Exercise XXV 



COMPLETION OF THE GENETICS EXPERIMENT 127 



Are all genes on the same chromosome? How 

 do you know? If they do appear linked, calcu- 

 late the percentage of crossing over between 

 them. Prepare a map indicating relative posi- 

 tions of these genes on the chromosome(s). Dia- 

 gram two generations of crosses giving rise to 

 these offspring. 



Interference of crossing over in one region 

 with crossing over in another region can be tested 

 in the following way : 



Coincidence = 



% double crossovers 

 (% crossovers in region I) 

 X {% crossovers in region 1 1) 



(The denominator is the percentage of double 

 crossovers that is expected.) 



If the coincidence is less than 1.0, crossing 

 over in one region interferes with that in an- 

 other. One sometimes expresses what is called 

 the "interference" as (1 — coincidence). Is 

 there interference in this test cross? 



PROBABILITY IN GENETICS 



The interpretation of breeding experiments in 

 genetics often requires statistical analysis; with- 

 out the use of statistics it is sometimes impos- 

 sible to decide whether the results of an experi- 

 ment agree with those predicted by theory. A 

 thorough treatment of the mathematics of 

 genetics is beyond the scope of this course, but 

 it will be helpful to consider a few elementary 

 principles of probability in interpreting the 

 Drosophila experiment and in understanding 

 many aspects of segregation of genes. 



The probability (P) that some event (.v) will 

 occur can be represented by a fraction between 

 and 1. This fraction is the proportion of 

 times the event occurs {m) in a very large num- 

 ber of trials («), or 



nix 

 riz 



When in a very large number of trials, every 

 trial yields the event, then m = n and P = \\ 

 the event is inevitable. When the event does not 



occur at all in a very large number of trials, 

 P = 0; the event is impossible. Everything 

 that happens has a probability that lies between 

 these limits. The nearer Pj is to 1, the more 

 probable the event. 



Probability values are theoretical; they are 

 merely mathematical expressions of expecta- 

 tions. It is necessary to perform a very large 

 number of trials, and for an event to occur 

 many times, for the observed frequency of suc- 

 cesses to equal the probability. That is, the 

 more trials and more often an event takes place, 

 the more closely the proportion of successes 

 will approach P^. 



To illustrate this, perform the following tests: 



(a) Flip a coin four times and record the 

 number of heads and of tails; repeat this four 

 times. Note the variation in results. 



(b) Flip the coin 10 times and again record 

 the number of heads and of tails. 



(c) Flip the coin 50 times and record the 

 results. 



(d) If you have time, extend this to 100 or 

 more flips. 



(e) Sum up the totals for heads and tails 

 from (a), (b), (c), and (d) above. 



(f) Calculate the ratio of heads (or tails) to 

 the total number of tosses in each of (a), (b), 

 (c), (d), and (e) above. 



Just from the shape of a coin we expect the 

 probability of a head (or tail) coming up on 

 any flip to be about 0.5. Which coin-flipping 

 test above provides the most reliable agreement 

 with the theoretical value of P? 



Simultaneous occurrence of independent 

 events 



The probability that several independent 

 events will occur together is equal to the product 

 of their separate probabilities, or 



Px.y.z... —P X X P ,j X Pz... 



For instance, when two dice are tossed the 



