Was it : a) infants, interacting with their mothers; b) toddlers; c) children, playing with other children; d) adults; e) a select band of clever adults, sages, shamans, etc?
Possibly the making of language-like sounds spread among different members of a mixed family group and all of them contributed to the development. This might be more plausible than restriction of language development to a certain social group over several generations. I would expect children to be involved in any case (by learning through imitation).
You have described a likely scenario for the spread of language, but how did it start in the first place? By saying that children learn language by imitation, you assume that it was invented by adults. Or was it " invented" at all?
What I wanted to say is that even the most ancient steps of language evolution were carried by all members of a society. Before something arose which we call 'language' the use of sounds or a combination of gestures and sounds spread among members of a tribe and every new step towards a more sophisticated communication was again passed around to all members and not only to a well-defined social group. Perhaps were was a special group or a particular group activity - like group hunting - that gave the impulses. (But why not assume that signals passed between hunters or children or chieftains or wise old women during the day were shared with everyone else in the evening?)
I agree that language developed from a woman to her children. First language develops from a mother to her descendants. Another possibility is that there was an advanced foreign language female teacher :) who developed a language that she later taught to some people and kids and kids got better at it than her. I believe that it had to be a woman because women are definitely better negotiators than us males. If you disagree, just look at the world. What is happening in the Middle East, Colombia, and what have you? Aren't men basically sending other people to war? So language as a negotiating tool was developed by a woman to defend herself and her offspring against other preying creatures.
I agree with M. Buchwitz and I don't think that using the word "invented" would be appropriated in this context: language has certainly evolved from earlier forms of communication. There are theories about which was the driver to more advanced forms of communication, like the social complexity or the alarm calls hypothesis. There is a quite abundant literature about that question.
You might want to look into this recent review of the social complexity hypothesis: "Freeberg, Dunbar & Ord. 2012. Social complexity as a proximate and ultimate factor in communicative complexity."
This more general review would also be a good starter: "Fitch. 2005. The evolution of language: A comparative review"
But to answer your question more directly, I think, as M. Buchwitz, that you can't really attribute the language to a specific age or sex class. It's just a too great step in evolution to be specific to only one type of interaction.
"..language has certainly evolved from earlier forms of communication".
Would it not be best at this limited state of knowledge to keep all options open? I am not familiar with all the literature, but recall two examples of the formation of new languages, creoles started by toddlers (Bickerton), and sign language created by deaf children when boarding schools first started up (in Nicaragua?). I don't think these can be said to have evolved from earlier forms of communication. Are there any modern examples of languages created by adults? OK, Esperanto, but then that did not catch on.
Language is such a unique and unlikely facility that it does not seem likely that it started in gradual analog fashion in widely different contexts, any more than humans had multiple origins. As with the rest of biology, there may be some unsuspected digital and discrete origin. If we don't look for simple explanations, we will not find them.
I think the border between primate vocalizations and human language is too blurry to define a specific point of origin for the latter, even if a precise definition of "language" is formulated.
There is a well-researched, multidisciplinary, and fairly recent treatment of this problem that I can recommend:
Deacon, Terrence W., The symbolic species, the co-evolution of language and the brain, reprint, New York/London, W. W. Norton & Company, 1998.
Again, should we not be keeping all options open? Are we quite sure that primate vocalizations and human language lie on the same smooth continuum?
I have not read Deacon's book, but there is already a problem in the title. Did not the human brain increase in size for a very long period before language is believed to have initiated?
Anthony: I don't see any problem in the title. Deacon anticipates and addresses your question about brain size, especially in chapter 6. Check it out; I expect you'll be pleasantly surprised.
I hesitate to get off the subject here, but the symbolic thought inherent in the use of spoken language seems to be related to that of visual communication, which of course has left earlier and more abundant traces in the archaeological record. I won't say any more on that here, except that there are other threads on this site that discusses the earliest evidence of the use of certain mineral pigments, especially red ochre, by early Homo sapiens:
Here is another example of a new language, Light Warlpiri, being formed:
"The development of the language, Dr. O’Shannessy says, was a two-step process. It began with parents using baby talk with their children in a combination of the three languages. But then the children took that language as their native tongue by adding radical innovations to the syntax, especially in the use of verb structures, that are not present in any of the source languages".
It now looks as if toddlers or children are definitely the driving force in establishing new languages, and thus the most likely candidates for starting language off in the first place. Any role of infants is not yet clarified.