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Eusociality, particularly focusing on the presence of certain altruistic sterile organisms within the social set-up creates questions as to why would the process of natural selection have favoured the persistence of such genes especially in hymenopteric species. One explanation (provided probably by Hamilton) pertains to very similar genetic constitutions of females of such species (owing to haploid nature of males), which increases genetic similarity between the female members of the social group. Thus it would be more "beneficial" (i.e., favourable for the persistence of similar genetic builds) for a female worker to help the fellow siblings, to which it bears greater genetic similarity, than its own offspring to which it bears a lesser genetic similarity. This might in a deeper way explain altruism in case of hymenopterans where the male is a parthenogenetic haploid and the female is diploid.

But why would the sterile condition of the workers in case of almost all eusocial groups be favoured by natural selection on grounds that it improves the 'fitness' of the 'genetic build' of the workers and ultimately the sterile altruists benefit the persistence of its genetic traits? Moreover the altruistic nature of the haploid males also goes unexplained.

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In what way are the haploid males altruistic? In the eusocial insects that I know about (not many) they act only as drones i.e. sperm donors, making no contribution to the success of the colony. –  Alan Boyd Jul 10 '13 at 18:16
The female workers are altruists in the true sense. The drones, though not altruists by definition, follow or rather hold a social position wherein they take a part only in the societies' development through mating with the queen and do not improve their personal 'fitness' directly. Moreover, a number of drones might not even mate with the queen but still their presence has not been eliminated by natural selection. –  Satwik Pasani Jul 11 '13 at 1:33
I might be misunderstanding, but it seems as though "mating with the queen" is best possible thing you could do to improve 'fitness'! Remember, fitness is number of children, or grandchildren, or great-grandchildren, and in that sense while it applies to an individual, it doesn't manifest except through mating. –  Oreotrephes Jul 31 '13 at 7:01
A related post: biology.stackexchange.com/questions/13693/… –  hello_there_andy Dec 13 '13 at 15:09
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I hope I've interpreted your question properly... It's an interesting question, but I think it's important to remember that evolution doesn't act on the two sexes separately. Sterile males might evolve and be maintained simply because they're good for their sisters or mothers. Sometimes genes that are advantageous for one sex are linked with genes that are disadvantageous for the other sex, leading to maladaptative traits in one sex. And of course, individuals don't necessarily forego opportunities willingly. If subordinates that attempt to mate are killed by the dominant individuals, then that trait is not advantageous. They'd be better advised to be altruistic and help their relatives, rather than be selfish and be killed (thereby depriving their colony of a worker). This would lead to selection for sterility.

It's also worth noting that while haploidy makes it easier for kin selection to evolve by increasing relatedness, it's not crucial. It all depends on the relative costs and benefits.

In these eusocial situations, nothing really makes sense until you summed the fitness of the whole lineage, not just one caste or one sex or one individual.

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There are also a lot of systems where the "satellite/helper" males do just fine by sneaking in copulations when the dominants aren't looking. –  Oreotrephes Jul 31 '13 at 7:06
True, but I'm not aware of many examples of sneaking in properly eusocial species? –  atrichornis Jul 31 '13 at 7:14
Fair enough, but maybe that's just the terminology we use. There are, for instance, female cheater worker bees (they call them, I'm not joking, "anarchists") who decide to start reproducing on the sly. –  Oreotrephes Jul 31 '13 at 7:19
+1 for anarchists. I've heard of this - I believe they get very harshly punished if they're caught! –  atrichornis Jul 31 '13 at 8:50
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Group selection, in the extreme, yields eusociality due to the shared fate of the replicators in the group. In a multicellular sexual organism, this "shared fate" of the "group" is the shared prospect that all replicators (alleles) have for making it into the next generation via the meotic lottery that produces the gamete. Since they share this prospective fate they have an evolutionary incentive to cooperate in the construction of specialized cells that are, in effect, "sterile caste" members of the total "hive". Similarly, if it is possible to subject all members of a group of individuals to a shared fate through multiple generations -- they will tend to evolve highly cooperative social structures. However, one of the confusing aspects of the eusocial insect colonies is whether they evolved to be that way through shared fate of individual organisms, or some variant on the meotic lottery's shared fate of alleles. The answer appears to be, primarily, that it is a peculiar form of meotic lottery in which the genes of the parents have extended phenotypes in the children that, in essence, parasitically castrate the vast majority of the children to help rear more offspring for the parents -- in particular the queen. In this respect, one can view the evolution of eusociality in the social insects as a perverse form of individual selection where the genes of, say, the queen, cooperate in constructing not just the queen's body but, also, the entire hive. The sterile castes are simply extended phenotypes of the queen (and the drone with which she mates).

See "The Social Conquest of Earth" by E. O. Wilson for an in-depth treatment of eusociality and its evolution as set forth by Nowak et al in their recent paper "The Evolution of Eusociality". See also "The Extended Phenotype" by Richard Dawkins -- in particular the chapter "Host Phenotypes of Parasite Genes".

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