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Chapter 2: Problem 26

Francis Galton, a geneticist of the pre-Mendelian era, devised the principle that half of our genetic makeup is derived from each parent, one-quarter from each grandparent, one-eighth from each great-grandparent, and so forth. Was he right? Explain.

Short Answer

Expert verified
Galton's principle is mathematically correct; each generation's genetic contribution sums to 100%.

Step by step solution

01

Understanding Galton's Principle

Francis Galton proposed that each generation contributes half the genetic makeup to the following generation. This means that if you sum these contributions from parents, grandparents, great-grandparents, etc., the total should equal 1 or 100% of the genetic makeup.
02

Calculate Genetic Contribution of Parents

According to Galton, half of our genetic material comes from each parent. Therefore, mathematically, this is represented as \( \frac{1}{2} + \frac{1}{2} = 1 \).
03

Calculate Genetic Contribution of Grandparents

Each grandparent contributes one-quarter of our genes. There are four grandparents, so \( 4 \times \frac{1}{4} = 1 \). This also sums to 100% of the genetic contribution.
04

Calculate Genetic Contribution of Great-Grandparents

Each great-grandparent contributes one-eighth of our genetics, and there are eight great-grandparents: \( 8 \times \frac{1}{8} = 1 \). This again totals to 100% of the genetic makeup.
05

Checking for Infinite Series

Each generation contributes as a sum of fractions that decreases as \( \frac{1}{2^n} \), where \( n \) is the number of generations from the individual (parents: \( n=1 \), grandparents: \( n=2 \), etc.). Sum this infinite geometric series: \( \sum_{n=1}^{ ext{infinity}} \frac{1}{2^n} = 1 \). This means each generation's genetic contribution properly adds to 100%, according to this model.
06

Conclusion on Galton's Principle

Mathematically, adding the infinite series confirms that each prior generation contributes proportionally to the genetics of the individual, totaling 100%. Hence, Galton's idea correctly forms a complete genetic system without missing or overlapping contributions.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Generation Contributions
Understanding how genetics is passed down through generations is key to comprehending genetic inheritance. Each generation contributes a specific portion of genetic material to the next. Starting with parents, half of a person's genetic material is derived from each鈥攖his is known as a basic principle in genetics. As we delve further into genetic ancestry:
  • Grandparents contribute one-quarter of the genetic makeup,
  • Great-grandparents contribute one-eighth,
  • Each previous generation continues to contribute half of the genetic material to the subsequent generation.
This contribution system is akin to pie pieces getting smaller with each generation, yet all these pieces together always complete the whole pie鈥攔epresenting 100% of one's genetic makeup. It's mathematical proof of family bonds cemented in our DNA.
Genetic Material Distribution
The distribution of genetic material across generations follows a predictable pattern, ensuring genetic diversity and continuation.By mathematically analyzing this, each generation's genetic contribution forms part of a series. In essence, the genetic material distribution is an infinite geometric series where each generation contributes a fraction:
  • The parents contribute one-half, represented as \( \frac{1}{2} \),
  • Grandparents contribute one-quarter, or \( \frac{1}{4} \) each from two grandparents,
  • Great-grandparents contribute one-eighth, or \( \frac{1}{8} \) each from four great-grandparents.
This series further aligns with the mathematical sequence of \( \frac{1}{2^n} \), where \( n \) signifies the generational level in question.Adding these terms, each generation's contributions accrue logically to the full 100% of genetic material in an individual, confirming a seamless distribution from ancestral figures.
Francis Galton's Principle
Francis Galton, a notable figure in early genetics, proposed a principle outlining how genetic materials are inherited across generations. This principle shapes our understanding of inheritance even before Mendel's laws gained traction. Galton's principle asserts that:
  • Each parent's contribution to an individual's genetic makeup is half,
  • Grandparents' contributions stand at a quarter each
  • And, this pattern proceeds systematically with further ancestors each contributing a fraction diminishing by half in each generational step.
This concept established the early foundation for genetic studies and underlines the modulating factor of inherited traits. Galton's perspective essentially foresaw the mathematical model of genetic inheritance, highlighting a pivotal moment in scientific history. His work, though initially conceptual, interacts harmoniously with modern genetic theory, emphasizing continuity in inheritance without overlap or unaccounted portions.

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Most popular questions from this chapter

Design a different nuclear-division system that would achieve the same outcome as that of meiosis.

In the plant Arabidopsis thaliana, a geneticist is interested in the development of trichomes (small projections). A large screen turns up two mutant plants (A and B) that have no trichomes, and these mutants seem to be potentially useful in studying trichome development. (If they were determined by single-gene mutations, then finding the normal and abnormal functions of these genes would be instructive.) Each plant is crossed with wild type; in both cases, the next generation \(\left(\mathrm{F}_{1}\right)\) had normal trichomes. When \(\mathrm{F}_{1}\) plants were selfed, the resulting \(\mathrm{F}_{2}\) 's were as follows: \(\mathrm{F}_{2}\) from mutant \(\mathrm{A}: 602\) normal; 198 no trichomes \(\mathrm{F}_{2}\) from mutant \(\mathrm{B}: 267\) normal; 93 no trichomes a. What do these results show? Include proposed genotypes of all plants in your answer b. Under your explanation to part \(a\), is it possible to confidently predict the \(\mathrm{F}_{1}\) from crossing the original mutant \(A\) with the original mutant \(\mathrm{B} ?\)

A plant geneticist has two pure lines, one with purple petals and one with blue. She hypothesizes that the phenotypic difference is due to two alleles of one gene. To test this idea, she aims to look for a 3: 1 ratio in the \(\mathrm{F}_{2} .\) She crosses the lines and finds that all the \(\mathrm{F}_{1}\) proge ny are purple. The \(\mathrm{F}_{1}\) plants are selfed, and \(400 \mathrm{F}_{2}\) plants are obtained. Of these \(\mathrm{F}_{2}\) plants, 320 are purple and 80 are blue. Do these results fit her hypothesis well? If not, suggest why.

a. The ability to taste the chemical phenylthiocarbamide is an autosomal dominant phenotype, and the inability to taste it is recessive. If a taster woman with a nontaster father marries a taster man who in a previous marriage had a nontaster daughter, what is the probability that their first child will be (1) A nontaster girl (2) A taster girl (3) A taster boy b. What is the probability that their first two children will be tasters of either sex?

In a possible future scenario, male fertility drops to zero, but, luckily, scientists develop a way for women to produce babies by virgin birth. Meiocytes are converted di rectly (without undergoing meiosis) into zygotes, which implant in the usual way. What would be the short-and long-term effects in such a society?
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