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A population approach to the study of repair of genetic radiation damage in mature spermatozoa of Drosophila melanogaster
Mutation Research, 22 (I974) 287-293 ©'Elsevier Scientific Publishing Company, Amsterdam - Printed in The Netherlands
287
SHORT COMMUNICATIONS A population approach to the study of repair of genetic radiation damage in mature spermatozoa of Drosophila rnelanogaster If Drosophila males are X-irradiated in nitrogen and post-treated with either nitrogen or oxygen, the observed frequencies of sexqinked recessive lethals and autosomal translocations in mature spermatozoa (sampled from such treated males) are reduced after post-treatment with nitrogen4, 5. This observation has been interpreted as due to the repair of genetic radiation damage in spermatozoa which is favored by nitrogen post-treatment. The experiments reported in the present paper were designed to extend these results using a population approach which on theoretical grounds, would be expected to permit a better delineation of the differential effects of the contrasting post-treatments. The approach is based on the following lines of reasoning : (i) in populations irradiated generation after generation, the magnitude of genetic loads can be built up to levels that are much higher than what is possible in experiments aimed at a direct measurement of mutation rates following irradiation; (ii) ii in two populations, males are irradiated in every generation and if these are similar in all respects except in the kind of post-treatment received, then in such populations, the differential effects of post-treatments should lead to a progressive divergence in the magnitude of genetic loads until different levels of equilibria are reached and (iii) the temporal changes in the magnitude of genetic loads would provide an opportunity to measure the differential effects of post-treatments over a time scale of several generations during which the absolute effects are expected to be magnified. Briefly the material used and the methodology employed are as follows: A stock of flies was established from 20 lethal- and semi-lethal-free second chromosomes derived from the laboratory wild-type Oregon-K stock. This was divided into three groups at the commencement of the experiments (generation o). In the first group designated at the N population, males aged 6- 7 days were pre-treated with nitrogen (20 min), irradiated in nitrogen (2000 R) and then post-treated with nitrogen (25 rain). The treated males were mated to females (in sugar-agar vials; 50 males to 25 females per vial; 20 vials) for one overnight period after which the males were discarded; the females were transferred to regular culture bottles and allowed to lay eggs for a day. The flies that eclosed from these bottles constituted those of generation I. The females were collected as virgins and the males were aged for 6- 7 days and subjected to the same radiation-gas treatment regimen as in generation o to raise the next generation. The procedure was repeated in every generation for 64 generations. The second group (the o population) was handled in all respects similar to the N population except that after irradiation, the males received post treatment with oxygen for 25 min. The third group (the C population) served as control and was neither irradiated nor gas treated. In every population, the number of parents used to propagate the next generation was 500 females and IOOO males taken at random from all the eclosed flies. Each population was carried in 20 bottles~ the higher male to female ratio was intended to ensure single inseminations and the sampling of germ cells that were mature spermatozoa at the time of irradiation. The magnitude of genetic loads in the different populations was measured using
288
SHORT
COMMUNICATI01~ S
egg-hatchability a n d the frequencies of second chromosome recessive lethals as criteria. H a t c h a b i l i t y tests were carried out in every generation for the irradiated populations up to a n d including generation 57 and then at generation 64 . Between generations 57 a n d 64 there was an infection of mites a n d no tests were carried out. Control hatchability tests were performed in generations i, 3o a n d 64. The technique used in these tests was the same as the one described b y the a u t h o r in an earlier publication 3. Between 5o a n d IOO females provided the eggs per test in each population a n d the n u m ber of eggs collected varied from a b o u t 2oo to well over 15oo in some tests. Periodically tests were conducted to ascertain the frequencies of second chromosome recessive lethals using the s t a n d a r d Cy L/Pro technique. The males used for these tests were themselves not irradiated or gas-treated. R a d i a t i o n exposures were administered using an E N R A F X - r a y machine operated at IOO kV, 4 m A a n d I m m A1 filtration at a n exposure rate of a b o u t 45 R/sec. The exposures a n d exposure rates were m o n i t o r e d using a Philips dosimeter. The results of h a t c h a b i l i t y tests are presented in Fig. I. The three regression lines shown in the figure (i) pertain to the d a t a of the N a n d O populations considered
50
f
o
0
•
o
0
•
30
oOo O•
•
•
•
O•
0
0
O0 o
,0
O• o
oo- o 0 . .
D
O•
oo
o.o°o oo° o " .
• oo
"--- N+O
0.020
'"N
O
20 LU 0.
10 []
I
~0l
I
201
I
3=0
D
I
t0r
i
50/
I
6f0
I
GENERATIONS
Fig. i. Frequencies of unhatched eggs in the different experimental populations. Black circles, O population ; white circles, N population ; white squares, C population. The regression lines shown are for the data of O and N populations considered separately (top and bottom lines, respectively) and for the data of the two populations considered together, ignoring post-treatments (middle line). For regression equations, see text. separately a n d together (in the latter case weighted m e a n s were used ignoring posttreatments) a n d (ii) have been d r a w n on the a s s u m p t i o n t h a t the yield of u n h a t c h e d eggs varies with time according to the equation y = a+bt where y is the yield of u n h a t c h e d eggs in percent, a the Y intercept, b the slope a n d t, the time in generations. The values of a a n d b t h a t give the best fit are y ( N population) = 39.6+(0.05 q: o.o3)t y(o populationl = 41.9+(0.05 -! O.03)t y(pooled data) = 40.5 + (0.06 4- o.o2)t
Thus it is clear t h a t in none of the irradiated populations there is a n y statistically
SHORT COMMUNICATIONS TABLE
289
I
FREQUENCIES
Generation
OF
SECOND
CHROMOSOME
RECESSIVE
LETHALS
IN
THE
EXPERIMENTAL
POPULATIONS
Population C
N
0
Number Number Percent of chr. of lethals lethals
Number Number Percent of chr. o[lethals lethals
Number Number Percent o[ chr. of lethals lethals
684 665 742 527 522 507 504 560 532 531 371
771 727 645 539 553 446 507 551 539 429 321
5
--
9
--
13
--
17
.
21
- -
24
.
-
--
__ .
__
.
. - -
.
.
.
- .
3°
538
4 °
--
__
4° __
7.4
5 °
--
__
__
64
614
124
20.2
37 98 137 I44 I73 182 I7I 192 221 203 265
5.4 14.7 I8.5 27.3 33 "I 35.9 33.9 34.3 41.5 38.2 71.4
4° lO7 154 ISi 194 158 242 271 193 162 249
5.2 14.7 23.9 33.6 35 "t 35.4 47.7 49.2 35.8 37.8 77.8
significant change with time (in generations) in the frequencies of u n h a t c h e d eggs. The slopes of the regressions for the two p o p u l a t i o n s are the same; for the c o m b i n e d d a t a however, t h e regression coefficient is significantly different from zero, a l t h o u g h the m a g n i t u d e of the e s t i m a t e d increase per g e n e r a t i o n is quite small. The results of tests on the frequencies of second c h r o m o s o m e recessive lethals are given in Table I. I t can be seen t h a t the d a t a considered as a whole are too heterogeneous to p e r m i t a n y s o p h i s t i c a t e d s t a t i s t i c a l t r e a t m e n t or a n y firm conclusions a b o u t the differential effects of the c o n t r a s t i n g p o s t - t r e a t m e n t s ; the e x p e c t a t i o n t h a t the two i r r a d i a t e d p o p u l a t i o n s will progressively diverge from one a n o t h e r with respect to the frequencies of recessive lethals is not borne out b y the d a t a . The d a t a of SOBELS4 show t h a t the ratio of the o b s e r v e d frequencies of sexlinked recessive lethals after oxygen p o s t - t r e a t m e n t to males (following i r r a d i a t i o n u n d e r a n o x i a with 4ooo R) relative to t h a t with n i t r o g e n p o s t - t r e a t m e n t is 1.28 (number of X - c h r o m o s o m e s t e s t e d : 3896, o x y g e n p o s t - t r e a t m e n t ; 3943, n i t r o g e n postt r e a t m e n t ) . W h e n similar calculations are done for the present results, the m e a n r a t i o o b t a i n e d is 1.13 b a s e d on all the I I tests; if only the first 8 tests are included, t h e n it is i . i 8 . These calculations a l t h o u g h a d m i t t e d l y crude, suggest t h a t the frequencies o b t a i n e d with o x y g e n p o s t - t r e a t m e n t t e n d to be higher. A n o t h e r w a y to analyse the d a t a is to e s t i m a t e values of u ( m u t a t i o n rate) a n d h (selection a g a i n s t h e t e r o z y g o u s lethals) t h a t best fit the d a t a for the two i r r a d i a t e d p o p u l a t i o n s a n d then ask t h e question w h e t h e r there are a n y significant differences between these. If, because of the h e t e r o g e n e i t y of the o b s e r v e d recessive lethal frequencies, it t u r n s out t h a t the e s t i m a t e d values for the two p o p u l a t i o n s are not signific a n t l y different, t h e n it is justifiable to use the pooled d a t a (ignoring p o s t - t r e a t m e n t s ) , check which set of values for u a n d h s a t i s f a c t o r i l y explain the results a n d see w h e t h e r the values so e s t i m a t e d are reasonable. The m e t h o d to e s t i m a t e frequencies of recessive lethals in successive generations is briefly, as follows: L e t q be the p r o p o r t i o n of l e t h a l - b e a r i n g chromosomes after irradiation, h, selection against a h e t e r o z y g o u s lethal, u, m u t a t i o n r a t e to recessive lethals per second chromosome per g e n e r a t i o n a n d p=
IroN
290
SHORT
COMMUNICATIONS
The frequency of normal chromosomes in the next generation is p,
EP~+pq(I--h)](I-u) = p~+2pq(s--h) + (q2--A)(I--2h)
(r)
where A is the proportion of zygotes homozygous for the same lethal (for a derivation of the formula, see ref. I). The change in the frequency of lethal chromosomes from one generation to the next is given by /]q = (q--I) ~ q h ( I - - U ) - - u + A ( I - - 2 h ) l I - - 2 h q - - A ( I - - 2h)
(2)
In the present experiments in which the population sizes were large and the opport u n i t y for inbreeding negligible, at least in the early generations, A is small and can be neglected. Writing equation (2) as a differential equation and ignoring the denominator, dq - -
dt =
(3)
u--qFh(I + u) + u] +q~h(I + u ) u-q(u+z) +zq ~
where z h(I+U) This integrates into ----
zq--u Loge
-
-
zq--z
-- - ( u - z ) t + l o g e -
U
(4)
or
q--
C(I- - C
at )
I - - CC ~t
where a = u - - z = u - - h ( r + u ) and c ~ u/~ --
U
h(i+u)
(5)
The values of u and z that give the best fit to the data were estimated using a m a x i m u m likelihood method, b y regressing the difference in frequencies between successive generations on the frequencies observed at different times as the latter were taken to be statistically dependent (since the populations were of finite size). The values t h a t give the best fit to the data are: N population: u = 0.0397 q~ O.OLO2; and z = 0.0662 -4- 0.0380 O population: u = 0.0403 4- o.o138; and z = 0.0545 _~ o.o461 It is clear that the estimated values of u and z are not significantly different in the two populations. This also applies to the difference between u and z values, respectively. However, as the analysis shows, the data are not inconsistent with expectations based on SOBELS' results (which, as mentioned earlier, show a m u t a t i o n rate ratio (O/N) of 1.28) when the s t a n d a r d errors of the estimated u values are taken into consideration. Even if one makes the assumption t h a t the z values do not differ in the two populations, the expected difference in m u t a t i o n rates (o.oo13) does not reach statistical significance (standard error of 0.0065).
291
S~ORT COMMUNICATIONS
Since there was no statistically demonstrable difference between the two populations with respect to the estimated parameter values, the pooled data were considered and the best fitting curve corresponds to: u = o.o4ol ~ O.OLO5 and z ---- o.o615 + 0.0373 (and h = 0.0591 ~ 0.0358) Since the pattern of accumulation of recessive lethals in irradiated populations of the type studied can easily be predicted theoretically if appropriate values of u and h are used, this was a t t e m p t e d to illustrate t h a t suitable combinations of u and h will give fairly similar curves. Two such theoretical curves are shown in Fig. 2; Curve 1 is drawn under the assumption t h a t u = 0.04 and h = 0.06 (nearly the same values as those estimated tor the best fitting curve for the d a t a of the two populations) and Curve 2 is described b y u = 0.03 and h = 0.04. 90
70
J 50
30
///o~
10
......
~0
'
2'0
'
30'
'
~'0
'
s'0
'
60'
'
GENERATIONS
Fig. 2. F r e q u e n c i e s of I I - c h r o m o s o m e recessive l e t h a l s in t h e di ffe re nt e x p e r i m e n t a l p o p u l a t i o n s B l a c k circles, O p o p u l a t i o n s ; w h i t e circles, BT p o p u l a t i o n ; w h i t e s qua re s , C p o p u l a t i o n . The t o p c u r v e ( b r o k e n line) a n d t h e b o t t o m c u r v e (solid line) show t h e p a t t e r n of f r e q u e n c i e s of re c e s s i ve l e t h a l s in differen t g e n e r a t i o n s , e x p e c t e d u n d e r t h e a s s u m p t i o n t h a t u ~ 0.0 4 a n d h = 0.o6 a n d u ~ o.o 3 a n d h = 0.0 4, r e s p e c t i v e l y . F o r e x p l a n a t i o n , see t e x t .
Curve 3 (for the C population) shows the accumulation or spontaneous second chromosome recessive lethals with u = 0.005 and h ---- 0.04 (the u value is from CRow AND TEMINi). With the above combination of values, a good agreement with the d a t a for generation 30 is obtained; the observed frequency in generation 64 is higher but this is expected since the lethals persisting longer are those with a smaller h. If h z 0.025, one gets ~ = 0.20, roughly the final value. Rewriting equation (5), we get, u [x--e'U-z)t ] q =
[z--ueIu-zl*J
which shows t h a t the lethal frequency at a n y time is roughly proportional to the m u t a t i o n rate. In s u m m a r y , the results presented in the preceding pages show t h a t (i) in the two populations, irradiation of the males generation after generation does not strongly decrease egg-hatchability below the level observed, say, after one generation of irradia-
292
SHORT COMMUNICATION'S
tion and these levels are similar in the two populations; (ii) contrasting post-treatments to males does not seem to affect egg-hatchability in any differential way; (iii) there appears to be no consistent post-radiation modifying effects of nitrogen and oxygen on recessive lethals induced in the second chromosome and consequently, the populations, in spite of the different post treatments, do not diverge from one another and (iv) the pattern of accumulation of recessive lethals in the two populations is consistent with reasonable assumptions about the mutation rate and the intensity of selection acting against lethals in the heterozygous condition. WALLACE (personal communication) suggested that a semi-log plot of the frequency of non-lethal chromosomes with time (in generations) would be instructive since such a drawing would emphasize the abrupt change at about generation 24 (when lethal frequencies became more or less constant) followed by points (generation 64) which fall close to the projection of tile original slopes. This is true; however, such a trend is already illustrated in Fig. 2, although not as dramatically as it would be in the kind of figure envisaged by Wallace. Furthermore, since the drawing of a straight line in a semi-log plot involves the assumption that h - o and since the cause(s) of the abrupt changes are not known, a presentation of all the data together with tile fitted curves was chosen (Fig. 2). The finding that egg-hatchability remains at fairly stable levels in the two irradiated populations with no evidence for a decrease in spite of generations of irradiation is not unexpected (since dominant lc'~hals are not transmitted) and is in line with the finding reported by the author in an earlier study 2. Likewise, the lack of a measurable post treatment effect on egg-hatchability is also in accordance with earlier results '~. The lack of a clearly detectable differential accumulation of autosomal recessive lethals in the two populations however, is unexpected although, as mentioned earlier, the data are not inconsistent with SOBELS' results. The available data do not permit one to determine whether this discrepancy between prediction and observation is real or only an apparent one. It may be that since in most of SOBELS' studies on post-radiation modification of genetic damage in mature spermatozoa (by nitrogen and oxygen), males carrying ring-X chromosonLes were used (and recessive lethals induced in such chromosomes studied), the differences that he detected are somehow associated with some special properties of the ring-X chromosomes and consequently, the conclusions are not applicable to the rest of the genome. At any rate, it seems that population methods are perhaps not the best to study repair of genetic radiation damage (as measured by autosomal recessive lethals) in Drosophila spermatozoa. It is a pleasure to thank Prof. F. H. SOBELSfor his warm encouragement, Prof. J. F. CROW and Mr. W. S. VOLKERS for their most invaluable help in the statistical analysis of the data, Professors J. F. CROW, B. WALLACEand Mr. W. S. VOLKERS for their constructive comments on the manuscript and Mrs. A. VAN DUYN, C. DE GROOT and Miss M. J. Loos for their conscientious technical assistance. The work was supported by EURATOM Contract o52-64-I BIAN with the University of Leiden.
Department of Radiation Genetics and Chemical Mutagenesis, State University of Leiden, and J. A. Cohen Institute for Radiopathology and Radiation Protection, Leiden (]'he Netherlands)
K. SANKARANARAYANAN
SHORT COMMUNICATIONS
293
i CROW, J. F., AND R. G. TEMIN, E v i d e n c e for t h e p a r t i a l d o m i n a n c e of recessive lethal genes in n a t u r a l p o p u l a t i o n s of Drosophila, Am. Naturalist, 98 (1964) 21-33. 2 SANKARANARAYANAN, K., Genetic loads in i r r a d i a t e d e x p e r i m e n t a l p o p u l a t i o n s of Drosophila melanogaster, Genetics, 5 ° (1964) 131-15o. 3 SANKARANARAYANAN, I~., T h e effects of n i t r o g e n a n d o x y g e n t r e a t m e n t s on t h e frequencies of X - r a y - i n d u c e d d o m i n a n t lethals a n d on t h e p h y s i o l o g y of t h e s p e r m in Drosophila melanogaster, Mutation Res., 4 (1967) 641-6614 SOBELS, F. H., P o s t - r a d i a t i o n r e d u c t i o n of genetic d a m a g e in m a t u r e D r o s o p h i l a s p e r m b y nitrogen, Mutation Res., I (1964) 472-477 . 5 SOBELS, F. H., R a d i o s e n s i t i v i t y a n d repair in different germ-cell s t a g e s of Drosophila, in S. J. GEERTS (Ed.), Proe. X I Intern. Congr. Genet., The Hague I963, vol. 2, P e r g a m o n , Oxford, 1965, pp. 235 255Received
October
8th, 1973
287
SHORT COMMUNICATIONS A population approach to the study of repair of genetic radiation damage in mature spermatozoa of Drosophila rnelanogaster If Drosophila males are X-irradiated in nitrogen and post-treated with either nitrogen or oxygen, the observed frequencies of sexqinked recessive lethals and autosomal translocations in mature spermatozoa (sampled from such treated males) are reduced after post-treatment with nitrogen4, 5. This observation has been interpreted as due to the repair of genetic radiation damage in spermatozoa which is favored by nitrogen post-treatment. The experiments reported in the present paper were designed to extend these results using a population approach which on theoretical grounds, would be expected to permit a better delineation of the differential effects of the contrasting post-treatments. The approach is based on the following lines of reasoning : (i) in populations irradiated generation after generation, the magnitude of genetic loads can be built up to levels that are much higher than what is possible in experiments aimed at a direct measurement of mutation rates following irradiation; (ii) ii in two populations, males are irradiated in every generation and if these are similar in all respects except in the kind of post-treatment received, then in such populations, the differential effects of post-treatments should lead to a progressive divergence in the magnitude of genetic loads until different levels of equilibria are reached and (iii) the temporal changes in the magnitude of genetic loads would provide an opportunity to measure the differential effects of post-treatments over a time scale of several generations during which the absolute effects are expected to be magnified. Briefly the material used and the methodology employed are as follows: A stock of flies was established from 20 lethal- and semi-lethal-free second chromosomes derived from the laboratory wild-type Oregon-K stock. This was divided into three groups at the commencement of the experiments (generation o). In the first group designated at the N population, males aged 6- 7 days were pre-treated with nitrogen (20 min), irradiated in nitrogen (2000 R) and then post-treated with nitrogen (25 rain). The treated males were mated to females (in sugar-agar vials; 50 males to 25 females per vial; 20 vials) for one overnight period after which the males were discarded; the females were transferred to regular culture bottles and allowed to lay eggs for a day. The flies that eclosed from these bottles constituted those of generation I. The females were collected as virgins and the males were aged for 6- 7 days and subjected to the same radiation-gas treatment regimen as in generation o to raise the next generation. The procedure was repeated in every generation for 64 generations. The second group (the o population) was handled in all respects similar to the N population except that after irradiation, the males received post treatment with oxygen for 25 min. The third group (the C population) served as control and was neither irradiated nor gas treated. In every population, the number of parents used to propagate the next generation was 500 females and IOOO males taken at random from all the eclosed flies. Each population was carried in 20 bottles~ the higher male to female ratio was intended to ensure single inseminations and the sampling of germ cells that were mature spermatozoa at the time of irradiation. The magnitude of genetic loads in the different populations was measured using
288
SHORT
COMMUNICATI01~ S
egg-hatchability a n d the frequencies of second chromosome recessive lethals as criteria. H a t c h a b i l i t y tests were carried out in every generation for the irradiated populations up to a n d including generation 57 and then at generation 64 . Between generations 57 a n d 64 there was an infection of mites a n d no tests were carried out. Control hatchability tests were performed in generations i, 3o a n d 64. The technique used in these tests was the same as the one described b y the a u t h o r in an earlier publication 3. Between 5o a n d IOO females provided the eggs per test in each population a n d the n u m ber of eggs collected varied from a b o u t 2oo to well over 15oo in some tests. Periodically tests were conducted to ascertain the frequencies of second chromosome recessive lethals using the s t a n d a r d Cy L/Pro technique. The males used for these tests were themselves not irradiated or gas-treated. R a d i a t i o n exposures were administered using an E N R A F X - r a y machine operated at IOO kV, 4 m A a n d I m m A1 filtration at a n exposure rate of a b o u t 45 R/sec. The exposures a n d exposure rates were m o n i t o r e d using a Philips dosimeter. The results of h a t c h a b i l i t y tests are presented in Fig. I. The three regression lines shown in the figure (i) pertain to the d a t a of the N a n d O populations considered
50
f
o
0
•
o
0
•
30
oOo O•
•
•
•
O•
0
0
O0 o
,0
O• o
oo- o 0 . .
D
O•
oo
o.o°o oo° o " .
• oo
"--- N+O
0.020
'"N
O
20 LU 0.
10 []
I
~0l
I
201
I
3=0
D
I
t0r
i
50/
I
6f0
I
GENERATIONS
Fig. i. Frequencies of unhatched eggs in the different experimental populations. Black circles, O population ; white circles, N population ; white squares, C population. The regression lines shown are for the data of O and N populations considered separately (top and bottom lines, respectively) and for the data of the two populations considered together, ignoring post-treatments (middle line). For regression equations, see text. separately a n d together (in the latter case weighted m e a n s were used ignoring posttreatments) a n d (ii) have been d r a w n on the a s s u m p t i o n t h a t the yield of u n h a t c h e d eggs varies with time according to the equation y = a+bt where y is the yield of u n h a t c h e d eggs in percent, a the Y intercept, b the slope a n d t, the time in generations. The values of a a n d b t h a t give the best fit are y ( N population) = 39.6+(0.05 q: o.o3)t y(o populationl = 41.9+(0.05 -! O.03)t y(pooled data) = 40.5 + (0.06 4- o.o2)t
Thus it is clear t h a t in none of the irradiated populations there is a n y statistically
SHORT COMMUNICATIONS TABLE
289
I
FREQUENCIES
Generation
OF
SECOND
CHROMOSOME
RECESSIVE
LETHALS
IN
THE
EXPERIMENTAL
POPULATIONS
Population C
N
0
Number Number Percent of chr. of lethals lethals
Number Number Percent of chr. o[lethals lethals
Number Number Percent o[ chr. of lethals lethals
684 665 742 527 522 507 504 560 532 531 371
771 727 645 539 553 446 507 551 539 429 321
5
--
9
--
13
--
17
.
21
- -
24
.
-
--
__ .
__
.
. - -
.
.
.
- .
3°
538
4 °
--
__
4° __
7.4
5 °
--
__
__
64
614
124
20.2
37 98 137 I44 I73 182 I7I 192 221 203 265
5.4 14.7 I8.5 27.3 33 "I 35.9 33.9 34.3 41.5 38.2 71.4
4° lO7 154 ISi 194 158 242 271 193 162 249
5.2 14.7 23.9 33.6 35 "t 35.4 47.7 49.2 35.8 37.8 77.8
significant change with time (in generations) in the frequencies of u n h a t c h e d eggs. The slopes of the regressions for the two p o p u l a t i o n s are the same; for the c o m b i n e d d a t a however, t h e regression coefficient is significantly different from zero, a l t h o u g h the m a g n i t u d e of the e s t i m a t e d increase per g e n e r a t i o n is quite small. The results of tests on the frequencies of second c h r o m o s o m e recessive lethals are given in Table I. I t can be seen t h a t the d a t a considered as a whole are too heterogeneous to p e r m i t a n y s o p h i s t i c a t e d s t a t i s t i c a l t r e a t m e n t or a n y firm conclusions a b o u t the differential effects of the c o n t r a s t i n g p o s t - t r e a t m e n t s ; the e x p e c t a t i o n t h a t the two i r r a d i a t e d p o p u l a t i o n s will progressively diverge from one a n o t h e r with respect to the frequencies of recessive lethals is not borne out b y the d a t a . The d a t a of SOBELS4 show t h a t the ratio of the o b s e r v e d frequencies of sexlinked recessive lethals after oxygen p o s t - t r e a t m e n t to males (following i r r a d i a t i o n u n d e r a n o x i a with 4ooo R) relative to t h a t with n i t r o g e n p o s t - t r e a t m e n t is 1.28 (number of X - c h r o m o s o m e s t e s t e d : 3896, o x y g e n p o s t - t r e a t m e n t ; 3943, n i t r o g e n postt r e a t m e n t ) . W h e n similar calculations are done for the present results, the m e a n r a t i o o b t a i n e d is 1.13 b a s e d on all the I I tests; if only the first 8 tests are included, t h e n it is i . i 8 . These calculations a l t h o u g h a d m i t t e d l y crude, suggest t h a t the frequencies o b t a i n e d with o x y g e n p o s t - t r e a t m e n t t e n d to be higher. A n o t h e r w a y to analyse the d a t a is to e s t i m a t e values of u ( m u t a t i o n rate) a n d h (selection a g a i n s t h e t e r o z y g o u s lethals) t h a t best fit the d a t a for the two i r r a d i a t e d p o p u l a t i o n s a n d then ask t h e question w h e t h e r there are a n y significant differences between these. If, because of the h e t e r o g e n e i t y of the o b s e r v e d recessive lethal frequencies, it t u r n s out t h a t the e s t i m a t e d values for the two p o p u l a t i o n s are not signific a n t l y different, t h e n it is justifiable to use the pooled d a t a (ignoring p o s t - t r e a t m e n t s ) , check which set of values for u a n d h s a t i s f a c t o r i l y explain the results a n d see w h e t h e r the values so e s t i m a t e d are reasonable. The m e t h o d to e s t i m a t e frequencies of recessive lethals in successive generations is briefly, as follows: L e t q be the p r o p o r t i o n of l e t h a l - b e a r i n g chromosomes after irradiation, h, selection against a h e t e r o z y g o u s lethal, u, m u t a t i o n r a t e to recessive lethals per second chromosome per g e n e r a t i o n a n d p=
IroN
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The frequency of normal chromosomes in the next generation is p,
EP~+pq(I--h)](I-u) = p~+2pq(s--h) + (q2--A)(I--2h)
(r)
where A is the proportion of zygotes homozygous for the same lethal (for a derivation of the formula, see ref. I). The change in the frequency of lethal chromosomes from one generation to the next is given by /]q = (q--I) ~ q h ( I - - U ) - - u + A ( I - - 2 h ) l I - - 2 h q - - A ( I - - 2h)
(2)
In the present experiments in which the population sizes were large and the opport u n i t y for inbreeding negligible, at least in the early generations, A is small and can be neglected. Writing equation (2) as a differential equation and ignoring the denominator, dq - -
dt =
(3)
u--qFh(I + u) + u] +q~h(I + u ) u-q(u+z) +zq ~
where z h(I+U) This integrates into ----
zq--u Loge
-
-
zq--z
-- - ( u - z ) t + l o g e -
U
(4)
or
q--
C(I- - C
at )
I - - CC ~t
where a = u - - z = u - - h ( r + u ) and c ~ u/~ --
U
h(i+u)
(5)
The values of u and z that give the best fit to the data were estimated using a m a x i m u m likelihood method, b y regressing the difference in frequencies between successive generations on the frequencies observed at different times as the latter were taken to be statistically dependent (since the populations were of finite size). The values t h a t give the best fit to the data are: N population: u = 0.0397 q~ O.OLO2; and z = 0.0662 -4- 0.0380 O population: u = 0.0403 4- o.o138; and z = 0.0545 _~ o.o461 It is clear that the estimated values of u and z are not significantly different in the two populations. This also applies to the difference between u and z values, respectively. However, as the analysis shows, the data are not inconsistent with expectations based on SOBELS' results (which, as mentioned earlier, show a m u t a t i o n rate ratio (O/N) of 1.28) when the s t a n d a r d errors of the estimated u values are taken into consideration. Even if one makes the assumption t h a t the z values do not differ in the two populations, the expected difference in m u t a t i o n rates (o.oo13) does not reach statistical significance (standard error of 0.0065).
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S~ORT COMMUNICATIONS
Since there was no statistically demonstrable difference between the two populations with respect to the estimated parameter values, the pooled data were considered and the best fitting curve corresponds to: u = o.o4ol ~ O.OLO5 and z ---- o.o615 + 0.0373 (and h = 0.0591 ~ 0.0358) Since the pattern of accumulation of recessive lethals in irradiated populations of the type studied can easily be predicted theoretically if appropriate values of u and h are used, this was a t t e m p t e d to illustrate t h a t suitable combinations of u and h will give fairly similar curves. Two such theoretical curves are shown in Fig. 2; Curve 1 is drawn under the assumption t h a t u = 0.04 and h = 0.06 (nearly the same values as those estimated tor the best fitting curve for the d a t a of the two populations) and Curve 2 is described b y u = 0.03 and h = 0.04. 90
70
J 50
30
///o~
10
......
~0
'
2'0
'
30'
'
~'0
'
s'0
'
60'
'
GENERATIONS
Fig. 2. F r e q u e n c i e s of I I - c h r o m o s o m e recessive l e t h a l s in t h e di ffe re nt e x p e r i m e n t a l p o p u l a t i o n s B l a c k circles, O p o p u l a t i o n s ; w h i t e circles, BT p o p u l a t i o n ; w h i t e s qua re s , C p o p u l a t i o n . The t o p c u r v e ( b r o k e n line) a n d t h e b o t t o m c u r v e (solid line) show t h e p a t t e r n of f r e q u e n c i e s of re c e s s i ve l e t h a l s in differen t g e n e r a t i o n s , e x p e c t e d u n d e r t h e a s s u m p t i o n t h a t u ~ 0.0 4 a n d h = 0.o6 a n d u ~ o.o 3 a n d h = 0.0 4, r e s p e c t i v e l y . F o r e x p l a n a t i o n , see t e x t .
Curve 3 (for the C population) shows the accumulation or spontaneous second chromosome recessive lethals with u = 0.005 and h ---- 0.04 (the u value is from CRow AND TEMINi). With the above combination of values, a good agreement with the d a t a for generation 30 is obtained; the observed frequency in generation 64 is higher but this is expected since the lethals persisting longer are those with a smaller h. If h z 0.025, one gets ~ = 0.20, roughly the final value. Rewriting equation (5), we get, u [x--e'U-z)t ] q =
[z--ueIu-zl*J
which shows t h a t the lethal frequency at a n y time is roughly proportional to the m u t a t i o n rate. In s u m m a r y , the results presented in the preceding pages show t h a t (i) in the two populations, irradiation of the males generation after generation does not strongly decrease egg-hatchability below the level observed, say, after one generation of irradia-
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SHORT COMMUNICATION'S
tion and these levels are similar in the two populations; (ii) contrasting post-treatments to males does not seem to affect egg-hatchability in any differential way; (iii) there appears to be no consistent post-radiation modifying effects of nitrogen and oxygen on recessive lethals induced in the second chromosome and consequently, the populations, in spite of the different post treatments, do not diverge from one another and (iv) the pattern of accumulation of recessive lethals in the two populations is consistent with reasonable assumptions about the mutation rate and the intensity of selection acting against lethals in the heterozygous condition. WALLACE (personal communication) suggested that a semi-log plot of the frequency of non-lethal chromosomes with time (in generations) would be instructive since such a drawing would emphasize the abrupt change at about generation 24 (when lethal frequencies became more or less constant) followed by points (generation 64) which fall close to the projection of tile original slopes. This is true; however, such a trend is already illustrated in Fig. 2, although not as dramatically as it would be in the kind of figure envisaged by Wallace. Furthermore, since the drawing of a straight line in a semi-log plot involves the assumption that h - o and since the cause(s) of the abrupt changes are not known, a presentation of all the data together with tile fitted curves was chosen (Fig. 2). The finding that egg-hatchability remains at fairly stable levels in the two irradiated populations with no evidence for a decrease in spite of generations of irradiation is not unexpected (since dominant lc'~hals are not transmitted) and is in line with the finding reported by the author in an earlier study 2. Likewise, the lack of a measurable post treatment effect on egg-hatchability is also in accordance with earlier results '~. The lack of a clearly detectable differential accumulation of autosomal recessive lethals in the two populations however, is unexpected although, as mentioned earlier, the data are not inconsistent with SOBELS' results. The available data do not permit one to determine whether this discrepancy between prediction and observation is real or only an apparent one. It may be that since in most of SOBELS' studies on post-radiation modification of genetic damage in mature spermatozoa (by nitrogen and oxygen), males carrying ring-X chromosonLes were used (and recessive lethals induced in such chromosomes studied), the differences that he detected are somehow associated with some special properties of the ring-X chromosomes and consequently, the conclusions are not applicable to the rest of the genome. At any rate, it seems that population methods are perhaps not the best to study repair of genetic radiation damage (as measured by autosomal recessive lethals) in Drosophila spermatozoa. It is a pleasure to thank Prof. F. H. SOBELSfor his warm encouragement, Prof. J. F. CROW and Mr. W. S. VOLKERS for their most invaluable help in the statistical analysis of the data, Professors J. F. CROW, B. WALLACEand Mr. W. S. VOLKERS for their constructive comments on the manuscript and Mrs. A. VAN DUYN, C. DE GROOT and Miss M. J. Loos for their conscientious technical assistance. The work was supported by EURATOM Contract o52-64-I BIAN with the University of Leiden.
Department of Radiation Genetics and Chemical Mutagenesis, State University of Leiden, and J. A. Cohen Institute for Radiopathology and Radiation Protection, Leiden (]'he Netherlands)
K. SANKARANARAYANAN
SHORT COMMUNICATIONS
293
i CROW, J. F., AND R. G. TEMIN, E v i d e n c e for t h e p a r t i a l d o m i n a n c e of recessive lethal genes in n a t u r a l p o p u l a t i o n s of Drosophila, Am. Naturalist, 98 (1964) 21-33. 2 SANKARANARAYANAN, K., Genetic loads in i r r a d i a t e d e x p e r i m e n t a l p o p u l a t i o n s of Drosophila melanogaster, Genetics, 5 ° (1964) 131-15o. 3 SANKARANARAYANAN, I~., T h e effects of n i t r o g e n a n d o x y g e n t r e a t m e n t s on t h e frequencies of X - r a y - i n d u c e d d o m i n a n t lethals a n d on t h e p h y s i o l o g y of t h e s p e r m in Drosophila melanogaster, Mutation Res., 4 (1967) 641-6614 SOBELS, F. H., P o s t - r a d i a t i o n r e d u c t i o n of genetic d a m a g e in m a t u r e D r o s o p h i l a s p e r m b y nitrogen, Mutation Res., I (1964) 472-477 . 5 SOBELS, F. H., R a d i o s e n s i t i v i t y a n d repair in different germ-cell s t a g e s of Drosophila, in S. J. GEERTS (Ed.), Proe. X I Intern. Congr. Genet., The Hague I963, vol. 2, P e r g a m o n , Oxford, 1965, pp. 235 255Received
October
8th, 1973