Probability and Mendelian Genetics

Probability Definition: The likelihood that a particular even will occur Formula: # of times something occurs # of trials Important Rule: Previous Events DO NOT affect future outcomes. Example: Flipping a coin—each flip is a separate, independent event

Standard Deviation Definition: Calculation based on differences of expected and observed results over total number Formula: Expected-Observed Total Number **Provides a reference point for accuracy of results when compared to a standard (expected)**

Three Principles of Probability As the number of events increase, the standard deviation decreases (aka results improve) 2. Product Rule—the probability that two separate events will occur AT THE SAME TIME is equal to the product (multiplication) of their separate probabilities.

Product Rule Example Q: When flipping a coin twice, what are the chances that both times it will come up heads? Answer: ½ x ½ = ¼    chances of heads in 1 flip chances of heads in 1 flip chances of both happening AT THE SAME TIME

3rd Principle of Probability Sum Rule—when an event can occur in more than one way, the probability that it will occur EITHER ONE WAY OR ANOTHER is equal to the sum of the separate probabilities

Sum Example Q: What are the chances of rolling either a 5 or a 6 on a standard die (singular for dice) during one roll? Answer: 1/6 + 1/6 = 2/6 or 1/3    Probability of getting one or the other in a single roll Chances of rolling 5 Chances of rolling 6

Mendelian Genetics  HEREDITY is the transmission of genetic information from one generation to another.    The GENE is the basic unit of information passed from one generation to another and it also CONTROLS the basic functions of a cell.  All information in genes is stored in the sequence of NUCLEOTIDE BASES that make up DNA. PROBABILITY is one way that scientists determine whether a particular hereditary trait will appear in offspring. **Probability is an application of math that predicts the CHANCES that a certain event might occur**

Gregor Mendel “The Father of Genetics”  In the 1860’s, GREGOR MENDEL determined the BASIC PRINCIPLES OF HEREDITY. **He did this by the CROSS-POLLINATION of plants**   UNIQUE METHODS THAT LED TO HIS SUCCESS 1. He concentrated on one trait at a time. 2. He used LARGE numbers of organisms to minimize the influence of chance on his data. 3. He combined the results of many identical experiments. 4. He used the rules of probability to analyze his results.

The Experiment Mendel collected many types of pea plants and tested them for genetic purity (offspring are ALL identical to parents)   He then worked with strains that showed one of two different forms of the same trait. (EX. ROUND PEAS VS. WRINKLED PEAS) He crossed a pure strain of round peas with a pure strain of wrinkled peas (Parents of such a cross are called P1 for parental generation)  Result: All offspring were ROUND (the wrinkled trait seemed to have disappeared). The offspring are known as F1, for first filial generation)  He allowed the F1’s to grow and SELF-pollinate. Result: ¾ of the peas were ROUND, ¼ of the peas were WRINKLED (This filial generation is known as F2) **The wrinkled seeds that had disappeared seemed to have suddenly reappeared in the next generation**

P1 Generation P1 Generation F1 Generation F2 Generation Tall Short

F1 Generation P1 Generation F1 Generation F2 Generation Tall Short

F2 Generation P1 Generation F1 Generation F2 Generation Tall Short

Mendel’s Seven F1 Crosses on Pea Plants Seed Shape Seed Color Seed Coat Color Pod Shape Pod Color Flower Position Plant Height Round Yellow Gray Smooth Green Axial Tall Wrinkled Green White Constricted Yellow Terminal Short Round Yellow Gray Smooth Green Axial Tall

Principle of Dominance All ROUND peas were known as the DOMINANT form of the trait because they held the majority. All WRINKLED peas were known as the RECESSIVE form of the trait because there were so few present. The dominant trait will ALWAYS mask the recessive trait when present.   Many trials of this experiment were tried and all results were the same—with the round pea being dominant to the wrinkled pea and the ratio always remaining 3:1.

Segregation, cont.  HOMOZYGOUS: a pure strain of a plant/organism. (EX. Only round peas are found in both offspring and parent). **This is represented as R/R for both alleles of the offspring**    HETEROZYGOUS: a HYBRID or cross, of two strains of plant/organisms. (EX. One allele of offspring is from a ROUND parent, one allele of offspring is from a WRINKLED parent and there is a 50% chance either one will contribute a gamete during meiosis) **This is represented as R/r for the alleles of the offspring**  NOTE: ALWAYS WRITE THE CAPITAL LETTER FIRST, IF PRESENT

Principle of Segregation The offspring of a pure round and pure wrinkled cross would receive ONE FACTOR from each parent (one round and one wrinkled)   FACTORS are now known as ALLELES. Alleles are represented by a CAPITAL LETTER for the DOMINANT form (EX. Round=R) and by a LOWERCASE letter for the RECESSIVE form (EX. Wrinkled=r) The alleles form the GENETIC MAKEUP or GENOTYPE The genotype of an individual is responsible for its PHENOTYPE or PHYSICAL APPEARANCE

Punnett Squares P1 generation: R/R x r/r Gametes possible: F1 generation:   R r   R r Rr

Result from previous slide: 100% R/r (all round) Punnett Squares, cont. Result from previous slide: 100% R/r (all round) F2 generation: R/r x R/r   Gametes possible: So: ½ ½ R r R r R r   R r RR Rr rr Result: 3:1 (75% round, 25% wrinkled)

Punnett Squares, cont. When an offspring is HETEROZYGOUS, the DOMINANT forms PHENOTYPE is represented. (EX. R/r would look like a ROUND PEA)   Therefore, from the above square, a 3:1 ratio is evident with 75% of the peas phenotype being ROUND (RR or Rr) and 25% of the peas phenotype being WRINKLED (rr).

Patterns of Inheritance  Mendel also crossed plants that differed in TWO traits. These crosses were called DIHYBRID CROSSES.   In a dihybrid cross of two traits that are heterozygous, the ratio of genotypes is 9:3:3:1

Example of Dihybrid Cross P1 generation: RRYY x rryy RY   ry Gametes possible:   RY ry   RrYy   Ratio: 100% RrYy

Principle of Independent Assortment Definition: Alleles from one trait segregate INDEPENDENTLY of alleles for other traits during gamete formation.    Therefore, 4 combinations of alleles are possible in the F2 generational crosses.

Dihybrid Crosses, cont. F1 generation: RrYy (female) x RrYy (male) Gametes possible: RY rY Ry ry RY rY Ry ry

F2 generation:     Ry  rY ry RY RRYY  RRYy  RrYY  RrYy RRYy RRyy RrYy Rryy RrYY rrYY rrYy  ry rryy RY

Dihybrid Crosses, cont. Phenotype Ratio: 9/16 ROUND AND YELLOW   Phenotype Ratio: 9/16 ROUND AND YELLOW 3/16 ROUND AND GREEN 3/16 WRINKLED AND YELLOW 1/16 WRINKLED AND GREEN Ratio: 9:3:3:1 Genotype Ratio: 1/16 RRYY 1/16 rrYY 2/16 RRYy 2/16 rrYy 2/16 RrYY 1/16 rryy 4/16 RrYy 2/16 Rryy 1/16 RRyy **Remember if a CAPITAL LETTER is present it ALWAYS determines the phenotype as dominant**

 When alleles have more than two allelic forms, they are known as MULTIPLE ALLELES. EX: Blood types: A, AB, B, O