Elephantidae is a family of large, herbivorous mammals, belonging to the malla order of Proboscidea, collectively called elephants and mammoths first described by John Edward Gray in 1821.
The word elephant derives from the Greek word Elephas, with a non-Indo-European language lineage, likely Phoenician, and while Homer (Homerus) used it for ivory, from Herodotus it was also describing the animal itself.
It was earlier thought, that the family of Elephantidae developed during middle Miocene (16 million years ago) with its ancestor Primelephas. A later species, Primelephas gomphotheroides lived during middle Pliocene and split into three lineages, which became the present African elephant, the present Asian elephant, and the Mammoths, which lived alongside each others, during millions of years in Africa, where also all recent species has its origin, not really making one of them more "African" than the other, even if it may reflect a more recent situation.
The first mammoths (genus Mammuthus) appeared about 3 million years ago in africa. 120 000 years ago they started to migrate to northern europe, and adapt to colder climate, while in Africa, the mammoths developed into the genus elephas, which also spread to Asia and Europe, and is supposed to have forked into new species, among others, an extinct gigantic species known as "The Forest elephant" or "Straight-tusked elephant" Elephas antiquus, which is known from several fossils from Europe with recovered individuals as far west as Great Britain. Straight-tusked elephant inhabited interglacial Europe and Western Asia during the Middle and Late Pleistocene (781,000–30,000 years before present), reaching size up to 4–4.2 metres (13.1–13.8 ft) in height, and an estimated 11.3–15 tonnes (11.1–14.8 long tons; 12.5–16.5 short tons) in weight. (Systematic revision of Primelephas gomphotheroides (Mammalia: Elephantidae). Sanders, W.J., Mundinger, G.S., and Bloch, J. For Journal of Vertebrate Paleontology).
Humans coexistence, after they started hunting elephants, probably milion years ago, came into a new form, when wild elephants started to become captured alive, after they became tamed and trained, some 5 000 years ago. It has to be highlighted though, that theres no indication, that elephants ever was domesticated, and only during the last 50 years, has elephants been bred in Zoos and breeding centres in Asia, where they have reached som 8-9 generations, which is nothing in the time perspective needed to domesticate a species. Through hunting and capture, humans may partly have affected the wild elephants, which is easier, than through a domestication process, and behaviour and size of tusks can rather fast become a consequence of hunting and capture of living wild elephants.
Present taxonomy tree
(At the bottom of this page is the present taxonomy discussed, and some new suggestions of changes are made).
The family Elephantidae was named in 1821 by the british zoologist John Edward Gray (12 February 1800 – 7 March 1875), and is still valid today among taxonomists. The family was later assigned to taxonomic ranks within the mammalian order of Proboscidea (trunk-animals), with the present following tree of included genus and species, after a rather large number of elephants were transferred from genus Elephas to genus Palaeoloxodon:
- Probsocidea (order)
- Elephantidae (family; living)
- †Primelephas -(genus; extinct +)
- †Mammoths -(genus; extinct +)
- †Palaeoloxodon -(genus; extinct +)
- † Palaeoloxodon antiquus earlier Elephas antiquus - (species; extinct +)
- †Mediterranean dwarf elephant Palaeoloxodon falconeri - (species; extinct +)
- Elephas -(genus; living)
- Elephas maximus - (species; living)
- Loxodonta -(genus; living)
- † Choerolophodontidae (family; extinct)
- †Choerolophodon -(genus; extinct +)
Taxonomy of the surviving recent elephants
The taxonomy of the living recent elephants has followed a rather inconsistent and sometimes a confusing path, but since 1797, up until 2004, the present living elephants had been divided into two recent species: Asian and African, although a number of suggestions for new species were presented, which are not valid today, even if three of them are presently valid subspecies. Below is an attempt to incompltetely describe the various changes of the recent elephants scientific taxonomy names, since 1758. A large number of suggested names of less relevance has been omitted, in order to focus on suggestions and changes, which has greater relevance.
A specimen of fetus of the African elephant (on this website referred to as Sebas pickled elephant) in possession of the dutch collector Albertus Seba (1665 - 1736), who bought the elephant in Amsterdam harbour from the Dutch East India Company, was after Sebas death bought by the Swedish king Adolf Fredrik of Sweden (14 May 1710 – 12 February 1771) in 1753. Shortly after, it was examined by Swedish Zoologist and creator of the modern taxonomy, Carl Linnaeus (23 May 1707 – 10 January 1778), who actually thought this was an Asian elephant from Zeylonae paludosis, or Ceylon, the island now called Sri Lanka.
How, and why, Linneaus was confused about the elephants origin is unclear, but since Seba owned one of the larger naturalia collections in the world, from which large parts wre sold during at least two times, and it could be possible that he also had an Asian elephant in his posession, and that someone mixed up the records after his death. A similair confusion in Drottningholm Castle after his examinaion, is probably more unlikely. Apart from this, is it unclear if Linneus ever saw a living elephant in Europe. During his stay in Netherlands between 1735 and 1738, there are no records of living elephants in the country, the Princes of Orange kept several elephants at various menageries, but probably not after 1633 when Asian female elephant Hansken was sold, and before the elephants Hans and Grete was kept at Het kleine Loo menagerie, imported to the prince in 1784 by the Dutch East India company.
Carl Linnaeus named 1758 the species "Elephant" Elephas maximus and later when taxonomists regarded elephants as two species, an African and an Asian, as a scientific paradoxe, this fetus of an African elephant, became the archetype for the Asian elephant.Another paradox, is that he chose the name maximus, since he thought elephants from Ceylon were considered larger than other populations, which is also wrong since the largest recorded elephants are from the mainland in Indian peninsular, why the entire naming of the first elephantine species, can be viewed as rather complicated. when applied for an Asian elephant, but when and if we would view all present elephants as same species, it comes different. And Linneus may actually have been right, there may be only one species!
In the beginning of the 1800s, when this fetus was transferred from Drottningholm Palace to The Swedish Museum of Natural History, doubts were given that this was an error, and that the fetus was in fact not an Asian elephant but an African elephant, and therefore mislabelled. This fetus speciment is until today in posession of the museum, with museum accession number; NRM 532062, and later research by among others, an ancient-DNA expert at the University of Copenhagen Tom Gilbert, and Italian protein chemist Enrico Cappellini, detected that one protein, a portion of the haemoglobin complex that carries oxygen in red blood cells, differed by a single amino acid, between the two species; among Asian elephants it is aspartate, whereas in African elephants it is glutamate. Their tests confirmed that Linnaeus’s elephant encoded glutamate, which is in a publication from 2013 considered evidence that the fetus that the specimen labelled as the archetype of the Asian elephant was in fact, an African elephant!
For this reason, a new archetype has been identified, with the oldest preserved Asian elephant in Europe, the Asian female elephant Hansken, imported 1633 from Ceylon by the Dutch East India company to Frederick Henry of Orange (29 January 1584 – 14 March 1647). His heir, John Maurice of Orange (17 June 1604 – 20 December 1679) sold Hansken, who toured Europe with different owners and died 1655 in Florence in Italy, where the remins were sold by her last owner Cornelis Jacobs van Groenevelt, to Ferdinand II, Grand Duke of Tuscany, who bought the dead elephant for his collection.. Hansken is located in La Specola Museum of Zoology and Natural History, Florence, Italy with museum accession number; MZUF-734.
As described above, Carl Linnaeus proposed 1758 the scientific name Elephas maximus for a fetus of an elephant, which he considered to the species "elephant".
The Asian, or asiatic, elephant
The German naturalist and professor in Göttingen, Johann Friedrich Blumenbach (11 May 1752 – 22 January 1840), described in 1797 one elephant from Asia, for which he proposed Elephas asiaticus, and one elephant from Africa, for which he proposed Elephas africanus, and while Linneus naming is cennected to various problems, Blumenbachs suggestion for those names has no issues what so ever, as long as we consider Asian and African elephants as two different species.
The French naturalist and zoologist, baron Georges Cuvier (23 August 1769 – 13 May 1832) described shortly afterwards, in 1798, an elephant from India, for which he proposed Elephas indicus, and although suggested later, this scientific name became far more populair in use than Blumenbachs, as the common name Indian elephant was more commonly used in the past, than Asian elephant.
The Dutch aristocrat, zoologist, and museum director Coenraad Jacob Temminck named in 1847 an elephant from Sumatra as Elephas sumatranus.
Then in 1940, English zoologist Frederick Nutter Chasen (1896 – 13 February 1942) renamed all previous three species as subspecies to Elephas maximus, Elephas maximus maximus, Elephas maximus indicus and Elephas maximus sumatranus. Those three subspecies are still, currently recognised as valid taxa, but later research gives an indication that their differences are not distinct enough to warrant classification as separate subspecies. He also named the Borneo elephants, but belonging to subspecies Elephas maximus indicus in 1940.
The Sri Lankan paleontologist, zoologist and Dean of the Faculty of Arts at the Vidyodaya University, Paulus Edward Pieris Deraniyagala (1900–1976) proposed in 1950 Elephas maximus borneensis for the Borneo elephant, based on an illustration published in the National Geographic magazine, which has been claimed as unvalid with the rules of the International Code of Zoological Nomenclature. During the same year he described another three species, Syrian elephant (E. m. asurus), which was based on Bronze Age illustrations, the Chinese elephant (E. m. rubridens), based on a bronze statuette of an elephant and the Javan elephant (E. m. sondaicus), based from a an illustration of a carving on the Buddhist monument of Borobudur. All those suggestions are today debated, the Javan elephant is considered synonymous with the Indian elephant (E. maximus indicus), but the question of when elephants became extinct on Java is unsettled, and it has been proposed that if the Borneo elephants are descended from now exctinct Javan elephants, then the Javan elephants presumably would have also been genetically distinct from other Asian elephant populations. The Syrian elephants status is still debated, and suggestions have been made that they were anthropogenically introduced during the Bronze Age, which has been disputed, based on later findings. The Syrian elephants seems to have been wide larger then most Asian elephants today, measuring 3.5 metres (11 ft 6 in) or more at the shoulder, and they seem to have been still existing as late as 700 BC. 3500 year old skeletons from Kahramanmaraş in Turkey, show a unique DNA: carryig a rare mitochondrial haplotype that was only found before with one single elephant in Thailand. The "Chinese elephant" which Deraniyagala from a statue described as E. m. rubridens, has been researched in 2011 by a team of scientists from China, who claim that the bronze statue is not an Elephant, but belong to the genus Palaeoloxodon.
The African elephant
The African elephant was officially first time described in 1797 by the German naturalist and professor in Göttingen, Johann Friedrich Blumenbach (11 May 1752 – 22 January 1840), with the proposed scientific name Elephas africanus. 28 years later, the French zoologist and paleontologist Frédéric Cuvier (28 June 1773 – 24 July 1838) proposed Loxodonte as generic name for African elephants, and an anonymous author used the Latinized spelling Loxodonta in 1827. But later taxonomists did not always follow Cuviers suggestion, and new descriptions of specimens of African elephants should follow, with the genus Elephas, described 1753 and still being used about 100 years ago, in 1907, and only as late as in 1999, the genus name Loxodonta became commonly used and recognized as authority by the International Code of Zoological Nomenclature.
Elephas oxyotis and Elephas knochenhaueri was described by German zoologist Paul Matschie (11 August 1861 - 7 March 1926) in 1900, and in 1907 Matschie suggested a name for the Forest elephant, Elephas cyclotis, based on two or three specimens from Cameroon, whose skulls differed in shape from elephant skulls collected elsewhere in Africa.
Subspecies of the African elephant
The English naturalist and geologist Richard Lydekker 25 July 1849 – 16 April 1915) assumed that ear size is a distinguishing character for a race (here used for subspecies?), and after specimens were shot in South Africa, Zimbabwe, Kenya, and in Sudan, respectively, he named them in 1907 as Elephas africanus toxotis, Elephas africanus selousi, Elephas africanus peeli, Elephas africanus cavendishi, Elephas africanus orleansi and Elephas africanus rothschildi.
Deraniyagala (mentioned above), described in 1948 the subspecies North African elephant (also called Carthaginian elephant, and Atlas elephant) with the scientific name Loxodonta africana pharaohensis, from a specimen from Fayum in Egypt. This population from north of Sahara, are suggested to be the famous war elephants used by Carthage in the Punic Wars, in their conflict with the Roman Republic. This subspecies has not been widely recognized by taxonomists, but it has been said, that given the relatively recent date of its disappearance, the status of this population as species, or subspecies, can probably be resolved through ancient DNA sequence analyses.
Later revisions of the forest elephant, upgrading it to its own species
DNA research, reported in the August 24, 2004 issue of the journal Science, claimed to provide a definitive answer to the long-debated controversy. It was claimed that DNA tests had shown, as an evidence, that the forest elephant was not a subspecies of the African elephant but a true species. and the taxomomy of the families taxonomy tree was again, changed. (for sources, see links , ).
This move has been criticized as a non-valid species, and suggestions has been made that the article, which claimed to bear implications for both international law and conservation strategies, had the primarly goal to decribe Forest elephant as a new species, in order to enable a change of the Forest elephants appendix iin CITES, and therefore rather as a conservation strategy, than with a taxonomic validity, rename the Forest elephant as a new species.
A hybride casts doubts on elephants taxonomy
During the early days of Internet, the author of this website and the above article, Dan Koehl, got in contact with DVM Derek Lyon, previous Veteriarian in Chester Zoo. Mr Lyon was then kind enough to provide prime sources and facts about Motty, born in 1977 as the first documented hybrid between an African, and an Asian elephant in the world, which after permission from Lyon to me, resulted in a longer article about Motty the elephant crossbreed which has since then been spread on Internet by many others, without mentioning of their source. In the article I already back then mentioned in the intro, that crossbreeds between two individuals, belonging to the same genus, but different species, are in most cases sterile, like the the mule, while a crossbreed between to different genus was regarded as impossible.
Already then, in late nineties, I was skeptical towrds the existence of the two different genus of elephants, and started to see Loxodonta as unvalid since the hybrid indicated that they should belong to the same genus Elephas, since they could produce offspring, like in the case of horse and donkey, both belonging to the genus Equus, tigers and lions, both belonging to the genus Panthera, but while all those hybrids become sterile, since their parents have different number of chromosomes, all recent elephants have the same number of chromosomes, making it likely that a hybrid can be fertile, when the chromosomes can pair properly during meiosis to allow crossing over and successful segretation of homologs into new daughter cells, like in the case with Polar bears and Brown bears, who previously was regarded as belnging to different genus, but recently was changed and now they both belong to the genus Ursus again:
- Constantine John Phipps was the first to describe the polar bear as a distinct species in 1774. He chose the scientific name Ursus maritimus, the Latin for 'maritime bear, and thereby put it in the same genus as the Brown bear, Ursus arctos. The polar bear was later considered to belong to its own genus, Thalarctos. However, evidence of hybrids between polar bears and brown bears, and of the recent evolutionary divergence of the two species, does not support the establishment of this separate genus, and the accepted scientific name is now therefore Ursus maritimus, as Phipps originally proposed.
I find this case similair with the elephants, and claim that they belong in the same genus, the original Elephas.
An article in the scientific journal Nature, Elephant history rewritten by ancient genomes DNA from extinct species forces rethink of elephants’ family tree, by Ewen Callaway in 2016, describing findings announced at the 7th International Symposium on Biomolecular Archaeology meeting in Oxford, UK, on 15 September, calls for a need of change for taxonomy names for different species withing the family Elephantidae, and the palaeogeneticist and professor in evolutionary genetics at the Swedish Museum of Natural History in Stockholm, Love Dalén, says in the article (citation):
- The study will force a reshuffle of the elephant family tree. “Basically Loxodonta is not valid as a genus name,” he says. He thinks that taxonomists may need to come up with new names for the different species, to better represent the relationship between savannah, forest and straight-tusked elephants.
The authors suggestions for recent species new taxonomy names
All previous suggestions of names, has been largely due to if the taxonomists where what we call today inclusionists, who tend to make subspecies of populations that others may regard as species, or exclusionists, who tend to make species of what other consider subspecies. Their reasons, and their arguments has been very inconsequent and varied a lot since 1758, and has still today, not reached a common approach on which principles a population should be regarded as a species or a subspecies, instead different taxonomists try to argue with different means, and meanwhile, some members of a new discipline, the moluciar biologists, who analyse DNA, sometimes claim that they have better insight in Taxonomy than the taxonomists, by using measurable differences in DNA, or how long time a go they measure that two populations split from each other in time, sometimes neglecting facts of if different populations breed in the wild, can produce offspring, or even fertile offspring, or even having large present populations of intermediate genetaical character. Some scientists may claim that it was easier in the past, when a species was defined as two individuals who can produce a fertile offspring, and where populations that interbreed, producing a hybrid that is a sterile offspring, should belong to the same genus. Others may claim that new methods, more precise can define what a species is. Also, the limited number of specimens availabla during most times when populations was named by taxonomists, were mosly very small, with difficulties to compare a finding with another. Today, we can see that most different "types" of Asian elephants exist alongside in most known range countries, and the origin of a single elephant can not be decided based on its "type". All we can see, is that the Asian elephants in general get smaller in east direction, and has less variation in types, but are as group, rather heterogene, since different "types" can be seen in a mixture, in most recent local populations throughout Asia, with a larger variation in the west, and a maybe smaller variation in the east, and insulair populations.
My understanding from this, is that the present taxonomy, dividing the Asian and the African elephant into two different genus, Elephas and Loxodonta, in any case should be reconsidered, like the case of scientific name for the Polar bear, and that the name Loxodonta is not valid, from a number of reasons, of which some has been described above.
As a consequence of this, the taxonomy of the family needs an oversight, bringing consequence to the different naming of species and subspecies, in order to be compatible, with the latest knowledge, about the living recent species, their relation to each other, based on equal classical taxonomy, moleculair research, as well as what we know about their intra-breeding patterns, and the populations productions of fertile offspring, which with new insight, gives a new view on their taxonomy, which should be changed accordingly. Whatever people 200 years ago, considered valid for scientific naming of mammal populations, like the shape of ears, colors, etc, may have a value, but it has undoubtly since long time, also made us neglect later knowledge and research.
Two main stream strategies can be used for such a change.
- A minimal change, which largely follows the strategy since 1779, when Blumenbach separated Linneus "Elephant" from 1758 into two branches, an African, and an Asian. All later taxonomy large follows this strategy, and a mild version of changes are suggested below under Suggested taxonomy tree for recent species within subfamily Elephantinae.
- A second strategy, is to totally reconsider the taxonomy of the family in a more inclusionist way, motivated by later knowledge that many of the populations had a gene flow between them, and their ancestry could be polyform, and not follow a straight line, as earlier taxonomists belived was the case of the different populations evolution. An example of this strategy is presented below under Discussion
1. Identical numbers of chromosomes, and evidence of hybrids between Asian elephant and African elephant (with unknown fertility), as well as the recent evolutionary divergence of the two species, does not support the establishment of the separate genus Loxodonta, and the accepted scientific name for the African elephant should in my opinion therefore be returned to the original Elephas africanus, as Blumenbach proposed in 1797, during the very first naming of the species. I regard changes since then, as unvalid, especially the genus Loxodonta, which has by many been confirmed as unvalid, and likely with our present knowledge, should be regarded as nothing than a synonyme to Elephas, why by rule of priority, the African elephant automatically, becomes Elephas africanus again.
2. Likewise evidence of fertile hybrids between African bush elephant and African forest elephants, which have in range regions widely living intermediate populations, does also not support the establishment of the present two present separate species Loxodonta, and the accepted scientific name for the African forest elephant should in my opinion, also therefore be Elephas africanus, as above. I regard changes since then, as unvalid.
3. With the possible need of still naming Savanna elephants and Forest elephants as two forking subspecies, the names can be Elephas africanus cyclotis or Elephas africanus silvestris and for the Savanna elephant Elephas africanus africanus.
4. For the Asian elephant, with its troubled history of taxonomy, a return back to Blumenbachs 1797 suggested Elephas asiaticus which today describes the species well, is in my eyes the easiest, and I regard changes since Blumenbachs suggestion, as unvalid.
5. Regarding subspecies of Asian elephant, this seems to be a matter of different opinions. Lately, opinions has risen that especially the Borneo elephant should be more highlighted for its smaller size, unique anatomy, and possibly long time isolation from other populations. Apart from this, theres presently three valid subspecies within the present species Elephas maximus. If they are still considered valid, it seems the Borneo elephant should be classed as a fourth subspecies.
Personally, I find subspecies a tricky issue. It is easy to say, that geographical isolation, clear differences in anatomy, a certain climate adapatation, or with DNA see when a certain grop did split from other gruops may be indications. But where do they start become such an indication that they motivate a subspecies, and not? If Sumatra elephants should be considered subspecies, then how many populations in Africa are equally so unique? Should the desert elephant in Namibia also become a subspecies? Or the elephants in Etosha, who survive -15 degrees during 4-5 hours during the night? It seems different criteria has during time been used as criteria for subspecies, and lately even species conservation has been arguments as to wether a population is a species, or subspecies. Below I suggest subspecies, from a POV, where I think less taxonomists would argue against, after the possibility that genus Loxodonta officially becomes unvalid.
Suggested taxonomy tree for recent species within subfamily Elephantinae
- Probsocidea Illiger, 1811 (order; living)
- Elephantidae Gray, 1821 (family; living)
- Elephantinae Gray, 1821 (subfamily; living)
- Elephas Linnaeus, 1758 (genus; living)
- Elephas africanus Blumenbach, 1797 (species; living)
- Elephas africanus africanus - (subspecies; living)
- Elephas africanus cyclotis - (subspecies; living)
- Elephas asiaticus Blumenbach, 1797 (species; living)
- Elephas asiaticus borneensis - (subspecies; living)
- Elephas asiaticus indicus - (subspecies; living)
- Elephas asiaticus maximus - (subspecies; living)
- Elephas asiaticus sumatranus - (subspecies; living)
- Probsocidea Illiger, 1811 (order; living)
- Elephantidae Gray, 1821 (family; living)
- Elephantinae Gray, 1821 (subfamily; living)
- Elephas Linnaeus, 1758 (genus; living)
- "The elephant" Elephas maximus Linnaeus, 1758 (species; living)
Later research has turned upside down on many things we thought we knew about elephantidaes evolution and hybridization. Earlier it was though that The straight-tusked elephant (Paleoloxodon antiquus) was a close relative of Asian elephants, but later it has been proven by genetical analyze, that they were most closely related to African forest elephants, especially a population around the Congo Basin, which have far more genetical distance to the savanna elephant, than the The straight-tusked.Furthermore, analysis also reveals that many different elephant and mammoth species interbred in the past. (Callaway, 2016: Elephant history rewritten by ancient genomes)
What we dont know, is wether the African and the Asian elephant hybrid is fertile, but its probably possible, consider that all living elephants today have same number of chromosomes.. Lately, recent research indicate that hybridization was rather common in the past, with populations that we have either regarded as belonging to different species, or even different genus. Theres also a gap in knowledge regarding those different animals number of chromosomes. Furthermore, it may be argued that Linnaeus suggestion Elephas maximus for what he considered was "The elephant" is considered valid because we may later have overestimated differences between different elephantine forms, not motivating that we separate them as far as before.
was Linneus right, is there only one species of elephant?
It could be speculated, wether all present elephants, maybe even together with other populations which we have given different species (or even genus) names, actually should be viewd as a "ring species", which is connected through series of neighbouring populations, each of which can sexually interbreed with adjacent related populations, but for which there exist at least two "end" populations in the series, which are too distantly related to interbreed, though there is a potential gene flow between each "linked" population. We actually dont know yet about the gene flow between east and west, since we have a gap of recent populations between Africa and Asia. But we do know that the Syrian elephant (which went extinct not long ago) was almost as large as the present African, and may have interbred along a ring chain, with connection to both African and Asian populations. There may also be possibilities to get more DNA information from the extinct North African elephant that may add knowledge to the puzzle.
It is to hope, that more knowledge through DNA from the extinct elephants between present most western populations of recent Asian elephant, and most northern of Savanna and Forest elephants, respectively, as well as other populations, which we have regarded as other species or even belonging to other genus. New research here may spread more light regarding their exchange of genes, and means of evolution.
This would affect a larger number of populations, which before were considered more unique, than they in reality is. If future research indicate that the present living forms in reality had a larger gene flow between them, than we earlier knew, and did not develop through straight cladistic lines, but had genetical input from different populations during their evolution. This may indicate that what we have regarded as different species or even genus, need to be closer together, since they were much closer related, than we knew before.
Such a scenario would make a large number of different species and subspecies, unvalid, since they can not be motivated as unique anymore, and should be downgraded to subspecies of one species, The elephant, which in fact was what Linneus described in 1758.
A very alternative example of a future tree from an inclusionists point of view, but presently with an unlikely scenario, could be as follows:
Alternative taxonomy tree for recent species within subfamily Elephantinae
Dan Koehl, 2021-03-11.
This article is dedicated in the memory of Dr. Jeheskel Shoshani.