Page 161 - Genetics_From_Genes_to_Genomes_6th_FULL_Part1

5.4 The Chi-Square Test and Linkage Analysis 153

the mean values expected of unlinked genes that assort
essential concepts
independently? Such questions become more important in
• A series of two-point crosses can establish the order of cases where linkage is not all that tight, so that even though
linked genes and the distances between them through the genes are linked, the percentage of recombinant classes
pairwise analysis of recombination frequencies. approaches 50%.
• Three-point testcrosses can refine map distances and
reveal the existence of crossover interference, a
phenomenon that distributes among all chromosomes the The Chi-Square Test Evaluates the
limited number of crossovers that occur in each meiosis. Significance of Differences Between
• Although genetic maps provide an accurate picture of Predicted and Observed Values
gene order on a chromosome, the distances measured
between genes can be misleading. To answer these kinds of questions, statisticians have de-
• Genes in a linkage group are by definition syntenic. With vised several different ways to quantify the likelihood that
enough mapped genes, the entire chromosome becomes an experimentally observed deviation from the predictions
a single linkage group. of a particular hypothesis could have occurred solely by
chance. One of these probabilistic methods is known as the
chi-square test for goodness of fit. This test measures how
well observed results conform to predicted ones, and it is
5.4 The Chi-Square Test designed to account for the fact that the size of an experi-
and Linkage Analysis mental population (the sample size) is an important com-
ponent of statistical significance. To appreciate the role of
sample size, let’s return to the proverbial coin toss before
learning objectives examining the details of the chi-square test.
In 10 tosses of a coin, an outcome of 6 heads (60%)
1. Explain the purpose of the chi-square test. and 4 tails (40%) is not unexpected because of the effects of
2. Discuss the concept of the null hypothesis and its use in chance. However, with 1000 tosses of the coin, a result of
data analysis. 600 heads (60%) and 400 tails (40%) would intuitively be
3. Evaluate the significance of experimental data based on highly unlikely. In the first case, a change in the results of
the chi-square test. one coin toss would alter the expected 5:5 ratio to the ob-
served 6:4 ratio. In the second case, 100 tosses would have
to change from tails to heads to generate the stated devia-
How do you know from a particular experiment whether tion from the predicted 500:500 ratio. Chance events could
two genes assort independently or are genetically linked? reasonably, and even likely, cause one deviation from the
At first glance, this question should pose no problem. Dis- predicted number, but not 100.
criminating between the two possibilities involves straight- Two important concepts emerge from this simple ex-
forward calculations based on assumptions well supported ample. First, a comparison of percentages or ratios alone
by observations. For independently assorting genes, a dihy- will never allow you to determine whether or not observed
brid F 1 female produces four types of gametes in equal data are significantly different from predicted values. Sec-
numbers, so one-half of the F 2 progeny are of the parental ond, the absolute numbers obtained are important because
classes and the other half are of the recombinant classes. In they reflect the size of the experiment. The larger the sam-
contrast, for linked genes, the two types of parental classes ple size, the closer the observed percentages can be ex-
by definition always outnumber the two types of recombi- pected to match the values predicted by the experimental
nant classes in the F 2 generation. hypothesis, if the hypothesis is correct. The chi-square test
The problem is that because real-world genetic trans- is therefore always calculated with numbers—actual data—
mission is based on chance events, in a particular study and not percentages or proportions.
even unlinked, independently assorting genes can produce The chi-square test cannot prove a hypothesis, but it can
deviations from the 1:1:1:1 ratio, just as in 10 tosses of a allow researchers to reject a hypothesis. For this reason, a
coin, you may easily get 6 heads and 4 tails (rather than the crucial prerequisite of the chi-square test is the framing of a
predicted 5 and 5). Thus, if a breeding experiment analyz- null hypothesis: a model that might possibly be refuted by
ing the transmission of two genes shows a deviation from the test and that leads to clear-cut numerical predictions.
the equal ratios of parentals and recombinants expected of Although contemporary geneticists use the chi-square test
independent assortment, can we necessarily conclude the to interpret many kinds of genetic experiments, they use it
two genes are linked? Is it instead possible that the results most often to discover whether data obtained from breeding
represent a statistically acceptable chance fluctuation from experiments provide evidence for or against the hypothesis