Population control potential of heterozygous translocations as determined by computer simulations*

Bull. Org. mond. Sant) 1971, 44, 829-845Bull. Wid Hith Org.f Population Control Potential of Heterozygous Translocations as Determined by Computer Simulations* P. T. McDONALD 1 & K. S. RAI 2 A possible methodfor genetic control of insect vector species involves the use of trans- location heterozygotes. The potential of single and double heterozygotes already available in Aedes aegypti has been investigated with computer simulations of release strategies. Such simulations indicate a possible role for translocation heterozygotes of these types in an insect population characterized by a S-fold population growth per generation, or less. For several years, the possibility of genetic control of insect vectors has received much attention (Knip- ling et al., 1968). Heritable chromosomal aberrations, reciprocal translocations in particular, have been con- sidered for the genetic control of mosquitos (Rai, 1967; Laven, 1969), tsetse flies (Curtis, 1968), house- flies (Wagoner, 1969), and sheep blowflies (Whitten, unpublished data). In Aedes aegypti, two sex-linked reciprocal trans- locations have recently been induced by irradiation, and translocation heterozygotes of both forms have been studied with respect to their genetics (K. S. Rai and others, unpublished data) and cytology (Mc- Donald & Rai, 1970a). One translocation, RT (1: 2), involves linkage groups I and II with the original break points 0.3 cross-over unit from the male-deter- mining allele (M) on group I and 1.6 units from the wild-type allele of spot abdomen (s+) on group II. The other translocation, RT(1 3), involves linkage groups I and III with the original break points 0.4 cross-over unit from the wild-type allele of the red-eye gene (re+) on group I and 0.6 unit from the normal allele of black-tarsi (blt+) on group III. Although originally both these translocations in- volved the male-determining chromosomes, female * This work received support from Atomic Energy Com- mission Contract AT(11-1)-38 with the Radiation Labora- tory, University of Notre Dame, Notre Dame, Ind., USA, and from an NSF Traineeship awarded to the senior author. This is AEC Document No. COO-38-756. 1 Post-Doctoral Research Associate, Department of Bio- logy, University of Notre Dame. This work was done in partial fulfilment of the requirements for the Ph.D. degree at the University of Notre Dame. ' Professor of Biology and Director, Mosquito Biology Training Program, University of Notre Dame. translocation heterozygotes have been established by appropriate crosses. Furthermore, 2 types of male heterozygous for each translocation have been con- structed. In one type (M-linked) the male-determin- ing chromosome is translocated and in the other (m-linked) the female-determining chromosome is translocated. In Aedes aegypti sex is determined by a single gene, Mm being the male genotype and mm the female genotype (McClelland, 1962). Crossings of two individuals heterozygous for the same trans- location failed to produce translocation homozy- gotes, both for RT(1: 2) and RT(1: 3). Double heterozygotes, having both translocations in the heterozygous form, were produced. A genetic exchange in the double heterozygote produced a " new " chromosome, bearing parts of all 3 linkage groups. In both the double heterozygotes and the " new " karyotypes, an apparent enhancement of crossing-over occurred in the region between the break points of RT(1: 2) and RT(1: 3) on linkage group I (McDonald & Rai, 1970b). As a result, the double heterozygote produced a high frequency of " new " karyotypes and the " new " karyotypes pro- duced a high frequency of single reciprocal-trans- location heterozygotes. Whereas each translocation heterozygote was associated with semisterility, the fertility of double heterozygous males was approxi- mately 12.5 %. These translocation heterozygotes have been evalu- ated with regard to their applicability for population control, using a model for computer simulations under several different release strategies. The results of these simulations are included in this paper. The model itself was made available by Dr Max Whitten, 2696 - 829- P. T. MCDONALD & K. S. RAI Commonwealth Scientific and Industrial Research Organization, Canberra, Australia. Such computer simulations are expected to be very useful in terms of realistic and long-term evaluations of the theoret- ical potential that a particular genetic technique may provide. It is for this reason that considerable atten- tion has been paid to such simulations in recent years (Berryman, 1967; Cuellar, 1969; Curtis & Hill, 1968; Watt, 1964). At a meeting of a WHO Scien- tific Group on the Cytogenetics of Vectors of Dis- ease in Man in 1967, Rai suggested a possible role for translocation heterozygotes in insect control. Rai & Asman (1968), using sterility and competitive abil- ity data from the sex-linked translocation RT(l : 2) in Ae. aegypti, indicated that an idealized population could be controlled through the use of such males, a population size replacement potential of 1: 1 in each generation being assumed. Working with Culex pipiens fatigans, Laven (1969) similarly suggested the use of translocation heterozygotes in control programmes based on studies with competition be- tween translocation heterozygotes and normal males. As in the work of Rai & Asman (1968), the assump- tion was made of a potential 1: 1 population size replacement in each generation. Wagoner (1969) was able to simulate a successful control programme using laboratory cage competi- tion experiments with Musca domestica. Transloca- tion heterozygotes of both sexes were introduced in a 9: 1 ratio and a population size of 0.25% of the control size in the second generation was thereby attained. MATERIALS AND METHODS General description of the model The computer model used for testing the effective- ness of releases of translocation heterozygotes is ad- aptable and easily allows for changing the patterns of introductions. In addition, various assumptions of population size influences on population growth can readily be accommodated. A brief outline of the sequence of steps in Whitten's model for the effect of an introduction of translocated males on zygotic lethality, genotype frequencies, and population growth is as follows: (1) Enter initial numbers of each genotype, their fit- nesses; enter pattern of introductions. (2) Determine the frequencies of each genotype in this generation. (3) Replace this generation with the " next generation (a) Select male parent; (b) Select female parent; (c) Determine if viable; (d) Assign genotype; (e) Register this individual; (f) Repeat a-e for all of next generation; (g) Total next generation; determine load (fraction of zygotic lethals). (4) Set size of the " next generation (5) Add introduced males, based on pattern designated. (6) Compute new frequencies of each genotype. (7) Repeat 3-6 for desired number of generations. At the outset of a release programme, the resident population was considered to have all standard karyotypes (non-translocated) with a normal fitness of 1. Translocation heterozygotes with a fitness of less than 1 are introduced in various ratios to the normal and may later be reintroduced in desirable numbers. The total mating population, including resident and introduced individuals, then produces the succeeding generation by random matings and fertilization of random gametes from parentals. Zygotic lethals are accumulated and the inviable fraction of the next generation constitutes the genetic load. The members of the new generation are now con- sidered as the resident population; reintroductions are made, and the subsequent generation is deter- mined in similar fashion. The model has no provi- sion for overlapping generations; however, it per- mits any number of generations to be produced. Assumptions of the programmes Two programmes have been written for the model. Programme 1 has been designed for single reciprocal translocations and is based on the following assump- tions, which themselves are derived from actual data: (1) A designated crossing-over between the trans- location break point and the sex locus occurs (values obtained from actual data). (2) Translocation homozygotes are lethal. (3) Fitness (=fertility) of a translocation hetero- zygote is 0.5 while that of a normal (non-trans- located) individual is 1.0. (4) Transmission of the translocation from a heterozygote is 50%. Programme 2 accommodates the double-hetero- zygote-" new "-karyotype system. It assumes fit- nesses of 1.0, 0.5, and 0.125 for normal, single, and double/" new " system heterozygotes, respectively. Cross-over rates in the sex-RT(1 : 2) break point region are assumed to be absent for RT(1 : 2), and 830 COMPUTER SIMULATIONS OF VECTOR CONTROL BY HETEROZYGOUS TRANSLOCATIONS 6% in the double/" new " system; and for the sex- RT(1: 3) break point region, 7% for RT(1: 3), 44% for double/" new " males, and 40% for double/ "new " females. These values are based on the data available to date for the two translocations (McDonald, 1970). One limitation in the second programme is that no provision is made for the production of viable zygotes from a fertilization of 2 unbalanced, but complementary, gametes. These would occur and contribute to the total number of translocation heterozygotes produced in a particular generation. Programme 1 was used for assaying loads of zygotic lethals for single heterozygotes and for determining the effectiveness of release of single heterozygotes for population suppression under con- ditions of 1: 1 population size replacement each generation. Programme 2 was used for assaying loads of zygotic lethals for double heterozygotes as well as for determining the effectiveness of releases of single and double heterozygotes for population suppression under conditions of various population growth rates. A copy of one of the two alternative programmes for exercising the model is provided in the Annex. As such, the programme is written in FORTRAN IV and designed to be consistent with the current usage employed for the Univac 1107 at the University of Notre Dame Computing Center. The subprogramme RANDOM generates random floating point numbers between 0. and 1. with uniform distribution. This subprogramme is initiated with the argument I and continued with the argument 0. RESULTS Zygotic lethality in single-heterozygote matings In order to study the effects of releases of different types of translocation heterozygotes on zygotic lethal- ity in subsequent generations, programme 1 was set up so that a constant potential of 2000 individuals was available for each generation producing a next generation. The results of two strategies for RT (1: 2) with programme 1 are shown in Table 1. Introduc- tions were made at a relatively high ratio in order to flood the population with translocated males. Introductions at 8: 1 and reintroductions of the same number of translocation heterozygote males, repeated 5 times, were made. Under these circum- stances, the data indicate that the M-linked trans- location quickly becomes fixed in the population and a permanent load of approximately 0.5 is achieved because all males in the population are semisterile. The behaviour of the m-linked translocation is quite different from that of the M-linked transloca- tion. When the population was initially flooded with translocated males of the m-linked type, a much higher load was achieved. However, the transloca- tion arrangement never became fixed (because the translocation homozygotes were lethal), and when the population was released from the pressure of the introductions, the load declined. When single translocation heterozygote males are released, an increased load with the flooding of the population with m-linked translocations is due to matings between 2 translocation heterozygote indi- viduals. According to the programme, such matings are 75% sterile. Furthermore, of the 25% of indi- viduals resulting from balanced gametes, one-fourth would be homozygotes for the translocation, and lethals. The total lethality would then be 81.25% for matings of 2 single-translocation heterozygotes. This is approached in the results of one of the programmes (Table 1). Effect of linkage of translocation on load Programme 1 was reset to test the production of loads with assumptions of 25% and 50% recombina- tion between the translocation and the sex-determin- ing locus. The 50% recombination would simulate the use of an autosome-autosome transiocation, two ofwhich have recently been isolated in this laboratory. The results of these strategies are shown in Table 2. When the loads generated at generation 6 (when the maximum effect would be expected) are compared, it is seen that the autosomal translocation generates a load intermediate between those of the two sex- linked translocations. The load generated by the 25% sex-linked translocation is intermediate between those of the sex-linked and autosomal translocations. As would be expected, only the M-linked transloca- tion can be fixed, thereby producing a fixed load per- manently. Effect offertilizations of aneuploid gametes In actual practice, the zygotic lethality entered in Table 2 would not be obtained, as up to 12.5% (assuming all unbalanced gametes result from segre- gation of homologous centromeres) of fertilizations, those involving 2 unbalanced and complementary gametes, would produce viable translocation hetero- zygotes. If such were the case, a load of 68.75% for matings of 2 single translocation heterozygotes 831 832 P. T. MCDONALD & K. S. RAI Table 1. Load measurements from simulation of releases of 6 generations of single- translocation heterozygous males a Genotype frequencies for the following normal and translocation males and females: Genera-| Load >malemsab RT (1 : 2) |RT (11: 2) |femaalese RT (I1: 2) A. Releases of M-linked translocation heterozygote males 1 .4385 99 463 0 561 0 2 .4870 8 507 0 511 0 3 .5060 3 460 0 525 0 4 .5125 0 500 0 475 0 5 .4995 0 498 0 503 0 6 .4985 0 502 0 501 0 7 .5080 0 504 0 480 0 8 .4875 0 495 0 530 0 9 .5010 0 515 0 483 0 10 .4825 0 500 0 535 0 11 .5075 0 507 0 478 0 12 .5070 0 486 0 500 0 B. Releases of m-linked translocation heterozygote males 1 .4420 574 0 0 108 434 2 .7295 229 0 84 27 201 3 .7686 165 0 107 10 181 4 .7835 142 0 130 3 158 5 .8025 127 0 133 5 130 6 .7940 138 0 131 2 141 7 .6370 199 0 182 143 202 8 .4620 434 0 115 296 231 9 .3080 591 0 81 554 158 10 .1695 786 0 47 725 103 11 .0890 878 0 32 859 53 12 .0415 966 0 18 911 22 a Initial ratio of 8:1 with 5 reintroductions of the same number of males. b Initial frequency 1000, fitness 1.0000 for A and B. c Initial frequency 8000, fitness 0.5000 for A; -0 and 0.5000 for B. d Initial frequency -0, fitness 0.5000 for A; 8000 and 0.5000 for B. e Initial frequency 1000, fitness 1.0000 for A and B. f Initial frequency -0, fitness 0.5000 for A and B. COMPUTER SIMULATIONS OF VECTOR CONTOL BY HETEROZYGOUS TRANSLOCATIONS would obtain rather than the load of 81.25 %. The effect of aneuploid fertilizations on the loads pro- duced by the sex-linked and the autosomal trans- locations was higher for the m-linked than for the autosomal translocation, and was absent for the M-linked translocations (Table 3). Zygotic lethality in double-heterozygote matings The results of the introductions of double hetero- zygotes (Table 4) indicated that the double heterozy- gote has the features of the m-type of single hetero- zygote. No long-range load is maintained through the introduction of the M-linked translocation, but a much increased load is produced by the presence of both M-linked and m-linked translocations. Population control potential of single translocation heterozygotes Several strategies of release of single translocation heterozygote males were simulated using pro- gramme l. The assumption was made that each generation had the maximum potential for replacing itself. If any zygotic inviability occurred, the poten- tial was not realized. The results of computer runs are entered in Table 5. These results indicated the following: Table 2. Load measurements from simulation of releases of 6 generations of various types or single-translocation heterozygous males a Sex- 25% 25% Sex-Genera- linked sex- Auto- sex- linkedtion with M witheM somal withem with m 1 .4385 .4415 .4425 .4470 .4420 2 .4870 .5645 .6105 .6555 .7295 3 .5060 .5960 .6485 .7070 .7685 4 .5125 .5705 .6610 .7165 .7835 5 .4995 .5670 .6410 .7200 .8025 6 .4985 .5795 .6495 .7510 .7940 7 .5085 .4925 .4750 .5545 .6370 8 .4875 .3425 .3035 .3610 .4620 9 .5010 .2095 .1560 .2060 .3080 10 .4825 .1260 .0785 .1385 .1695 11 .5075 .0625 .0430 .0630 .0890 12 .5070 .0240 .0180 .0350 .0415 a Initial ratio of 8: 1 with 5 reintroductions of the same number of males. Table 3. Load measurements from simulation of releases of 6 generations of various types of single-translocation heterozygous males a Sex-linked with M Autosomal Sex-linked with m Generation No aneuploid Aneuploid No aneuploid Aneuploid No aneuploid Aneuploid fertilization tfertilization fertilization fertilization fertilization fertilization 1 .4385 .4505 .4425 .4500 .4420 .4365 2 .4870 .4925 .6105 .5610 .7295 .6370 3 .5060 .4960 .6485 .5905 .7685 .6690 4 .5125 .4720 .6610 .6120 .7835 .6795 5 .4995 .5030 .6410 .6095 .8025 .6585 6 .4985 .4965 .6495 .5980 .7940 .6800 7 .5080 .5080 .4750 .5275 .6370 .6020 8 .4875 .4990 .3035 .3970 .4620 .5000 9 .5010 .5090 .1560 .2830 .3080 .3920 10 .4825 .5040 .0785 .1740 .1695 .2770 11 .5075 .5085 .0430 .0915 .0890 .1560 12 .5070 .4900 .0180 .0340 .0415 .0715 a Initial ratio of 8: 1 with 5 reintroductions of the same number of males. 833 P. T. MCDONALD & K. S. RAI Table 4. Load measurements from simulation of releases of 6 generations of various types of translocated males a Genro ISex-linked Sex-linked DoubleGeneration with M with m heterozygote 1 .4330 .4430 .7710 2 .4875 .7245 .9050 3 .5170 .7530 .9537 4 .5045 .7910 .9477 5 .5230 .7835 .9348 6 .4800 .8165 .9567 7 .4980 .6215 .6615 8 .4800 .4790 .4636 9 .4755 .3060 .3175 10 .4400 .1685 .1795 11 .3850 .1035 .0820 12 .2915 .0460 .0495 a Initial ratio of 8: 1 with 5 reintroductions of the same number of males. (1) In all, 6 introductions are needed to " eradi- cate" the idealized population. (2) The release of m-linked translocation hetero- zygotes is more effective than the release of M-linked translocation heterozygotes or alternating the two. (3) The optimum ratio of released to resident males is 4: 1 at the time of the first release, with each succeeding release of the same size. The pattern of population control following con- tinued releases of 4000 translocated males of either the M-linked type or the m-linked type is presented in Fig. 1. As expected, this graph shows greater control effectiveness of the m-linked translocation when the population is constantly flooded with translocation heterozygotes. For single releases, the M-linked translocation is more effective. When the effectiveness of autosomal translocation heterozygotes was compared with that of sex-linked translocation heterozygotes, it appeared that the autosomal translocation is more effective in sup- pressing a population than the M-linked transloca- tion and less effective than the m-linked translocation (Fig. 2). The translocations characterized by 25% linkage to the sex locus have a suppressing effect that is intermediate between those of the autosomal and sex-linked translocations. The effect of 2 aneuploid gametes giving rise to a translocation heterozygote is the lessening of the effectiveness of both the m-linked and the autosomal translocation heterozygotes in suppressing popula- tion size (Fig. 3). As would be expected, the assump- tion of the fertilization of 2 complementary aneup- loid gametes giving rise to a translocation hetero- zygote has no effect for the M-linked situation since 2 translocation heterozygotes never mate together in this situation. Table 5. Results of introductions of single-translocation heterozygote males for population control assuming an initial population of 2 000 a Number Repetitions Males introduced Results(thousands) 0 0 0 No reduction 4 0 RT (1: 2) at M Reduced to 16 in 7 generations 4 5 RT (1: 2) at M Eradication in 11 generations 4 5 RT (1: 2) alternating atm Eradication in 8 generations 4 5 RT (1: 2) at m Eradication in 6 generations 2 5 RT (1: 2) at m Eradication in 9 generations 6 5 RT (1: 2) at m Eradication in 6 generations 4 I _______ - RT (1: 3) at m Eradication in 6 generations a 1000 females + 1000 males. 834 COMPUTER SIMULATIONS OF VECTOR CONTOL BY HETEROZYGOUS TRANSLOCATIONS (1) In all, 5 introductions are necessary for eradi- cation. (2) The double heterozygote is more effective than the single heterozygote, with eradication occurring 1 generation earlier. (3) The optimum ratio of released double-hetero- zygote to resident males is 4: 1 at the time of the first release, with each succeeding release of the same size. (4) Both double-heterozygote and " new "-karyo- 1 2 3 4 5 6 7 8 9 10 11 12 Generation after i niti al releaSo Fig. 1. Population reduction following the release of sex-linked single-translocation heterozygote males. The initial ratio of introduced to resident males was 4: 1, with reintroductions of the same number of males. A- M-linked 11 release B = rn-linked AB' M-linked 6 releases A' rn-linked Population control potential ofdouble heterozygotes Simulations of the releases of double-heterozygote or "new "-karyotype males in various strategies were carried out with programme 2. Again, the assumption was made that each generation had a maximum potential for replacing itself and the poten- tial was not realized when zygotic lethals were pro- duced. The results of the computer runs are entered in Table 6. These results indicated the following: IC .C @ 3 a I C ".2 .0 z 2 3 4 s 6 7 8 9 lt 11 12 Generation after initial rel*ase Fig. 2. Population reduction following the release of sex-linked or autosomal single-translocation hetero- zygote males. The initial ratio of introduced to resident males was 4: 1, with reintroductions of the same number of males. A' = M-linked l B' = m-linked 6 releases C' = autosomal J 835 8-I P. T. MCDONALD & K. S. RAI 10 6 IC .C 3 E is2' I.II.ti;.in1. ~ ~ ~ ID ~ ~ ~~~~~noa euptolid fort ilIizations z 1 2 3 4 5 6 7 8 9 10 I 1 12 Generation after initial release Fig. 3. Effect of fertilizations of aneuploid gametes on population reduction following releases of m-linked or autosomal single-translocation heterozygote males. The initial ratio of introduced to resident males was 4: 1, with reintroductions of the same number of males. B' = m-linked 6 rC' = autosomal I reeases type males are equally effective for bringing about eradication. The patterns of population size reduction for the release of 4000 males of both types of single hetero- zygotes (M-linked, m-linked) and the double hetero- zygote are included in Fig. 4, 5, and 6. These graphs show the superiority of the double heterozygote over the single heterozygotes in affecting eradication. Similar results were obtained for a double hetero- zygote with a fitness of 0.25. These programmes were repeated using an initial population of 20 000. Release strategies of the same ratio of introduced to resident males gave results similar to those obtained with an initial population of 2000. Several multiple-introduction strategies were simu- lated using programme 2. Again, the same limita- tions of density independence on population growth were made. The results are included in Table 7. A comparison of the results from multiple introduc- tions with those for double heterozygotes alone indi- cated that the introduction of several types does not have an advantage over the introduction of double heterozygotes alone. Population suppression with varying population growth potentials The effectiveness of releases of translocation het- erozygotes in suppressing population growth under various assumed population size replacements per generation has been tested using programme 2. In the programme, an upper ceiling (the initial population size) on the potential population size of a next generation is established. The x-fold in- crease in individuals based on the number of indivi- duals in a generation is then calculated. If that num- ber is less than the ceiling, it is permitted. If the x-fold increased size exceeds the ceiling it is ignored and the maximum size potential of the next generation Table 6. Results of introductions of double-heterozygote or ' new males for population control assuming an initial population of 2 000 a Numbers ) Repetitions Males introduced Results 4 0 Double heterozygote Reduced to 1/10 in 5 generations 4 4 Double heterozygote Eradication in 5 generations 2 5 Double heterozygote Eradication in 6 generations 6 4 Double heterozygote Eradication in 5 generations 4 4 - New ' at M Eradication in 5 generations a 1000 females + 1000 males. 836 COMPUTER SIMULATIONS OF VECTOR CONTROL BY HETEROZYGOUS TRANSLOCATIONS DISCUSSION Consideration of the applicability of translocation heterozygotes for control of Ae. aegypti populations is made in the context of the inviability of transloca- tion homozygotes for these translocations. This is true for the translocations studied to date in this species. Although the simulations were undertaken for Ae. aegypti, they should also be applicable to other species of insect with a sex-determination mechanism similar to that of Ae. aegypti, e.g., C. p. fatigans, a species in which several translocations have been induced (Laven, 1969). 1 2 3 4 5 6 7 8 9 10 11 12 Generation after initial release Fig. 4. Effect of population growth rate on population reduction following the releases of M-linked single- translocation heterozygote males. The initial ratio of introduced to resident males was 4: 1, with reintroduc- tions of the same number of males. A' = growth rate of 1 times 6 releases; A" = growth rate of 2 times-10 times M-linked is established as the ceiling. The manner in which the programme was designed to accommodate dif- ferent population growth rates simulates conditions under which one stage in the life-cycle, the adult female, is under selection pressure. According to the results obtained, the release of 4: 1 double heterozygotes maintained for 6 genera- tions would be successful in effecting eradication for a population capable of a 5: 1 population size replacement each generation (Fig. 6). However, for a greater than 5: 1 population size replacement capability, the double heterozygote would not effect eradication. C E.5 2 1 2 3 4 3 6 7B 9 10 11 12 Generation after initial release Fig. 5. Effect of population growth rate on population reduction following the releases of m-linked single- translocation heterozygote males. The initial ratio of introduced to resident males was 4: 1, with reintroduc- tions of the same number of males. B' = growth rate of I times6reas;B" = growth rate of 2 times m-rleases;B"'..= growth rate of 4 times-I10 times mlne 837 P. T. MCDONALD & K. S. RAI t0 . .C 'A 3 E E zD 1 2 3 4 5 6 7 8 9 10 11 12 Generation aft er i niti al rel e as e Fig. 6. Effect of population growth rate on population reduction following the releases of double heterozygote males. The initial ratio of introduced to resident males was 4: 1, with reintroductions of the same number of males. D' = growth rate of 1 times-2 times: 6 releases:D" = growth rate of 4 times-5 times double hetero- D"'= growth rate of 8 times-10 times zygotes Whitten, in a paper on the use of chromosome rearrangements for mosquito control read at an IAEA Symposium on sterility principles for insect control or eradication in Athens in 1970, pointed out that a limitation to the usefulness of M-linked translocation heterozygotes in mosquitos is that the load such heterozygotes can produce is too small. As computer simulations have indicated, however, such may not be the case with the m-linked trans- location heterozygote in a control programme. The programmes used for determining the effects of aneuploid fertilizations assumed the segregation of homologous centromeres from the translocation interchange complex. Whether this occurs or not would depend upon the frequencies of non-disjunc- tions from an interchange complex, and this fre- quency would be greatly influenced by the size of the exchange pieces, the centromere positions with regard to the break points, and the chiasma fre- quency. Two factors would tend to reduce the load- decreasing effect of fertilizations involving comple- mentary, aneuploid gametes. One is the occurrence of adjacent disjunction of non-homologous centro- meres; the other is the formation of aneuploid gametes from non-co-orientation. The higher loads in the case of the double hetero- zygotes are due to the matings between two indivi- duals, one of which is of the double-heterozygote and " new "-karyotype system. According to the programme, matings between a single and a double heterozygote would be associated with 6.25 % fertil- ity. Furthermore, 25% of the individuals resulting from balanced gametes (1.57%) would be homo- zygous for one or both of the translocations, and lethal. The total lethality would then be 95.32% for matings between a single and a double heterozygote. Also, according to the programme, matings between two double-heterozygote and " new "-karyotype sys- tem individuals would be associated with 1.56% fertility. Furthermore, 43% of the individuals result- ing from balanced gametes (0.67 %) would be homo- zygous for one or both of the translocations, and lethals. The total lethality would then be 99.11 % for matings between two individuals of the double- heterozygote and " new "-karyotype system. A load of 95.67% resulted primarily from the matings be- tween a single and a double heterozygote individual. In the release programme involving the release of double heterozygotes, aneuploid fertilizations pro- ducing translocation heterozygotes would also occur, but for several reasons would be much less frequent than might be expected. Matings between a single heterozygote for one translocation and a single heterozygote for the other translocation would not produce translocation heterozygotes from the fertil- ization of such aneuploid gametes. Furthermore, the double-heterozygote and " new "-karyotype sys- tem may favour a non-disjunction type of segrega- tion rather than strictly a segregation of homologous centromeres (McDonald, 1970). The source of the effectiveness of the translocation heterozygote method of control lies primarily in the partial sterility associated with matings between two translocated individuals. This is clearly seen 838 COMPUTER SIMULATIONS OF VECTOR CONTROL BY HETEROZYGOUS TRANSLOCATIONS Table 7. Results of simultaneous introductions of different translocation heterozygous males for population control assuming an initial population of 2 000 a Number Repetitions Males introduced Results(thousands) et on 2 5 RT(1:2)atm 2 No eradication 2 5 RT (1: 3) at MJ 4 5 RT (1:2) at m 4 Eradication in 7 generations 4 5 RT (1 :3) at M) 2 5 (RT (1:2) at m 2 5 RT (1:3) at M Eradication in 6 generations 2 5 Double heterozygote 4 5 RT (1:2) at m 4 5 RT (1:3) at M Eradication in 6 generations 4 5 Double heterozygote a 1000 females + 1000 males. in Fig. 7. Such an enhanced sterility requires the availability of the m-linked translocation or the autosome translocation. The effectiveness also depends upon continued reintroductions of trans- located individuals. The reintroductions provide translocation heterozygotes that mate with resident translocation heterozygotes, and this results in highly sterile matings. Whitten (loc. cit.) suggested that M-linked trans- locations heterozygotes would not be effective in control but he did not consider the m-linked trans- locations which, in a programme including reintro- ductions, would be more effective and could provide a cumulative load sufficient to eradicate a population characterized by a 1: 1 population size replacement per generation in 6 generations. If the cumulative loads are taken into consideration, even the M-linked translocation, following 6 introductions, resulted in theoretical " eradication ", assuming a 1: 1 popula- tion size replacement (Fig. 1). Nevertheless, the results of the programme runs indicate that the m-linked translocation heterozygote would be more successful than the M-linked and autosomal trans- location heterozygotes, and that a double hetero- zygote would be even more effective than the m-linked single heterozygote. The effect of the occurrence of aneuploid fertiliza- tions producing translocation heterozygotes is rather slight and would be expected to be almost negligible in the release of double heterozygotes for population suppression. It is difficult to determine the exact influence of this factor for a particular double hetero- zygote but, in view of the probably slight influence, it could be safely disregarded. To date, no attempt has been made precisely to adjust the number of males introduced each genera- tion so as to provide an optimum control procedure. This could profitably be undertaken. The fact that the curves from generations Z-3 and 3-4 in Fig. 7 are close to parallel suggests that the number of reintroduced males is greater than it needs to be in order to effect control. The reproductive potential of an insect species is generally regarded by Knipling (1960) to be a 5-fold increase per generation at times of maximum popula- tion growth. The maximum reproductive potential of a mosquito population has been estimated to be 10-fold for C. p. fatigans by Weidhaas et al. (1970). This 10-fold increase per generation was realized when the population was subjected to simultaneous stresses of egg-raft destruction and releases of chemo- sterilized males. At the time when this maximum reproductive potential was measured, the climatic conditions were optimum for population growth. In the C. p. fatigans experiment, the population had been undergoing 1.5-fold-3.5-fold increases per gen- eration during the month prior to treatment, and were presumably at or near population size stability. 839 P. T. MCDONALD & K. S. RAI Six Releases(m-IInked) Release ratio ___2 X .4X ^_6 X heerzyot mae.Inalcssthnubromle o10 .0. reintroduced each time was equal to the number originally released. At the other extreme from a mosquito population with a 10-fold increase in growth potential per gener- ation would be a tsetse fly population with a maxi- mum population growth potential of approximately I (Curtis & Hil, 1968). The multivoltine species would undoubtedly be characterized by a population growth potential that would be strongly influenced by environmental fluc- tuations. With such species, including many species of mosquito, the population growth potential would attain a maximum value under the most favourable conditions, but would be smaller at other times of the year and in less-than-optimum areas. The release of translocation heterozygotes should provide an effective means ofpopulation suppression, and possibly eradication, for isolated insect popula- tions when the population growth potential is suffi- ciently small. With the double heterozygote in Ae. aegypti, this method should be effective for up to 5-fold increases of population size per generation in the critical third, fourth, and fifth generations after the initial release, even if previous generations were characterized by a higher potential. The use of a single semisterile translocation hetero- zygote for control would be feasible for situations in which the population was characterized by ap- proximately 1-fold increases per generation at the time of the initial release as well as the reintro- ductions. The computer simulation programmes incorpo- rating various population growth rates reported here were based on the assumption that the selection is primarily on the adult stage and more specifically on the inseminated female. The validity of this assumption depends upon verification from further field test studies on various species of mosquito, but certainly seems valid for some other species of insect. The translocation heterozygote male could have a potential advantage over the sterilized male coun- terpart in that the released individual has not itself undergone a treatment or resulted from hybridiza- tion, both of which could seriously reduce its com- petitive abilities, especially in mating. Knipling (1967), although hopeful that progress would be made in the future, stated: " we do not yet know how to produce sterility without some adverse effect on the competitiveness of most insects ". One of the primary advantages of the transloca- tion heterozygotes compared with the homozygotes is the relative ease of producing the heterozygotes. Of 7 translocations induced in this laboratory, to date none has been rendered homozygous despite numerous attempts. However, with species of Droso- phila, approximately 40% of translocation homo- zygotes are fully viable and fertile (Bumham, 1962). A potential disadvantage of translocation hetero- zygotes would be the maintenance and selecting out ofthe translocated individuals, especially the m-linked single and the double heterozygotes. This disadvan- tage, however, could be alleviated if the translocation were maintained against a suitably marked stock. Considerably improved potential for the use of translocation heterozygotes in population control will accrue if and when viable homozygotes are obtained. The use of such homozygotes has been advocated by several authors for the control of insect 840 COMPUTER SIMULATIONS OF VECTOR CONTROL BY HETEROZYGOUS TRANSLOCATIONS pest species, and has many advantages over the translocation heterozygote. Serebrovskii (1940) argued that the introduction of both male and female single-translocation homo- zygotes of equal fitness to the normals would bring about a sterility of 43% in the first generation after release. This sterility would remain at 43 % as long as both translocated and non-translocated haploid sets of chromosomes were of equal frequency. The departure that might be expected from 50% would be due to the production of viable translocation heterozygotes from two unbalanced gametes. Serebrovskii (op. cit.) further theorized that per- manent sterilities of up to 75% could be achieved by using several fully fit translocation homozygotes, each with translocations involving the same pair of chromosomes, and each characterized by 50% steril- ity in the heterozygous condition. In organisms with higher chromosome numbers, with possibilities of more independent translocations (involving chromo- somes not involved in another reciprocal transloca- tion), a higher sterility could be achieved. This ste- rility would approach 98% when several different variants of 3 independent translocations were intro- duced in correct proportions. To achieve this level, a species haploid number of 6 or higher would be required. Whitten (loc. cit.) has stressed the potential role of several multiple-translocation homozygotes, each producing highly or completely sterile heterozygotes with the normal, or with each other. Together, they would effect a long-maintained sterility in a popu- lation. Although the use of translocation homozygotes for population control has been emphasized by various workers, one aspect of their use presents a problem. Once again this was originally suggested by Serebrovskii (1940). In order to obtain optimum control, it is necessary to have exactly 50% of trans- located chromosomes in the population. Whenever the frequency of either the translocated or the normal haploid set becomes more than 50%, it becomes fixed in the population. As a result, in time, the population becomes fully fertile again. However, Serebrovskii (op. cit.) pointed out that the decrease of sterility with the fixation of either type of haploid set would be gradual, and that adjustment in the planning of the control pro- gramme could reverse the fixation process. Curtis (1968) used computer simulations of single releases of translocation homozygotes of both sexes. He demonstrated that when single releases of steri- lized males are compared with single releases of equal numbers of translocation homozygotes of both sexes, the release of the translocated individuals is effective in producing theoretical eradication, whereas the single release of the sterilized males is not. With the assumption of a potential of 1: 1 population size replacement each generation, eradi- cation occurs in the twelfth generation after release, on condition that the frequencies of translocated and normal haploid sets were both 50%. Curtis & Hill (1968), in considering translocation homozygotes for tsetse fly control, investigated cer- tain critical factors for the success of this type of control. The success depends on the viabilities of translocation homozygotes and heterozygotes. Suc- cess also depends on the influence of population density and migration on the genetic structure and growth of the population. In addition to their population suppression poten- tial, Curtis (1968) proposed that translocation homo- zygotes might also be used to fix genes in popula- tions, when such genes are tightly linked to a trans- location and when the frequency of translocation chromosome sets is made higher than that of the normal chromosome sets. The natural fixation pro- cess for chromosome sets of higher frequency will eventually render the population homozygous for the translocation and thus for the gene. Curtis (op. cit.) pointed out that an inversion, acting as a cross- over suppressor, could be employed to tightly link the gene with the translocation. Whitten (loc. cit.) has recently produced designs for using insecticide-susceptible multiple homozy- gotes that would be alternately cycled into popula- tions at various intervals in association with different insecticide treatments. Two translocation systems with three different insecticide treatments would be capable of keeping a pest species at low levels. 841 842 P. T. MCDONALD & K. S. RAI RIeSUMt POTENTIEL D'EFFICACITt DES HtTtROZYGOTES DE TRANSLOCATION DANS LA LUTTE CONTRE UNE POPULATION D'INSECTES, JVALUP PAR SIMULATIONS SUR ORDINATEUR La simulation sur ordinateur de l'introduction d'insectes * heterozygotes de translocation * dans une population montre que les heterozygotes simples ou doubles sont potentiellement utilisables dans la lutte genetique. Les programmes ont ete elabores en fonction des translocations qui peuvent etre actuellement induites chez Aedes aegypti. Une translocation unique portant sur le chromosome qui determine le sexe male (M) et aboutissant 'a la produc- tion de males partiellement steriles entrainerait une morta- lite permanente de 50% des embryons. Grace a ce type de translocation, I'eradication serait obtenue en 11 genera- tions, a la condition d'introduire les miles h6tdrozygotes dans la proportion de 4 pour 1 male normal et de repeter l'operation a cinq reprises avec le meme nombre de males. Ces calculs sont applicables A une population d'insectes dont le potentiel de reproduction est de 1 fois a chaque generation. On obtiendrait une mortalite des embryons beaucoup plus dlevee en utilisant des males heterozygotes pour une translocation int6ressant le chromosome qui determine le sexe femelle (m). Ce type de manipulation permettrait d'eliminer une population, disposant d'un potentiel de reproduction de 1 fois, en 6 generations, les males partiel- lement st6riles etant introduits dans la proportion de 4: 1 et l'operation etant renouvelee cinq fois avec le meme nombre de males. Les simulations indiquent que dans la lutte genetique contre une population d'insectes les heterozygotes de translocation de type m sont plus efficaces que les hMt& rozygotes de translocation autosomique, lesquels a leur tour se revelent superieurs aux heterozygotes de transloca- tion de type M. L'heterozygote double - hdterozygote pour deux translocations differentes liees au sexe - est fertile dans la proportion de 12,5 %. Son introduction dans une population entrainerait une mortalite des embryons de loin plus 6levee que celle qui r6sulte de l'emploi d'hetero- zygotes de type m, en raison principalement d'apparie- ments entre het6rozygotes simples et heterozygotes dou- bles. Les h6terozygotes doubles seraient capables d'era- diquer une population en 5 generations, a la condition de les incorporer a raison de 4 males h6terozygotes pour I male normal, l'operation etant repetee a quatre reprises. Lorsque les programmes sont etablis sur l'hypothese d'un potentiel de reproduction plus eleve, les avantages de l'heterozygote double deviennent manifestes. Introduit dans une population a raison de 4 males heterozygotes doubles pour 1 male normal, il peut assurer l'eradication en 7 generations grace a 6 traitements consecutifs lorsque le potentiel de reproduction est de 5 fois par generation; dans les memes conditions, l'heterozygote simple ne par- vient a eliminer qu'une population a potentiel de repro- duction de 1 fois; il echoue si le potentiel est de 2 fois. L'opportunite de la mise au point de programmes de lutte gen6tique par les heterozygotes dependra d'un cer- tain nombre de facteurs: a) facilite d'obtention et d'entre- tien des heterozygotes de translocation; b) action sur l'aptitude a la concurrence sexuelle des traitements steri- lisants; c) obtention eventuelle d'homozygotes de trans- location; d) potentiel de reproduction et de croissance de la population a eradiquer. REFERENCES Berryman, A. A. (1967) Canad. Ent., 99, 858-865 Burmham, C. R. (1962) Discussions in cytogenetics, Min- neapolis, Burgess Press Cuellar, C. B. (1969) Bull. Wld Hlth Org., 40, 205-212 Curtis, C. F. (1968) Bull. ent. Res., 57, 509-523 Curtis, C. F. & Hill, W. G. (1968) Theoretical and prac- tical studies on a possible genetic method for tsetse fly control. In: Isotopes and radiation in entomology, Vienna, International Atomic Energy Agency Knipling, E. F. (1960) J. econ. Ent., 53, 415-420 Knipling, E. F. (1967) Sterile technique-principles in- volved, current application, limitations, andfuture appli- cation. In: Wright, J. W. & Pal, R., ed., Genetics of insect vectors ofdisease, New York, Elsevier, pp. 587-616 Knipling, E. F., Laven, H., Craig, G. B. Jr., Pal, R., Kitzmiller, J. B., Smith, C. N. & Brown, A. W. A. (1968) Bull. Wld Hlth Org., 38, 421-438 Laven, H. (1969) Nature (Lond.), 221, 958-959 McClelland, G. A. H. (1962) A contribution to the genet- ics of the mosquito Aedes aegypti with particular refer- ence to factors determining colour, Ph.D. thesis, Uni- versity of London McDonald, P. T. (1970) Cytogenetics andpopulation con- trol potential of two reciprocal translocations in Aedes aegypti (Diptera: Culicidae), Ph.D. dissertation, Uni- versity of Notre Dame, Notre Dame, Ind., USA McDonald, P. T. & Rai K. S. (1970a) Genetics, 66, 475-485 McDonald, P. T. & Rai, K. S. (1970b) Science, 168, 1229-1230 Rai, K. S. (1967) Bull. Wld Hlth Org., 36, 563-565 Rai, K. S. & Asman, S. M. (1968) Possible application of a reciprocal translocation for genetic control of the mosquito Aedes aegypti. In: Proceedings of the 12th International Congress ofGenetics, Tokyo, vol. 1, p. 164 Serebrovskii, A. S. (1940) Zool. Zh., 19, 618-630 Wagoner, D. E. (1969) Bull. ent. Soc. Amer., 15, 220 Watt, K. (1964) Canad. Ent., 96, 202-220 Weidhaas, D. E. et al. (1970) Proc. N. J. Mosq. Exterm. Ass., 57 COMPUTER SIMULATIONS OF VECTOR CONTROL BY HETEROZYGOUS TRANSLOCATIONS 843 Annex ALTERNATIVE FORTRAN IV MODEL PROGRAMME FOR TESTING THE EFFECTIVENESS OF RELEASES OF TRANSLOCATION HETEROZYGOTES DIMENSION JEN(5),G(5),W(5),KEN(5) DIMENSION IRNT(20),IRN(20) R= RANDOM(1) 198 READ(5,199)LA 199 FORMAT(12) IF (LA) 162,162,163 163 READ(5,100)IGEN,IPOP, (KEN(I),I= 1 ,5),(W(I),I = 1,5) 100 FORMAT (12X,2I5,5I5,/5F7.4) READ(5,300)(IRNT(I),I=1,20) READ(5,300)(IRN(I),I= 1,20) 300 FORMAT(2014) LAP= 0 JSUM = 0 KSUM=O DO 1 J=1,3 1 JSUM=JSUM+KEN(J) DO 2 J=4,5 2 KSUM=KSUM+KEN(J) R=JSUM DO 3 J=1,3 3 G(J) = FLOAT(KEN(J))/R R=KSUM DO 4 J=4,5 4 G(J) = FLOAT(KEN(J))/R WRITE(6,383) (KEN(,I = 1,5),(W(I),I = 1,5) 383 FORMAT(/////,IX,8HGENOTYPE,///,lX,12HINITIAL FREQ,6X,51I2,//,lX, *7HFITNESS,1 1X,5F12.4) WRITE(6,101) 101 FORMAT(1X,3HGEN,10X,4HLOAD,30X,1 8HGENOTYPE FREQUENCY) 191 DO 161 L=1,IGEN DO 27 J=1,5 27 JEN(J) = 0 IPOP= 20001 DO 68 KZ=1,IPOP R=RANDOM(0) 211 AM=G(1) IF(R-AM)86,86,29 86 ML=1 GO TO 13 This card is used for assaying loads. When the card is removed, the assumption of a potential of 1: 1 population size replacement per generation is made. P. T. MCDONALD & K. S. RAI 29 AM =AM+ G(2) IF(R-AM)8,8,19 8 ML=2 GO TO 13 19 ML=3 13 CONTINUE R=RANDOM(O) AM = G(4) IF(R-AM)84,84,16 84 MF=4 GO TO 26 16 MF=5 26 CONTINUE WA= W(ML)*W(MF) R=RANDOM(0) IF(R-WA)37,37,68 37 R=RANDOM(O) M=ML*MF MM=M+1 GO TO (6,6,6,6,5,6,6,6,9,6,11,6,90,6,6,91),MM 5 IF(R-0.5) 61,61,64 6 IF(R-.25) 61,61,36 36 IF(R-0.5) 63,63,38 38 IF(R-.75) 64,64,65 9 IF(R-0.5) 62,62,64 11 IF(R-.25) 62,62,49 49 IF(R-0.5) 66,66,51 51 IF(R-.75) 64,64,65 90 IF(R-0.5) 61,61,65 91 IF(R-.25) 61,61,71 71 IF(R-0.5) 63,63,72 72 IF(R-.75) 65,65,66 61 JEN(1)=JEN(1)+1 GO TO 68 62 JEN(2) =JEN(2)+1 GO TO 68 63 JEN(3) =JEN(3)+ 1 GO TO 68 64 JEN(4)=JEN(4)+1 GO TO 68 65 JEN(5)=JEN(5)+1 GO TO 68 66 CONTINUE 68 CONTINUE JSUM=0 KSUM=0 DO 81 J=1,3 844 COMPUTER SIMULATIONS OF VECTOR CONTROL BY HETEROZYGOUS TRANSLOCATIONS 81 JSUM=JSUM+JEN(J) DO 82 J=4,5 82 KSUM=KSUM+JEN(J) TOT=JSUM+KSUM Z=IPOP ALODE= (Z-TOT)/Z 603 WRITE(6,102)L,ALODE,(JEN(,I = 1,5) IPOP=TOT IF(IPOP) 198,198,301 301 CONTINUE JSUM = 0 KSUM=0 LAP=LAP+1 I= LAP JEN(2) = JEN(2)+IRNT(I) JEN(3) = JEN(3)+IRN(I) 232 DO 234 J= 1,3 234 JSUM =JSUM+JEN(J) DO 235 J=4,5 235 KSUM =KSUM+JEN(J) 102 FORMAT(lX,I3,7X,F8.4,51l2) R=JSUM IF(R) 198,198,302 302 CONTINUE DO 200 J=1,3 G(J) = JEN(J) 200 G(J)=G(J)/R R=KSUM IF(R) 198,198,303 303 CONTINUE DO 201 J=4,5 G(J) = JEN(J) 201 G(J) = G(J)/R 161 CONTINUE GO TO 198 162 CONTINUE STOP END 845