group assignment in a class you’re taking where each person is allowed only $200. The group doles out specific preliminary tasks to each member to decide where to go, what sort of trip to take, and how to keep costs low, all in the name of a fun fantasy vacation. In this scenario, whose plan demonstrates the most effective critical thinking?
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DeRhonda creates an elaborate invitation for a dinner party she’ll coordinate at an exclusive mountain cabin.
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Patrick researches cruises, cabin rentals, and staycation options, considering costs for various trip lengths.
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Rodrigio puts down a deposit for a private dining room for 25 at an expensive local restaurant for a date six weeks from the end of the semester.
Write out what each person’s thinking reflects about their expectations for this trip and why their actions may or may not help the group at this stage of the planning.
Critical thinking differs according to the subject you’re thinking about, and as such it can be difficult to pin down any sort of formula to make sure you are doing a good job of thinking critically in all situations. While you may need to adapt this list of critical thinking components, you can get started if you do the following:
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Question everything
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Conduct legitimate research
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Limit your assumptions
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Recognize your own biases
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Gather and weigh all options
Additionally, you must recognize that changes will occur and may alter your conclusions now and in the future. You may eventually have to revisit an issue you effectively resolved previously and adapt to changing conditions. Knowing when to do that is another example of critical thinking. Informed flexibility, or knowing that parts of the plan may need to change and how those changes can work into the overall goal, is also a recognized element of thinking critically.
For example, early in the 20th century, many people considered cigarette smoking a relaxing social pastime that didn’t have many negative consequences. Some people may still consider smoking a way to relax; however, years of medical research have proven with mounting evidence that smoking causes cancer and exacerbates numerous other medical conditions. Researchers asked questions about the impact of smoking on people’s overall health, conducted regulated experiments, tracked smokers’ reactions, and concluded that smoking did impact health. Over time, attitudes, evidence, and opinions change, and as a critical thinker, you must continue to research, synthesize newly discovered evidence, and adapt to that new information.
Figure 8.11: Information, attitudes, laws, and acceptance of smoking changed dramatically over time. More recently, vaping and related practices have rekindled debates and launched new research into safety. (Credit: Satish Krishnamurthy / Flickr / Attribution 2.0 Generic (CC-BY 2.0))
Defending against Bias
Once you have all your information gathered and you have checked your sources for currency and validity, you need to direct your attention to how you’re going to present your now well-informed analysis. Be careful on this step to recognize your own possible biases. Facts are verifiable; opinions are beliefs without supporting evidence. Stating an opinion is just that. You could say “Blue is the best color,” and that’s your opinion. If you were to conduct research and find evidence to support this claim, you could say, “Researchers at Oxford University recognize that the use of blue paint in mental hospitals reduces heart rates by 25% and contributes to fewer angry outbursts from patients.” This would be an informed analysis with credible evidence to support the claim.
Not everyone will accept your analysis, which can be frustrating. Most people resist change and have firm beliefs on both important issues and less significant preferences. With all the competing information surfacing online, on the news, and in general conversation, you can understand how confusing it can be to make any decisions. Look at all the reliable, valid sources that claim different approaches to be the
best
diet for healthy living: ketogenic, low-carb, vegan, vegetarian, high fat, raw foods, paleo, Mediterranean, etc. All you can do in this sort of situation is conduct your own serious research, check your sources, and write clearly and concisely to provide your analysis of the information for consideration. You cannot force others to accept your stance, but you can show your evidence in support of your thinking, being as persuasive as possible without lapsing into your own personal biases. Then the rest is up to the person reading or viewing your analysis.
Factual Arguments vs. Opinions
Thinking and constructing analyses based on your thinking will bring you in contact with a great deal of information. Some of that information will be factual, and some will not be. You need to be able to distinguish between facts and opinions so you know how to support your arguments. Begin with basic definitions:
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Fact:
a statement that is true and backed up with evidence; facts can be verified through observation or research
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Opinion:
a statement someone holds to be true without supporting evidence; opinions express beliefs, assumptions, perceptions, or judgements
Of course, the tricky part is that most people do not label statements as fact and opinion, so you need to be aware and recognize the difference as you go about honing your critical thinking skills.
You probably have heard the old saying “Everyone is entitled to their own opinions,” which may be true, but conversely, not everyone is entitled to their own facts. Facts are true for everyone, not just those who want to believe in them. For example,
mice are animals
is a fact;
mice make the best pets
is an opinion.
ACTIVITY
Determine if the following statements are facts or opinions based on just the information provided here, referring to the basic definitions above. Some people consider scientific findings to be opinions even when they are convincingly backed by reputable evidence and experimentation. However, remember the definition of
fact
—verifiable by research or observation. Think about what other research you may have to conduct to make an informed decision.
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Oregon is a state in the United States. (How would this be proven?)
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Beef is made from cattle. (See current legislation concerning vegetarian “burgers.”)
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Increased street lighting decreases criminal behavior. (What information would you need to validate this claim?)
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In 1952, Elizabeth became Queen of England. (What documents could validate this?)
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Oatmeal tastes plain. (What factors might play into this claim?)
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Acne is an embarrassing skin condition. (Who might verify this claim?)
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Kindergarten decreases student dropout rates. (Think of different interest groups that may take sides on this issue.)
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Carbohydrates promote weight gain. (Can you determine if this is a valid statement?)
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Cell phones cause brain tumors. (What research considers this claim?)
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Immigration is good for the US economy. (What research would help you make an informed decision on this topic?)
Many people become very attached to their opinions, even stating them as facts despite the lack of verifiable evidence. Think about political campaigns, sporting rivalries, musical preferences, and religious or philosophical beliefs. When you are reading, writing, and thinking critically, you must be on the lookout for sophisticated opinions others may present as factual information. While it’s possible to be polite when questioning another person's opinions when engaging in intellectual debate, thinking critically requires that you do conduct this questioning.
For instance, someone may say or write that a particular political party should move its offices to different cities every year—that’s an opinion regardless of whether you side with one party or the other. If, on the other hand, the same person said that one political party is headquartered in a specific city, that is a fact you can verify. You could find sources that can validate or discredit the statement. Even if the city the person lists as the party headquarters is incorrect, the statement itself is still a fact—just an erroneous one. If you use biased and opinionated information or even incorrect facts as your evidence to support your factual arguments, then you have not validated your sources or checked your facts well enough. At this point, you would need to keep researching.
Tips for Critical Thinking
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Consider all points of view; seriously consider more than two (look for grey areas).
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Keep an open mind.
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Answer three questions about your supporting data:
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Is it enough support?
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Is it the right support?
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Is it credible?
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Look for evidence that contradicts your point of view. Pretend to disagree with the position you are supporting. What parts of your argument are weak? Do you have the supporting facts to overcome that evidence?
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Create a set of criteria you will use to evaluate the strength of information you want to use to support your argument. Ask questions like these:
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What is the source of this information?
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Is the author well respected in the field?
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When was this information developed? Is that important? Why?
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Does the author or publisher have an agenda for publishing the information? How does that agenda affect the credibility of the information?
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Create a table on which you list your main points, then for each one, list the evidence you have to support it. This method will help you visually identify where you have weak evidence and what points actually lack evidence.
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Be willing to admit that you lack information to support a point of view or make a decision. Ask questions or do some focused research to get what you still need.
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Make sure that your assumptions and points of view are supported by facts, not opinions.
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Learn what types of fallacies you use habitually, and then be on the lookout for them. Writers will often rely on certain types of arguments as a matter of habit. Review some of your old papers to identify which fallacies you need to avoid.
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Question your characterizations of others. Are those authorities truly competent in the area you are considering? Are you attacking the opponents of your point of view rather than attacking their arguments?
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Be careful of broad generalizations. Claims that use absolute words like “all,” “none,” “always,” “never,” “no one,” and “everyone” require much more proof than claims that use words like “most,” “some,” “often,” “rarely,” “sometimes,” and so on.


4.1: Precipitation of group II cations
The bases of Group II cations separation
The solubility guideline#1 of insoluble ions states “Hydroxide (\(\ce{OH^{-}}\)) and sulfides (\(\ce{S^{2-}}\)) are insoluble except when the cation is alkali metal, ammonia, or a heavy alkaline earth metal ion, i.e., \(\ce{Ca^{2+}}\), \(\ce{Ba^{2+}}\), and \(\ce{Sr^{2+}}\)”. The sulfide of \(\ce{Cr^{3+}}\) is also in the exceptions list as its sulfide is unstable in water. It is obvious that the number of insoluble sulfides and hydroxides is large. The solution is made acidic to decrease [\(\ce{OH^{-}}\)] to below the level that can cause precipitation of any ion. The [\(\ce{S^{2-}}\)] also remains low due to the common ion effect of \(\ce{H3O^{+}}\) in the acidic medium as explained in the next section. Therefore among the insoluble sulfides, only those that have very low solubility limits are selectively precipitated. These include \(\ce{Bi^{3+}}\), \(\ce{Cd^{2+}}\), \(\ce{Cu^{2+}}\), and \(\ce{Sn^{4+}}\) among the cations selected in this study that are left in the solution after group I cations have been separated. Group II comprise of \(\ce{Bi^{3+}}\), \(\ce{Cd^{2+}}\), \(\ce{Cu^{2+}}\), and \(\ce{Sn^{4+}}\).
Precipitation of group II cations
Among the ions in the initial solution after removal of group I cations, the following ions form insoluble sulfides: \(\ce{Bi^{3+}}\), \(\ce{Cd^{2+}}\), \(\ce{Cu^{2+}}\), \(\ce{Fe^{2+}}\), \(\ce{Fe^{3+}}\), \(\ce{Ni^{2+}}\), and \(\ce{Sn^{4+}}\). Among these, \(\ce{Bi^{3+}}\), \(\ce{Cd^{2+}}\), \(\ce{Cu^{2+}}\), and \(\ce{Sn^{4+}}\) are in group II that form very insoluble sulfides, and \(\ce{Cr^{3+}}\), \(\ce{Fe^{2+}}\), \(\ce{Fe^{3+}}\), and \(\ce{Ni^{2+}}\) are in group III form insoluble hydroxides and sulfides in basic medium, as reflected by their solubility product constants (\(\ce{K_{sp}}\)) listed in Table 1. The minimum concentration of \(\ce{S^{2-}}\) needed to start precipitation of the cation can be calculated from the \(\ce{K_{sp}}\) expressions as shown in Table 1. It can be observed from Table 1 that there is a huge difference in the minimum \(\ce{S^{2-}}\) concentration (1.8 x 10 - 20 M) needed to precipitate \(\ce{Ni^{2+}}\) -the least soluble sulfide of group III and \(\ce{Cd^{2+}}\) (7.8 x 10 -26 ) -the most soluble sulfide of group II. If the \(\ce{S^{2-}}\) is kept more than 1.8 x 10 -20 M but less than 7.8 x 10 -26 M group II cations will selectively precipitate while group III cations and the rest of the cations will remain dissolved.
|
Ion |
Sulfide |
K sp at 25 o C |
Minimum [S -2 ] needed to precipitate |
|---|---|---|---|
| \(\ce{Fe^{2+}}\) | \(\ce{FeS}\) |
\(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Fe}^{2+}\right]\left[\mathrm{S}^{2-}\right]=4.9 \times 10^{-18}\) |
\(\left[\mathrm{S}^{-2}\right]=\mathrm{K}_{\mathrm{sp}} /\left[\mathrm{Fe}^{2+}\right]=4.9 \times 10^{-17}\) |
|
\(\ce{Ni^{2+}}\) |
\(\ce{NiS}\) |
\(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Ni}^{2+}\right]\left[\mathrm{S}^{2-}\right]=1.8 \times 10^{-21}\) |
\(\left[\mathrm{S}^{-2}\right]=\mathrm{K}_{\mathrm{sp}} /\left[\mathrm{Ni}^{2+}\right]=1.8 \times 10^{-20}\) |
|
\(\ce{Cd^{2+}}\) |
\(\ce{NiS}\) |
\(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Cd}^{2+}\right]\left[\mathrm{S}^{2-}\right]=7.8 \times 10^{-27}\) |
\(\left[\mathrm{S}^{-2}\right]=\mathrm{K}_{\mathrm{sp}} /\left[\mathrm{Cd}^{2+}\right]=7.8 \times 10^{-26}\) |
|
\(\ce{Bi^{3+}}\) |
\(\ce{Ba2S3}\) |
\(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Bi}^{3+}\right]^{2}\left[\mathrm{~S}^{2-}\right]^{3}=6.8 \times 10^{-97}\) |
\(\left[\mathrm{S}^{-2}\right]=\sqrt[3]{\mathrm{K}_{\mathrm{sp}} /\left[\mathrm{Bi}^{3+}\right]^{2}}=4.1 \times 10^{-32}\) |
|
\(\ce{Sn^{4+}}\) |
\(\ce{SnS2}\) |
\(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Sn}^{4+}\right]\left[\mathrm{S}^{2-}\right]^{2}=1.0 \times 10^{-70}\) |
\(\left[\mathrm{S}^{-2}\right]=\sqrt[2]{\mathrm{K}_{\mathrm{sp}} /\left[\mathrm{Sn}^{4+}\right]}=3.2 \times 10^{-35}\) |
|
\(\ce{Cu^{2+}}\) |
\(\ce{CuS}\) |
\(\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Cu}^{2+}\right]\left[\mathrm{S}^{2-}\right]=8.7 \times 10^{-36}\) |
\(\left[\mathrm{S}^{-2}\right]=\mathrm{K}_{\mathrm{sp}} /\left[\mathrm{Fe}^{2+}\right]=8.7 \times 10^{-35}\) |
- * Following cations that may be present the initial solution are not listed in this table due to the following reasons: i) group I cations, i.e., \(\ce{Pb^{2+}}\), \(\ce{Hg2^{2+}}\), and \(\ce{Ag^{+}}\) are already removed, ii) \(\ce{Ca^{2+}}\) and \(\ce{Ba^{2+}}\) for soluble sulfides, iii) sulfide of \(\ce{Cr^{3+}}\) is not stable in water, and iv) \(\ce{Fe^{3+}}\) is reduced to \(\ce{Fe^{2+}}\) by \(\ce{H2S}\) in acidic medium: \(\ce{2Fe^{3+}(aq) + S^{2-} <=> 2Fe^{2+}(aq) + S(s)}\). Source of \(\ce{K_{sp}}\) values: chem 202 lab manual, 2008, by Michael Stranz, cengag learning, ISBN 13: 978-0-534-66904-1
Source of \(\ce{S^{2-}}\) is \(\ce{H2S}\) gas -a week diprotic acid that dissociated in water by the following equilibrium reactions:
\[\ce{H2S(g) + H2O(l) <=> H3O^{+}(aq) + HS^{-}(aq)}\quad \mathrm{K}_{\mathrm{a} 1}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{HS}^{-}\right] /\left[\mathrm{H}_{2} \mathrm{~S}\right]=1.0 \times 10^{-7}\nonumber\]
\[\ce{HS^{-}(aq) + H2O(l) <=> H3O^{+}(aq) + S^{2-}(aq)}\quad \mathrm{K}_{\mathrm{a} 2}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]\left[\mathrm{S}^{2-}\right] /\left[\mathrm{HS}^{-}\right]=1.3 \times 10^{-13}\nonumber\]
\[\text{Overall reaction: }\ce{H2S(g) + 2H2O(l) <=> 2H3O^{+}(aq) + S^{2-}(aq)}\quad\mathrm{K}_{\mathrm{a}}=\left[\mathrm{H}_{3} \mathrm{O}^{+}\right]^{2}\left[\mathrm{~S}^{2-}\right] /\left[\mathrm{H}_{2} \mathrm{~S}\right]=1.3 \times 10^{-20}\nonumber\]
Extent of \(\ce{H2S}\) dissociation, and, consequently, the concentration of \(\ce{S^{2-}}\) produced is dependent on \(\ce{H3O^{+}}\):
\[K_a = \frac{\ce{[H3O^{+}]^{2}[S^{2-}]}}{\ce{[H2S]}}\quad\quad\text{ rearranges to: }\quad\quad\ce{[S^{2-}]} = \frac{K_{a}\ce{[H2S]}}{\ce{[H3O^{+}]^{2}}}\nonumber\]
It is obvious from the above formula that \(\ce{[S^{2-}]}\) is dependent on \(\ce{[H3O^{+}]}\), which is related to pH ( \(pH = Log\frac{1}{\ce{[H3O^{+}]}} = \text{-Log}\ce{[H3O^{+}]}\). Therefore, \(\ce{[S^{2-}]}\) can be controlled by adjusting the pH.
\(\ce{H2S}\) is a toxic gas. To minimize the exposure, \(\ce{H2S}\) is produced in-situ by decomposition of thioacetamide (\(\ce{CH3CSNH2}\)) in water:
\[\ce{CH3CSNH2(aq) + 2H2O <=> CH3COO^{-} + NH4^{+}(aq) + H2S(aq)}\nonumber\]
The decomposition of thioacetamide is an endothermic reaction, which, according to Le Chatelier's principle, moves in the forward direction upon heating. An aqueous solution of thioacetamide is heated in a boiling water bath in a fume hood producing ~0.01M \(\ce{H2S}\) solution.
Rearranging acid dissociation constant of \(\ce{H2S}\) and plugging in 0.01M \(\ce{H2S}\) in the rearranged formula allows calculating \(\ce{S^{2-}}\) concentration at various concentrations of \(\ce{H3O^{+}}\), i.e., at various pH values:
\[\ce{[S^{2-}]} = \frac{K_{a}\ce{[H2S]}}{\ce{[H3O^{+}]^{2}}} = \frac{1.3\times10^{-20}\times0.01}{\ce{[H3O^{+}]^{2}}} = \frac{1.3\times10^{-22}}{\ce{[H3O^{+}]^{2}}}\nonumber\]
It shows that \(\ce{S^{2-}}\) concentration can be varied by [\(\ce{H3O^{+}}\)], i.e., by varying pH. At pH 1 and 0, \(\ce{H3O^{+}}\) is 0.10 M and 1.0 M, respectively, that produces [\(\ce{S^{2-}}\)] in the range of 1.3 x 10 - 20 M S 2- and 1.3 x 10 - 22 M S 2- :
\[\ce{[S^{2-}]} = \frac{1.3\times10^{-22}}{(0.10)^{2}} = 1.3\times10^{-20} ~M\quad\quad\text{ and }\quad\quad\ce{[S^{2-}]} = \frac{1.3\times10^{-22}}{(1.0)^{2}} = 1.3\times10^{-22}~M\nonumber\]
This range of [\(\ce{S^{2-}}\)] is less than the solubility limit of \(\ce{Ni^{2+}}\) -the least soluble cation of group III but more than the solubility limit of \(\ce{Cd^{2+}}\) -the most soluble cation of group II. If pH of the test solution is maintained between 0 and 1, group II cations will precipitate and group III and higher group cations will remain dissolved. At pH 0.5, S 2- is 5.2 x 10 - 22 M that will precipitate more than 99.99% \(\ce{Cd^{2+}}\):
\[\mathrm{K}_{\mathrm{sp}}=\left[\mathrm{Cd}^{2+}\right]\left[\mathrm{S}^{2-}\right]=7.8 \times 10^{-27}\quad\quad\text{gives:}\quad\quad\ce{[Cd^{2+}]} = \frac{7.8\times 10^{-27}}{\ce{[S^{-2}]}} = \frac{7.8\times 10^{-27}}{5.2\times10^{-22}} = 1.5\times10^{-5}~M\nonumber\]
, which is 0.0002% of the initial [\(\ce{Cd^{2+}}\)].
The supernatant after removal of group I chlorides is usually within the pH range of 0.5 ±0.3, which is the appropriate pH for precipitation of group II cations under the conditions of this study. If the pH of the test sample is outside this range, the pH can be increased to ~0.5 by adding 0.5M \(\ce{NH3(aq)}\) drop by drop under stirring. Determine pH by using a pH paper after each drop of 0.5M \(\ce{NH3(aq)}\) is added and thoroughly mixed. Keep in mind that \(\ce{NH3}\) solution in water is also labeled as \(\ce{NH4OH}\). Similarly, the pH can be decreased to ~0.5 by adding 0.5M \(\ce{HCl(aq)}\) drop by drop under stirring. Determine pH by using a pH paper after each drop of 0.5M \(\ce{HCl(aq)}\) is added and thoroughly mixed.
Thioacetamide reagent is added to the test solution at pH ~0.5 and heated in a boiling water bath to precipitate out group II cations.
The precipitates include \(\ce{SnS2}\) (yellow), \(\ce{CdS}\) (yellow-orange), \(\ce{CuS}\) (Black-brown), \(\ce{Bi2S3}\) (black), formed by the following precipitation reactions:
\[\ce{SnCl6^{2-}(aq) + 2S^{2-}(aq) <=> 6Cl^{-}(aq) + SnS2(s, yellow)}\nonumber\]
\[\ce{Cd^{2+}(aq) + S^{2-}(aq) <=> CdS(s, yellow-orange)}\nonumber\]
\[\ce{Cu^{2+}(aq) + S^{2-}(aq) <=> CuS(s, black-brown)}\nonumber\]
\[\ce{2Bi^{3+}(aq) + 3S^{2-}(aq) <=> Bi2S3(s, black)}\nonumber\]
The overall color of the combined precipitate may vary depending on its composition. Black color dominates, i.e., if all precipitates are present, the color of the mixture will be black as shown in Figure \(\PageIndex{1}\).
The solution is cooled to room temperature by using a room temperature water bath. Cooling helps precipitation of \(\ce{CdS}\). A drop of 0.5 M \(\ce{NH3(aq)}\) is added while stirring, which promotes precipitation of \(\ce{CdS}\) and \(\ce{CnS2}\), as both tend to stay dissolved in a supersaturated solution. The mixture is centrifuged and decanted to separate the supernatant that is used for the analysis of group III and higher group cations. The precipitate is washed with 0.1M \(\ce{NH4Cl}\) solution and the washed precipitate is used to separate and confirm individual cations of group II.


14: Nervous System
After completing this section, you should know:
- the role of the nervous system in coordinating an animal’s response to the environment
- that the nervous system gathers, sorts and stores information and initiates movement
- the basic structure and function of a neuron
- the structure and function of a synapse and neurotransmitter chemicals
- the nervous pathway known as a reflex with examples
- that training can develop conditioned reflexes in animals
- that the nervous system can be divided into the central and peripheral nervous systems
- that the brain is surrounded by membranes called meninges
- the basic parts of the brain and the function of the cerebral hemispheres, hypothalamus, pituitary, cerebellum and medulla oblongata
- the structure and function of the spinal cord
- that the peripheral nervous system consists of cranial and spinal nerves and the autonomic nervous system
- that the autonomic nervous system consists of sympathetic and parasympathetic parts with different functions
Thumbnail: Brain human lateral view. (CC BY 2.5; Patrick J. Lynch , medical illustrator).


19.2: Population Genetics
Skills to Develop
- Describe the different types of variation in a population
- Explain why only heritable variation can be acted upon by natural selection
- Describe genetic drift and the bottleneck effect
- Explain how each evolutionary force can influence the allele frequencies of a population
Individuals of a population often display different phenotypes, or express different alleles of a particular gene, referred to as polymorphisms. Populations with two or more variations of particular characteristics are called polymorphic. The distribution of phenotypes among individuals, known as the population variation , is influenced by a number of factors, including the population’s genetic structure and the environment (Figure \(\PageIndex{1}\)). Understanding the sources of a phenotypic variation in a population is important for determining how a population will evolve in response to different evolutionary pressures.
Genetic Variance
Natural selection and some of the other evolutionary forces can only act on heritable traits, namely an organism’s genetic code. Because alleles are passed from parent to offspring, those that confer beneficial traits or behaviors may be selected for, while deleterious alleles may be selected against. Acquired traits, for the most part, are not heritable. For example, if an athlete works out in the gym every day, building up muscle strength, the athlete’s offspring will not necessarily grow up to be a body builder. If there is a genetic basis for the ability to run fast, on the other hand, this may be passed to a child.
Heritability is the fraction of phenotype variation that can be attributed to genetic differences, or genetic variance, among individuals in a population. The greater the hereditability of a population’s phenotypic variation, the more susceptible it is to the evolutionary forces that act on heritable variation.
The diversity of alleles and genotypes within a population is called genetic variance . When scientists are involved in the breeding of a species, such as with animals in zoos and nature preserves, they try to increase a population’s genetic variance to preserve as much of the phenotypic diversity as they can. This also helps reduce the risks associated with inbreeding , the mating of closely related individuals, which can have the undesirable effect of bringing together deleterious recessive mutations that can cause abnormalities and susceptibility to disease. For example, a disease that is caused by a rare, recessive allele might exist in a population, but it will only manifest itself when an individual carries two copies of the allele. Because the allele is rare in a normal, healthy population with unrestricted habitat, the chance that two carriers will mate is low, and even then, only 25 percent of their offspring will inherit the disease allele from both parents. While it is likely to happen at some point, it will not happen frequently enough for natural selection to be able to swiftly eliminate the allele from the population, and as a result, the allele will be maintained at low levels in the gene pool. However, if a family of carriers begins to interbreed with each other, this will dramatically increase the likelihood of two carriers mating and eventually producing diseased offspring, a phenomenon known as inbreeding depression .
Changes in allele frequencies that are identified in a population can shed light on how it is evolving. In addition to natural selection, there are other evolutionary forces that could be in play: genetic drift, gene flow, mutation, nonrandom mating, and environmental variances.
Genetic Drift
The theory of natural selection stems from the observation that some individuals in a population are more likely to survive longer and have more offspring than others; thus, they will pass on more of their genes to the next generation. A big, powerful male gorilla, for example, is much more likely than a smaller, weaker one to become the population’s silverback, the pack’s leader who mates far more than the other males of the group. The pack leader will father more offspring, who share half of his genes, and are likely to also grow bigger and stronger like their father. Over time, the genes for bigger size will increase in frequency in the population, and the population will, as a result, grow larger on average. That is, this would occur if this particular selection pressure , or driving selective force, were the only one acting on the population. In other examples, better camouflage or a stronger resistance to drought might pose a selection pressure.
Another way a population’s allele and genotype frequencies can change is genetic drift (Figure \(\PageIndex{2}\)), which is simply the effect of chance. By chance, some individuals will have more offspring than others—not due to an advantage conferred by some genetically-encoded trait, but just because one male happened to be in the right place at the right time (when the receptive female walked by) or because the other one happened to be in the wrong place at the wrong time (when a fox was hunting).
Exercise \(\PageIndex{1}\)
Do you think genetic drift would happen more quickly on an island or on the mainland?
- Answer
-
Genetic drift is likely to occur more rapidly on an island where smaller populations are expected to occur.
Small populations are more susceptible to the forces of genetic drift. Large populations, on the other hand, are buffered against the effects of chance. If one individual of a population of 10 individuals happens to die at a young age before it leaves any offspring to the next generation, all of its genes—1/10 of the population’s gene pool—will be suddenly lost. In a population of 100, that’s only 1 percent of the overall gene pool; therefore, it is much less impactful on the population’s genetic structure.
Genetic drift can also be magnified by natural events, such as a natural disaster that kills—at random—a large portion of the population. Known as the bottleneck effect , it results in a large portion of the genome suddenly being wiped out (Figure \(\PageIndex{3}\)). In one fell swoop, the genetic structure of the survivors becomes the genetic structure of the entire population, which may be very different from the pre-disaster population.
Another scenario in which populations might experience a strong influence of genetic drift is if some portion of the population leaves to start a new population in a new location or if a population gets divided by a physical barrier of some kind. In this situation, those individuals are unlikely to be representative of the entire population, which results in the founder effect. The founder effect occurs when the genetic structure changes to match that of the new population’s founding fathers and mothers. The founder effect is believed to have been a key factor in the genetic history of the Afrikaner population of Dutch settlers in South Africa, as evidenced by mutations that are common in Afrikaners but rare in most other populations. This is likely due to the fact that a higher-than-normal proportion of the founding colonists carried these mutations. As a result, the population expresses unusually high incidences of Huntington’s disease (HD) and Fanconi anemia (FA), a genetic disorder known to cause blood marrow and congenital abnormalities—even cancer. 1
Link to Learning
Watch this short video to learn more about the founder and bottleneck effects.
Scientific Method Connection: Testing the Bottleneck Effect
Question : How do natural disasters affect the genetic structure of a population?
Background : When much of a population is suddenly wiped out by an earthquake or hurricane, the individuals that survive the event are usually a random sampling of the original group. As a result, the genetic makeup of the population can change dramatically. This phenomenon is known as the bottleneck effect.
Hypothesis : Repeated natural disasters will yield different population genetic structures; therefore, each time this experiment is run, the results will vary.
Test the hypothesis : Count out the original population using different colored beads. For example, red, blue, and yellow beads might represent red, blue, and yellow individuals. After recording the number of each individual in the original population, place them all in a bottle with a narrow neck that will only allow a few beads out at a time. Then, pour 1/3 of the bottle’s contents into a bowl. This represents the surviving individuals after a natural disaster kills a majority of the population. Count the number of the different colored beads in the bowl, and record it. Then, place all of the beads back in the bottle and repeat the experiment four more times.
Analyze the data : Compare the five populations that resulted from the experiment. Do the populations all contain the same number of different colored beads, or do they vary? Remember, these populations all came from the same exact parent population.
Form a conclusion : Most likely, the five resulting populations will differ quite dramatically.  Now think about how this might affect a real population. What happens when a hurricane hits the Mississippi Gulf Coast? How do the seabirds that live on the beach fare?
Gene Flow
Another important evolutionary force is gene flow : the flow of alleles in and out of a population due to the migration of individuals or gametes (Figure \(\PageIndex{4}\)). While some populations are fairly stable, others experience more flux. Many plants, for example, send their pollen far and wide, by wind or by bird, to pollinate other populations of the same species some distance away. Even a population that may initially appear to be stable, such as a pride of lions, can experience its fair share of immigration and emigration as developing males leave their mothers to seek out a new pride with genetically unrelated females. This variable flow of individuals in and out of the group not only changes the gene structure of the population, but it can also introduce new genetic variation to populations in different geological locations and habitats.
Mutation
Mutations are changes to an organism’s DNA and are an important driver of diversity in populations. Species evolve because of the accumulation of mutations that occur over time. The appearance of new mutations is the most common way to introduce novel genotypic and phenotypic variance. Some mutations are unfavorable or harmful and are quickly eliminated from the population by natural selection. Others are beneficial and will spread through the population. Whether or not a mutation is beneficial or harmful is determined by whether it helps an organism survive to sexual maturity and reproduce. Some mutations do not do anything and can linger, unaffected by natural selection, in the genome. Some can have a dramatic effect on a gene and the resulting phenotype.
Nonrandom Mating
If individuals nonrandomly mate with their peers, the result can be a changing population. There are many reasons nonrandom mating occurs. One reason is simple mate choice; for example, female peahens may prefer peacocks with bigger, brighter tails. Traits that lead to more matings for an individual become selected for by natural selection. One common form of mate choice, called assortative mating , is an individual’s preference to mate with partners who are phenotypically similar to themselves.
Another cause of nonrandom mating is physical location. This is especially true in large populations spread over large geographic distances where not all individuals will have equal access to one another. Some might be miles apart through woods or over rough terrain, while others might live immediately nearby.
Environmental Variance
Genes are not the only players involved in determining population variation. Phenotypes are also influenced by other factors, such as the environment (Figure \(\PageIndex{5}\)). A beachgoer is likely to have darker skin than a city dweller, for example, due to regular exposure to the sun, an environmental factor. Some major characteristics, such as gender, are determined by the environment for some species.  TSD means that individuals develop into males if their eggs are incubated within a certain temperature range, or females at a different temperature range.
Geographic separation between populations can lead to differences in the phenotypic variation between those populations. Such geographical variation is seen between most populations and can be significant. One type of geographic variation, called a cline , can be seen as populations of a given species vary gradually across an ecological gradient. Species of warm-blooded animals, for example, tend to have larger bodies in the cooler climates closer to the earth’s poles, allowing them to better conserve heat. This is considered a latitudinal cline. Alternatively, flowering plants tend to bloom at different times depending on where they are along the slope of a mountain, known as an altitudinal cline.
If there is gene flow between the populations, the individuals will likely show gradual differences in phenotype along the cline. Restricted gene flow, on the other hand, can lead to abrupt differences, even speciation.
Summary
Both genetic and environmental factors can cause phenotypic variation in a population. Different alleles can confer different phenotypes, and different environments can also cause individuals to look or act differently. Only those differences encoded in an individual’s genes, however, can be passed to its offspring and, thus, be a target of natural selection. Natural selection works by selecting for alleles that confer beneficial traits or behaviors, while selecting against those for deleterious qualities. Genetic drift stems from the chance occurrence that some individuals in the germ line have more offspring than others. When individuals leave or join the population, allele frequencies can change as a result of gene flow. Mutations to an individual’s DNA may introduce new variation into a population. Allele frequencies can also be altered when individuals do not randomly mate with others in the group.
Footnotes
- 1 A. J. Tipping et al., “Molecular and Genealogical Evidence for a Founder Effect in Fanconi Anemia Families of the Afrikaner Population of South Africa,” PNAS 98, no. 10 (2001): 5734-5739, doi: 10.1073/pnas.091402398.
Glossary
- assortative mating
- when individuals tend to mate with those who are phenotypically similar to themselves
- bottleneck effect
- magnification of genetic drift as a result of natural events or catastrophes
- cline
- gradual geographic variation across an ecological gradient
- gene flow
- flow of alleles in and out of a population due to the migration of individuals or gametes
- genetic drift
- effect of chance on a population’s gene pool
- genetic variance
- diversity of alleles and genotypes in a population
- geographical variation
- differences in the phenotypic variation between populations that are separated geographically
- heritability
- fraction of population variation that can be attributed to its genetic variance
- inbreeding
- mating of closely related individuals
- inbreeding depression
- increase in abnormalities and disease in inbreeding populations
- nonrandom mating
- changes in a population’s gene pool due to mate choice or other forces that cause individuals to mate with certain phenotypes more than others
- population variation
- distribution of phenotypes in a population
- selective pressure
- environmental factor that causes one phenotype to be better than another


6.7.2: Human-Induced Changes
Human activities have increased atmospheric carbon dioxide by about 40% over pre-industrial levels and more than doubled the amount of nitrogen available to ecosystems. Similar trends have been observed for phosphorus and other elements, and these changes have major consequences for biogeochemical cycles and climate change.
The human mobilization of carbon, nitrogen, and phosphorus from the Earth’s crust and atmosphere into the environment has increased 36, 9, and 13 times, respectively, compared to geological sources over pre-industrial times.[3] Fossil fuel burning, land-cover change, cement production, and the extraction and production of fertilizer to support agriculture are major causes of these increases.[4] Carbon dioxide (\(CO_2\)) is the most abundant of the heat-trapping greenhouse gases that are increasing due to human activities, and its production dominates atmospheric forcing of global climate change.5 However, methane (\(CH_4\)) and nitrous oxide (\(N_{2}O\)) have higher greenhouse-warming potential per molecule than \(CO_2\), and both are also increasing in the atmosphere. In the U.S. and Europe, sulfur emissions have declined over the past three decades, especially since the mid-1990s, because of efforts to reduce air pollution.[6] Changes in biogeochemical cycles of carbon, nitrogen, phosphorus, and other elements – and the coupling of those cycles – can influence climate. In turn, this can change atmospheric composition in other ways that affect how the planet absorbs and reflects sunlight (for example, by creating small particles known as aerosols that can reflect sunlight).
State of the Carbon Cycle
The U.S. was the world’s largest producer of human-caused \(CO_2\) emissions from 1950 until 2007, when it was surpassed by China. U.S. emissions account for approximately 85% of North American emissions of \(CO_2\) [7] and 18% of global emissions. [8,9] Ecosystems represent potential “sinks” for \(CO_2\), which are places where carbon can be stored over the short or long term (see “Estimating the U.S. Carbon Sink”). At the continental scale, there has been a large and relatively consistent increase in forest carbon stocks over the last two decades,[10] due to recovery from past forest harvest, net increases in forest area, improved forest management regimes, and faster growth driven by climate or fertilization by \(CO_2\) and nitrogen.[7,11] The largest rates of disturbance and “regrowth sinks” are in southeastern, south central, and Pacific northwestern regions.[11] However, emissions of \(CO_2\) from human activities in the U.S. continue to increase and exceed ecosystem \(CO_2\) uptake by more than three times. As a result, North America remains a net source of \(CO_2\) into the atmosphere[7] by a substantial margin.
Sources and Fates of Reactive Nitrogen
The nitrogen cycle has been dramatically altered by human activity, especially by the use of nitrogen fertilizers, which have increased agricultural production over the past half century.[1,2] Although fertilizer nitrogen inputs have begun to level off in the U.S. since 1980,[12] human-caused reactive nitrogen inputs are now at least five times greater than those from natural sources.[13,14,15,16] At least some of the added nitrogen is converted to nitrous oxide (\(N_{2}O\)), which adds to the greenhouse effect in Earth’s atmosphere.
An important characteristic of reactive nitrogen is its legacy. Once created, it can, in sequence, travel throughout the environment (for example, from land to rivers to coasts, sometimes via the atmosphere), contributing to environmental problems such as the formation of coastal low-oxygen “dead zones” in marine ecosystems in summer. These problems persist until the reactive nitrogen is either captured and stored in a long-term pool, like the mineral layers of soil or deep ocean sediments, or converted back to nitrogen gas.[17,18] The nitrogen cycle affects atmospheric concentrations of the three most important human-caused greenhouse gases: carbon dioxide, methane, and nitrous oxide. Increased available nitrogen stimulates the uptake of carbon dioxide by plants, the release of methane from wetland soils, and the production of nitrous oxide by soil microbes.
Phosphorus and other elements The phosphorus cycle has been greatly transformed in the United States, [19] primarily from the use of phosphorus fertilizers in agriculture. Phosphorus has no direct effects on climate, but does have indirect effects, such as increasing carbon sinks by fertilizing plants. Emissions of sulfur, as sulfur dioxide, can reduce the growth of plants and stimulate the leaching of soil nutrients needed by plants.[20]
Source:
Galloway, J. N., W. H. Schlesinger, C. M. Clark, N. B. Grimm, R. B. Jackson, B. E. Law, P. E. Thornton, A. R. Townsend, and R. Martin, 2014: Ch. 15: Biogeochemical Cycles. Climate Change Impacts in the United States: The Third National Climate Assessment, J. M. Melillo, Terese (T.C.) Richmond, and G. W. Yohe, Eds., U.S. Global Change Research Program, 350-368. doi:10.7930/J0X63JT0. : http://nca2014.globalchange.gov/report/sectors/biogeochemical-cycles


5.E: Curvature (Exercises)
- Example 6 discussed some examples in electrostatics where the charge density on the surface of a conductor depends on the Gaussian curvature, when the curvature is positive. In the case of a knife-edge formed by two half-planes at an exterior angle \(\beta > \pi\), there is a standard result 29 that the charge density at the edge blows up to infinity as \(R^{\frac{\pi}{\beta - 1}}\). Does this match up with the hypothesis that Gaussian curvature determines the charge density?
- Show that for polar coordinates in a Euclidean plane, \(\Gamma^{r}_{\phi \phi} = −r\) and \(\Gamma^{\phi}_{r \phi} = \frac{1}{r}\).
- In 1+1 dimensions, let the metric be ds 2 = \(\frac{1}{t}\) dt 2 − t d\(\theta^{2}\), where \(\theta\) is an angle running around the circle. Calculate all the nonvanishing Christoffel symbols by hand. These will be used in example 4 where we investigate some further properties of this interesting spacetime.
- Partial derivatives commute with partial derivatives. Covariant derivatives don’t commute with covariant derivatives. Do covariant derivatives commute with partial derivatives?
- Show that if the differential equation is satisfied for one affine parameter \(\lambda\), then it is also satisfied for any other affine parameter \(\lambda' = a \lambda+b\), where a and b are constants.
- Equation [2] gives a flat-spacetime metric in rotating polar coordinates. (a) Verify by explicit computation that this metric represents a flat spacetime. (b) Re-express the metric in rotating Cartesian coordinates, and check your answer by verifying that the Riemann tensor vanishes.
-
The purpose of this problem is to explore the difficulties inherent in finding anything in general relativity that represents a uniform gravitational field g. In
example 11
, we found, based on elementary arguments about the equivalence principle and photons in elevators, that gravitational time dilation must be given by e
\(\Phi\)
, where \(\Phi\) = gz is the gravitational potential. This results in a metric $$ds^{2} = e^{2gz} dt^{2} - dz^{2} \ldotp \tag{[1]}$$On the other hand,
example 19
derived the metric $$ds^{2} = (1 + gz)^{2} dt^{2} - dz^{2} \ldotp \tag{[2]}$$by transforming from a Lorentz frame to a frame whose origin moves with constant proper acceleration g. (These are known as Rindler coordinates.) Prove the following facts. None of the calculations are so complex as to require symbolic math software, so you might want to perform them by hand first, and then check yourself on a computer.
- The metrics [1] and [2] are approximately consistent with one another for z near 0.
- When a test particle is released from rest in either of these metrics, its initial proper acceleration is g.
- The two metrics are not exactly equivalent to one another under any change of coordinates.
- Both spacetimes are uniform in the sense that the curvature is constant. (In both cases, this can be proved without an explicit computation of the Riemann tensor.)
Note
The incompatibility between [1] and [2] can be interpreted as showing that general relativity does not admit any spacetime that has all the global properties we would like for a uniform gravitational field. This is related to Bell’s spaceship paradox ( example 15 ). Some further properties of the metric [1] are analyzed in section 7.5 .
- In a topological space T, the complement of a subset U is defined as the set of all points in T that are not members of U. A set whose complement is open is referred to as closed. On the real line, give (a) one example of a closed set and (b) one example of a set that is neither open nor closed. (c) Give an example of an inequality that defines an open set on the rational number line, but a closed set on the real line.
- Prove that a double cone (e.g., the surface r = z in cylindrical coordinates) is not a manifold.
- Prove that a torus is a manifold.
- Prove that a sphere is not homeomorphic to a torus.
-
Curvature on a Riemannian space in 2 dimensions is a topic that goes back to Gauss and has a simple interpretation: the only intrinsic measure of curvature is a single number, the Gaussian curvature. What about 1+1 dimensions? The simplest metrics I can think of are of the form ds
2
= dt
2
− f(t)dx
2
. (Something like ds
2
= f(t)dt
2
−dx
2
is obviously equivalent to Minkowski space under a change of coordinates, while ds
2
= f(x)dt
2
− dx
2
is the same as the original example except that we’ve swapped x and t.) Playing around with simple examples, one stumbles across the seemingly mysterious fact that the metric ds
2
= dt
2
−t
2
dx
2
is flat, while ds
2
= dt
2
− tdx
2
is not. This seems to require some simple explanation. Consider the metric ds
2
= dt
2
− t pdx
2
.
- Calculate the Christoffel symbols by hand.
- Use a computer algebra system such as Maxima to show that the Ricci tensor vanishes only when p = 2.
Note
The explanation is that in the case p = 2, the x coordinate is expanding in proportion to the t coordinate. This can be interpreted as a situation in which our length scale is defined by a lattice of test particles that expands inertially. Since their motion is inertial, no gravitational fields are required in order to explain the observed change in the length scale; cf. the Milne universe .
References
29 Jackson, Classical Electrodynamics


1.6: Thinking Like an Economist- Abstraction
Economics, and its offspring, Finance, are abstract (social) sciences. In order to study economics, it is essential that one understands what an abstraction is.
An abstraction is an idea, intended to mirror reality in its simplest form. The world is a very complicated place; there are many variables or inputs, some identifiable, others not, that affect an outcome, and which we endeavor to identify. In order to understand the outcome which is generally true, but not necessarily absolutely or always so, one must engage in a process of simplification that requires removing minor variables from a general idea in order to reduce the notion to its essential characteristics. Indeed, the Latin word, “abstract,” comes from “drawing” or “taking away from.”
The ever-changing kaleidoscope of raw reality would defeat the human mind by its complexity, except for the mind’s ability to abstract, to pick out parts and think of them as a whole.
Thomas Sowell
A Conflict of Visions (2002), p. 5
In this process, one is able to derive a broad, general conclusion, based on first principles from which is derived a general idea or rule. In economics, this requires a ceteris paribus assumption, that is to say, holding “ all else equal .” Initially, it is assumed that no other variables matter and are thus ignored away. It takes some discipline to do this at first, but it quickly becomes easy; you must merely keep it in mind.
In circumstances where little given or known information may be at hand, one must assume reasonable default assumptions , i.e., premises , which make sense in general and in the simplest, most common form possible. While it may be facile to imagine other considerations, or variables, that may come into play, one must avoid doing this, in order to focus on just a few key variables, which affect the outcome. Here is a relevant comment by Dr. Milton Friedman [1] :
A hypothesis is important if it “explains” much by little, that is, if it abstracts the common and crucial elements from the mass of complex and detailed circumstances surrounding the phenomena to be explained and permits valid predictions on the basis of them alone. To be important, therefore, a hypothesis must be descriptively false in its assumptions; it takes account of, and accounts for, none of the many other attendant circumstances, since its very success shows them to be irrelevant for the phenomena to be explained….
To be sure, Dr. Friedman’s comments are not without criticism, but nevertheless are adhered to, by and large, in the social sciences, including, of course, economics. In certain other disciplines, including law, political theory, history, philosophy, and possibly others, we do not engage in this mode of reasoning . In these fields, by contrast, we are often engaged in dialectical reasoning . There, we first state a thesis , then examine its antithesis . We go back and forth numerous times until we can arrive at a synthesis , which is conclusive or dispositive.
Those of you that are accustomed to dialectical reasoning must diligently avoid the natural instinct to quickly imagine the antithesis; rather you must remain steadfast to the line of reasoning demanded by the more linear manner of abstract argumentation, based on first principles and ceteris paribus delimitations. (A “delimitation” is a limitation that one person herself imposes on the scope of her reasoning.)
When, in certain instances, we deviate from abstract reasoning, we assume specific, more descriptive , circumstances in a contextual or “concrete” manner. The result may not be generalizable . If a conclusion is generalizable, we say that it is true in the overwhelming number of instances, although not necessarily all.
One of the beauties of abstract reasoning is that it enables us to employ other, more reasonable assumptions when we find that a model has poor predictive power.
Happy travels!
Religion without science is blind, science without religion is lame.
– Albert Einstein
- Friedman, Milton. (1953). Essays in Positive Economics. Chicago: University of Chicago Press. pp. 14-15. ↵


2.1.5: Il pronome "ne"
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The pronoun ne
Ne is a tricky little word because it is essential in Italian while there is no exact equivalent in English. Consider the example:
- Anna: Quanti pomodori usi per fare il sugo? [ How many tomatoes are you using to make the sauce? ]
- Giuseppe: Ne uso sei o sette. [ I use six or seven (of them). ]
As you can see, in English it is not necessary to say of them , but in Italian you absolutely have to use ne (which here means “of them” ) . Keep in mind the following:
- Ne means of it or of them .
- Ne usually answers the questions Quanto? Quanta? Quanti? Quante? [ How much? How many? ], whether the question is explicit or just implied.
- Ne is usually followed by a quantity of some kind, like a number or an amount.
Some more examples:
- Quanti anni hai? > Ne ho 19.
- Non mangio molto pesce: ne mangio solo un po’ la domenica.
- Hai della farina? > No, non ne ho.
As is the case for ci, ne always goes before the conjugated verb, i.e.: ne mangio , ne ho 20 , etc. However, when there is a verb + an infinitive, it can go either before the conjugated verb or be attached to the end of the infinitive after you have dropped the last letter of the infinite, as in comprare > comprar . Consider the two possible answers to the following question:
Hai già comprato la farina per fare la focaccia?
- Sì, ma ne devo comprare ancora un po’.
- Sì, ma devo comprarne ancora un po’.
Ne is also used in many common phrases not only to mean of it/of them , but also to mean about it . We are not going to go into detail on this in this course; simply memorize the following expressions:
- Cosa ne dici? [ What do you say about it? ]
- Cosa ne pensi? [ What do you think about it? ]
- Cosa ne sai? [ What do you know about it? ] and Ne sai qualcosa? [ Do you know anything about it? ]
- Non me ne importa ; non me ne importa niente [ I don’t care about it; I don’t care about it at all. ]
- Non me ne frega niente!  [ Who cares! ] which are not very nice things to tell someone.


15.6: Summarizing
- Describe when and how to summarize
What Does Summary Look Like?
Summarizing involves condensing the main idea of a source into a much shorter overview (anywhere from a single sentence to a page). A summary outlines a source’s most important points and general position. When summarizing a source, it’s important to give credit to the original author. You should reference the author or source in the appropriate citation method at the end of the summary.
A good summary accomplishes the following:
-
It identifies or names the piece and its author(s) and states the main purpose of the text.
Example: In his essay, “ Consider the Lobster ,” writer David Foster Wallace asks readers to consider the ethical implications of feasting on lobsters. - It captures the text’s main points.
- It does not include the reader’s opinions, feelings, beliefs, counterarguments, etc.
- It is short. The idea of a summary is to “boil down” or condense a text to just a few sentences.
How to Construct a Summary
- Decide what part of the source is most relevant to your argument.
- Pick out the most important sentences in that part of the source. In most cases, you’ll focus on the main points.
- Paraphrase those sentences. If they include any important or memorable phrases, quote those in your paraphrases. List the paraphrased sentences in the order they occur in the original.
- Add any other information that readers might need to understand how your paraphrased sentences connect to one another.
- Revise the list so that it reads not like a list but like a paragraph.
Don’t cut and paste summaries from other articles and use them as your own. Many of the periodical indexes that are available as part of your library’s computer system include abstracts of articles. Do not cut this abstract material and then paste it into your own annotated bibliography. For one thing, this is plagiarism. Second, cutting and pasting from the abstract defeats one of the purposes of writing summaries and creating an annotated bibliography in the first place, which is to help you understand and explain your research.
When you summarize, you reword and condense another author’s writing. Be aware, though, that summary also requires individual thought: when you reword, it should be a result of you processing the idea yourself, and when you condense, you must think critically about which parts of the text are most important.
How to Mix Quotation with Summary
A long summary can make readers feel that you and they are too distant from an important source. So when you write a long summary, look for memorable phrases that you can quote within your summary. For example:
- “Colomb and Williams emphasize that drafting is `an act of discovery’ that can fuel a writer’s creative thinking. They acknowledge that some writers have to draft carefully and stick closely to their outlines, but they advise writers to draft as freely and as openly as they can…they show writers how to make the best of a plan while hoping that you will `discover what your storyboard has missed.’” [1]
When you add a few quotations to your summary, you seem a more lively writer. You give readers an idea of your source without quoting so much that your paper reads like a cut-and-paste job. If you have pages that are mostly summary and paraphrase, add a few notable quotations that will liven up your writing.
Look at some more examples of appropriate summaries in the exercise below.
https://lumenlearning.h5p.com/content/1290979705130201808/embed
Quote, Paraphrase, or Summarize?
The best way to start to understand the different rhetorical affordances of paraphrase, summary, and quotation is to see how they work together in actual writing. In this practice activity, you will read a passage from a student research paper and identify where you see paraphrase, summary, and quotation at work.
Use the following paragraphs to answer the questions that follow.
The history of the Mississippi Delta centers around one thing: farming. During the transition from segregated to integrated schools, small towns in the Delta were home to illustrious plantations and booming manufacturing plants. The economy was not spectacular, but it was habitable. Now, most of the manufacturing plants have closed their doors and farm jobs are becoming more and more sparse (Elliott). NPR’s Debbie Elliott notes that “the decline of manual labor and exodus of manufacturing jobs have made difficult conditions worse in one of the nation’s poorest regions.” Six Deltan counties have seen a population decline greater than 20% since 1970.
The declining economy is another contributing factor to the decline of Deltan schools. In a Washington Post article about schools in the Delta, writer Peter Whoriskey explains how rural schools that are primarily comprised of at-risk youth and offer substantially lower salaries than nearby schools have a difficult time finding and preserving qualified teachers. One section of Whoriskey’s article includes a story of an untrained teacher hired through an “emergency license” who was “found hiding” when his third-grade students tossed papers in his direction.
There are no hard and fast rules for when to use direct quotations, when to paraphrase, and when to summarize. Like so many other parts of the writing process, this rhetorical decision will become easier with practice. Keep in mind that the goal of including sources in your writing is to build your credibility (you’ll learn more about this later) and to make your purpose more clear and concise to your audience. These factors should influence the source integration decisions you make.
As you are writing your own paper, use this checklist to help you decide when to paraphrase, summarize, or directly quote from sources.
-
Use direct quotations . . .
- sparingly and when the original language has a strong impact
- with set-up (signal phase), context, and proper citation
- followed by commentary, analysis, or explanation
-
Use paraphrase . . .
- to contextualize the information (who said it, when, and where)
- to restate all the supporting points to develop the main idea of the original text
- to share important information from the source while maintaining your own voice
-
Use summary . . .
- to contextualize the information (who said it, when, and where)
- by condensing the source to its main ideas and without using quotations or citing specific supporting points of the passage
- to support your claims
- Kate L. Turabian. A Manual for Writers of Research Papers, Theses, and Dissertations, Seventh Edition: Chicago Style for Students and Researchers. Revised by Wayne C. Booth, Gregory G. Colomb, Joseph M. Williams, and University of Chicago Press Editorial Staff. (University of Chicago Press, 2007), 83-7. ↵
Contributors and Attributions
- How to Summarize Accurately, section on summary. Located at : www.groundsforargument.org/drupal/evidence/sidebar/summarize. Project : Grounds for Argument. License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Summary and Plagiarism Activity. Provided by : Excelsior College Online Writing Lab. Located at : https://owl.excelsior.edu/plagiarism/plagiarism-how-to-avoid-it/plagiarism-summarizing/ . License : CC BY: Attribution
- Image of tulip field. Authored by : 272447. Provided by : Pixabay. Located at : pixabay.com/photos/flowers-tulips-field-varieties-569648/. License : Other . License Terms : pixabay.com/service/terms/#license
- Caution section. Authored by : Steven D. Krause. Located at : https://openoregon.pressbooks.pub/oregonwrites/chapter/quoting-paraphrasing-and-avoiding-plagiarism/ . License : CC BY-NC-SA: Attribution-NonCommercial-ShareAlike
- Expression and Inquiry. Authored by : Chris Manning, Sally Pierce, and Melissa Lucken. Located at : https://pb.openlcc.net/expressionandinquiry/chapter/10-3-5-paraphrase-summary-and-direct-quotes/ . License : CC BY: Attribution