Steve Davis is worried about the theoretical foundations of evolution.  Fear not.  The cdesign proponentsists did not develop a real critique of evolutionary theory while you were sleeping.  Davis is worried that evolutionary theory is overly dependent on widespread, unremitting competition, but that such competition does not exist.  How is that foundation doing?

I always like to start by being pedantic, even in the shower.  Davis isn't really worrying about the theoretical foundation of evolution.  He is worrying about the theoretical foundation of natural selection.  The two are frequently confused, but they are not synonyms for each other.  Evolution was a widely observed phenomenon, not a theory, even before Darwin.  Today we define evolution in molecular terms as the change in allele frequencies in a population over time.   That definition describes an observation, not a mechanism.

The title On the Origin of Species by Means of Natural Selection (emphasis mine), makes it clear that Darwin proposed natural selection as a mechanism for evolution.  Darwin was not the first to propose a mechanism of evolution.  He (along with Wallace) was simply the first to propose one that didn't suck.  For some time, it was the only mechanism we had to explain the phenomenon.  In the modern evolutionary theory, selection is only one of four forces that drive evolution.  The other three, oft forgotten, forces are drift, mutation, and migration.  

Of course, it is perfectly legitimate to worry about the theoretical foundation of one of the mechanisms of evolution.  So, how is it doing?  Is it overly reliant on competition within species?  How prevalent is within species competition?

We could look for examples of competition and cooperation.   Davis discusses Dawkins' example of robins competing for territory (Holy Property Lines, Batman!) from The Selfish Gene.  Dawkins find this example compelling.   Others disagree:
This is simplistic to the point of silliness, for if robins repel all robins then the species dies out. But robin territoriality has been observed, so what’s it all about. Rather than being a battle for resources, I would suggest that it’s a battle for one resource only – potential sexual partners.
Now, Davis makes no secret of disliking Richard Dawkins, which is fair enough given that Dawkins makes some effort to be dislikable.  The reductio ad absurdum argument above may work for the debating society, but it does not accurately reflect the potential complexity of animal behavior.  This falsely represents a binary choice between constant, unrelenting competition or no competition.

The fact is that I can find anecdotes of within species competition (e.g., dolphins killing dolphins) or cooperation between species (e.g., groupers and giant moray eels in the Red Sea) easily and can interpret those anecdotes to support my preconceived notions.
The plural of anecdotes is not data.
    -Randy Pausch
In the robin example, the robins do not compete for every single resource in their niche.  They compete for a limited resource, sexual partners.  This example is consistent with both our current understanding of natural selection and Darwin's thinking on the subject..

The history of natural selection as an idea is filled with interesting stories and characters (ok, mostly Thomas Huxley on both counts).  Among those historical tidbits is the fact that we can identify and date Charles Darwin's flash of insight:
In October 1838, that is, fifteen months after I had begun my systematic inquiry, I happened to read for amusement Malthus on Population, and being well prepared to appreciate the struggle
for existence which everywhere goes on from long-continued observation of the habits of animals and plants, it at once struck me that under these circumstances favourable variations would tend to be preserved, and unfavourable ones to be destroyed. The results of this would be the formation of a new species. Here, then I had at last got a theory by which to work.
    - Charles Darwin, from his autobiography. (1876)              (http://www.ucmp.berkeley.edu/history/malthus.html)
The "struggle for existence which everywhere goes on" easily becomes the cliche "nature red in tooth and claw," where competition is the rule and cooperation should be rarer than a three-eyed fish.  Much as the "To be or not to be" speech is not the most important in Hamlet (the most important is the speech at the end of Act IV, Scene iv), the "struggle" line above is not the key line in this passage.  Darwin put in a qualifier, ". . .it at once struck me that under these circumstances. . ."  What were the circumstances that Malthus inspired Darwin to think about?  

Malthus had observed that many plants and animals produce far more offspring than can survive.  He was concerned that humans could suffer the same problem.  But, Malthus was not really worrying about competition.  His fundamental concern was that the human population would outstrip its ability to produce food.  Malthus was concerned with the effects of limited resources on humanity.

The theoretical foundation of natural selection is that some, but not all, resources will be limited.  Given the finite nature of the Earth, this seems a reasonable foundation.  Extreme forms of competition and cooperation are simply two possibilities in a spectrum of strategies for dealing with limited resources.

Instead of debating the plausibility of extreme strategies of competition and cooperation, let's start by thinking about the effect limited resources have on one's strategy.  Biological systems require resources to survive and reproduce.  Life, however, does not require infinite resources.  There is a minimum and, likewise, it is reasonable to assume that there is a maximum above which the continued acquisition of resources is no longer provides additional benefit.  In Davis' example of grazing animal herds:
For grazing animals, sharing of resources is their mode of operation. There could well be isolated instances of jostling for a particularly juicy bit of herbage, but such would be rare, certainly not typical. The cost in energy is just not worth the effort.
individuals are neither competing nor cooperating for grass.  Grass is not a limited resource in this case. 

Let's try a gedankenexperiment to understand competition and cooperation as strategies for dealing with limited resources.  Michael White of Adaptive Complexity fame and I sit back-to-back in the same lab (accordingly, all his good ideas are actually mine, and all my bad ideas are his).  On Fridays, a neighboring lab regularly fails to eat all the donuts at lab meeting (they shall remain nameless to save them this undying shame).  Assuming that Michael and I want to eat no more than one donut (a fallacious assumption, but work with me), one donut represents the maximum benefit we can receive from this resource.  If the neighboring lab leaves two or more donuts, then Michael and I can each derive maximum donut benefits in the absence both competition and cooperation.  Call this the benign neglect strategy (A).   You will recognize below and to the side the donut as a donut, the pasty-faced smiley as Michael, the  red-faced interloper, and the pleasant skin tones of myself.

If only one donut is left, the options become more complicated.  Michael and I could share the donut, each receiving half a donut benefit (B).  Alternatively, Michael and I could fight for the donut, in which case I would receive
maximum donut benefit (C); unless an interloping, third lab member swept in
while Michael and I engaged in Mortal Kombat to steal the donut, in which case I would receive no benefit (D).  If the donut gets stolen half the time Michael and I battle, then sharing becomes a more effective strategy than fighting. 

In this context, we can precisely define competition and cooperation.  Competition exists when one individual obtains a benefit to themselves (the donut), by denying benefit to another (Michael's beat down), usually at a cost to themselves (risk of a third party stealing the donut).  Cooperation is not the absence of competition.  Cooperation is when an individual allows another to obtain a benefit (half a donut) at some cost to themselves (half a donut).  The best strategy depends on the parameters of the environment, in this case third lab member frequency. 

This highly simplified example looked at only two choices.  In reality, I not only have the option to choose a 100% competitive strategy or a 100% competitive strategy, but I can choose to compete, cooperate, or neglect at any frequencies in between.  The effect that the circumstances have on the resulting strategy in scenarios similar to the one above have been explored extensively using the iterated Prisoner's Dilemma from game theory.   I believe it even finds its way into Dawkins' much-maligned Selfish Gene.

For a real life example, let's take a look at the most famous* natural selection research project around, namely the long-term observation of Darwin's finches on the Galapagos Islands by Peter and Rosemary Grant.  As it so happens, I had lunch with the Grants not too long ago and got to talk a bit about the details of their research program. 707-11.

The Grants observed dramatic changes in body size, beak size, and beak shape among the finch populations they studied.  Those results were highly dependent on the weather.  During periods with plenty of rain, the Grants observed minimal selection on beak shape, because food was not a limiting resource.  During droughts, they observed rapid evolution of beak shape as food became limited in quantity and diversity of size.  The finches move from benign neglect to competition, depending entirely on the parameters of their environment.

Like in our thought experiment, the results of a real world evolutionary process depends on the details of the dynamic environment of the individuals being studied.  Natural selection is not dependent on widespread competition.  Competition and cooperation are simply two of many possible strategies for dealing with the problem of limited resources.

I do, however, tend to agree with Michael Lynch that in discussions of evolution we are too reliant on adaptive explanations:
The vast majority of biologists engaged in evolutionary studies interpret virtually every aspect of biodiversity in adaptive terms. This narrow view of evolution has become untenable in light of recent observations from genomic sequencing and population-genetic theory. Numerous aspects of genomic architecture, gene structure, and developmental pathways are difficult to explain without invoking the nonadaptive forces of genetic drift and mutation.
This adaptionist focus, rooted in the tendency of researchers to systematically ignore the explanatory power of the three other forces of evolution, leads to an oversimplification of evolutionary theory's public face.  It is as if I tried to explain all of physics through gravity alone.  Indeed, the proposed lack of widespread competition poses a grave threat to the foundation this oversimplified impression of evolutionary theory.  The foundations of the real evolutionary theory?  They remain solid. 

Now, stop worrying.  It's bad for your blood pressure.

*Thanks to the wildly popular, much lauded, and apparently execrable, book The Beak of the Finch.