GENETICS, 6: 663-670 (1920)
IS CROSSING OVER A FUNCTION OF DISTANCE?1
By J. A. DETLEFSEN

LABORATORY OF GENETICS, ILLINOIS AGRICULTURAL EXPERIMENT STATION
Communicated by C. B. Davenport, September 24, 1920

There is a well intrenched concept of recent genetics that hereditary factors or genes may be given fairly definite loci on chromosome maps and that these maps correspond to or represent, roughly perhaps, the actual conditions in the chromosome. The basis for this attractive and suggestive view is the premise that the distance between two genes is necessarily proportional to the percentage of crossing over which these two genes show — other things being equal. If the distance which gives one per cent of crossovers is used as an arbitrary unit of measurement, then it follows that distances on the chromosome may be calculated in terms of this unit. It has seemed to me for some time that the antecedent in this hypothetical proposition contains a more or less gratuitous assumption. We do not know that the distance which gives 1% (or n%) of crossovers is a fixed unit. Staled differently, we do not know how constant the percentage of crossing over may be between two genes to which we give a fixed distance, i.e., our arbitrary unit of measurement may itself prove to be a variable. It may be possible for the distance which gives 1% of crossing over to differ in different females of the same population, or differ between stocks. In order to throw some light on these questions I began a set of experiments in 1916 in collaboration with my colleague, Dr. E. Roberts, and several students. Although a number of these experiments are still in progress, data involving the classification of over 400,000 individuals have been accumulated and some conclusions seem warranted. A more detailed account of these experiments will appear in the current numbers of the Journal of Experimental Zo÷logy.

In observing a large number of females (Drosophila melanogaster) of the generalized zygotic formula ab/AB, it is common to find great differences between individual females with respect to the amount of crossing over. Some of the variability may be due to sheer fluctuations of sampling, to age, and to environmental conditions, but sometimes the deviations are so wide as to arouse a suspicion that hitherto unknown causes may be effective. If this variability is due at least in part to genetic modifiers then selection should be effective, particularly if environmental fluctuations do not mask or obliterate the effects of genetic modifiers. It was with this thought in mind that I began to select for high and low crossover value. Pour selection experiments were undertaken. Series A, A' and B were low selection experiments and Series C was a high selection experiment. Each series began with a single white-eyed, miniature-winged female mated to a wild, red, long male. The F1 females were red, long double heterogzyotes wm/WM and the F1 males were white, miniature double recessives wm. These were mated in pairs, giving the parental classes (red long and white miniature) and the crossovers (red miniature and white long) with the usual ratio of approximately 33% crossovers — the same value used in plotting chromosome maps. The same mating was made in successive generations, always selecting as far as was possible the widest deviates to perpetuate the line of selection. At the same time, the closest possible inbreeding was maintained, the details of which are given in our longer papers. The results indicate that selection was effective in all series.

Series A was reduced to 0% in F10 and remained at about 0% for two more generations. Series A', derived from Series A as a side line of selection in the F7, began with a female showing 1: 91 = 1.10%.2 This line was carried for 9 generations (F7-F15) and also bred true to about 0%. The grand total for this entire series gave 33 : 5156 = 0.64% — actually less than 1%. There can be no doubt but that an original crossover value of about 33% has been changed by selection, at least a marked change has followed selection.

Series B was entirely independent in its origin from Series A and A'; and low selection was also effective, as in the case of the preceding series. Curiously enough we have not been able as yet to reduce the crossover value to zero, or approximately zero, as in the other series. Since experiments with this series form the basis of the present paper, table 1 is given to show in condensed form the progress during selection. After the F28, selection was discontinued, and the stock has bred practically true to about 5 or 6% crossing over for 22 generations (i.e., through F50). Table 1 gives the percentage of crossovers for every fifth generation, and also for the total offspring in each block of five successive generations.

TABLE I
CROSSOVER VALUES FOR EVERY FIFTH GENERATION, AND FOR THE TOTALS IN EACH
BLOCK OF FIVE SUCCESSIVE GENERATIONS, IN SERIES B (LOW SELECTION)

GENERATIONS CROSSOVER
VALUES
GENERATIONS
INCLUDED
CROSSOVERS TOTALS CROSSOVER
VALUES
1 28.60 1- 5 10517 40567 25.93
5 24.55 6-10 10344 47295 21.87
10 16.99 11-15 3687 25333 14.55
15 11.17 16-20 4869 48277 10.09
20 9.81 21-25 3386 36693 9.23
25 7.15 26-30 576 8007 7.19
30 5.62 31-35 121 2089 6.79
35 4.18 36-40 267 4571 5.84
40 6.70 41-45 750 12453 6.02
45 6.51 46-50 350 5203 6.73
50 6.98        

Series C, high selection, was carried for 8 generations, but we were unable to make progress in selecting upward. On the contrary, we were greatly astonished to find in the F7, 9 out of 72 pairs, which gave almost no crossing over at all, although they produced a large number of offspring. The remaining 63 pairs gave about the usual crossover value. The totals for these 9 paired matings were:

26 crossovers : 1055 total = 2.46% Crossing over.

These same genes should have given 33% crossing over if they agreed with the usual values used in plotting chromosome maps. The natural inference is that any attempt to increase crossing over leads to double crossing over and thus to very low crossover values (practically zero). The explanation implies that these 9 females showed a marked decrease in crossover values, despite high selection, because they gave almost nothing but double crossovers. Series C was dropped, but we hope to repeat the experiment and test out the region between white and miniature in such females.

The effects of selection on crossover values may be due to one or a number of causes, some of which suggest themselves almost immediately. The most promising and probable explanation seemed to me to be that crossing over is either due to or markedly modified by multiple factors. In order to test out this view, I crossed the low crossover stock of Series B, which shows 5-6% crossing over, to ordinary stock which shows 33% crossing over. Table 2 gives the results of this experiment. The first line of the table gives for comparison the frequency distribution of crossover values in an ordinary population. There were 90 females in this sample but I have eliminated two very wide deviates from the distribution, because the number of offspring on which their crossover values were based was extremely small. One of them showed 1: 8 = 12.5%; and the other showed 6 : 8 = 75%. The population as a whole showed 30.68% crossing over and the mean female had a value of 30.55%. The average number of offspring per female and the totals show that the values for the females both individually and collectively are as reliable as can be reasonably expected. The second line of the table shows the first generation in Series B, which resembles closely the sample just described. After 28 generations, selection was discontinued. Thereafter the generations were perpetuated by en masse matings. In the F42, I mated 50 red, long females heterozygous in white miniature wm/WM to stock white miniature males wm. All except one were fertile and the distribution of their crossover values is given as the low P1 parent in table 2. Mating them to ordinary stock males would not change the crossover values which such low females show. We cannot know positively what the crossover value of each white miniature male parent was, but we have no reason to suppose it differs greatly from the values given for the first generation of Series B or the ordinary stock, both shown in table 2. We have used this same white miniature stock in class work and have always found it to give the regular "map value" of about 33%.

It was virtually impossible to breed all of the F1 hybrid females from each pair separately. I decided to breed exhaustively 50 red long F1 females wm/WM to their F1 white miniature brothers wm to obtain a sample frequency distribution of F1 females coming from a single P1 pair (pair No. 18). Forty-seven of these 50 females were fertile and gave an average of 465 offspring per female.3 The range of F1 crossover values shows quite clearly that they lie between the low and the high parents. The value of the mean female and the crossover value of this total F1 population show the same thing. One F1 female showed a ratio of 1 : 36 = 2.77%, but since the ratio is based upon such a small total we need not lay much stress on this wide variate.

TABLE 2
THE DISTRIBUTION OF CROSSOVER VALUES IN NORMAL POPULATION,
| IN LOW CROSSOVER STOCK, AND P1 HYBRIDS BETWEEN THESE

GENERATIONS NUMBER OF
VARIATES
THE DISTRIBUTION OF CROSSOVER VALUES MEAN
VARIATE
σ CROSS-
OVERS
TOTAL % OF CROSS-
OVERS
AVERAGE NUMBER
OF PROGENY PER
VARIATE
1.5 4.5 7.5 10.5 13.5 16.5 19.5 22.5 25.5 28.5 31.5 34.5 37.5 40.5
Sample population 88               7 11 19 28 15 5 3 30.55 4.28 6465 21071 30.68 239.4
1st generation Series B 34             3 5 3 10 6 3 2 2 28.85 5.58 2056 7189 28.60 211.4
P1 low patent 49 7 26 15 1                     5.11 2.10 425 7948 5.35 162.2
F1 hybrid females 47 1   2 10 16 12 6               13.88 3.64 3216 21853 14.72 465.0
F1 samples of each P1 45     10 18 10 6 1               11.50 3.10 5213 39416 13.23 875.9
F2 from P1 No 2 33 2 1 5 8 8 5 3 1             12.24 4.90 1060 7812 13.57 236.7
F2 from P1 No 5 39       5 13 12 5 1 2     1     16.19 4.70 1477 9001 16.41 230.8
F2 from P1 No 6 76   1 3 14 23 22 6 3 3 1         14.96 4.39 3161 21701 14.57 285.5
F2 total 148 2 2 8 27 44 39 14 5 5 1   1     14.66 4.81 5698 38514 14. 79 260.2

In addition to the F1 distribution coming from a single P1 pair, I also obtained a sample crossover value of the F1 coming from each of 44 other P1 females. I chose at random four F1 red, long double heterozygotes from each P1 pair. Each group of four F1 females was mated to white miniature F1 brothers. Thus we secured crossover values for 45 different F1 groups, each group coming from a single P1 pair. These F1 crossover values are put in the form of a frequency distribution in the fifth row of table 2. Here again we find the F1 values intermediate between the low stock and the original population. In no case was an F1 value as low as the mean or mode of the low parent nor as high as the mean or mode of the original population.

Three distinct and separate F2 distributions were reared, coming from P1 pairs No. 2, 5 and 6. The value of each original P1 female, together with the crossover ratio of its F1 and F2 progeny, is given in table 3.

TABLE 3
THE DATA ON P1 PAIRS No. 2, 5, AND 6, FROM WHICH THE F2 DISTRIBUTIONS WERE OBTAINED

P1
PAIR NO.
CROSSOVER
VALUE
F1 CROSSOVER
VALUE
F2 CROSSOVER
VALUE
2 21:382 = 5.50 29: 464 = 6.25 1060: 7812 = 13.57
5 7:193 = 3.63 72: 530 = 13.59 1477: 9001 = 16.41
6 6:178 = 3.37 251:1730 = 14.51 3161:21701 = 14.57

The F2 distributions of table 2 show a wider range than the low parent or the F1. In fact, the total F2 population with 148 pairs gives some females as low as the low parent and some as high as the original population. The mode is between the two stocks. It is clear that the results of these hybridization experiments bear the distinctive features of multiple factor inheritance with incomplete dominance; for the F1 is intermediate and the F2 is likewise intermediate in its average but the F2 shows a conspicuous increase in range which easily overlaps both original P1 distributions. The increase in the standard deviation of each F2 population and of the total F2 distribution over that of the F1 or P1 puts these facts in concrete terms. Therefore, we can hardly escape the conclusion that multiple factors have a striking influence upon crossover values. In the frequency distributions of table 2, some variates will necessarily have little meaning because their crossover values are based upon small totals. I have thought it desirable to include every variate and thus withhold no data rather than include only such females as produced more than a fixed minimum of offspring. However, in order to show that the extremes in the F2 population are segregates, rather than fluctuations of sampling, I have given in table 4, detailed data on the highest and lowest 12 variates in the total F2 frequency distribution of table 2. The lowest 12 variates have values from 0%-9% and cover about the same range as the low parent; while the highest 12 have values above 21% and cover about the same range as the high parent. The values for both low and high F2 variates are based upon totals which are just as satisfactory as any in the population, where the average number of progeny per female was 260. The total F1 included 61,000 offspring and the total F2 distribution is based upon 38,500 offspring.

TABLE 4
THE HIGH AND LOW VARIATES OF THE TOTAL F2 DISTRIBUTION IN TABLE 2

LOW VARIATES  HIGH VARIATES
RECORD
NUMBER
CROSS-
OVERS :
TOTAL = CROSSOVER
VALUE
RECORD
NUMBER
CROSS-
OVERS :
TOTAL = CROSSOVER
VALUE
2- 2 1 : 35 = 2.86 2-32 66 : 287 = 23.00
2- 6 18 : 216 = 8.33 5-21 52 : 154 = 33.77
2-19 14 : 223 = 6.28 5-22 45 : 178 = 25.28
2-22 0 : 19 = 0.00 5-24 69 : 325 = 21.23
2-25 8 : 168 = 4.76 5-28 112 : 466 = 24.03
2-28 14 : 174 = 8.05 6-10 107 : 416 = 25.72
2-33 22 : 329 = 6.69 6-21 56 : 241 = 23.24
2-34 25 : 280 = 8.93 6-23 71 : 287 = 24.74
6-8 11 : 281 = 3.91 6-24 61 : 251 = 24.30
6- la 32 : 394 = 8.12 6-11a 33 : 145 = 22.76
6- 2a 23 : 275 = 8.36 6-13a 26 : 89 = 29.21
6-35a 20 : 272 = 7.35 6-16a 62 : 295 = 21.02
Total 188 : 2666 = 7.05 Total 760 : 3134 = 24.25

In obtaining a crossover value for any two genes like white and miniature we find much variability among the females which serve to make up the general population from which our map value is derived. This variability is due to numerous modifying factors. Selection has evidently sifted out certain relatively pure combinations of these modifiers, hence the low variability of our low crossover stock. The hybridization experiments indicate that the amount of crossing over is at least markedly influenced if indeed it is not actually determined by multiple factors. There are several ways in which multiple factors might possibly change the crossover value which two genes show. In modifying the crossover value of white and miniature from 33% to 6% or to 0% we might suppose that we had either moved the locus of genes or that we had eliminated the usual single chromosomal twist between these two genes. Since the allelomorphic relationships between red and white and between long and miniature have not been disturbed when we mate low crossover stock to the original population, the latter alternative explanation seems preferable. We can evidently change by selection the amount of twisting which members of an homologous pair of chromosomes show. Now, if the difference between practically no crossing over (Series A and A') or between 6% crossing over (Series B) and normal crossing over (33%) is due to multiple factors, we then naturally wonder just what part "distance between two genes" on a chromosome map may play in determining linkage values. Our current view is that "the percentage of cases in which two linked genes separate (amount of crossing over between them) is necessarily proportional to the distance between these genes, — other things being equal," i.e., under ordinary circumstances and in the absence of unusual factors or environmental conditions which geneticists recognize. But evidently under ordinary circumstances, the percentage of crossing over is a variable which is determined by the different possible combinations of multiple modifying factors; hence the percentage of crossing over cannot be proportional to the distance if the distance remain constant. For example in Series B we find 6% crossing over, and so we should conclude that the distance is less than one-fifth of what it originally was before we began selection. To maintain our original position, we must conclude that the percentage of crossing over and the distance are correlated variables, if the proportion is to remain reasonably constant. The dilemma will hardly aid us in determining what had happened to almost all of the distance and the genes between 0 and 33 in Series A and A', where crossing over was practically eliminated. In view of these considerations it would perhaps be simpler to conclude that linkage is not a function of distance, i.e., crossing over is not necessarily proportional to distance. The distance between two genes may remain fairly constant, but the amount of crossing over depends upon numerous hereditary factors.

  1. Paper No. 14 from the Laboratory of Genetics, Illinois Agricultural Experiment Station.
  2. In giving crossover values, I shall put the data in the following form throughout this paper — crossovers: total = per cent of crossing over. Since the classes are always the same, repetition can be avoided.
  3. I am indebted to Dr. E. Roberts and Mr. P. M. Woodworth for carrying this generation in part.