Dialectical materialism appears to go all the way to the "bare metal" of reality: motion is a synthesis of quanta's dialectically opposed material properties of being "smeared in a wavefunction" and "observed as an eigenstate", but quantum mechanics is weird and obscure. Evolution is much more amenable to philosophical study.
The fundamental dialectic of evolution is the opposition of heritable variation and natural selection. Both of these dialectical elements are material: heritable variation is a physical, material, independently observable change in an organism's genotype, an eminently material substance (composed mostly of DNA). Natural selection is also a material process: physical properties of an organism's physical phenotype determine whether it will run faster or slower, have more or less acute vision and hearing, stronger or weaker teeth, etc. Furthermore, an individual organism's reproductive success is directly a material property: The organism has to physically reproduce to be reproductively successful.
Because heritable variation is uncorrelated with natural selection, these two elements are in true dialectical contradiction*. Heritable variation doesn't "care" whether it makes the organism more or less susceptible to adverse selection; selection doesn't "care" whether some heritable variation might be intrinsically good. (For example, it's intrinsically bad that human beings can't internally synthesize vitamin C — whether or not we can eat it, it would be better if we could synthesize it at need — but because our ancestors' diet was abundant in vitamin C, the loss of the ability wasn't selected against.)
*A dialectical contradiction is different from a logical contradiction. The use of the term "contradiction" is mostly historical — Marx's dialectic materialism springs from Hegel's dialectical idealism, where logical contradiction powered the synthesis, but also because while "contradiction" might be too strong the alternatives — conflict, opposition, etc. — seem too weak.It's instructive to consider Mendelian (established at conception) vs. Lamarkian (acquired during life) variation. It happens to be the case that terrestrial organisms exhibit Mendelian variation, but we might have exhibited Lamarkian variation. If so, there would have to be something uncorrelated with natural selection about how an organism acquired traits for there to be a true dialectical contradiction between Lamarkian variation and natural selection. If this contradiction didn't exist, if an organism deterministically and predictably acquired just those traits that improved its survival, we would not see the pattern of complex, emergent behavior in the long-term development of species.
There are also important dialectical relationships in biological evolution at more abstract levels. A fundamental dialectic is between predator and prey. Again, the elements are material: the predator must physically catch and eat the prey, or the prey must physically escape the predator. And the elements are in true dialectical contradiction: the predator wants to eat the prey, the prey does not want to be eaten. Yet another is the parasite-host dialectic, which often results in symbiosis.
An important consequence of evolution is that it's neither predictable nor random. In my most important quibble with canonical communist terminology, I assert that dialectical relationships and historical factors do not determine the synthesis, they constrain it. There are specific features, for example, that would make predators ineffective: lack of speed, poor vision, poor quality weapons (such as teeth and claws); we will never see a predator with a predominance of features that poorly afford predation in its usual environment. We can predict to some extent where evolution won't go, but we cannot predict where evolution will go, even retrospectively. If we took a snapshot of any historical evolutionary epoch, we could not predict with confidence much of how the contemporaneous species would change.
Indeed the parallels between dialectical materialism and biological evolution are so strong that the following bold conjecture suggests itself: all dialectical material relationships are fundamentally evolutionary: they consist of a dialectical relationship between some form of heritable variation uncorrelated with some form natural selection.