Genetics in Life

Genetics and Heredity Fundamentals

Course 1 · Chapter 10 · Capstone: Genetics in Everyday Life

This last chapter takes what the course built and points it at the places where most people actually meet genetics: a test result, an ancestry report, a news headline about a "gene for" something. The biology from Genetics and Heredity Fundamentals 1 to 9 gives you the vocabulary. What matters now is the arithmetic and the habits of thought that stop you being misled. All the programs here are Python 3.

What was run, and what was not

Every program in this chapter was run and the output shown is what it printed. The numbers in the examples are invented to make a point, not real test or disease figures. The biology and ethics are written from general knowledge; items marked (check) are the ones to verify first. Where a program uses random numbers it fixes the seed, so the same output appears each time. Nothing here is medical advice: for a real result, talk to a doctor or a genetic counsellor.

What a Genetic Test Can and Cannot Tell You

A genetic test looks for something specific: one changed letter, a missing piece, an unusual number of chromosomes, or a pattern across many positions at once. Different tests answer different questions (check).

Diagnostic: does this person have the change that explains their symptoms?
Carrier: does this healthy person carry one copy of a recessive allele (Genetics and Heredity Fundamentals 1 and 8)?
Screening: a cheap test applied to many people to pick out those who need a closer look.
Predictive or risk: does this person have variants that raise the chance of a condition later, without making it certain?

Two numbers describe how good a test is. Sensitivity is the share of people who have the thing that the test correctly flags. Specificity is the share of people who do not have it that the test correctly clears. A test with 99% of both sounds nearly perfect, and people often assume that a positive result then means a 99% chance of having the condition. That is wrong, and the reason is how common the condition is. The share of positive results that are real is the positive predictive value, and it depends on the prevalence, how common the condition is in the group tested.

def ppv(prev, sens, spec):
    tp = prev * sens
    fp = (1 - prev) * (1 - spec)
    return tp / (tp + fp)

for prev in (0.5, 0.1, 0.01, 0.001):
    print(prev, round(ppv(prev, 0.99, 0.99), 3))

n = 100000
prev, sens, spec = 0.001, 0.99, 0.99
have = n * prev
true_pos = have * sens
false_pos = (n - have) * (1 - spec)
print(round(have), round(true_pos), round(false_pos))
print(round(true_pos / (true_pos + false_pos), 3))
    

The same test gives a 99% chance that a positive is real when half the group has the condition, but only 9% when one person in a thousand has it. The last three lines show why using "natural frequencies": of 100,000 people, 100 have the condition and the test finds 99 of them, but it also wrongly flags 1 in 100 of the 99,900 healthy people, which is 999 false alarms. So about 99 of every 1,098 positives are real. Rare conditions and screening tests are a poor mix for this reason, and it is why a positive screen is normally followed by a second, more specific test (check).

The base rate is easy to forget

The common mistake is to remember the accuracy of the test and forget how rare the condition is. Before trusting a positive (or a negative) result, ask two questions: how accurate is the test, and how common is this in people like me? The answer to the second one can change the meaning of the first completely.

Ancestry Claims and the Shrinking Share

Ancestry reports compare your DNA with reference groups and give percentages, or list possible relatives (check). They rest on real genetics, but a few facts make the headline claims easy to misread. You inherit half your DNA from each parent, about a quarter from each grandparent, an eighth from each great-grandparent, and so on: the expected share from one ancestor n generations back is 1 / 2ⁿ. Crucially that is an average. Genetics and Heredity Fundamentals 4 showed that each chromosome is a random mixture, so the real share varies, and from far enough back a particular ancestor may have left you no DNA at all, even though they are certainly your ancestor.

The simplified model below pretends each of the 22 non-sex chromosomes is passed down whole, with no crossing over. At each generation a chromosome comes from one of the two parents with probability one half, so a chromosome comes from a chosen ancestor with probability 1 / 2ⁿ. The first table is the chance, by formula, that none of the 22 does. The second runs 1,000 simulated people for each of three depths.

import random
for n in range(1, 8):
    print(n, 1 / 2**n, round((1 - 1 / 2**n) ** 22, 3))

rng = random.Random(5)
def shared_fraction(n, chroms=22):
    hits = sum(1 for _ in range(chroms) if all(rng.random() < 0.5 for _ in range(n)))
    return hits / chroms

for n in (2, 4, 6):
    results = [shared_fraction(n) for _ in range(1000)]
    zero = sum(1 for r in results if r == 0) / 1000
    print(n, round(sum(results) / 1000, 4), round(1 / 2**n, 4), zero)
    

0.5 0.0
0.25 0.002
0.125 0.053
0.0625 0.242
0.03125 0.497
0.015625 0.707
0.0078125 0.842
0.2488 0.25 0.002
0.066 0.0625 0.234
0.0161 0.0156 0.7
    

In the second block the columns are the depth, the average simulated share, the formula's expected share, and the fraction of simulated people who got nothing from that ancestor. The averages match the formula. But at six generations back (the great-great-great-great-grandparents), about 70% of people would share no whole chromosome with a given ancestor. In real DNA, crossing over cuts chromosomes into pieces, so ancestors tend to leave many small segments rather than a few whole chromosomes, and the exact chances differ (check). The lesson holds either way: the further back you go, the less reliably DNA can confirm a particular ancestor, so a claim such as "you are descended from this famous person" is mostly unfalsifiable by the DNA alone.

Claim	What it can mean	Question to ask
"You are 30% from region X"	your DNA resembles a reference group of people living there now	how was the reference group chosen, and how big is it? (check)
"A relative match"	a stretch of shared DNA larger than chance	how much is shared, and what range of relationships fits it? (check)
"Descended from a famous person"	perhaps a paper trail, rarely the DNA	what is the evidence apart from the DNA?
"No DNA from that ancestor"	quite possible many generations back	does it contradict the family records at all?

Risk Headlines: Relative and Absolute

"Gene variant doubles the risk of X" is a classic headline. A relative risk compares two groups: here, 2 means twice as likely. It says nothing about how likely X was in the first place. The absolute risk is the actual chance. The difference between the new and the old absolute risk is the extra risk, and its reciprocal is the number of people among whom one extra case is expected.

def risks(base, rr):
    new = base * rr
    return new, new - base

for base, rr in ((0.01, 2.0), (0.10, 2.0), (0.0001, 1.5)):
    new, extra = risks(base, rr)
    print(base, rr, round(new, 5), round(extra, 5), round(1 / extra))
    

01 2.0 0.02 0.01 100
1 2.0 0.2 0.1 10
0001 1.5 0.00015 5e-05 20000
    

The columns are the baseline risk, the relative risk, the new risk, the extra risk, and one extra case per that many people. "Doubles" turns a 1-in-100 risk into 2-in-100 (one extra case in 100 people), but turns a 1-in-10 risk into 2-in-10 (one in 10). A relative risk of 1.5 on a baseline of 1 in 10,000 means an extra case in 20,000 people. Note too that most common traits and conditions are polygenic (Genetics and Heredity Fundamentals 6) and depend on environment as well, so a single variant rarely behaves like the single gene of a pea. A "gene for" a complex trait is almost always shorthand for a small statistical nudge (check).

Ethics and Privacy

Genetic data is unusual because it is permanent, it is partly shared with relatives, and it can say things the person did not ask about. Several questions follow, and they do not have simple answers (check).

Privacy and consent. Your result also says something about your parents, siblings and children, who did not agree to be tested. Who may see it, and who may keep it?
Discrimination. Should an insurer or an employer be allowed to use genetic results? Laws differ between countries and change over time (check).
The right not to know. Some people want to know their risk of a serious late-onset condition, and some do not. Tests can reveal findings that were not being looked for.
Children. Testing a child for a condition that would only appear in adulthood takes the choice away from the adult they will become. Practice and guidance vary (check).
Fairness of the science. Reference data has historically over-represented some groups, so tests and risk scores can work less well for others (check).
Reading too much into DNA. Genetic determinism, the idea that genes alone fix traits, is not what the science says. Genes and environment work together, and a high-risk variant is not a sentence.

Counselling exists for a reason

Many health services offer genetic counselling before and after a test, to explain what a result can and cannot say and what the options are. The code in this course is for understanding the arithmetic. It is not a substitute for that conversation (check what is offered where you live).

A Checklist for Reading Genetics in the News

Pulling the whole course together, here are the questions to put to a story before believing it.

Who and how many were studied? A small sample can give striking results by chance, as the coin and pea simulations in Genetics and Heredity Fundamentals 1 showed.
Relative or absolute? Find the baseline risk. "Doubles" of a tiny risk is still tiny.
What does "gene for" mean here? One gene, as with a pea colour, or a small nudge among many, as with height?
Correlation or cause? A variant being more common in a group does not by itself show the variant causes the trait (check).
Which population? Results from one group do not always carry over to another, because allele frequencies differ (Genetics and Heredity Fundamentals 8).
How good is the test, and how common is the condition? Remember the 9% positive predictive value above.
Was it in humans, in mice, or in a dish? Many headlines describe work in animals or cells (check).
Is it peer reviewed, and has anyone repeated it? A single study is a starting point.
What are the limits the authors state? Good reports and good papers say what they cannot show.

Chapter	The idea you now have	Where it protects you
Genetics and Heredity Fundamentals 1	chance and sample size	small studies and "my family proves it"
Genetics and Heredity Fundamentals 2 and 3	DNA, genes and what proteins do	knowing what a "mutation" is and is not
Genetics and Heredity Fundamentals 4	shuffling by meiosis	ancestry claims and why siblings differ
Genetics and Heredity Fundamentals 6 and 7	beyond dominant and recessive, and sex-linked traits	"a gene for" headlines and pedigree questions
Genetics and Heredity Fundamentals 8	allele frequencies	carrier numbers and population claims
Genetics and Heredity Fundamentals 9	sequences as data	understanding what a test actually reads

Challenges

Exercise 1

A recessive allele has frequency q = 0.01 in a population of 200,000. Using Hardy-Weinberg, print the fraction of carriers and of affected people. A carrier test has sensitivity 0.95 and specificity 0.98. Print the number of carriers, true positives and false positives, and the share of positive results that are real. Finish by printing the chance that a random couple are both carriers, and the chance that a child of a random couple is affected.

📄 View solution

Exercise 2

Write a headline decoder. Given a list of (headline, baseline risk, relative risk) tuples, for each print the headline, the new absolute risk, the extra risk, and "about 1 extra case per N people". Use three headlines with baseline risks 0.01, 0.20 and 0.0002, and print a warning if any new risk would be above 100%.

📄 View solution

Exercise 3

With random.Random(11) and 5,000 simulated people per depth, use the whole-chromosome model to estimate, for 3 to 8 generations back, the share of people who inherit no chromosome from a chosen ancestor. Print it next to the formula's value, and finish by printing the first depth at which more than half of people share nothing.

📄 View solution

Quick Reference

Sensitivity and specificity: correct flags among those who have it; correct clears among those who do not
Positive predictive value: the share of positives that are real; it falls when the condition is rare
Ancestry: the expected share from an ancestor n generations back is 1 / 2ⁿ, but the real share varies and can be zero
Relative and absolute risk: always find the baseline; extra risk is new minus baseline
Ethics: privacy, discrimination, the right not to know, testing children, fairness of the data
In the news: sample size, baseline, population, correlation or cause, repeated or not
Check: test types, ancestry methods, the model's limits and the ethics and law details

Course complete

That is the end of Genetics and Heredity Fundamentals. You can now follow a trait from a pair of alleles through the chromosomes, the protein and the population, read a sequence as data, and ask sensible questions of a genetics story. A good next step is to take one real health or ancestry article and run the checklist above against it, writing down your answers.