A plausible account of the evolution of syntax is coming into view. I had almost despaired.
Most syntacticians (I believe) still hold the view that syntax must have come as an all or nothing package, a proposition I consider an evolutionary absurdity.
Second, even when it is discussed in evolutionary or biological contexts syntax is presented in syntactically formal terms that provides no clue as to how the formal operation can be translated into something important to natural selection.
Finally, I don’t believe syntax, as formally described, is much of a help to people when they are trying to figure out the best way to say something. I know that whenever I give editorial advice, I talk about a completely different set of issues from technical discussions about moving phrases, etc. The formal system is great for mechanical operations in which the machine has no awareness of what it is doing, but does not really address the experience of using language. If editing really worked best at the unconscious level, all these thoughts about helping the reader follow along should just get in the way. Instead, they help get it right.
At the same time, syntax is obviously important and has to be accounted for. “Syntax” was one of the original categories for posting on this blog, but I have long doubted that I would have much to report. Lately, however, things are looking more promising. I am especially encouraged by a paper, “Sex and Syntax” (here) by Ljiljana Progovac in the current Biolinguistics.
The paper begins with a technical discussion of “what differentiates constructions that allow Move from those that do not.” [p. 307] For example, the sentence Penguins eat fish can be transformed to a question—What do penguins eat?—by moving the word fish to the front and transforming it to what do. On the other hand, the correct way to transform Peter ate fish and tartar sauce into a question is to ask Peter ate fish and what? Why is there a Move operation in one sentence and not the other?
Among syntacticians, Progovac says, the standard approach to the problem is to assume that Move operations are normal, and to look for reasons why certain structures do not allow them. Progovac has flipped that reasoning around: saying that originally, nothing could be Moved, and then Move operations were allowed for certain structures. This explanation is fundamental to an evolutionary perspective, and is antithetical to the proposition that syntax is the result of some great leap forward in which the whole system appeared as the result of a single step.* Progovac is one of the very few linguists who has concentrated her study on identifying primitive examples of syntax and in the Biolinguistics paper she has assembled her observations into a picture of syntactical evolution (see: Fossilized Syntax; The Eternal Duality; A Protolinguistic Fossil).
Much of her work has been with “root small clauses” which are characterized by unconjugated verbs, undeclined nouns, and no Move operations within the clause. In her Biolinguistics paper, she looks at how clauses are organized and proposes that the first clause combinations were joined without conjunctions and without the ability to insert something into the clause. Examples of such holdover constructions include:
- Nothing ventured, nothing gained.
- Easy come, easy go.
- Monkey see, monkey do.
- Card laid, card played.
All of these statements have, to our ears, the sound of proverbial truth The absence of conjugations or subject/object distinction gives them a ring of eternity, but if remarks like this were routine at some time in human history they must have addressed more prosaic events—e.g., Jane come, Jane eat. This could mean: Jane came and ate; Come on over, Jane, and eat; Jane will come and eat; Jane has come and is eating. Some might object, therefore, that the speech is too ambiguous to serve, but Progovac says:
If language developed gradually, then it is to be expected that not all the grammatical tools that we use today to express logical relations with some precision were available in the previous stages of grammar. This should not have prevented our ancestors from speaking in however imprecise and underspecified ways. 
Saying the currently unsayable is one of the things language change is about.
Progovac argues that, thanks to gradual evolutionary development, grammars show “a range of constructions” that fall between making completely separate utterances and making full integrated expressions. She notes three stages for organizing clauses:
- Parataxis: Jane came. Jane ate.
- Coordination: Jane came and she ate.
- Subordination: Jane ate after she came.
Notice, by the way, that the full integration of the expression (i.e., stating the idea without relying on a conjunction) used a Move of the eating to the front of the sentence. Progovac argues, “Only the most integrated of constructions (subordination) allow Move across clause boundaries” 
This account does not automatically rule out the existence of an innate Universal Grammar. We might have evolved a special ability to create clauses, then added a neurological ability to link by conjunction, and finally added a new capacity to move clauses. My impression is that Progovac believes this process happened. I’m skeptical, leaning more towards James Hurford’s focus on pragmatics and cultural evolution, but whatever your opinion you had better be open to the possibility of being proved wrong by new data. More important is that we have a plausible series of intermediate steps for marking and combining words that make
- evolutionary sense (shows how to get from words to sentences),
- linguistic sense (explains the diversity of observable structures), and
- editorial sense (explains why reorganizing ideas commonly requires moving them about).
*Progovac quotes Berwick 1998: “there is no possibility of an ‘intermediate’ syntax between a noncombinatorial one and full natural language — one either has Merge in all its generative glory, or one has no combinatorial syntax at all”