Non-Mendelian Inheritance Patterns

COMPLEX INHERITANCE ( Non-Mendelian) PATTERNS AND PROBABILITIES

In the last couple of lessons, we learned the meaning of dominant and recessive and how to use Punnetts Square for a simple monohybrid cross- a cross where there is one trait being considered that is dominant or recessive.  Not every trait is so simple to determine.  Let's first review Mendel's work. 

MENDEL'S MODEL AND LAWS

There are four key elements to Mendels' study of Observable Patterns of Inheritance:

1. There are heritable traits determined by heritable factors, which we now call genes, and they come in pairs.

2. Genes come in different versions called alleles. The dominant allele will hide the presence of a recessive allele.

3. Mendels Law of Segregation- during gamete production each egg or sperm receives one of two alleles.  That allocation is random.

4. Mendels Law of Independent Assortment- genes for different traits are inherited independently of one another.

We also learned that a Genotype- is the set of alleles an organism has, and the Phenotype- is the observable traits that an organism has. 

Now, a century and a half later, we know there are exceptions, variations, extensions, and unusual patterns of inheritance.  Mendel's work is not wrong, but we have to expand our understanding to account for every pattern of inheritance we see in organisms. 

Non-Mendelian Inheritance- Complex inheritance patterns
Of course, human eyes do not come in multi-color, but they do come in many colors. How do eyes come in so many colors? That brings us to complex inheritance patterns, known as non-Mendelian inheritance. Many times inheritance is more complicated than the simple patterns observed by Mendel.
Each characteristic Mendel investigated was controlled by one gene that had two possible alleles, one of which was completely dominant to the other. This resulted in just two possible phenotypes for each characteristic. Each characteristic Mendel studied was also controlled by a gene on a different (non-homologous) chromosome. As a result, each characteristic was inherited independently of the other characteristics. Though Mendel did note that flower color, seed color, and axis color ( where a branch meets the stem) seemed to be correlated, he could not know for certain why.  Today we do......this is a case where one gene affects more than one trait. We now know that inheritance is often more complex than this.

Variations Involving Single Genes

Multiple Alleles

An organism may only get two alleles, one from Mom and one from Dad, but consider that many versions of those alleles may exist in a population. For instance, in rabbits, there are four common alleles for fur color.  Black fur comes from the Dominant allele "C".  When present it is always expressed.  Then there are four recessive alleles.  c^ch, c^h, and c. The first is grey fur, the second is white fur with black ears, tail, feet, and nose, and the third is a pure white albino bunny.  The c^ch is incompletely dominant to the ch and c alleles...making for a lighter-colored Himalayan or lighter grey bunny.  The c^h is completely dominant to the c allele.  This leads to a wide variety of bunny fur colors.  

INCOMPLETE DOMINANCE and CODOMINANCE

A characteristic may be controlled by one gene with two alleles, but the two alleles may have a different relationship than the simple dominant-recessive relationship that you have read about so far. 

Incomplete Dominance
Incomplete dominance occurs when the phenotype of the offspring is somewhere in between the phenotypes of both parents; a completely dominant allele
does not occur. Two alleles may produce an intermediate phenotype where both are partially expressed. For example, when red snapdragons are crossed with white snapdragons, the offspring are all pink. The pink color is an intermediate between the two parent colors. When two plants with pink flowers are crossed, they will produce red, pink, and white flowers. The genotype of an organism with incomplete dominance can be determined from its phenotype.  Here is where Mendel got it wrong, but only because his studies were limited to pea plants.  Sometimes there is a blending of traits. 

Codominance

 Codominance occurs when both alleles are expressed equally in the phenotype of the heterozygote. The red and white flower in the figure has codominant alleles for red petals and white petals. Two alleles a simultaneously expressed when both are present, rather than one fully determining the phenotype.  Here is a chart showing the possible outcomes of ABO blood typing.  A and B self-markers are both dominant.  When a person gets AB blood type both self markers are equally present on a blood cell.  A and B are always expressed over O. O is recessive, and will not be expressed unless there are two O alleles.  Here is also a picture of a flower in which White and Red alleles are codominant and both expressed. 

PLEIOTROPY 

Pleiotropy is when one gene affects multiple different traits.  Mendel did note this in his work.  He saw that  flower color, seed pod color, and axil color ( the junction where leaves met the stem) seemed to all be correlated.  

Lethal Alleles

Many genes are necesary for survival.  If an allele of a gene is not functional or functions abnormally, it may not result in a living organism.  The organism may die in utero, meaning inside the mothers womb, or it may have a very short life.  There are two types of Lethal Allele conditions, Recessive Lethal Alleles and Dominant Lethal Alleles.  

Recessive Lethal Allele is lethal ( leads to death) when the organism is homozygous for the allele, but not when it is heterozygous.  One famous example is the yellow mice studied by French geneticist Lucion Cuenot.  Yellow fur is a mutation in mice. "A^Y "is the allele for yellow fur. "A^y" represents brown fur.  When yellow mice were crossed with brown mice, it was found that the yellow allele is dominant to the brown allele.   One half of the mice born were yellow and half were born brown.  This meant that the Yellow mice were heterozygous ( A^YA^y), because if they had been homozygous, the dominant yellow gene would have made 100% yellow mice.  However, when Yellow mice were crossed with yellow mice, an unusual ratio was the result.  You would expect 100% yellow mice.  Instead 2 were yellow and 1 was brown.  The yellow mice didnt "breed true".  What was happening.  When a mouse receives two A^Y alleles, the mouse dies in utero.  Only three of four live to birth, leaving a ratio of 2:1......two heterozygous yellow mice and one homozygous brown mouse. Examples of other diseases caused by recessive lethal alleles are cystic fibrosis, Tay-Sachs disease, sickle-cell anemia, and brachydactyly.

Dominant Lethal Alleles can cause death with just a single copy of the allele, so as a heterozygote a often lethal condition is expressed.   Frequently we do not see organisms alive in the population with a dominant lethal allele, because they die before birth.  They do not live to pass on their alleles, so they are rare in populations. However there are a few that will allow an organism to live a few years.  And still fewer, are the dominant lethal alleles that express themselves late in life.  Huntingtons Disease and Epiloia are examples of a dominant lethal allele that is survived past birth.  In huntingtons disease, a person does not experience symptoms until they are around 40 years old, which are nuerological deterioration, dementia, and involuntary movments.  By that time they have often passed the genetic condition to some of their children.  In Epiloia a person has many defermations of epidermial tissue, on their skins surface and on their organs.  With good medical access they can live a normal life span. It is very disfiguring. 

Sex-Linked Traits
Traits controlled by genes on the sex chromosomes are called sex-linked traits. Single-gene X-linked traits have a different pattern of inheritance than single-gene autosomal traits. Do you know why? It’s because males only have one X chromosome. In addition, they always inherit their X chromosome from their mother, and they pass it on to all their daughters but none of their sons. Inheritance of Sex Chromosomes. Mothers pass on only X chromosomes to their children. Fathers always pass their X chromosome to their daughters
and their Y chromosome to their sons. Can you explain why fathers always determine the sex of the offspring?  Because males have only one X chromosome, they have only one allele for any X-linked trait. Therefore, a recessive X-linked allele is always expressed in males. Because females have two X chromosomes, they have two alleles for any 
X-linked trait. Therefore, they must inherit two copies of the recessive allele to express the recessive trait. This explains why X-linked
recessive traits are less common in females than males. Red-green color blindness is an example of a recessive X-linked trait. People with this trait cannot distinguish between the colors red and green. More than one recessive gene on the X chromosome codes for this trait, which is fairly common in males but relatively rare in females. About 1 in 10 men have some form of color blindness, however, very few women are color blind.  The X Chromosome is large and contains upwards of 1200 genes, 5% of the human genome.  The Y Chromosome is smaller and carries 100 to 200 genes.  The Y chromosome carries the genes for male sex determination and development.

Barr Bodies:

While a female embryo is forming, one of the X-chromosomes is less active, essentially a crumpled-up ball called a Barr Body. Many of the genes are not used.  The level of gene activity produced by a single X chromosome is the normal "dosage" for a human. Men have this dosage because, well, they only have one X chromosome! Women have the same dosage for a different reason: they shut down one of their two X chromosomes in a process called X-inactivation. Which X is shut down is random.  Shut down begins about 16 hours after mitosis begins so there are several cells at this point.  It could shut down the one the Father contributed, or it could be the one the Mother contributed, and it happens during the embryo stage of development.  All of the cells that the original cell divides into follow the same shutdown pattern of the first cell........so if a cell made a barr body out of Moms X chromosome...all the decedents of that cell shut down Moms X.  A classic example of this is is a calico cat.  All calico cats are female.  The cat is heterozygous for black and tan coat color.  They are considered a mosaic.  So are human females a mosaic? 

VARIATIONS INVOLVING MULTIPLE GENES

Some traits are controlled by more than one gene and can interact in a few different ways.

Complimentary Genes

With complimentary genes, two genes with their two dominant alleles are required to produce the trait.  For instance, Gene C codes for an enzyme that makes a precursor substance.  Then Gene P codes for an enzyme that uses the precursor to make the particular trait.  This is the case in Sweat Pea Plants, Two genes and their dominant alleles must be present for the plant to have a purple flower.   Here is an excellent explanation from NAGWA:¹

In complementary gene action, it is the dominant alleles of the two genes that work together to contribute to the phenotype. If either gene is missing the dominant allele, the phenotype cannot be observed. Dominant alleles in both genes are necessary “to complete” the pathway and produce the specific trait.

To explain this complementary action between genes, let’s take a closer look at the sweet pea flower experiment performed by William Bateson and Reginald Punnett to discover complementary genes.

Bateson and Punnett performed their experiments on Lathyrus odoratus, a sweet pea that normally has purple flowers. In  experiments, they used two varieties of the plant that had white flowers. In the first step of their experiments, they crossed the two varieties of white sweet pea flowers and produced a first generation of flowers that were purple

Epistasis

Epistasis is where the allele of one gene may mask or conceal the allele of another gene.  Labrador Retrievers' coat color is affected by this.  There are Black, Brown, and Yellow versions of a Labrador retriever coat.  

UC Davis Veterinary Medicine has an excerpt explaining this well: ²

The gene that determines if a Labrador Retriever is black or chocolate is Tyrosinase-related protein 1, or TYRP1 for short. There are four known alleles at this gene in the Labrador Retriever: one is the allele for black (designated as B) and three different alleles that result in chocolate (collectively designated as b). In determining if your puppies will be black or chocolate, the black coat color (B) is dominant to the chocolate (b). Therefore, a puppy will only be chocolate if each parent contributes a chocolate allele (bb). If one or both parents (Bb or BB) contribute the black (dominant) allele, the puppy will be black (BB or Bb), although a Bb puppy would carry chocolate and could therefore produce chocolate puppies.

The gene that determines if your Labrador puppies will be yellow is a different gene from the one that determines black/chocolate color and is known as melanocortin 1 receptor, or MC1R for short. There are several known alleles of this gene in dogs, but for Labradors the most common are E (produces black and brown pigment) and e (only produces yellow pigment). An e allele at the MC1R gene prevents expression of the black or chocolate color in the hair follicle and the puppy's hair ends up yellow. This is epistasis.  Interestingly, the black or chocolate pigment is still expressed in the skin, just not in the hair. To be yellow, a Labrador must have two recessive alleles of the MC1R gene (ee). This means both parents contributed a yellow allele (e). However, if only one (Ee) or no (EE) yellow-causing alleles are contributed, this puppy will be either black or chocolate depending on which alleles are present at the TYRP1 gene (see above). Two yellow labs can only have yellow puppies (ee) since they both only have the yellow allele (e) to contribute to their offspring. Some black (BbEe or BBEe) and chocolate (bbEe) Labradors carry one copy of the yellow-causing allele (e). If they are bred to each other, there is a chance that some puppies will get a copy of e from each parent and have yellow hair.

POLYGENIC INHERITANCE AND ENVIRONMENTAL EFFECTS

Some traits like height, skin color, and eye color are controlled by many genes.  This is called polygenic inheritance. Because of this, the traits are a spectrum rather than two options.  Over 400 genes contribute to a person's height, and human height is a spectrum from short to very tall, and every measure in between.  Height can also be impacted by the environment.  A person's health and nutrition greatly impact height.   Eye color is one of these as well.  We have learned about the big B for brown and the little b for blue, but 16 genes impact the color of our eyes.  Human eyes have a range of colors.  If you think about it, you know people with almost black-brown eyes, light brown eyes, gray-blue eyes, and very blue eyes.  Some of the genes decrease or increase pigments in the iris, turning a brown eye into a hazel eye.   

Environment affects the expression of genetic traits as well.  Flamingos are born white or grey, and they turn pink over the first couple of years.  They eat a diet of algae, crustaceans, and shrimp, which have a lot of the orange pigment Beta Carotene in them.  The pigment is absorbed into the fat and feathers of the flamingo.  Flamingos that don't get this special diet have their bright pink fade back toward white over time.  

FINDING THE PROBABILITY OF TRAITS- Dihybrid Cross, Forked Line Method, and Probability Method.

Dihybrid Cross

We studied and practiced  monohybrid crosses. A dihybrid cross is a test mating of individuals looking at two traits with a Punnetts Square. This uses 16 boxes in the Punnet Square. You could even do a trihybrid cross for three traits- using 64 boxes in the Punnetts Square, or a tetrahybrid cross of four traits- using 256 boxes. As you can see, the use of Punnetts Square becomes unweildy the more traits we look at, so we will learn a few different methods for calculating ratio/probability, when we are looking are larger numbers of traits. 

Lets first understand some terminology before looking at these charts.  "P" stands for the Parent Generation.  "F1" stands for the first generation of offspring.  "F2" stands for the second generation of offspring.  Two traits Mendel studied was the shape of the pea wrinkled or round, and the color of the pea, green or yellow.  Look at the chart below to see how a dihybrid cross is done.

Forked Line Method

Another method for studying ratios and probabilities of genetic crosses is the forked line method.  Lets follow three traits through the forked line method, Plant height- tall (T) or dwarf (t), pea shape round (R) or wrinkled (r), and pea color yellow (Y) or green (y).   After crossing these individuals we get the following results

ratio 27:9:9:3:9:3:1

Probability Method

Instead of writing out every possible genotype we can use the probability method.  Probability is a mathematical measure of likelihood.  

The Product Rule- States the probability of two or more independent events occuring together can be calculated by multiplying the individual probabilities of the events.  It is the "and" rule- both event A and event B must happen for a certain outcome to occur.  Since event A and event B happen independently, the product rule says you can calculate probability of the outcome by multiplying the probabilities of X and Y occuring, to get a total probability of both occuring. 

We know that for any heterozygous cross,  Bb x Bb, the fraction of homozygous recessive offspring will be 1/4.  Therefore, if say we wanted to know the probability of a plant having four recessive traits,  you can multiply  this fraction for 4 genes 1/4 x 1/4 x 1/4 x 1/4= 1/256 of offspring will be homozygous recessive.  

The Sum Rule- States the probability that any of several mutually exclusive events will occur is equal to the sum of the events individual probabilities.   This is the "or" rule.  Look for the word "or " in these problems. You add your fractions together in this case. Mutually exclusive events can't happen at the same time.   You either get this OR that outcome.  To show the probability of getting either this OR that outcome, you ADD the probabilities together.  If I want to know the probability of getting offspring which are Dominant homozygous for both traits or a Recessive homozygous for both traits from parents AaBb x AaBb.  I might first do a simple punnets square for the first trait Aa.  Then a simple punnets square for Bb.  So we are looking for offspring number one AABB  OR  offspring  number two aabb.  For offspring number two mulitply 1/4 x 1/4 to get the probability of gettin THAT offspring.  This is 1/16.  Do the same for offspring number 2.  1/4 x 1/4= 1/16 .  What is the probability of getting homozygous dominant OR homozygous recessive offspring:

1/16 + 1/16= 2/16= 1/8 chance of getting one OR the other. 

The probability of being  homozygous dominant is 1/4.  The probability of being homozygous recessive is 1/4.  The same if the B trait below.  

Here is an excellent video for explaning this further:

https://www.youtube.com/watch?v=y4Ne9DXk_Jc

1. https://www.nagwa.com/en/explainers/714121243707/

2. https://healthtopics.vetmed.ucdavis.edu/health-topics/canine/inheritance-coat-color-labrador-retriever