With our modern understanding of genes, chromosomes, and cellularreproduction, we can explain the biological basis of Mendel’sobservations and make pretty accurate predictions about the offspringthat any given cross (short for crossbreeding) will produce.
Alleles
Each of the traits that Mendel observed inhis pea plants came in one of two varieties; modern science calls anygene that gives rise to more than one version of the same trait anallele. So, for example, the tall gene and the short gene are differentalleles (variations) of the height gene.
Every somatic cell contains two completesets of chromosomes, one from each parent. Now you can understand whyhomologous chromosomes are similar, but not identical: although theycontain the same genes, they may not contain the same alleles for thesegenes.
Homozygous and Heterozygous
Going back to Mendel’s plants, we can nowsay that all of his true-breeding plants contained two of the samealleles for each of the observed genes. Tall plants in this Pgeneration had two alleles for tallness (TT), and short P generationplants had two alleles for shortness (tt). Anytime an organism’s twoalleles for a specific trait are identical, that the individual is saidto be
homozygous (“homo” means same) for that trait.
On the other hand, crossing the tall and short plants to produce F1hybrids created a generation of plants with one tall allele and oneshort allele (Tt). An organism with two opposing alleles for a singlegene is said to be
heterozygous for that trait.
Genotype and Phenotype
Although the P generation of pure-breeding tall plants
looked the same as their hybrid F1 offspring, the P and F1generations did not have identical genetic makeups. The genetic makeupof a certain trait (e.g., TT, Tt, or tt) is called its genotype, whilethe physical expression of these traits (e.g., short or tall) is calleda phenotype.
For any given trait, an organism’sgenotype will indicate alleles from both parents, while the phenotypeonly indicates the allelic form that is physically expressed in thatindividual. This distinction between genetic makeup and physicalappearance explains the apparent “disappearance” of the recessivealleles in the F1 generation. Mendel’s results for the F2 generation can also be reinterpreted in light of these new distinctions. Mendel’s results showed that 75 percent of the F2 offspring exhibited the dominant phenotype, a ratio of 3:1 dominant to recessive. But from a genetic perspective, the breakdown would actually be around 25 percent homozygous dominant (TT), 50 percent heterozygous with a dominant phenotype (Tt), and 25 percent homozygous recessive (tt)—a ratio of 1:2:1.
Punnett Squares
The Punnett square is a convenientgraphical method for representing the genotypes of the parental gametesand all the possible offspring they produce. The Punnett square belowshows the mating of two F1 hybrids (Aa genotype). We call this mating a
monohybrid cross,because it involves only one gene. According to the law of se
gregation,two possible gametes are formed: A and a. The paternal gametes arelisted as columns across the top of the square, and maternal gametesare listed as rows down the left side of the square. Combining thegametes in the intersecting boxes provides the genotypes of allpossible offspring.
In this case, 25 percent of the F2 offspring will be AA, 50 percent will be Aa, and 25 percent will be aa. Both AA and Aa will have the dominant phenotype, giving the 3:1 ratio (75 percent to 25 percent) of dominant to recessive phenotypes that Mendel observed.
For the
SAT II
Biology, if you are given thegenotypes of two parents, you should be able to predict the genotypesand phenotypes of their offspring by using a Punnett square.
The Law of Independent Assortment
After finishing his monohybrid crosses, Mendel moved on to
dihybrid crosses,in which he bred pure, parental varieties that had two traitsdistinguishing them from each other. He wanted to determine whether theinheritance of one trait was connected in any way to the inheritance ofthe other.
The color and shape of the pea seedsprovided two convenient traits to study. The seeds were either yellowor green, with yellow dominant; in shape, they were either round orwrinkled, with round dominant. Mendel crossed double dominant(phenotype yellow and round, genotype RRYY) plants with doublerecessive (phenotype green and wrinkled, genotype rryy) plants. Asexpected, the F1generation consisted of hybrid offspring all with the double dominant(round yellow) phenotype and a heterozygous genotype (RrYy). The keytest came in the proportions of different phenotypes in the F2generation. If the inheritance of one trait did not influence theinheritance of the other, then each parent should make equal numbers ofthe four possible gametes, and sixteen different genotypes would beequally represented in the offspring. As seen in the Punnett squarebelow, there should be four different phenotypes (yellow and round,green and round, yellow and wrinkled, green and wrinkled) occurring inthe proportions 9:3:3:1.
Mendel’s phenotype counts of F2 seeds did indeed show the 9:3:3:1proportions anticipated in the Punnett square for the dihybrid cross.From these results, he concluded that the inheritance of one trait wasunrelated to the inheritance of a second trait. The units from any onehereditary pair segregate into the gametes independently of thesegregation of the units from any other pair. This principle is knownas the law of independent assortment.
Calculating Probabilities
Drawing Punnett squares is a helpful way tovisualize simple genetics problems, but with problems involving severaldifferent genes, it is often easier to use the rules of probability. (APunnett square for a three-gene hybrid cross would have 64squares!) There are two rules of probability that you will need tosolve genetics problems. First, the probability of an outcome thatdepends on the occurrence of two or more independent events is obtainedby multiplying together the probability of each necessary independentevent. This is the
and rule of probability:
If A and B must occur in order to bring about outcome C, then the probability of 
In contrast, if an outcome depends on theoccurrence of any one of several mutually exclusive alternatives, thenthe probability of the outcome is obtained by adding together theprobabilities of the alternatives. This is the
or rule of probability:
If A or B must occur to get outcome C, then the probability of 
As an example, we can calculate the probability of getting an 11 when rolling two dice, die A and die B. In order to roll an 11, we need a 5
and a 6. The probability of rolling a 5 on die A and a 6 on die B is
But we can also roll an 11 with a 6 on die A and a 5 on die B. This is a mutually exclusive alternative to the first roll we considered; its probability is also 1/ 36. Since either A5, B6
or A6, B5 gives us a total of 11, the final probability of rolling an 11 using two dice is 1 /36 + 1/36 = 2/36 = 1/18.
Moving from gambling to genetics, we cancalculate the probability that a cross between genotypes AABBCc andaaBbCc will produce an offspring with genotype AaBbcc. Taking one geneat a time, the probability of the Aa combination is a perfect 1, since an AA and aa cross can produce only Aa offspring.
The probability of the Bb combination is 1/2, because the BB and Bb cross will produce Bb offspring 50 percent of the time.
The probability of the cc combination is 1/4, because the Cc and Cc cross gives cc offspring 25 percent of the time.
[
Since Aa
and Bb
and cc must occur to produce our desired outcome, the probability is
Test Crossing (Back Crossing)
A test cross is the means by which ascientist can determine whether an individual with a dominant phenotypehas a homozygous (AA) or heterozygous (Aa) dominant genotype. The testcross involves mating the individual with the dominant phenotype to anindividual with a recessive (aa) phenotype and observing the offspringproduced. If the individual being tested is homozygous dominant, thenall offspring will have a dominant phenotype, since all the offspringwill have at least one A allele and the A is dominant.
If the tested individual is heterozygousdominant, then half of the offspring will show the dominant phenotype,while the other half show the recessive phenotype.
Incomplete Dominance and Codominance
Mendel’s law of dominance is generally true, butthere are many exceptions to the law. In some instances, instead of aheterozygote expressing only one of two alleles, both alleles could bepartially expressed. For example, the flower color of the four o’clockplant is determined by a single gene with two alleles: plantshomozygous for the R1 allele have red flowers, while plants homozygous for the R2 allele have white flowers. If interbred, the heterozygous R1R2 plants have pink flowers. Incomplete dominanceisthe term used to describe the situation in which the heterozygotephenotype is intermediate between the two homozygous phenotypes.
If the heterozygote form simultaneouslyexpresses both alleles fully, then the relationship between the twoalleles is called codominance. An example of codominance appears inhuman blood type. Blood type is determined by two alleles, A and B,that code for the presence of antigen A and antigen B on the surface ofred blood cells. Allele A and B are codominant. If only the allele A ispresent, then only antigen A exists on the blood cell. If only allele Bis present, then only antigen B exists on the blood cell. If bothalleles A and B are present, neither dominates the other and bothantigens appear on the red blood cell. A third allele,
i, isrecessive: if only it appears, then the blood is of type O. Thefollowing is a summary of the genotypes that result in the fourdifferent blood types:
AA and Ai
type A blood
BB and Bi
type B blood
AB and BA
type AB blood
ii
type O blood
Linkage and Crossing-Over
Fortunately for Mendel, the genes encoding hisselected traits did not reside close together on the same chromosome.If they had, his dihybrid cross results would have been much moreconfusing, and he might not have discovered the law of independentassortment. The law of independent assortment
holds true as long as twodifferent genes are on separate chromosomes. When the genes are onseparate chromosomes, the two alleles of one gene (A and a) willsegregate into gametes independently of the two alleles of the othergene (B and b). Equal numbers of four different gametes will result:AB, aB, Ab, ab. But if the two genes are on the same chromosome, thenthey will be linked and will segregate together during meoisis,producing only two kinds of gametes.
For instance, if the genes for seed shapeand seed color were on the same chromosome and a homozygous doubledominant (yellow and round, RRYY) plant was crossed with a homozygousdouble recessive (green and wrinkled, rryy), the F1hybrid offspring, as usual, would be double heterozygous dominant(yellow and round, RrYy). However, since in this example the R and Yare linked together on the chromosome inherited from the dominantparent, with r and y linked together on the other chromosome, only twodifferent gametes can be formed: RY and ry. Therefore, instead of 16 different genotypes in the F2offspring, only three are possible: RRYY, RrYy, rryy. And instead offour different phenotypes, only the original two will exist. Noticethat the inheritance pattern now resembles that seen in a monohybridcross, with a 3:1 phenotypic ratio, rather than the 9:3:3:1ratio expected from the dihybrid cross. If physically linked on asingle chromosome, the round and yellow alleles would segregatetogether, and the wrinkled and green alleles would segregate together:no round green seeds or wrinkled yellow seeds would ever appear.
The above explanation, however, neglects theinfluence of the crossing over of genetic material that occurs duringmeiosis. The farther away two genes are from one another, the morelikely an exchange point for crossing over will form between them. Atthese exchange points, the alleles of one gene switch to the oppositehomologous chromosome, while the other gene alleles remain with theiroriginal chromosomes. When alleles switch places like this, theresulting gametes are called recombinant. In the example above, theoriginal parental gametes would be RY and ry, while the recombinantgametes would be Ry and rY. Thus four different kinds of gametes willbe formed, instead of only two formed when the genes were linked.
If two genes are extremely close together,crossing over will almost never occur between them, and recombinantgametes will almost never form. If they are very far apart on thechromosome, crossing over will almost certainly occur between them, andrecombinant gametes will form just as often as if the genes were ondifferent chromosomes (50 percentof the time). If the genes are at an intermediate distance from eachother, crossing over may sometimes occur between them and sometimesnot. Therefore, the percentage of recombinant gametes (reflected in thepercentage of recombinant offspring) correlates with the distancebetween two genes on a chromosome. By comparing the recombination ratesof multiple different pairs of genes on the same chromosome, therelative position of each gene along the chromosome can be determined.This method of ordering genes on a chromosome is called a linkage map.
