In botany, apomixis was defined by Hans Winkler as replacement of the normal sexual reproduction by asexual reproduction, without fertilization.  Etymology of the word Apomixis is Greek for "away from" + "mixing". This definition notably does not mention meiosis. Thus "normal asexual reproduction" of plants, such as propagation from cuttings or leaves, has never been considered to be apomixis, but replacement of the seed by a plantlet or replacement of the flower by bulbils are types of apomixis. Apomictically produced offspring are genetically identical to the parent plant.

A) For evolution it is mandatory to add new characters to the existing organism then it becomes an evolved organisms and able to coup with the changing environment  which ultimately leadsto wards the formation of the new species.  for this entire process sexual reproduction is mandatory as in this process due to formation of the gametes new characters are added by crossing over process but in the apomixis it is not happen so it is said that it blocks the evolution.

B) It is also considered as the road blocks to the plant breeding as due to lack of the sexual reproduction introduction of the new characters in the gene traits is not possible.  so no hybrids or heterozygous plants are produced.  

Yes, indeed, apomixis has been seen as evolutionary non-promising, to say the least.

It was Darlington, far back in1939, who stated this for the first time (as far as I know). He was of the opinion that apomixis is...‘‘...an escape from sterility, but it is an escape in a blind alley of evolution.’’

See: Darlington CD. 1939. The evolution of genetic systems. Cambridge: Cambridge Univ. Press.

Among other authors, also Stebbins, in his classical contribution to biosystematics of plants was still of this opinion, see:  Stebbins (1950) Variation and evolution in plants. New York: Columbia Univ Press.

Hi Kawther,

the situation is a bit more complex than that – first, apomixis is often connected to hybridization (and polyploidy, in particular aneuploidy), as it is one way out of hybrid sterility. Incompatibility between the two "parental" genomes of a hybrid (or multiple genomes of a polyploid) sometimes leads to an inability to perform normal meiosis, so that reproduction without sex becomes the only way to reproduce at all. Especially for plants, hybridization and polyploidization may have been major drivers of evolution, although their overall importance is still controversial. 

Second, and this may also answer your question about breeding of apomictic plants, apomixis need not be obligatory and/or its prevalence not 100%. This means that even plants labelled as "apomictic" can occasionally produce normal egg cells and pollen and produce seeds sexually. However, the sometimes very low frequency with which this happens can be very frustrating for plant breeders: the most famous example may be Gregor Mendel, the "father of genetics" himself, trying for years to cross different (apomictic) Hieracium species with only very little success. I recently heard that the great effort of these experiments may even have contributed to the deterioration of his eyesight - I wish all breeders of tropical grasses a happier fate.

So, yes, apomixis has been considered an evolutionary dead-end, and may in some cases have been one. But the current opinion among plant evolutionary biologists is rather different - beside the "escape from sterility" and "partial apomixis" aspects I described above, there is also the third point that apomictic offspring may still acquire mutations and thus continue to evolve (rather similar to some bacteria or viruses). Among (not just) plant breeders, there is even a strong interest to create "artificial apomicts" by genetic engineering - to fix & propagate hybrid varieties that show some desired quality, e.g. hybrid vigor.

I hope this helps you somewhat, or at least gives some new ideas for your further search (good luck!). I'm afraid I can't help you with any specific tropical grass references, but about apomixis and plant breeding / artificial apomixis I can suggest articles by e.g. Anna Koltunow, Timothy Sharbel or Peter Van Dijk, and for a somewhat more modern ("post-Stebbins") view on the role of apomixis for evolution the book "Plant speciation" by Verne Grant (1981; he also wrote a historic appraisal of his own book in 2003, which may be interesting).

Cheers, Katja