Mendelian Inheritance, Basic probability - AndersenLab/Genetic-Analysis GitHub Wiki

Lecture 1 slides

Gregor Mendel

What is Genetics

Genetics is the study of heredity. The basic unit of heredity is a gene. The founder of genetics, Gregor Mendel (1822–1884), never knew what a gene was, but he was able to formulate some of the basic principles of genetics that we still use today. These discoveries, like many in science, were made by doing two things:

  1. Applying a new idea or way of thinking to an old problem.
  2. Being lucky.

Humans had been selectively breeding and domesticating organisms for tens of thousands of years prior to Mendel's time, but the basic rules that governed inheritance were not known. Mendel's "new idea applied to an old problem" was to quantify the results of genetic crosses in pea plants. From the results, he was able to establish some basic rules that are fundamental to genetic analysis today. See below to find out why he was lucky.

Mendel's Laws

Mendel established fundamentals of genetics by performing crosses between pea plants with different traits. Mendel chose to use pea plants for a two reasons:

  1. Ease of experimental manipulation - Control over which strains crossed. In other words - the ability to experimentally manipulate generations of individuals.
  2. A reproducible strain. When a true-breeding strain is bred to itself, it produces offspring with the same phenotype. This reproducibility is essential for experimental validation.

The simplest cross Mendel performed was a monohybrid cross which involves crossing two individuals with different alleles in the same gene.

Monohybrid Cross

Mendel also performed a dihybrid cross:

Dihybrid Cross

From these crosses, he was able to deduce three basic principles of genetics still in use today.

The Law of Segregation - During gamete formation, the alleles for each gene segregate from each other so that each gamete carries only one allele for each gene.

The Law of Independent Assortment - Genes for different traits can segregate independently during the formation of gametes.

The Law of Dominance - Some alleles confer dominant phenotypes while others confer recessive phenotypes; an organism with at least one allele that confers a dominant phenotype will express the dominant phenotype.

Mendel's Luck

Mendel applied a new method to an existing problem - crossing pea plants; but he was also quite lucky to identify some of the fundamental principles of genetics. Below are some reasons why he was lucky:

  1. Pea plants are diploid, meaning they have two copies (alleles) of every autosomal chromosome.
  2. Mendel examined seven traits and identified the same patterns of inheritance in each. All seven of the traits he examined were not linked. It turns out that when genes are close together on chromosomes - they do not segregate independently. Therefore, Mendel's second law does not apply in all cases. He chose traits controlled by genes that were unlinked.
  3. The traits examined were not complex, or under the control of many genes or environmental inputs.
  4. The traits did not follow inheritance patterns such as codominance or incomplete dominance.

Codominance and Incomplete Dominance

In addition to a Dominant/Recessive relationship between alleles in the same gene, it is possible to have additional relationship types.

Incomplete Dominance - Occurs when both alleles contribute to a phenotype.

For example, two flowers (one red, one white) bred together produce offspring that are pink.

Codominance - Occurs when both alleles produce a phenotype independent of one another.

The best example of this human ABO blood type. ABO blood type is controlled by the ABO gene. We have three alleles of the ABO gene: A, B, and O. The A and B alleles express A and B antigens that are expressed on the surface of erythrocytes (red blood cells), and the O type does not result in expression of any antigen. Crucially, the phenotype is the antigen or antigens expressed. The following genotypes produce differing phenotypes:

Genotype Phenotype
AA A
BB B
AB AB
OO O

Basic Probability

p(A) is shorthand notation for "The probability of event A occurring"

The Product Rules states that the probability of any two independent events co-occurring is the product of their individual probabilities. For example, the probability of rolling a 12 with two dice is the probability of rolling a six on each die (1/6 * 1/6 = 1/36).

The Sum Rule states that the probability of two or more events occurring is the sum of their individual probabilities. For example, using a six-sided die, the p(1 or 2) = 2/6 or 33.333%

Further Resources