If I flip a coin, what are the chances it will land on heads? Find out all about probability according to Mendel in Episode 64.
If I flip a coin, what are the chances it will land on heads? Find out all about probability according to Mendel in Episode 64. Two of Mendel’s major observations are highly rooted in meiosis and the manner in which homologous chromosomes separate (2:08). Get some Chi-Square testing with some awesome brave corn (4:34). The rules of probability can be applied to study the passing of single-gene traits through generations (7:06).
The Question of the Day asks (8:23) What male plant structure produces pollen?
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064 Mendel’s Rules
Hi and welcome to the APsolute Recap: Biology Edition. Today’s episode will recap Mendel’s Rules
Zoom out:
Unit 5 - Heredity
Topic - 5.3
Big idea - Information Storage and Transmission
I’ve got a very difficult question to ask you. If I flip a coin, what are the chances it will land on heads? (long pause) Ok yes, 50%. How about this one? What if I flip two coins - what are the chances they will both land on heads? 0.5 times 0.5 is 0.25, so 25%! Congratulations, you did a probability. Ok, when two heterozygotes cross, what are the chances that their offspring will be homozygous recessive? One out of four is 25%! Or, each parent has a 50% chance of passing on the recessive allele….0.5 x 0.5 is also, 25%. Now, what are the chances that they will have TWO offspring that are homozygous recessive...hmm…. so two independent events, happening consecutively…... you’ll need to wait until the end to find out!
Let’s Zoom in:
Time to talk about Gregor - not Sir Gregor Clagaine a la Game of thrones, but the COMPLETE opposite of a 250 pound assassin. Gregor Mendel was an Austrian monk and farmer who had the power of keen observation. While tending the monastery garden, Mendel noticed that certain traits appeared more often than others (ie purple flowers) while some traits seemed to disappear and reappear with time (ie recessive alleles). For his contributions to genetics, Mendel is regarded as the Father of Heredity. Not that he knew anything really about DNA, but I digress.
Two of Mendel’s major observations are highly rooted in meiosis and the manner in which homologous chromosomes separate. The first is the law of independent assortment which states that alleles of genes located on non-homologous chromosomes will separate during meiosis I without influencing each other. For example, so long as two genes are on different chromosomes - there won’t be a greater chance of inheriting them together, they are not linked. Just like flipping two coins next to each other won’t influence how they land. The second is the law of segregation which states that the two alleles for each gene will separate during meiosis, as diploid cells become haploid.
It's really convenient that Mendel experimented with pea plants. They are small with very observable phenotypes, quick generation times, and make tons of offspring. Also - you can easily control mating through self and cross fertilization. Yes, plants mate. Yes, there are male and female anatomical parts of a plant. Yes, plants have egg and sperm. Its sexual reproduction after all. How would Mendel’s laws have been affected if he had studied a different type of plant? Data would not have been as consistent that's for sure and he couldn’t have created true breeding plants for controlled experiments. Polygenetic traits? codominance? sex-linked recessive traits? - All in our next episode.
Ok, we can’t finish up without mentioning Chi-Square hypothesis testing. AKA, the statistical test which looks at a set of experimental data and asks the BIG question….umm…. is that close enough to what we expected to happen? Or are their other (cough …. evolutionary) factors at play? Don’t be scared of the equation That big pointed “E” is sigma, which means sum. And then its just a fraction. observed - expected, all squared, divided expected. Observed represents your actual experimental outcomes, genetic ratios etc while expected would be the calculated values from a punnett square. Don’t memorize the equation, or the table of critical values - it's all on the formula sheet provided for the exam.
Here are the primary steps for chi-Square hypothesis testing. Imagine you are completing a dihybrid cross of two heterozygotes for the traits offfff…... begin Awesome (capital A) and Brave (capitalB). So both parents are Awesome and Brave. Sweet. Let’s make these parents um….. corn. Because corn makes lots offspring (all those kernels are each the result of fertilization!). Now we have awesome, brave corn, mating - just go with it. You are expecting to see a 9:3:3:1 phenotypic ratio since you completed your Punnett square, but GASP! The numbers seem a bit “off” - how off? Formulate a null hypothesis and perform a chi-square test. You should conclude by stating whether you should reject (calculated value exceeded the critical value for 3 degrees of freedom) or fail to reject the null hypothesis. Don’t forget to justify your reasoning!
Time for unit connections. Correlation to Unit 1 with DNA structure and Unit 7: Natural Selection. After all, fertilization involves the fusion of two haploid gametes, restoring the diploid number of chromosomes and increasing genetic variation in populations. And variation is a crucial part of evolution.
Alright - what about the exam? Practice, practice, practice. You may need to Punnett square, probability express, and Chi-square in both the multiple choice and FRQ sections. This is a good topic to provide experimental data and pull in information from multiple units. Oftentimes these are represented as “word problems” like in math class, so feel free to use your own letters to represent the alleles. Oh and did we mention pedigrees? Be on the lookout for application there too.
Oh right - the introductory question. Don’t want to leave you hanging. What are the chances of TWO offspring that are homozygous recessive when heterozygous parents cross - 0.25 x 0.25 is ⅛, or 12.5%. The rules of probability can be applied to analyze passage of single-gene traits from parent to offspring. If the events are independent, like with this example - than you multiple the independent probabilities. If the two events are mutually exclusive, than you add your probabilities. As in “what are the probabilities of the offspring inheriting a dominant allele from two heterozygous parents” That would be ¼ + ¼ + ¼ - or 75%. You’ll likely use the multiplication rule more often in genetics problems, but don’t worry, these equations are also on the formula sheet.
To recap……
Mendel was a farmer who is credited with the Law of Independent assortment and the law of segregation. Chi-square testing compares expected from Punnett Squares and experimentally observed data. The rules of probability can be applied to analyze passage of single-gene traits from parent to offspring.
Coming up next on the Apsolute RecAP Biology Edition: Breaking Mendel’s Rules
Today’s question of the day is about plant reproduction.
Question of the day: What male plant structure produces pollen?