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Loitlogical Journalofthe Lznnean Society, 69 87-109 With 16 figures June 1980 Heterosis, epistasis and linkage disequilibrium in a wild population of the polymorphic butterfly Danaus chrysippus (L.) D. A. S. SMITH Department of BioLogy, Eton CoLLege, Windsor, Berks. SL4 6 E W , England Arrepted fOr publication J u l ~1979 The colour polymorphism of the Danaus r h y i p p u s population at Dar es Salaam, East Africa, is controlled at three major loci, each with two alleles. Two of the loci, one governing ground colour and the other forewing pattern, are closely linked. Th e third locus, determining hindwing pattern, assorts independently. Thirty-eight broods raised from wild mated pairs, F1 and F2 generations gave 857 offspring of 23 genotypes (out of 27 possible). The forewing length, taken as an index of size, was investigated in relation to the genotype. Heterosis is evident at all three loci. The two linked lori show epistatir interaction of an unexperted kind : double heterozygotes are smaller than heterozygotes at only one locus but larger than double homozygotes. The hrterotic effert at the third, unlinked locus is the most pronounced and is additive to that at the other two. Heterosis is more marked in males than females. The possibility that body size has importance in connexion with sexual selection, food recources and mimetic relationships is discussed. Analysis of gene and chromosome frequenries in the wild parents of 61 broods suggests that double heterozygotes for the two iinked loci may have heterozygous advantage. Seventy-eight per c-ent of chromosomes are repulsion phase: thus, there is pronounced linkage disequilibrium which must be maintained by selection as crossing over is almost 2%. In particular, the chromosome carrying both dominant alleles in coupling is rare. Consideration of the centres of distribution and present ranges of the alleles at all three loci suggests that three geographiral races, aegyptzus, dorippus and alczppus, were isolated by forest barriers, during wet periods in the Pleistocene, in south-west, north-east and north-west Africa respectively. They have probably expanded their ranges in the post-glacial period to overlap and interbreed in central and east Africa. Either heterozygous advantage o r seasonal (directional) selection or a combination of both is responsible for the persistence of the polymorphism. KEY WORDS: - polymorphism - genetirs - Danaus chryslppus - heterosis - epistasis - sexual selection - mimicry - heterozygous advantage - linkage disequilibrium - subspecision Pleistocene. CONTENTS . . . . . . . . . . . . Introdurtion Materials and methods . . . . . . . . Breeding methods . . . . . . . . Statistical analysis . . . . . . . . The population sample . . . . . . . Scoring the genotypes . . . . . . . 0024-4082/80/06008 7 6 + 23$02.00/0 97 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 9I 91 92 92 92 0 1980 The Linnean Society of London D. A. S . SMITH 88 Breeding results . . . . . . . . . Population genetics . . Randomness of mating Sex ratio . . . . . . Hardy-Weinberg equilibrium The A locus . . . . . Discussion . . . . . . . Acknowledgements . . . . References . . . . . . . Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 99 99 100 10 1 102 102 . . . . . . . . . . . . . . . . 107 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . I08 109 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTRO DUCT10 N The Old World queen butterfly, Dunuus chrysippus (L.1, is an exception to the generalization that aposematic models belonging to Mullerian mimicry rings are monomorphic (Fisher, 1930; Ford, 1971; Turner, 1977). In Uganda it participates with Acrueu encedon L. and other acraeids in no less than four distinct, sympatric Mullerian assemblages (Owen, 197 11, each with its attendant Batesian members. These are by no means local phenomena, for at least two of the Mullerian groupings are found throughout East Africa and Pierre (1974) has demonstrated an impressive geographical correlation between the various comimetic forms of D. chvsippus and A . encedon. This situation is quite unlike that pertaining for example, in the Neotropical genus Heliconius in which numerous Mullerian rings are believed to have evolved in forest refuges, isolated during dry periods in the Pleistocene. Most forms of Heliconius species are thus allopatric races, sometimes giving rise to narrow hybrid zones where they meet (Turner, 1976). In contrast, the biogeography of the forms of D. chrysippus in Africa suggests that race formation could have occurred in wet periods of the Pleistocene (Smith, 1976a) when areas of dry grassland (the species does not inhabit forest) in west, north-east and south-west Africa were isolated by intervening lowland forest and montane vegetation (Moreau, 1963). Studies of speciation and race formation in savannah birds (Moreau, 1966) support this hypothesis. Subsequent contraction of the forests following both climatic change and human activity has opened up vast new tracts of country to grassland species. The races of D. chrysippus, having expanded out of their Quaternary refuges, could have created the central and east African polymorphic populations by admixture and hybridization. If this argument is correct, it is important to know why the polymorphism has persisted and how it is maintained. The mechanism most commonly postulated to maintain genetic polymorphisms, particularly if alternatives are not readily demonstrable, is heterosis or heterozygous advantage. In this paper, I examine the evidence from two principal sources for heterosis in D. chrysippus: ( 1) broods reared from known parents in the laboratory and (2) some aspects of the population genetics of the wild population from which the breeding stock was taken. Dobzhansky (1950, 1952) drew attention to the importance of distinguishing two kinds of heterosis, namely, ‘euheterosis’ in whichfitness is improved in F1 hybrids and ‘luxuriance’ where the offspring are enhanced in a purely metric sense. The former is now better known as ‘heterozygous advantage’ (Sheppard, 1967; Ford, 1971) or ‘overdominance’ (Wallace, 1970) while the latter is synonymous with ‘hybrid vigour’. To distinguish the two phenomena, which GENETICS OF POLYMORPHISM I N DANALJS 89 are quite different, I use respectively the terms ‘heterozygous advantage’ and ‘heterosis’. By definition, heterozygous advantage occurs when the heterozygote exceeds both homozygotes injtness. On the other hand, heterosis is defined as the amount by which the mean of an F1 family exceeds, in a metric sense, its better parent (Mather 8c Jinks, 1971). Here, I use the latter term to cover any segregation in which the heterozygote d@ers significantly, for a metric character, either positively or negatively, from both its parental genoQpes. The terms positive and negative heterosis are used to distinguish the alternatives. The latter has been reported in wide crosses between species or allopatric subspecies of Drosophila (Dobzhansky, 1950; Wallace 8c Vetukhiv, 1955) but its occurrence in a monospecific, sympatric population, as I show here for D. chrysifipus, is probably unusual and may indicate its recent origin. The basic genetics of the colour polymorphism in African D. chrysippus are published (Owen 8c Chanter, 1968; Clarke, Sheppard & Smith, 1973; Smith, 1975a).The following facts are relevant to this paper (Figs 1-16). The B locus has two alleles, B giving a brown ground colour and bb orange on both wings. B is semi-dominant to dominant, heterozygotes being recognizable in some cases; but BB and Bb butterflies cannot be reliably separated in 3 : 1 segregations. Forewing pattern is determined by the C locus, C giving a wing uniformly coloured (orange or brown) except for a narrow black margin (form dorippus Klug.) and cc a large black apical area traversed by a row of, sometimes confluent, white apical spots (form aegvptius Schreber). Cc heterozygotes are phenotypically close to CC butterflies but are often distinguishable by the row of ‘uegvptius’ subapical spots visible on the underside and occasionally the upper side of the forewing (form transiens Suffert). The expressivity of c in heterozygotes is modified by the B locus: 74.6% ( N = 173) of known B-Cc butterflies were f. transiens compared with only 45% ( N = 129) of bbCc (unpublished data) and the difference is significant (xf=26.2; P<O.OOl) with no sex difference. The B and C loci are linked with a cross-over value of approximately 1.9% (Smith, 1975a, 1976b). As the known recombinants all resulted from cross-over in the male parents, achiasmatic oogenesis is suspected as in other Lepidoptera (Suomalainen, Cook 8c Turner, 1974; Turner 8c Sheppard, 1975). The A locus has a recessive allele a giving, in the homozygous state, a large white area on the hindwing (form alcippus Cramer when combined with the aegvptius forewing and form albinus Lanz when combined with the dorippus forewing). Au heterozygotes are often phenotypically distinct from both homozygotes, having a small white patch o r a few white scales. The intermediate phenotypes are named alcippoides Moore and semialbinus Strand. Dominance of A is modified by both the B locus and sex (unpublished data). Of the known Aa butterflies reared, the following proportions were intermediate phenotypes : Aabb males, 77.8% (N=36); A d b females, 53.3% ( N = 3 0 ) ; AuB- males, 65.7% ( N = 70); AuB- females, 28.1% (N=64). Thus, a significantly higher proportion of males (xT=21.4; P(O.001) and of orange (x!=5.6; P(O.02) butterflies than offemales or browns are intermediate. Clarke et al. (1973)found a modifying action of the B locus opposite to my result in wide crosses between butterflies from Australia and Sierra Leone. There is no evidence for linkage between the A locus and either the B or C loci (Clarke et al., 1973; Smith, 1975a, and unpublished data): independent assortment is assumed. 90 D. A. S . SMITH GENETICS OF POLYMORPHISM IN DANAUS 91 MATERIALS AND METHODS Breeding methods The area of rough grassland at Dar es Salaam, Tanzania, from which all the breeding stock was obtained, has been described before (Smith, 1976a). D . chrysippus is not ideal for formal genetical studies. Laboratory reared males are rarely able to mate until 7-10 days old because they lack the pheromone necessary to elicit a female response to courtship (Seibt, Schneider 8c Eisner, 1972; Schneider et al., 1975) and mating will only occur in a spacious outdoor flight cage. As females emerge from the pupa on average 1-2 days before their brothers, they must be kept alive for 8-12 days to obtain sib matings. Therefore, most broods were obtained either from wild mated females or laboratory reared females mated to older wild males. As wild females were known from marking studies to be polygamous, mainly fresh looking ones in copula were taken for breeding. Parker (1970) showed that, in polygamous insects, most eggs are fertilized by sperm from the most recent mating which, in the present context, implies that they would be provided by the male observed in copula. The segregations obtained suggest that multiple matings have not affected the genetical interpretations (Smith, 1975a). Eggs were obtained by sleeving individual females on a branch of the main local foodplant, Calotropis gigantea (L.) Ait. (Asclepiadaceae). The broods were then reared separately in indoor cages. The 38 broods included in the genetical analysis comprised 857 butterflies. Selection of the colour phenotypes of the wild female parents is unlikely to be random with respect to the wild population but is not deliberately biased. All healthy butterflies bred between September 1974 and May 1975 and fed as larvae upon C. gigantea are included. Broods reared on other milkweeds are excluded as t6e larvd-foodplant is an important source of phenotypic variation (Smith, 1978). The forewing length, measured on the day of emergence after the wings had fully expanded and dried out, is taken as an index of size. The genotypes are known to the extent that they can be inferred directly from their phenotype and/or that of their parent(s) and/or the segregations obtained. The dominant phenotype classes at all three loci studied inevitably include both homozygotes and heterozygotes in 3 : 1 segregations. Fortunately, the expressitivity of the Figures 1 to 16. The colour forms of Danaus chryszppus occurring naturally around Dar es Salaam, Tanzania. All the specimens illustrated were bred at D ar es Salaam. To p row, left to right: I , brown dorippus 9,genotype A A B- C-. 2 , orange dompus 9 , genotype AQ bb CC (with some white scales on hindwing veins). 3, orange dorippus 8, genotype A A bb CC. 4, orange aeg~ptius8.genotype A- bb cc. Second row: 5, brown aegyptius 9 , genotype A A B- cc. 6 , orange albinus 8, genotype aa bb CC. I, orange semi-albinus 8,genotype An bb C-. 8, orange alcippus 9 , genotype aa bb cc. Third row: 9, brown a l t i p p ~8, genotype QQ BB cc. 10, brown akippoides 8, genotype Aa BB cc. 11, brown albinus 6, genotype aa Bb Cc. 12, orange semi-albinus 9,Aa bb CC. Bottom row: 13, orange aegyptius 3 with a little white scaling on the hindwing, genotype AQ bb cc. This specimen is of the type named liboria Hulstaert in which the white sub-apical spots are enlarged and confluent. This specimen (and no. 4 ) is more or less identical with the Asiatic race chrysippus L. 14, brown liborla 9 , genotype A A B- cc. Note the hold white spot in the brown area offorewing space 3 typical of this form. 15, brown liboria 8 (underside). 16, brown transiens (dorippus) (underside) showing the “aegyptzuJ” sub-apical spots, genotype A A B- Cc. Variation in the amount of white in AQ genotypes is seen by comparing nos 2 (white scarcely visible), 7, 10, 12 and 13 (white scarcely visible). Magnification ofall specimens is x 6/7. 92 D. A. S. SMITH recessive alleles in heterozygotes is fairly high for the A and C loci (see Introduction) and many heterozygotes can be classified on phenotypic grounds alone. At the B locus, reliable separation of BB and Bb butterflies is impossible although some heterozygotes are detectable. Consequently, the B- phenotype and genotype classes are more heavily contaminated with heterozygotes than are either the A- or C- classes. The impossibility of identifying all heterozygotes has inevitably blunted the impact of the analysis. Statistical analysis The breeding data are analysed by Analysis of Variance to distinguish the effects of the A, B and C loci, sex and their interactions on forewing length. The data for both phenotypes (Table 1) and genotypes (Table 4) are far from orthogonal so that a standard 4-way analysis for sex and the three loci, using all the data, is impossible. Alternative methods are used (Snedecor & Cochran, 19671, two of which necessarily involve the sacrifice of some data. First, I use unweighted class means (i.e. disregarding the size of and variance within classes). Of the 27 genotypes possible, four are missing in both sexes and an additional one in males. Thus, a single analysis including all A and B genotypes is impossible. Secondly, a random sample of individuals from each genotype is taken, using the maximum replication which the data will permit for an orthogonal analysis. With the missing A/B genotypes, it is possible to analyse only A with C or B with C. Finally, one-way analyses and calculation of least significant differences (LSD) use all the data. The population sample Some aspects of the population genetics of D . chrysippus at Dar es Salaam can be deduced from a larger sample of butterflies from which 151 broods were obtained between July 1972 and August 1975. Thirty broods gave no adult offspring due to virus disease ( 1 7 ) , parasitism (12) and ant predation (1). Of the remaining 12 1, 36 are excluded because the female parent was not wild and 24 because the full genotype of both parents was unknown. There are several reasons for the latter including small broods (9), male parent not seen (4),double mating (1) and my failure to score the B locus" in early broods (10). Sixty-one pairs remain for which a full B/C genotype can be deduced and 66 pairs can be used for the A locus analysis. Scoring the genotypes Before presenting the results, the reader needs reassurance that the problems involved in distinguishing genotypes, when heterozygotes are not always phenotypically distinct from homozygotes, have been solved. In ten broods where both parents were dorippus (CC or Cc) and there was no segregation for aeoptius (cc) in the progeny, there is only one case where transiens (the Cc phenotype) is absent from both parents and offspring. This brood is assumed to * 1 first recognized the B locus in a backcross (brood 281 in February 1973, independently of Clarke el ~ l . (1973)whose paper was not then published. Many of the earlier broods could be interpreted retrospectively as they had been preserved zn lolo. GENETICS OF POLYMORPHISM IN DANAUS 93 Table 1. Mean forewing length (mm)with sample size (in parentheses), classified by colour phenotype, males in roman type and females in italics 6 locus C locus A locus A- 3- C- cc CC bh C- Aa 42.60 (42) 43.33 (6) 42.29 (17) 42.58 (65) 41.63 ( 3 0 ) 4 2 . 0 0 (2) 42.50 (14) 41.91 ( 4 6 ) 41.49 (49) 43.60 (20) 41.25 (53) 43.50 ( 4 ) 41.85 (61) 40.21 (56) 40.81 ( I 13) 41.46 (11) 39.50 ( 4 ) 40.94 ( 1 5 0 ) 41.47 (70) 42.75 (24) 40.83 (126) 41.95 (20) 40.42 (26) 4 0 . 7 9 (43) cc 41.50 (6) 41.89 (26) CC 42.00 (1) 41.60 ( I S ) Total Total aa 41.98 (130) 41.76(105) 43.80 15) (8) 45.00 (6) 41.88 (481 41.52 (79) 40.79 (68) 40.96 (119) 43.00 (1) 43.23 1131 433! 43.00 (3) 42.13 (32) 43.25 (3) 43.50 (2) 41.50 (4) 42.14 41.60 ( 5 ) 42.00 (I) 41.62 (21) (7) 41.58 (194) 43.40 (63) 41.88 (1421 41.97 (399) 41.11 (293) 4 2 . 4 1 (42) 40.75 ( 1 4 6 ) 41.17 ( 4 8 1 ) result from a CC x CC cross. In the other nine crosses, known to be CC x Cc, the heterozygous parent is identifiable from its phenotype in seven of them and in the remaining two it is arbitrarily assigned, one to each sex. The B locus presents greater problems. In 15 broods where both parents are brown ( E B or Eb) and there are no orange (bb)segregants in the progeny, in every case at least one of the parents or offpsring has orange on the hindwing, the trailing edge of the forewing, or both. As this condition is always common in backcross broods, where brown segregants must be Bb, such crosses are all scored as BB x Bb. In 11 of these cases, all of which must be either Ec/bC x Bc/Bc or B C / B c x Bc/bc as they are backcrosses at the C locus, neither parent has any orange (some males were not seen) and the heterozygous one cannot, therefore, be determined by inspection. However, in every case, the traces of orange occurred in the dorippus but not the aegyptius offspring, proving the first alternative to be correct. Thus, the dorippus parent is the carrier of the 6 allele in all these broods. In crosses between double heterozygotes, coupling x coupling and repulsion x repulsion phase broods are easily distinguished as the former gives an orange aegyptius class W b c ) in F1 (Smith, 1975a).Coupling x repulsion broods are identified by the occurrence of orange transiens (bC/bc), which is rarely produced by crossing-over in repulsion x repulsion crosses, and a lower than expected proportion ofbrown transiens in F1. In the four crosses of this type, it is impossible to match parental sex with linkage phase and they are arbitrarily assigned, two to each sex, for the sex comparison. As the BC chromosome was otherwise recorded only in males, it is possible that it does not occur in females. These comments show that small errors are expected in the sex comparison which do not affect the combined estimates of gene, chromosome or genotype frequency. 94 D. A. S . SMITH BREEDING RESULTS T h e classification and analysis of phenotypes (Tables 1, 2) show that F is significant for sex (males average 0.8 mm larger than females), the A and C loci and for the interaction between the B and C loci. Examination of the phenotype means (Table 3) shows that the effect at both A and C loci is due to the superior size of the heterozygotes. AS the A/C interaction is not significant,' the separate effects are likely to be additive. The nature of the significant B/C interaction is unknown at this stage as BB and Bb butterflies are not distinguished. The use of the two sexes to provide replication of phenotype classes is justified as their ranks are significantly correlated (7=0.672; P < 0.001) by Kendall's method (Kendall, 1962). Table 4 shows the reclassification of the butterflies using the genetic evidence. The 3-way variance analysis of a random sample for the A and C loci and sex (Table 5 ) may suffer interference from the B locus but the risk is minimized by random allocation of the available B genotypes among the different A/C genotypes. Heterosis at the A and C loci and the sex difference are again significant. The small mean square for A/C interaction supports the inference above (Table 2) that the effect is additive rather than epistatic. The first order interactions are not significant but the significant value for the second order Table 2. Three-way analysis of variance for the A, B and C loci, using the cell mean values in Table 1 Source of variation Sums of squares Degrees of freedom Mean square Replicates (sexes) A locus B locus c locus A/B interaction A/C interaction B/C interaction A/B/C interaction Error Total 3.560 20.53 1 1.047 4.157 1.155 2.340 5.912 3.903 6.288 46.892 I 2 1 2 2 4 2 4 17 35 3.560 10.266 1.047 2.079 0.578 0.585 1.956 0.976 0.370 F ratio 9.62.' 21.15*** 2.85 5.62' 1.56 1.58 5.29. 2.64 " P <0.05, * ' P < O . O l , **'P<O.OOl and insubsequent tables. Table 3. Forewing length (mm) at the A, B and C loci for the sexes combined, averaged over the cell means in Table 1 Locus A C B Phenotypes Homozygous dominant Heterozygote Homozygous recessive 4 1.46 42.11 43.13 42.47 4 1.62 4 I .64 41.90 42.24 GENETICS OF POLYMORPHISM IN D A N A U S 95 interaction undoubtedly reflects the fact that that double heterozygote AaCc shows marked heterosis in the male but not in the female. Table 6 summarizes three separate analyses for sex and the B and C loci. Interference from the A locus is minimized either by random selection from the A genotypes available (3-way analysis) or by using the cell means (Table 41, both unweighted and weighted over the A genotypes. There is fair agreement between the three methods: the C locus is significant in each case and the B locus, the B/C interaction and sex in two of the three. The results suggest that there is heterosis at both B and C loci with epistatic interaction between them. Table 4. Mean forewing length (mm)with sample size (in parentheses), classified by genotype, males in roman type and females in italics B locus C locus A locus Aa A- ~ B- Bb ~~~~ - (3) 41.00 (1) 42.00 (2) - 41.00 40.20 cc 41.89 (18) 41.86 (14) 43.32 (25) 43.21 (24) - 42.72 (43) 42.71 (38) cc 41.04 (48) 40.69 (87) 42.88 (33) 41.84 (32) C- 43 06 (16) 41.09 (11) 43.33 (6) 4200 ( I ) - 43 14 (22) 41 1 7 (12) Cr 41.68 40.54 42.70 4136 (28) 43.58 (12) 42.86 (7) 41 90 (76) 40 69 (70) 4280 ( 5 ) - 42.02 (1 16) 40 80 (103) 42 70 (10) 4 1 81 (16) C- CC bb Total aa 41.00 39.00 (3) (26) (10) (11) 41.46 38.25 (11) (4) (4) (5) 41.75 (92) 40.91 (123) C- 39.95 (20) 39.96 (23) 43.10 (10) 43.43 (7) 41.88 (501 40.80 (70) 41.55 (80) 40.79 (100) Cr 41.44 (9) 42.05 (38) 44.71 ( 7 ) 43.86 (7) 43.00 43.00 (1) (3) 42.88 (17) 42.38 (48) cc 42.00 (1) 41.60 (15) 43.50 (2) 41.60 ( 5 ) 41.50 42.00 (4) (I) 42.14 (7) 41.62 (21) 41.46 (153) 40.99 (228) 43.26 (96) 42.61 (90) 41.85 (142) 40.73 (148) 42.05 (391) 41.22 (466) Total Table 5. Three-way analysis of variance for the A and C loci and sex with five replicates per treatment ( N = 9 0 ) Source of variation Replicates A locus C locus Sex A/C interaction A/sex interaction C/sex interaction AICIsex interaction Error Total Sums of squares 6.51 70.56 31.62 9.34 6.84 12.29 2.02 28.44 169.49 337.12 Degrees of freedom Mean square 4 2 1.63 35.28 15.81 9.34 1.7 I 2 1 4 2 2 4 68 89 6.15 1.01 7.11 2.49 - F ratio 0.65 14.16" 6.35". 3.75' 0.69 2.47 0.41 2.85* - Table 6. Variance analyses for the B and C loci and sex Source of variation Replications B locus c locus Sex B/C interaction B/sex interaction C/sex interaction B/C/sex interaction Error Total 2-way analyses? 3-way analysis Unweighted means Degrees of freedom Surnsof squares Mean square F ratio 3 2 2 1 4 2 2 4 51 71 0.78 17.03 21.86 0.50 7.89 1.75 I .08 3.66 133.22 187.77 0.26 8.52 10.93 0.50 1.97 0.88 0.54 0.92 2.61 0.10 3.26' 4.19. 0.19 0.76 (1 2 2 1 0.34 - 0.21 0.35 - - t In the 2-way analyses, the sexes are the replicates. Degrees of freedom Sumsof squares Mean square 3.14 0.54 2.68 3.14 4.93 3.14 0.27 1.54 3.14 1.23 - - - 8 17 1.17 12.46 0.15 4 - Weighted means F ratio 21.50 1.86 9.16** 21.50"' 8.45.' - Sumsof squares Mean square 2.23 2.26 2.80 2.23 3.69 2.23 1.13 1.40 2.23 0.92 - - 1.37 12.34 - 0.17 - F ratio 13.00) 6.60' 8.16' 13.00*' 5.39' - - P ? ? GENETICS OF POLYMORPHISM I N D A N A U S 97 Finally, one-way variance analyses make use of all the genotype data. At the A locus (Table 71, the heterozygote is very significantly larger than both homozygotes in both sexes and positive heterosis is beyond dispute. The B/C interaction indicated in Table 6 is analysed in Table 8. One-way analysis of variance for the nine genotypes, based on all the data for the combined sexes, shows that there are highly significant size differences. Individual comparisons are made by the LSD method, which involves in this case calculating a parameter No to correct for unequal sample sizes (Snedecor. & Cochran, 1967). The comparisons made are between the heterozygote (at one or both loci) and the two homozygotes in each of the eight arrays, three rows (R1-3),three columns (Cl-3) and two diagonals (D1-2), i.e. 16 comparisons in all. Examination of rows shows that, when the B locus does not segregate, there is positive heterosis at the C locus in R1 and R3 and negative heterosis in R2, the Table 7. One-way analysis of variance for A locus genotypes F ratio R (mm) and [ N )for genotypes Sax d P A- Aa aa 41.46(153) 40.99 1228) 43.26 (96) 42.6 1 190) 41.85 1142) 40.73 (148) 29.69 * * * 28.26*** Table 8 . Mean forewing length (mm) (in heavy type) and sample sizes (in parenthesis) for the B/C genotypes (sexes combined) which would segregate in F2 from monohybrid crosses at the B locus (columns), the C locus (rows) and dihybrid crosses in coupling and repulsion (diagonals) Pairntal genotypes, crosses giving F2 results and array number (C, D or R ) BC/bc x BC/bc D1 BC/Bc x BC/Bc BC/bC x BC/bC BC/bC x Bc/bc Bdbc x Bdbc Bc/bC x Bc/bC c1 c2 c3 D2 B B CC BB Cc B B cr 40.556 42.716 41.270 R1 (9) (81) (215) BC/Bc x bC/bc Bb CC Bb Cc Bb cc 42.441 41.438 42.154 *** *** cc < c c > cc R1 ** (I CC > cc < cc R2 R2 (34) (219) (26) bC/bc x bC/bc bb CC bb Cc bb cc 41.128 42.508 41.750 cc < Cc> cc R3 ( 1 80) (65) (28) R3 *** ** *** *** * * * *** .** Bc/Bc =Bc/bC =bC/bC B B < B b > bb B B > Bb < bb D2 c1 C2 BC/BC tf B B < Bb=bb = bc/bc cs ~ < BC/bc D1 ~~ ~~ Type of heternsis (ifany),level of probability (asterisked)and array One-way variance analysis for the table gives F=8.428, d.f. 8/848, P<O.OOl. Critical LSD levels are 0.598 mm f n r P < 0 . 0 5 ( ' ) , 0 . 7 8 6 m m f o r P < 0 . 0 1(**)and1.004mmforP<0.001(***). 98 D . A. S. SMITH only array with the double heterozygote. The column results (C locus not segregating) are similar. C1 shows positive heterosis, C3 has the heterozygote superior to the dominant homozygote only but there is again negative heterosis in the C2 array which includes double heterozygotes. These results show that, in monohybrid crosses, 7/8 comparisons of single locus heterozygotes with their homozygous segregants are positive whereas 4/4 comparisons between two locus heterozygotes and their single locus segregants are negative. Comparing the distribution of negative and positive differences between the two types of cross by Fisher’s Exact Test gives P= 0.0000 1. Examination of the dihybrid crosses on the two diagonals shows no heterosis. On D 1 (coupling x coupling crosses), the homozygous dominant for both loci is markedly inferior, as it is to all other genotypes, but the homozygous double recessive is not. On D2 (repulsion x repulsion crosses), the three genotypes are very similar in size and it is the only array in which no significant differences occur (positive heterosis occurs in males only). Comparison by the Exact Test of the 11/12 significant differences (in both directions) in the monohybrid crosses with only 1/4 in dihybrid crosses gives P= 0.027. Finally, comparing positive and negative significant deviations between all arrays producing single locus heterozygotes ( R l , R3, C1, C3) with those giving double heterozygotes (R2, C2, D1, D2) gives P = O . O l by the Exact Test. Table 9. Mean forewing length in F1 from different types of cross and in F2 assuming random mating among the F1 genotypes Type of cross I I1 111 V Deviation from meant F1 F2 41.26 42.94. 42.10 +1.18 +0.34 41.24 40.89 40.97 41.25 41.61 41.53 4 1.44 42.16* 42.72+ 41.44 42.26. 42.63. 41.33 41.53 41.84 4 1.33 41.93 42.08 -0.32 +0.40 -0.43 -0.23 +0.96 +0.08 -0.32 +0.50 +0.87 -0.43 +0.17 +0.32 42.66 42.21 42.40 42.44 42.45 42.49 41.81 42.03 41.84 41.72 42.05 41.93 41.76 41.76 41.82 41.70 42.02 41.91 +0.05 +0.27 +0.08 -0.04 +0.29 +O. 1 7 0.00 0.00 +0.06 -0.06 +0.26 +0.15 x bC/bc x Bdbc 42.72 42.16 42.63 42.26 41.84 41.52 42.08 4 1.93 41.84 41.52 42.08 4 1.93 +0.08 -0.24 +0.32 +0.17 +0.08 -0.24 +0.32 +O. 1 7 BC/bc x BC/bc BdbC x Bc/bC BC/bc x BdbC 4 1.44 41.44 41.44 4 1.33 41.33 42.44’ 41.33 4 1.33 41.76 -0.43 -0.43 +0.68 -0.43 -0.43 A A x aa BC/BC BC/BC BC/BC BdBc Bc/Bc bC/bC x bdbc bC/bC x Bc/Bc x bC/bC X bc/bc x bc/bc X BC/Bc BC/bC BC/bC BC/bC x bC/bc BC/Bc BC/bC bC/bc Bc/bc x BC/Bc x BC/bC x Bc/bc x bC/bc x BC/Bc B d b c x bC/bc BC/Bc x Bc/bc IV ic for forewing length (mm) Parental F1 F2 genotypes genotypes genotypes 0.00 ’ Heterosis statistically significant. t Mean of all classes (sexes combined) is 41.76 mm. A wild population mean, weighted according to the frequency of genotypes, would be substantially less. GENETICS OF POLYMORPHISM IN DANAC’S 99 The major conclusions from the data in Table 8 are as follows : ( 1 ) Single locus heterozygotes show positive heterosis compared with the homozygotes from which they segregate. ( 2 ) Double heterozygotes show negative heterosis compared with all single locus heterozygotes in monohybrid crosses but no heterosis in dihybrid crosses. (3)The double heterozygotes in repulsion produce an F2 close to the overall mean with minimal variance: stabilizing selection for body size will thus favour the BdbC genotype. The average effect of parental genotype on size in the F1 and F2 (sexes combined) are given in Table 9. In homotypic crosses between homozygotes (groups 1-11] there is always heterosis in F1 except when double heterozygotes are produced (crosses BC/BC x bdbc and Bc/Bc x bC/bC. Assuming random mating among the F1, there is regression to the mean in F2. Heterogametic (group 111) and homogametic (group IV)crosses between single heterozygotes, the genotypes showing maximum heterosis in F1, show regression to the mean over one or two generations. Homogametic coupling and repulsion crosses (group V) both produce an F1 averaging slightly less than the parents on account of the homozygous segregants. The coupling x repulsion cross produces a 1 : 1 : 1 : I segregation for all four single heterozygotes (BC/Bc, Bdbc, BC/bC and bC/bc) with strong heterosis in F1 followed by sharp regression to the mean in F2. These results show that epistasis between the B and C loci produces a balanced double heterozygote, intermediate in size between the smaller double homozygotes and the larger single heterozygotes (Table 10). Although there are sex differences, the genotypes are significantly correlated by rank (7 =0.667 ; P=0.013). I t is important to realize that the heterotic effects at all three loci are probably greater than the analysis shows as each dominant class contains a proportion of heterozygotes which must reduce any difference between the means of the two classes. Thus, all the inferences are likely to err in the direction of caution. Table 10. Rankings for forewing length (mm)of the ten B/C genotypes in the two sexes Genotype BUbC bC/bc EUBc Ec/bc bc/hc Bc/bC BC/bc BdEc bC/bC BC/BC Mean of all genotypes Males Mean forewing length Rank Females Mean forewing length 43.14 42.88 42.12 42.70 42.14 1 2 3 4 5 41.17 42.38 42.7 1 41.81 4 1.62 42.02 6 40.80 41.75 4 1.55 41.00 42.05 1 8 9 40.91 40.79 40.20 4 1.22 - Rank POPULATION GENETICS Randomness $mating There are ten different B/C genotypes of which nine occurred in wild male and seven in wild female parents. Thus, 100 different pair combinations are possible D . A. S. SMITH 100 of which 31 occurred in my sample of 61 wild mated pairs giving offspring. Expected frequencies of the various pairings were calculated in a detailed matrix from the genotype frequencies within each sex. They suggest that mating is random. Much the commonest pairings, as expected from the high frequencies of the genotypes, are Bc/bC x Bc/bC ( 10) and BdbC male x B d B c female (10).Of the remaining 29 pair combinations, none has above three occurrences. As most expectations are small, the null hypothesis that mating is random can be tested only by combining data. The following results of 2 x 2 xz tests were obtained for the B and C loci, both of which support random mating: brown (B-) v. orange ( b b ) ; ~ f = l . 0l ;. 3 > P > 0 . 2 : dorippus(C-) u. aegyptius (cc);x:=1.5; 0 . 3 > P > 0 . 2 . Sex ratio At the B locus, the two alleles are of equal frequency in the sexes Cx!=0.4; 0.7 > P > 0.5) but at the C locus the C allele is more frequent in males (48.4%) than females (32.8%).Therefore, male dorippus are more frequent (82%)than female (57.4%)(x:= 7.6; P > 0.01). It follows that mating frequencies are significantly different from expectation on a null hypothesis that the genes have equal frequency in the two sexes (Table 11).The departure from expectation is main1 due to the heterotypic pairings which make the largest contribution to x . Although mating is random, as there is a surplus of dorippus males and mgyptius females unable to find mates of their own kind, hybridization and thus gene exchange between the lines, is an enforced consequence of the sex-ratio within each morph. This result does not invalidate earlier findings of non-random mating and sexual selection (Smith, 1973a, 1975~) as these are strictly seasonal phenomena. Furthermore, it is clear from Table 12 that there is a genetic component to the sex-ratio imbalance. In backcross broods at the C locus, the sex-ratio is J Table 1 1 . Mating frequencies at the C locus tested against the null hypothesis that allele frequencies are identical in the two sexes Male genotype Ccc 19 12.9 2.904 CC31 Female genotype Pairs observed Pairs expected Contributions to,$ 29.6 0.063 cc cc C4 12.9 6.125 CC 7 5.6 0.350 Totals - 61 61 9.4429 (3 d.f.) Table 12. Comparison of the sex ratios obtained from three types of cross Number of broods lot 4 10tt Parental genotyues Offspring d 9 6 9 N X2 Bc/bC BdBc BdbC BdBc Bc/bC Bc/bC 39 65 99 72 58 65 111 9.81 1" 0.398 7.049" 123 164 t There is heterogeneity, 4 of the broods being either all-female o r significantly biased to females. tt There is heterogeneity, 3 of the broods being significantly biased to males and the others normal. GENETICS OF. POLYMORPHISM IN D A N A ( / S 101 significantly biassed towards females if the female parent is aegyptius (Bc/Bc) but not if it is dorippus ( B d b C ) ; on the other hand, the dihybrid crosses give a significant excess of males. Thus, the female parental genotype affects the sexratio (Smith, 1975b, 1976b1, the genetic control of which will be discussed in another paper. As there is seasonal selection which favours dorippus in the dry season and aegyptius in the wet (Smith, 1975b), the sex-ratio also changes dramatically being dominated by males in the former and females in the latter season. Comparing the BdbC male x B d B c female with the dihybrid crosses (Table 12), which together comprised 33% of the wild matings giving progeny, it is easy to see how a seasonal shift in the selective value of the two female genotypes will automatically alter the sex-ratio. Hardy- Weinberg equilibrium When the B and C genotypes are examined together (Table 131, the double heterozygotes exceed expectation and all other genotypes except bdbc are rarer than predicted (x:= 14.4; P<O.O5). On the other hand, the heterozygotes at neither the B nor the C locus alone are in significant excess. This suggests the possibility of heterozygous advantage dependent on epistatic interaction between the two loci. As expected, there is a significant sex difference in chromosome frequencies (Table 14): the BC and bC chromosomes are commoner in males and the Bc and bc chromosomes in females (xi=8.4; P < 0.05). The excess of repulsion (77.5%) over coupling chromosomes is very highly significant (xi= 82.3 ; P < 0.00 11, Table 13. Goodness of fit to Hardy-Weinberg ratios for B/C genotypes in 6 1 wild mated pairs Geriotype BC/BC BC/Bc BC/bC BC/bc BdbC Number observed expected 0 2 2 50 6 4.10 o'21 3.65 3;:;; 1 1 X2 1.970 8.123 Genotype Number obselved expected I7 Bc/Bc Bc/bc bC/bC bC/bc bc/bc Total 14 12 I3 6 122 20.51 18.41 16.25 16.39 4.13 122.00 X* 0.601 1.056 1.112 0.701 0.84 7 14.410' Chi-omosome frequencies: EC=0.041, Ec=0.4 10, bC=0.365, bc=0.184. Gene frequencies: B=0.451, b=0.549, C=0.406. c=0.594. Table 14. Number of coupling and repulsion phase chromosomes in a sample of 80 male and 64 female wild butterflies Chromosome Males observed BC BC bC bc Totals 11 59 64 26 160 ~~~~~ xt3,for the sex difference=8.397; Females expected 7.2 65.0 57.8 30.0 160.0 ~~ Totals observed expected 2 58 40 28 I28 5.8 52.0 46.2 24.0 128.0 ~ P<0.05 by Brandt & Snedecor's formula. 13 117 104 54 288 D. A. S . SMITH I02 indicating gametic excess (Turner, 1967 1 or linkage disequilibrium. From the data in Table 14, the gametic determinant D is -0.142 (maximum_+0.25, equilibrium zero). D’ (Lewontin, 1964) is - 0.7 76 (maximum k 1, equilibrium zero) (see Appendix). Linkage disequilibrium of this magnitude must be maintained by both restricted recombination (close linkage) and strong selection. In particular, there must be powerful selection against the coupling chromosomes as 1.9% recombination in each generation is sufficient, in the absence of selection, to establish linkage equilibrium quite rapidly (Lewontin 8c Kojima, 1960; Bodmer 8c Parsons, 1962; Arunachalam 8c Owen, 197 11, especially as there are 12 overlapping generations a year. The A Locus Accurate scoring of the A alleles is impossible in field specimens. If traces of white are visible on the hindwing, the a allele is known to be present in the heterozygous state but absence of white does not imply the reverse. Moreover, traces of white scaling, which can be scored with confidence in freshly emerged butterflies, would be undetectable in even slightly worn wild specimens. Variation in the expressivity of a in heterozygotes, due both to sex and the modifying action of the B alleles, further complicates the task. In the 66 wild matings from which five or more offspring were obtained, one Aa parent is inferred if white scaling is detectable on either parent or any of the offspring. The data in Table 15 do not indicate heterozygous advantage: indeed the observed values are a good fit with the Hardy-Weinberg expectations. However, the frequency of aa butterflies in the sample is approximately three times their known field frequency (1.2%) and the fit is, therefore, probably fortuitous. Table 15. Goodness of fit to Hardy-Weinberg ratio for A locus genotypes in 66 wild mated pairs Genotype Observed ( N ) Expected ( N ) X2 AA 110 107.4 0.063 Aa aa Totals 18 23.3 4 1.3 132 132.0 0.338 0.275 DISCUSS1 ON Danaus chrysippus is probably the most abundant and widespread of all tropical butterflies. It also supports the greatest array of mimics, both Batesian and Mullerian, of any butterfly: the list in Africa alone embraces, on a conservative estimate, some 30 species from the families Nymphalidae (12), Acraeidae (numerous), Hypsidae (several), Papilionidae (1) and Lycaenidae (1 (Rothschild, Von Euw, Reichstein, Smith & Pierre, 1975: pl. 1). It is not unusual to find half a dozen co-mimics flying together. Although the combination of unconcealed lifestyle and aposematic colouration have convinced most observers that D . chryszppus is distasteful to predators, hard evidence was until recently somewhat scanty. Swynnerton (1915) was the first to observe birds vomit after swallowing African Queens. However, the chemical weaponry, which is the mainstay of the species’ defensive system, is a comparatively recent discovery. GENETICS OF POLYMORPHISM IN DANAUS 103 Two distinct classes of deterrent plant products are known to be stored by the adult insects : (1) cardiac glycosides (cardenolides),which are well known for their cardioactive, emetic and noxious properties, are sequestered by larvae from their foodplants, mainly members of the Asclepiadaceae (milkweeds), and subsequently stored in all stages of the life-cycle (Rothschild et al., 1975; Brower, Edmunds 8c Moffitt, 1975); (2) pyrrolizidine alkaloids are ingested, mainly by males, from the dead or dying parts of plants from several families including the Boraginaceae, Compositae and Leguminosae. These alkaloids, which are potent hepatotoxins and often lethal to domestic stock (Bull, Culvenor & Dick, 1968), are also known to be distasteful to some predators when stored in their prey (T. Eisner, in lztt.). Male danaids of many species metabolize the alkaloids into a component of the aphrodisiac pheromone, without which courtship is unsuccessful (Schneider, 1975; Schneider et al., 1975; Meinwald et al., 1974): however, Edgar, Cockrum & Frahn (1976)found that adult D.chrysippus, of both sexes but principally males, store pyrrolizidine alkaloids unaltered in their tissues. This means that despite the fact that D. chrysippus larvae may feed on milkweeds not containing cardenolides (in some populations predominantly so-Brower et al., 19751, adult males might, nevertheless, be distasteful due to their alkaloid content (Boppri., 1978). In East Africa, a high proportion of both sexes may contain deterrent amounts of cardenolide (Rothschild et al., 1975)and the males are presumably doubly protected by the presence of the alkaloid in addition. Overall, there are no longer grounds for doubting that D . chrysippus is a well protected species, even in areas such as West Africa, where cardenolide storage is often dispensed with. The colour polymorphisms of D.chrysippus in East Africa have been described by Owen & Chanter (1968) and Smith (197313, 1975a, 1976a). That a widely mimicked and proven unpalatable species should also be highly polymorphic constitutes something of a puzzle. The function of the aposematic life-style is surely to convey to experienced predators an image easily perceived from afar and instantly associated with an unpleasant experience; and one which is, moreover, frequently reinforced to the mutual benefit of predators and prey. While accepting that avian predators may generalize images (Duncan & Sheppard, 1965), economy in their education is probably jeopardized if they must learn to avoid as many as eight distinct phenotypes (excluding intermediates) such as occur in D.ch7ysippus around Dar es Salaam (Figs 1-16). The rare phenotypes are likely to be particularly at risk as few predators will have experienced them. Owen & Chanter ( 1968) attribute the polymorphism to the disadvantage attached to a model which supports an excessive load of Batesian (edible)mimics. They argue that mutations which alter the appearance of the model, to an extent that weakens mimetic resemblance, may be beneficial to the possessor by allowing it to escape (in the evolutionary sense) from its mimics. Thus, selection pressure favouring diversity may lead to a stable polymorphism maintained by frequency-dependent selection. A second possibility is the acquisition of heterozygous advantage, allowing the mutant alleles to increase in frequency to an extent not wholly determined by the pressures of mimicry and predation. This explanation is favoured by Ford (197 1) without facts to support it. Thirdly, the mutants might increase through other advantages, such as superior adaptation to part of a diverse habitat or to a particular seasonal climate, and become in time 7 104 D. A. S SMITH sufficiently common to be established as distinct models. There is strong evidence for seasonal changes in the selective value of forms uegyptius and dorippus in Tanzania (Smith, 1975b). Other possibilities include frequency-dependent selection in response to Miillerian mimics (Smith, 1976a), and density-dependent selection (Smith, 1975b,c). Should Ford’s suggestion prove correct, none of the other possibilities is thereby invalidated: on the contrary, the stability of the polymorphism is guaranteed. The study of size, which is, in D. chrysippus, at least partly a pleiotropic effect of the major colour genes, provides some important clues to the nature of the polymorphism. Assuming that size in a butterfly is not selectively neutral, there must be selection for an optimum size, or perhaps for several optima, which might differ between sexes and phenotypes, from season to season or within parts of a diverse habitat. The breeding results show that mean size does indeed vary with sex and phenotype but the possibility of seasonal or habitat variation has not been studied. Environmental factors which might select for size in the African Queen are to some extent speculative as none has been positively identified. It is generally easier to visualize or demonstrate factors favouring large size than small (Cook & O’Donald, 197 1). Factors conducive to large size in females are enhanced reproductive output and heightened visual attractiveness to males (Crane, 1955, 1957). Large males may achieve, through faster flight, a competitive edge in seeking out mates. In aposematic species especially, large size improves the individual’s chances of being recognized by an experienced predator at a distance sufficient to prevent its being molested. It is noteworthy that the male is the larger sex in most danaids as it is arguably the more generally distasteful one (Edgar et al., 1976). In populations not storing cardenolides, where males may be protected mainly by pyrrolizidine alkaloids, females are, in effect, potentially their Batesian mimics. On the other hand, small genotypes are preadapted to food shortage which is experienced by butterflies in the tropical dry season when both larval foodplant and nectar sources for adults are relatively scarce. Also, Rothschild (1971) has pointed out that the less distasteful species of a pair of Mullerian mimics is expected to be the smaller. At Dar es Salaam, both the uegyptius and dorippus forms of D . chrysippus are respective co-mimics of forms acedon and dairu of Acrueu encedon, a smaller species which is thought to be well protected by a noxious secretion of yellow fluid, containing HCN, released from a thoracic gland. As female D. chrysippus may contain neither cardenolides nor alkaloids, the species as a whole is possibly the less effectively protected of the pair, a factor which could favour small size, particularly in females, where they are syrnpatric. The breeding results show that the mean size of BdbC males is almost identical with the overall mean although in Bc/bC females it is somewhat (but not significantly) below (Table 10). The excess of heterozygotes in this multilocus system might indicate heterozygous advantage if there is also stabilizing selection for size as seems likely to be the case. Stabilizing selection would also embrace the genotypes produced from the commonest crosses, BdbC x BdbC and BdbC male x BdBc female (Tables 8,9). The three genotypes from a dihybrid repulsion x repulsion cross, Bc/Bc, BdbC and bC/bC, are of almost identical size in females although in males the double heterozygote shows significant heterosis. In contrast, a dihybrid cross between coupling phases produces unbalanced GENETICS OF POLYMORPHISM I N D A N A U S 105 progeny including the two extreme genotypes, B U B C (small) and W b c (large). Assuming no position effect (differences of viability or phenotype between coupling and repulsion phases), the repulsion phase will be selected for its more balanced progeny, thus creating linkage disequilibrium. In other words, the breeding results show that the two pairings found to have the highest frequencies in the wild population both produce progenies with an array of genotypes giving a good approximation to the population mean size and a low brood variance. Inbreeding between double homozygotes will always depress the mean whereas all types of outcross will produce a heterotic F1 followed by regression to the mean under random mating in F2. Protogyny and wide scattering of the eggs by laying females both tend to enforce out-breeding. Thus, the genetic architecture of the wild population is superbly adapted to the maintenance of the average, balanced phenotype, in the manner predicted for two linked loci by Mather (1973). Moreover, the flow of variability from the potential to the free state (Mather, 1973) is stemmed by the restriction of recombination, which produces coupling chromosomes, to about 4% in males and probably zero in females. The B/C polymorphism in D. chvsippus gives impressive support in general terms to the model for two loci proposed by Turner (1967). In particular, it agrees with his prediction that close linkage, with epistasis and linkage disequilibrium, would be expected. On the other hand, the African Queen population at Dar es Salaam has an extraordinarily complex population genetics which is known to include many factors invariably omitted from non-verbal models in the interest of tractable mathematics. Such factors include at least the following (Smith, 1973a,b, 1975a,b,c, 1976a,b): ( 1 ) overlapping generations; (2) seasonal non-random mating and sexual selection, affecting both sexes; (3) deviant sex and morph ratios, probably caused by meiotic drive in the female; (4) cyclic selection acting on both colour and sex-ratio polymorphisms and possibly density-dependent ; ( 5 ) possible frequency-dependent selection in response to both Batesian and Mullerian mimics; (6) different selective values between sexes within morphs (present paper), suggested by sex differences in gene, chromosome and genotype frequencies, recombination values, expressivity of the a gene in heterozygotes, size and heterotic effects; ( 7 ) pleiotropy for size and colour; ( 8 ) interaction between the linked complex and unlinked loci (e.g. the A locus). Any of the factors 4-8 alone could underpin a genetic polymorphism and their relative importance in D.chlysippus is impossible to assess at present. Factors 2-3 are probably parts of the machinery involved in the adjustment of equilibria. The very marked heterosis at the A locus in both sexes (Table 7 ) is not easily accounted for. Analysis of the wild parental genotypes (Table 16) gives no evidence for heterozygous advantage. Moreover, evidence obtained from reared broods is conflicting. In five monohybrid crosses (broods 60-62, &2,99), which gave 65 A- and 13 aa offspring, the departure from the expected 3: l,ratio is not significant Cx!= 2.9; 0.1 > P > 0.05 with no heterogeneity). However, if the Aclass is corrected for expressivity (only 24 being Aa phenotypes), the segregation is AA 15: Aa 50: aa 13, a significant deviation to the heterozygote from the expected 1 :2: 1 ratio (xi=6.3; P < 0.05). On the other hand, three backcross broods (6, 7, 93) gave 36 Aa and 40 ~1 offspring, a result very close to 1: 1 (x:=O.2; 0 . 9 > P > 0.8). Therefore, it is impossible to draw any conclusion from these results without postulating another interacting factor to account for the difference between the monohybrid and backcrosses. I06 D. A. S. SMITH As all D. chrysippus south of the Sahara and west of Cameroun are homozygous for a, the mutation probably occurred in West Africa and went to fixation. Yet the a allele occurs at various lower frequencies, both eastwards across Africa to the coast, and sporadically in Asia as far east as Sumatra: it has also spread southwards, in an arc around the northern and eastern fringes of the Congo basin, to Natal (distribution maps in Rothschild et ul., 1975: 2-4). Although I am unable to prove heterozygous advantage at the A locus, it is the most likely explanation for both the heterosis described here and the extensive distribution of the a allele outside its heartland. Eventually, analysis of extensive field data from Dar es Salaam may help to resolve this matter. The substantial proportion of Aa butterflies which are of intermediate phenotype are poor mimics. In Uganda, Owen & Chanter (1968) have shown that they are less frequent in the field than predicted from rearing wild larvae, thus suggesting selection against them. The white hind-winged forms of A . encedon (forms alcippina and alcippina-dairu), which are Mullerian mimics of the D. chrysippus aa genotypes, are common around Kampala in Uganda but absent from Dar es Salaam, where the a allele is rare, and also from most parts of West Africa where it is fixed. Consequently, Aa phenotypes may suffer disadvantage in Uganda where they impair Miillerian mimicry with some forms of A . encedon, but not in other areas, such as the Dar es Salaam region, where the only mimics of the ua phenotypes are forms of Hypolimnas misippus L. (Smith, 1976a). The intermediate D. chrysippus phenotype may have the advantage of escaping some Batesian mimics although intermediate phenotypes are also present in H . misippus. Double homozygotes in coupling are rare (Table 14): no proven BC/BC individual was recorded and bc/bc butterflies from Africa are rare in the field and in museum collections. Through much of Asia, however, the species is monomorphic for bc/bc (form=race chrysippttus L.). Examination of the collections in the British Museum (Natural History) and the University Museum, Oxford, suggests the b and C alleles have gone to fixation in north-east Africa, especially in the Somali Arid. On the other hand, in west-central and south-west Africa, southwards from the Bight of Biafra to the Namib desert (Gabon, Congo Republic, west Zaire, Angola and Namibia), only the B and c alleles occur. The causes of the gene biogeography at the present time must be sought in the Pleistocene history of Africa. Between 25,000 and 18,000 B.P., there is good evidence for a barrier of montane vegetation which stretched more or less without a break from the Ethiopian highlands to Cape Province and Angola, with a western arm reaching across from Ruwenzori to Mount Cameroun. Both east and west of this barrier, but particularly in the north-east (Somalia) and the extreme south-west (Namib Desert), dry conditions seem to have held throughout the Pleistocene (Moreau, 1966). Furthermore, the late Pleistocene history of the Chad basin shows that, from 22,000 until as recently as 8500 years ago, it was occupied by the vast Lake Mega-Chad, which was as big as the Caspian, with a northern shore 400 miles north of the present lake. A contemporary northward extension of the equatorial rainbelt, by some 300 miles, over the ridge dividing the Congo and Chad basins, would have produced a continuous belt of evergreen forest extending quite possibly from the coast to the Tibesti mountains. As both montane and lowland forest present an impenetrable barrier to D. chrysippus, the importance of these GENETICS OF POLYMORPHISM IN DANAUS 107 recent and sweeping changes in climate and vegetation for the evolution of the species can hardly be exaggerated. Moreover, although the primary cause of the massive extension of grassland and desert in the last 5000 years has undoubtedly been climatic, the unprecedented impoverishment of the vegetation from human interference must have greatly accelerated the process. Thus, both the biogeographical and genetic evidence point to the conclusion that the polymorphism has originated since the Pleistocene, by hybridization between three until recently allopatric races, alcippus (aa E- cc) to the west of the Chad basin, dorippus ( A A bb CC) in the north-east and aegyPtius ( A A BB cc) in the south. The establishment of heterozygous advantage could account for its persistence. I t follows that neither Batesian nor Mullerian mimetic relationships are likely to have had much to d o with the origin of the polymorphism; on the contrary, they probably result from it. Subsequently, frequency-dependent, density-dependent and cyclic selection have become important in fixing equilibria, which vary at each locus throughout the east and central African region and, in the Dar es Salaam area at least, with the season of the year. A curious fact emphasized by Rothschild et al. (1975) is the dearth of species mimicking D . chrysippus form alcippus in West Africa (or, indeed, anywhere else) where it nevertheless retains the aposematic life-style. The same applies to some extent to form dorippus which lacks Batesian mimics compared with form aegyptius in East Africa. In Batesian mimics which are dimorphic ( H . misippus, Pseudacraea poggei, Mimacraea murshalli, Papilio dardanus), having forms matching both models, the one mimicking dorippus is always rarer, if present at all, even in areas where its model is commoner as in Tanzania (Smith, 1976a). These facts support the idea that the a and C alleles are recent mutations, good mimics of which have in some cases not yet evolved and in others had insufficient time to match the geographical range or frequency of their models. The larger size of single locus heterozygotes compared with both homozygotes and two locus heterozygotes shows that heterosis and heterozygous advantage (if it occurs) must be distinct phenomena. The two locus heterozygotes, which are in excess, exhibit either zero or negative heterosis with respect to their fellow segregants. Thus, the multiple heterozygotes are of intermediate size as a result of epistatic interaction between linked loci and additive effects between unlinked ones and are the average and balanced phenotypes. As cyclic, directional selection favours the bC chromosome in the dry season and Bc in the wet (Smith 1975b, 1976b, and unpublished data), the BclbC genotype is the reservoir of potential variation, providing a steady output of Bc/Bc and bC/bC segregants which are favoured in alternate seasons. The double heterozygote in repulsion is possibly protected by heterozygous advantage although seasonal (directional) selection for a dominant gene could alone produce an excess of heterozygotes. The hybridization between two races monomorphic for Ec and bC, which is probably post-Pleistocene in origin, would provide the array of genotypes on which seasonal selection could act. The B and C loci may not initially have been linked and the present rather close linkage is possibly due to selection. ACKNOWLEDGEMENTS I am grateful to Professor A. S. Msangi, Head of the Department of Zoology, University of Dar es Salaam, for providing the facilities for this research. D. A. S. SMITH 108 Professor G. C. Varley and Mr R. I. Vane-Wright have been most helpful in allowing me access to the museum collections in their care. REFERENCES ARUNACHALAN, V. & OWEN, A. R. G., 1971. Polymorphisms with Linked Loci. London: Chapman & Hall. BODMER, W. F. & PARSONS, P. A,, 1962. Linkage and recombination in evolution. Advances in Genetics, 11: 1-100. BOPPRE, M. 1978. Chemical communication, plant relationships and mimicry in the evolution of danaid butterflies. Entomologia Experimentalis et Appliccata, 24: 1641-1721. BROWER. L. P., EDMUNDS, M. & MOFFITT, C. M., 1975. Cardenolide content and palatability of a population of Danaus chrysippus butterflies from West Africa. Journal of Entomology (A), 49: 183-196. BULL, L. B., CULVENOR, C. C. J . & DICK, A. T., 1968. The Pyrrolizidine Alkaloids. 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APPENDIX To derive the basic parameters for a system of two loci, each with two alleles, I follow Lewontin & Kojima (19601, Lewontin (1964) and Turner (1967). The frequencies of the genes A , B, a, b are q A , q B , ya, 46. The frequencies of the gametes AB, aB, Ab, ab are v, x, y, z. D , the gametic determinant, is defined as D = v z - XY or, the difference between the frequencies of the coupling and repulsion gametes. If the frequency of each gamete is the product of the frequencies of the genes composing it, then the alleles at the loci are distributed at random with respect to each other. In other words, they are in linkage equilibrium and D=O. If D is positive, the coupling gametes are in excess; if negative, there is an excess of repulsion gametes. I f all the alleles have a frequency of 0.5, it is easy to show that the maximum values of D are 0.25 (coupling chromosomes only) and -0.25 (repulsion chromosomes only). The maximum value D can attain depends on the gene frequencies. The parameter D’(Lewontin, 1964)is the value of D divided by the maximum value it can attain at the observed gene frequencies. D’is zero at linkage equilibrium and otherwise lies in the range f 1.