To the blowfly, horse dung makes a delightful, nourishing meal; to you, horse dung tastes like...well, like what it is -- plus, it might make you sick. In this way, value is species relative.
As I pointed out in my last post, though, such relativism about value encompasses properly moral value. I showed this by appeal to the imaginary alien species Homo atrox ("cruel man"), a species of human-like moral agents endowed with a morality incommensurable with our own in at least one respect: For atrox, exquisite cruelty to animals is a virtue. 
But the notion that a demarcation based on species membership can neatly and reliably cabin a "morality" (grounded, we must take it, on specific  hereditary traits) rests on a benighted essentialism about species categories. A genetic trait is "essential" to a species in the relevant sense only if it is immutably universal and particular to that species. And we've known for almost 150 years that that can't be. First, even if a selectable genetic trait is universal among members of a species class, a given, viable offspring -- by definition  a member of that species class -- could nonetheless be born without that trait.  And second, even if a selectable trait were particular to a species class, it could nonetheless be passed along to members that branch off and eventually become a distinct species class, so that the trait is no longer particular to the original class; of course the same trait could also develop independently in other species groups, either through convergent or parallel evolution.
Furthermore, species categories also have an inherent, sorites vagueness. To see this, consider that my mother and I are (again, by definition) of the same species, as were my mother and her mother (I'll call my mother's mother my "mother2"), my mother2 and mother3, my mother10 and mother11, my mother242 and mother243, and so on. In general,
Now, of course in extending my matrilineage back in time, we'll want to say that at some point we will have reached my last direct matrilineal ancestor who was a bona fide Homo sapiens. Let's stipulate that this ancestor is my mother10,000. But then by (S), above, my mother10,000 and my mother10,001 are of the same species. Thus (by the above-noted specific transitivity between parent and offspring), my mother10,001 must be Homo sapiens too. But then this contradicts our stipulation that my mother10,000 was the last Homo sapiens in the lineage. In sum, then, there can be no identifiable point at which one species gives way to another. Speciation "events" aren't discrete, momentary occurrences, but instead consist in gross shifts in gene frequencies that accrue over several generations and across (diachronically) overlapping sets of breeding populations.
The upshot of all this is that species categories can offer no stable conceptual ground upon which to situate a morality. At best, then, the claim that Homo sapiens has a distinctive, "universal" (species-wide) morality must be an empirical one. It is to that claim I'll turn in my next post.
1. My rhetorical choice here -- an appeal to an imaginary, human-like species, rather than to the proto-morality of bonobos, say, or dolphins -- was mostly to forestall objections that humans are the only ones with bona fide, full-blooded moral agency. I suspect that issue will ripen later on, but for now I want to leave it on the vine.
2. In this post, the term 'specific' pertains to species.
3. There are several alternative species concepts. To simplify things, I've adopted the biological species concept. I don't believe any arguments in this post turn on that choice.
4. Following this line of argument, it's easy to see how the trait could subsequently vanish from the species class altogether.