Page 30 - Genetics_From_Genes_to_Genomes_6th_FULL_Part1

22 Chapter 2 Mendel’s Principles of Heredity

And finally, if sperm carrying the allele for green peas Next, to visualize what happens when the Yy hybrids
fertilizes a green-carrying egg, the progeny will be a self-fertilize, we set up a Punnett square (named after the
pure-breeding green pea. British mathematician Reginald Punnett, who introduced it
Mendel’s law of segregation encapsulates this general in 1906; Fig. 2.11). The square provides a simple and con-
principle of heredity: The two alleles for each trait separate venient method for tracking the kinds of gametes produced
(segregate) during gamete formation, and then unite at ran- as well as all the possible combinations that might occur at
dom, one from each parent, at fertilization. Throughout this fertilization. As the Punnett square shows in the first column
book, the term segregation refers to such equal segregation and the first row, each hybrid produces two kinds of gam-
in which one allele, and only one allele, of each gene goes etes, Y and y, in a ratio of 1:1. Thus, half the sperm and half
to each gamete. Note that the law of segregation makes a the eggs carry Y, the other half of each gamete type carries y.
clear distinction between the somatic cells (body cells) of Each box in the Punnett square in Fig. 2.11 containing
an organism, which have two copies of each gene, and the a colored pea represents one possible fertilization event. At
gametes, which bear only a single copy of each gene. fertilization, 1/4 of the progeny will be YY, 1/4 Yy, 1/4 yY,
and 1/4 yy. Because the gametic source of an allele (egg or
The Punnett square sperm) for the traits Mendel studied had no influence on
Figure 2.11 shows a simple way of visualizing the results the allele’s effect, Yy and yY are equivalent. This means
of the segregation and random union of alleles during gam- that 1/2 of the progeny are yellow Yy hybrids, 1/4 YY
ete formation and fertilization. Mendel invented a system true-breeding yellows, and 1/4 true-breeding yy greens.
of symbols that allowed him to analyze all his crosses in the The diagram illustrates how the segregation of alleles dur-
same way. He designated dominant alleles with a capital A, ing gamete formation and the random union of egg and
B, or C and recessive ones with a lowercase a, b, or c. sperm at fertilization can produce the 3:1 ratio of yellow to
Modern geneticists have adopted this convention for nam- green that Mendel observed in the F 2 generation.
ing genes in peas and many other organisms, but they often
choose a symbol with some reference to the trait in question—
a Y for yellow or an R for round. Throughout this book, we Mendel’s Results Reflect Basic
present gene symbols in italics. In Fig. 2.11, we denote the Rules of Probability
dominant yellow allele with a capital Y and the recessive Though you may not have realized it, the Punnett square
green allele with a lowercase y. The pure-breeding plants illustrates two simple rules of probability—the product
of the parental generation are either YY (yellow peas) or yy rule and the sum rule—that are central to the analysis of
(green peas). The YY parent can produce only Y gametes, genetic crosses. These rules predict the likelihood that a
the yy parent only y gametes. You can see in Fig. 2.11 why particular combination of events will occur.
every cross between YY and yy produces exactly the same
result—a Yy hybrid—no matter which parent (male or
female) contributes which particular allele. The product rule
The product rule states that the probability of two or more
independent events occurring together is the product of the
Figure 2.11 The Punnett square: Visual summary of a probabilities that each event will occur by itself. With inde-
cross. This Punnett square illustrates the combinations that can arise pendent events:
when an F 1 hybrid undergoes gamete formation and self-fertilization.
The F 2 generation should have a 3:1 ratio of yellow to green peas. Probability of event 1 and event 2 =

P YY yy Probability of event 1 × probability of event 2.
Consecutive coin tosses are obviously independent
events; a heads in one toss neither increases nor decreases
Gametes Y y
the probability of a heads in the next toss. If you toss two
coins at the same time, the results are also independent
F (all identical) Yy Yy events. A heads for one coin neither increases nor decreases
1
the probability of a heads for the other coin. Thus, the prob-
Sperm 1/2 1/2 ability of a given combination is the product of their inde-
F 2 pendent probabilities. For example, the probability that
Y y Each box: both coins will turn up heads is:
Eggs 1/2 × 1/2 = 1/4
1/2 Y YY Yy 1/2 × 1/2 = 1/4.
Similarly, the formation of egg and sperm are independent
1/2 y yY yy
events; in a hybrid plant, the probability is 1/2 that a given