Cytotaxonomy and evolution in Cryptocoryne (Araceae) J. W. F. Reumer Institute for Earth Sciences, Budapestlaan 4, Utrecht, The Netherlands Present address: Station de Zoologic expbrimentale, 154, route de Malagnou, 1224 CH, ChOne-Bougeries, Genbve, Switzerland Abstract A hypothetical phylogeny is presented for the genus Cryptocoryne (Araceae, Cryptocoryninae). This scheme is based on both geographical and cytological data. Therefore the geography of S. E. Asia, the distribution of the various base numbers and the possible relationships between the base numbers are discussed. In the resulting phylogeny the various base numbers of Crvptocorvne (and the one of Lagenandra) are thought to have been derived from a hypothetical primary base number x I = 9. As a consequence of the scheme, Cryptocoryne is assumed to have a diphyletic character. Introduction Many chromosome numbers are known within the Asiatic monocotyledon genus Crvptocorvne. In the literature the following diploid numbers have been mentioned: 20, 22, 28, 30, 33, 34, 36, 42, 54, 60, 66, 68, 72, 85, 88, 90, 102 and 132 (Jacobsen, 1976, 1977a, 1979, 1980; Arends et al., 1982; De Wit, 1983). Some of these numbers (viz. 60 and 90, see below) are questionable; on the other hand not all species of Cryptoeoryne have been studied yet. The chromosome numbers mentioned above can be related to six different base numbers, viz. x = 10, 11, 14, 15, 17 and 18 (Jacobsen, 1977a; Arends et al., 1982; see Table 1). It has been proposed (Arends et al., 1982) that this series of base numbers originated as an aneuploid series, starting at x = 18 and decreasing to x = 10. This suggestion is based on the assumption that x = 18 is the most primitive c h r o m o s o m e condition, which seems to be confirmed by the fact that the closely related genus Lagenandra has 2n = 36, x --- 18 in all known species (Arends & Van der Laan, 1978). However, when this suggestion is considered toGenetica 65. 149-158 (1984). © Dr W. Junk Publishers. Dordrecht. Printed in the Netherlands. gether with biogeographical facts, it appears that the situation is rather more complicated. This article attempts to combine cytological and biogeographical data into a hypothetical phylogeny of the genus Cryptocoryne. Geography The distribution area of the genus Co'ptocoryne includes continental S. Asia from W. India to S. China, and comprises Bangladesh, Burma, Thailand, lndochina and Malaysia, as well as the islands of Sri Lanka (Ceylon), Sumatra, Borneo, Java, Sulawesi (Celebes), the Philippines and I r i a n / P a pua (New Guinea). The distributions of the six base numbers are more restricted, in many cases quite considerably (Figs. 1-6). The area under consideration is geographically rather incoherent, different parts having a different paleogeographical origin. In Figure 7 the area is shown divided into four sectors: (A) The mainland sector. This sector comprises continental Asia, including the islands of Sri Lan- 150 Table 1. List of Cryptocoryne species of which the chromosome number is known. Compiled atter Jacobsen, 1977a, 1980; Arends et al., 1982; De Wit, 1983. Base number Species Chromosome number Area x = 10 striolata Engler keei Jacobsen 20 20 Borneo Borneo x = 11 eiliata (Roxb.) Schott spiralis (Retz.) Wydler 22, 33 33, 66, 88, 132 entire SE Asia India x = 14 wendtii De Wit beckettii Thwaites ex Trimen undulata Wendt walkeri Schott (incl. lutea Alston) x willisii Reitz (incl. lucens De Wit) parva De Wit nevillii Trimen ex Hooker f. 28, 28, 28, 28, Sri Sri Sri Sri 42 42 42 42 Lanka Lanka Lanka Lanka 28 Sri Lanka 28 28 Sri Lanka Sri Lanka x = 15 pontederiifolia Schott moehlmannii De Wit villosa Jacobsen longicauda Beccari ex Engler (incl. johorensis En~ler 30 30 30 30 Sumatra Sumatra Sumatra Borneo, Johore x = 17 amicorum De Wit et Jacobsen gasseri Jacobsen scurrilis De Wit griffithii Schott zewaldiae De Wit minima Ridley purpurea Ridley jacobsenii De Wit zukalii Rataj diderici De Wit schulzei De Wit nurii Furtado affinis Brown ex Hooker f. cordata Griffith (incl. blassii De Wit, siamensis Gagnepain) edithiae De Wit grabowskii Engler zonata De Wit versteegii Engler ferruginea Engler (incl. sarawacensis (Rat.) Jac.) fusca De Wit tortilis De Wit auriculata Engler bullosa Engler pallidinervia Engler usteriana Engler pygmaea Merrill 34 34 68 34 34 34 34 34 34 34 34 34 34 34, 68, 85, 102 Sumatra Sumatra Sumatra Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula Malay Peninsula 68 68 68 34 34 Borneo Borneo Borneo New Guinea Borneo 34 34 34 34 34 34 34 Borneo Borneo Borneo Borneo Borneo Philippines Philippines 36 36, 54 Thailand, Birma India to SE China 36, 72 36 36 36 36 India Sri Lanka Sri Lanka Sri Lanka Borneo x = 18 albida Parker crispatula Engler (incl. balansae Gagnepain) retrospiralis (Roxb.) K u n t h thwaitesii Schott bogneri Rataj alba De Wit lingua Beccari ex Engler 151 Fig. l. D i s t r i b u t i o n o f t h e b a s e n u m b e r x = 10. q Fig. 2. D i s t r i b u t i o n o f t h e b a s e n u m b e r x = ! 1. ka, Hainan and Taiwan (Formosa), but without the Malay Peninsula. This area has always been continental and underwent only minor changes in its geographical structure during the Quaternary (Pleistocene and Holocene; Dunn & Dunn, 1977). (B) The Sunda sector. This sector consists of the Malay Peninsula, Sumatra, Palawan (not according to Dunn & Dunn (1977), but according to Hooijer (1967), whose opinion is followed here), Borneo, Java, Bali and the many smaller islands in between these larger ones. The influence of fluctuations in the sea level has been large in this sector during the Quaternary. At certain times the area consisted of one big land mass (Sundaland) attached to the mainland; at other moments it became separated and was split into many different islands, as is the case today (Dunn & Dunn, 1977). (C) The island sector, comprising the Philip- 152 Fig. 3. Distribution of the base number x = 14. Fig. 4. Distribution of the base number x = 15. pines (without Palawan), Sulawesi, the Moluccan Islands, the Lombok-Timor range, the Tanimbar Islands and the Kai Islands. In contrast to the straits between the islands of the Sunda sector (B), the straits between the islands in this sector are relatively deep. Throughout the Pleistocene the islands must have always been islands, which were not connected either to each other or to a continental shelf (Dunn & Dunn, 1977). (D) The Sahul sector. This sector comprises New Guinea, the Aru Islands and Australia, which are all situated on one continental shelf (Hooijer, 1967). It is worth noting that the boundary between sectors B and C coincides with the zoogeographical Wallace's line, and the C / D boundary coincides with Weber's line. Returning to C r y p t o c o r y n e , the following pie- 153 Fig. 5. Distribution of the base n u m b e r x = 17. Fig. 6. Distribution of the base n u m b e r x = 18. ture can be d r a w n of the distribution of the six base numbers (see Jacobsen, 1977a, 1980; Arends et al., 1982). x = 10 is f o u n d exclusively in one island, Borneo (Fig. 1). x = 11 is f o u n d in sectors A, B, C and D. It should be noted that in sectors B, C and D only one species is found: C. ciliata (Fig. 2). x = 14 is f o u n d exclusively in one island, Sri Lan'ka (Fig. 3). x = 15 is found in sector B only: in Sumatra, Borneo and J o h o r e on the Malay Peninsula (Fig. 4). x = 17 is f o u n d in sectors B, C and D; it is missing from sector A (Fig. 5). x = 18 is found exclusively in sector A, with one exception: C. lingua in Borneo in sector B (Fig. 6). It needs to be mentioned that the groups of base 154 I \ \\ J / Fig. 7. Sectoral subdivision of SE Asia, A: Mainland Sector, B: Sunda Sector, C: Island Sector, D: Sahul Sector. For further explanation see text. Fig. 8. Distribution of the genus Lagenandra. n u m b e r s are here considered to be coherent groups of m o r e or less related species. A d d i t i o n a l l y , the genus L a g e n a n d r a (which together with C r y p t o c o r y n e constitutes the subtribe C r y p t o c o r y n i n a e ) is f o u n d on the I n d i a n subcontinent and in Sri L a n k a (sector A, Fig. 8). The base numbers The x = 18 g r o u p A r e n d s et al. (1982) suggest that the different base n u m b e r s originate f r o m x = 18. It is generally a c c e p t e d t h a t the diversification of the C r y p t o c o r y ninae o r i g i n a t e d on the I n d i a n subcontinent. R a t a j 155 (1975) a d o p t s this view too, except with r e g a r d to his s u b g e n u s S u b m e r s i n a (op. cir., figs. 2 - 5 , pp. 118-119). T h e most i m p o r t a n t a r g u m e n t s s u p p o r t i n g this view are: the d i s t r i b u t i o n of Lagenandra in I n d i a and Sri Lanka; - the occurrence of several Cryptocorvne-species with primitive c h a r a c t e r s in I n d i a o r B a n g l a d e s h ( C. spiral&, C. huegelii, C. gomezii); - the d i s t r i b u t i o n of the x = 18 g r o u p of Cryptocoryne, which occurs a l m o s t exclusively in s e c t o r A. T h e present a u t h o r agrees that the C r y p t o c o r y ninae o r i g i n a t e d in the m a i n l a n d sector, but, as will be discussed below, he does n o t agree that there was simply an a n e u p l o i d series f r o m x = 18 to x = 10. T h e presence of C. lingua in B o r n e o must be e x p l a i n e d as the e a s t e r n m o s t occurrence o f the x = 18 group; there is an a p p a r e n t e a s t w a r d m i g r a t o r y t r e n d in this g r o u p (e.g. the presence of C. crispatula in S. E. China; J a c o b s e n , 1980). T h e x = 18 g r o u p m u s t have reached B o r n e o at a time when the S u n d a sector (B) was a t t a c h e d to the m a i n l a n d (A), i.e. d u r i n g a period of sea-level lowering c o r r e s p o n d i n g to a glaciation at higher latitudes. b e t w e e n the areas of the x = 14 and of the x = 15 g r o u p s and the fact that the Sri L a n k a n species have a y o u n g a n d e n d e m i c c h a r a c t e r m a k e the step x = 15 ~ x = 14 r a t h e r unlikely. The x = 11 group In a d d i t i o n to the x = 18 a n d x = 14 g r o u p s , x = 11 is the third one present in sector A. It is r a t h e r unclear how x = 11 could have originated f r o m x = 18, as one i n t e r m e d i a t e n u m b e r (x = 14) is k n o w n o n l y as a n island endemic, a n d three i n t e r m e d i a t e s (16, 13 a n d 12) are not k n o w n at all (which does not imply that these n u m b e r s c a n n o t exist or c a n n o t have existed). In o r d e r to e x p l a i n the existence of x = 11 (and x = 10, see below) we need a scheme o t h e r t h a n simply an a n e u p l o i d series f r o m x = 18 d o w n to x --- 10. A c c o r d i n g to A n d r e a s (1972; using G r a n t , 1963) plant t a x a are c h a r a c t e r i z e d on a d i p l o i d level by p r i m a r y base n u m b e r s Xl = 2 t h r o u g h Xl -~ 13. Base n u m b e r s a b o v e 13 are s e c o n d a r y base n u m b e r s (x2), which have evolved from c o m b i n a t i o n s of groups with lower ( p r i m a r y ) base n u m b e r s . T h e e v o l u t i o n a r y scheme to be presented here (Fig. 9) has the p r i m a r y base n u m b e r Xl = 9 as its starting point. F r o m this base n u m b e r x~ = 9 the s e c o n d a r y base The x = 14 group T h e g r o u p with x = 14 is restricted to Sri L a n k a a n d in this p a p e r it is a s s u m e d that it o r i g i n a t e d there after Sri L a n k a b e c a m e isolated f r o m the m a i n l a n d at the end of the Pleistocene. This w o u l d i m p l y t h a t the x = 14 g r o u p is r a t h e r a y o u n g one. T h i s is c o n f i r m e d by the instability of the g r o u p . T h e r e are quite a n u m b e r of hybrids, a n d the t a x o n o m i c status o f several species is s o m e w h a t u n c l e a r (Bastmeijer, 1981); this suggests t h a t we are d e a l i n g with a y o u n g a n d d e v e l o p i n g group. T h e only o t h e r g r o u p present in Sri L a n k a is the x = 18 g r o u p . It is t h e r e f o r e suggested that the x - - 14 g r o u p o r i g i n a t e d f r o m the x = 18 g r o u p , a l t h o u g h it r e m a i n s u n c l e a r how this h a p p e n e d . In the o p i n i o n of A r e n d s et al. (1982) x = 14 o r i g i n a t e d f r o m the x = 15 g r o u p (one of the steps in their a n e u p l o i d series). R a t a j (1975) is of the same o p i n ion, as can be d e d u c e d f r o m his figure 5 (op cit., p. 119). T h e g r o u p with x = 15 is k n o w n f r o m S u m a t r a , B o r n e o and J o h o r e . H o w e v e r , the vast d i s t a n c e /f -'~\ @ Fig. 9. Hypothetical phylogeny of the subtribe Cryptocoryninae, Araceae, showing the relations between the different base numbers. Above broken line: evolutionary steps taken place in the Indian subcontinent; below broken line: steps taken place in other areas and/or in islands. 156 n u m b e r x 2 = 18 originated by means of a simple euploid doubling; on the other hand the primary base n u m b e r xl = 11 developed as an aneuploidy (9 + 2). Whether or not this last step took place with x = 10 as an intermediate will be discussed below. The most likely mechanism for such aneuploid steps is c h r o m o s o m e fusion/fission. The distribution of C. spiralis (India to Bangladesh) more or less coincides with the supposed area of origin of the Cryptocoryninae; this finding supports the hypothesis stated above. Also, C. spiralis and the closely related C. huegelii have some noteworthy morphological characters of the inflorescence in c o m m o n with Lagenandra: the absence of a tube, the presence of a perforated wall closing off the kettle and a wrinkled surface of the limb. S a r k a r et al. (1976) report 2n = 90 for C. spiralis. We think this is a slight mistake and should have been 2n = 88. The other species belonging to the x = 11 group, C. ciliata, is the most widely distributed species of Crvptocoryne: it is found from India to P a p u a and it is the only species present in Sulawesi, J a v a (with the possible exception of C. cordata, see Rataj, 1975) and the Moluccan Islands. One obtains the impression that C. ciliata has the ability to cross considerable stretches of sea. This is explained as follows. The generative proliferation of Cryptocoryne species is restricted by the fact that the seed has no resting period prior to germination (Hermsen & Van Hasselt, 1982), but vegetative reproduction by means of runners is c o m m o n . C. ciliata is found in tidal-influenced rivers, and according to Rataj (1975) even in mangrove areas; the species has a tolerance for salt judging by its occurrence in brackish waters (op. cit.). A rather c o m m o n feature in river-mouths is the detachment of large pieces of vegetation, which f o r m floating islands. These are carried out to the open sea and can be transported over vast distances by currents and winds. In this way plants and animals can be distributed to distant islands (this form of distribution is known for e.g. mammals; Sondaar, 1977). It is tempting to suppose that the large distribution of C. ciliata came about in a similar way. The x = 10 group It is supposed here that the x = 10 group (comprising C. striolata and C. keei from Borneo) originated as an endemic group, c o m p a r a b l e to the x = 14 g r o u p f r o m Sri Lanka. It is likely to have the x = 11 g r o u p as ancestor, as this involves the least complicated step (x- 1). It is however a problem that the only representative of the x = 11 g r o u p in Borneo is C. ciliata; there are great morphological differences between C. ciliata on the one hand and C. striolata and C. keei on the other. Alternatively, it could be argued that the x = 10 g r o u p can be seen as an intermediate step in the x = 9 ~ x = 11 transition. There are two arguments against this idea. Firstly, there is a geographical argument. If we suppose that the x = 11 group originated from xz = 9 on the Indian subcontinent (see above), then the x = 10 group in Borneo should be a relict, far away f r o m the area of origin, from which it apparently disappeared. Such large-scale extinctions are rather unlikely as the genus is quite successful. Secondly, the x = 11 group contains the primitive C. spiralis which should be morphologically and hence also phylogenetically close to the c o m m o n ancestor of Cryptocoryne and Lagenandra, i.e. the hypothetical xl = 9. At present we prefer to adhere to the idea that the x = t0 g r o u p originated in Borneo as an endemic development, even t h o u g h this cannot be satisfactorily explained. The x = 17 group The g r o u p with x = 17 has a large distribution; species are k n o w n f r o m sector B (Malay Peninsula, S u m a t r a and Borneo), f r o m sector C (the Philippines) and from sector D (New Guinea). It is reasonable to assume that x = 17 originated f r o m x = 18; this implies only a simple step ( x - l ) . In general, the area of distribution of x = 17 is more easterly than that of x = 18, and apparently the x = 17 g r o u p continued the eastward migratory trend of the x = 18 group. The areas of both groups overlap in parts of the Malay Peninsula and in Borneo. A p a r t f r o m C. ciliata, the x = 17 group is the only taxon that has been able to cross the seastraits of sector C. Probably, the same mechanism as described above for C. eiliata operated here. The 157 enormous morphological differences between the various species (compare e.g.C, usteriana from the Philippines and C. versteegii from Papua) suggest that this process took place a long time ago. Some remarks should be made here. C. gasseri has 2n = 34; Jacobsen (1979) however mentioned 2n = 30 for this species. Arends et al. (1982) note that this was erroneous. De Wit (1983, in a section written by Arends) mentions the erroneous 2n -- 30. The same applies to C. scurrilis with 2n = 68 (Arends et al., 1982). Jacobsen (1979) as well as De Wit (1983) erroneously mention 2n -- 60 for this species. The great morphological resemblance between C. lingua (Borneo, 2n = 36, x = 18)and C. versteegii (New Guinea, 2n = 34, x = 17) should be interpreted as a parallel development and does not indicate any phylogenetic proximity. Rataj (1975) places both species together in one section (Linguae); his view is disputed here (see also Jacobsen, 1977a). Crusio (1982) and Arends et al. (1982) place C. versteegii in a separate group. On the basis of resemblances in the seedling, M iihlberg (1979) concludes that there is a relationship between C. versteegii and C. ciliata (x = 11, also on New Guinea). We consider this to be yet another parallel development. It would be interesting to know the chromosome number of the third Cryptocoryne in New Guinea (next to C. ciliata and C. versteegii): C. dewitii. This species is known from herbarium sheets only (Jacobsen, 1977b). Attempts should be made to relocate this species in order to verify whether or not C. dewitii belongs to the x = 17 group. It is likely that it does belong to this group on geographical grounds (Arends et al., 1982, are of the same view). The x = 15 group The x = 15 group is found in sector B only, where it shares its area with the x -- 17 group. It is likely that the x = 15 group originated from the x = 17 stock and that it spread over Johore, Sumatra and Borneo at a moment when this area formed one single land mass (Sundaland). The greatest polymorphism of the x = 15 group is found in Sumatra (three species). It will be clear that the suggestion of Crusio (1982) that C. villosa belongs to the C. scurrilis-group cannot be upheld. His suggestion is probably based on the erroneous publication of 2n = 60 for C. scurrilis. The C. scurrilis-group has the base number x = 17 and not x=15. One might have the impression that the four species of the x = 15 group, which all have the somatic chromosome number 2n = 30, belong to the x = 10 group (in which case they would be triploids). However, since all four species are fertile, this possibility can be virtually ruled out; triploids are nearly always sterile. Conclusions These discussions about the relationships between the various base numbers, together with the data from the geographical distribution of the base numbers, lead us to the hypothetical phylogeny shown in Figure 9. As stated above, the basis of this phylogeny is the hypothetical primary base number x~ = 9. From this base number it is thought that the following are derived: (a) xl = 11, possibly with or without x I = 10 as an intermediate step. The currently existing x = 10 group from Borneo however is here considered to have descended from x = 11. It will be evident that in the nomenclature of Andreas (1972) both groups (x = I0 and 11) have primary base numbers. (b) x2 = 18 by means of doubling. From this secondary base number it is thought that x = 14 (in Sri Lanka), x = 17 and from x = 17 again x = 15 are derived. In contrast to the former two groups, these four groups (I 8, 17, 15 and 14) have secondary base numbers. (c) the genus Lagenandra, also having x 2 = 18. The existence of two more or less separate parts (a and b) means that in its present form the genus Cryptocoryne is diphyletic. The origin of the Cryptocoryninae is supposedly on the Indian subcontinent; this is where the first evolutionary steps took place (the part of Figure 9 above the broken line). Further steps occurred in other areas a n d / o r on islands (the part of Figure 9 below the broken line). The phylogeny presented here gives a good explanation for the absence of the base numbers x = 12 and x = 13. Neither part of the phylogeny (the above-mentioned a and b) has x = 12 or x = 13 as (imaginary) intermediate steps. Several problems and questions are still to be solved or answered: 158 l) The explanation of the large step x = 18 -- x = 14 in Sri Lanka. 2) The relationship between x = 10 and x = 11. 3) The suggested diphyletic character of the genus. 4) Can the presented phylogeny be supported by other characters, such as the morphology of the inflorescence? 5) Many species have not been studied cytogenetically yet. Do their numbers fit in with the phylogeny presented here? 6) Hybrid studies should be undertaken in order to test chromosome homologies and relationships between different karyotypes. Acknowledgements The author is indebted to J. D. Bastmeijer, J. M. van Brink and J. de Vos for critically reading the original Dutch version of this article; S. M. McNab improved the English text. References Andreas, Ch. H., 1972. Experimentele plantensystematiek. Oosthoek, Utrecht: 148 pp. Arends, J. C., Bastmeijer, J. D. & Jacobsen, N., 1982. Chromosome numbers and taxonomy in Cryptocoryne (Araceae) II. Nord. J. Bot. 2: 453-463. Arends, J. C. & Van der Laan, F. M., 1978. Somatic chromosome numbers in Lagenandra Dalzell. Meded. Landb. Hoogesch. Wageningen 78-13:46 48. Bastmeijer, J. D., 1981. Naamgeving in Cryptocoryne van Sri View publication stats Lanka. Meded. Werkgrp. Aq. Planten l: 23-38. Crusio, W. E., 1982. Help, ik heb een Crypto! Aquarium 52 (2): 46-48 and ibidem 52 (3): 74-77. De Wit, H. C. D., 1983. Aquariumplanten. 4th ed. Hollandia, Baarn: 463 pp. Dunn, F. L, & Dunn, D. F., 1977. Maritime adaptations and exploitation of marine resources in Sundaic Southeast Asian prehistory. Mod. Quaternary Res. SE Asia 3: 1-28. Grant, V., 1963. The origin of adaptations. Columbia Univ. Press, New York/London: 606 pp. Hermsen, E & Van Hasselt; G., 1982. Kieming en verdere groei van Cryptocoryne walkeri-zaden in vitro. Meded. Werkgrp. Aq Planten 3:15-20. Hooijer, D. A., 1967. Indo-Australian insular elephants. Genetica 38: 143-162. Jacobsen, N., 1976. Notes on Cryptocoryne of Sri lanka (Ceylon). Bot. Notiser 129: 179-190. Jacobsen, N., 1977a. Chromosome numbers and taxonomy in Cryptocoryne (Araceae). Bot. Notiser 130: 71-87. Jacobsen, N., 1977b. Cryptocoryne dewitii N. Jacobsen sp. nov. (Araceae). Bot. Notiser 130:381 382. Jacobsen, N., 1979. Cryptocoryne gasseri N. Jacobsen, sp. nov. (Araceae). Bot. Notiser 132: 144. Jacobsen, N., 1980. The Cryptocoryne albida group of mainland Asia (Araceae). Misc. Papers Landb. Hoogesch. Wageningen 19:183 204. Mtihlberg, H., 1979. Cryptocoryne versteegii. Inform. ZAG Wasserpflanzen 9 (3): 5. Rataj, K., 1975. Revision of the genus Cryptocoryne Fischer. Studie ~SAV 3:174 pp. Sarkar, A. K., Datta, N., Mallick, R. & Chatterjee, U., 1976. Report in: A. L6ve, IOPB Chromosome number reports 54. Taxon 25:631-649. Sondaar, P. Y., 1977. Insularity and its effect on mammal evolution. In: Hecht, M. K., P. C. Goody & B. M. Hecht (eds.) Major patterns in vertebrate evolution. Plenum, New York: 671 707. Received 9 . 1 2 . 8 3 Accepted 13.7.84.