My argument is that if this passage is read in the light of Aristotle's biological works, we can see that it suggests, in contrast to Plato, that natural right arises not from the cosmological order of the universe, but from the biological order of human nature.
Here's the passage (1134b18-35a5):
Of the political sort of justice, one kind is natural [physikon] and another is legal/conventional [nomikos]. What is naturally just has the same power [dunamis] everywhere, and is not affected by whether it seems so to people or not, but what is conventionally/legally just is something that at first makes no difference to to this way or some other way, but when people have established it, does make a difference, such as being released for a ransom of one mina, or sacrificing a goat but not two sheep, and also those things that people set down by law for particular situations, such as sacrificing to Brasidas, and things of the sort that are decided by a vote. And it seems to some people that all justice is of this sort, because what is by nature is unchangeable and has the same power everywhere, just as fire burns both here and among the Persians, while they see what is just being changed. But this is not the way it is, though it is so in a certain sense, and while among the gods, no doubt, nothing changes at all, among us there is something that is by nature even though everything is changeable; nevertheless, one kind of thing is by nature and another kind is not by nature.
What sort of thing, among the things that are capable of happening in different ways, is by nature, and what sort is not but is legal/conventional and by agreement, even if both are equally changeable, is clear. And the same distinction will fit other things, for the right hand is stronger by nature, and yet it is possible for everyone to become ambidextrous. The things that are just by law/convention and expediency are like units of measure, for the measuring units for wine and grain are not equal everywhere, but where they are sold they are greater, and where they are bought they are less. Similarly, the things that are just not naturally but by human law/convention are not the same everywhere, since the kinds of regime are not the same either, but there is only one kind of regime that is by nature the best everywhere.
Notice that both natural justice and conventional justice are kinds of political justice. Since human beings are political animals by nature, human justice must be political justice. By contrast, much of what Plato seems to teach is that human justice must imitate some cosmic order of universal justice.
Notice also the contrast between the physical phenomenon of fire, which burns the same way in all human societies and the biological phenomenon of right-handedness, which is somewhat variable among human beings. In his biological writings, Aristotle observed that animals with bilateral symmetry manifested "sidedness" in their movements, favoring one side over the other. Human beings were by nature right-handed, and yet they could make themselves ambidextrous (497b30, 705b21). In the Laws (794d), Plato recommended that all children should be taught to be ambidextrous, because this would be advantageous for soldiers.
Beginning with Darwin, biological research has turned up evidence that right-handedness is a genetic propensity favored by human evolution. Much of this research is surveyed in Stanley Coren's The Left-Hander Syndrome: The Causes and Consequences of Left-Handedness (Vintage Books, 1993). Many animals show handedness--favoring one hand over the other. In all human societies throughout history, right-handers are probably roughly 90% of the population. So left-handedness is common, but it is always a trait of the minority. The human fossil record of tool-use suggests that these tools were used predominantly by right-handers. Historical evidence--such as human pictures over long periods of history--suggest the same right-hander dominance.
There is substantial evidence that right-handedness is a genetic propensity of the human species--a species-specific trait of human beings just like having two hands, two feet, and a visual system that perceives color. Although in recent years, there have been some reports of evidence that left-handedness is genetically determined, much research (such as Coren's) suggests that left-handedness is not genetically caused but rather a consequence of early developmental trauma--such as birth stress--that somehow alters the development of the brain towards left-handedness.
So this is an example of how our biological nature shows not natural necessities (like the burning of fire) but natural propensities that hold "for the most part" but not always. Moreover, it's also an example of how human learning--people forcing themselves to become ambidextrous--can counter the natural propensities.
This biological example points to how the natural biological desires of human beings support natural right as both universally true for human beings and yet always variable. So, for example, Aristotle stresses the natural desires for sexual mating, parental care, familial bonding, and friendship as supporting the virtues. And yet while these desires are natural propensities for most human beings, and thus constitute the generic goods of human life universally, there is great variation in these desires across individuals and societies.
This indicates that Strauss was wrong in his claim, in the Introduction to Natural Right and History, that Aristotelian natural right depended on a cosmic teleology of the universe that had been refuted by modern natural science. But this also indicates that Strauss was closer to the truth when he observed later in this book (94) that human nature could provide an immanent teleology for natural right: "However indifferent to moral distinctions the cosmic order may be thought to be, human nature, as distinguished from nature in general, may very well be the basis of such distinctions. . . . We must therefore distinguish between those human desires and inclinations which are natural and those which originate in convention."
This latter remark points to what I have defended as a Darwinian natural right rooted in the immanent teleology of evolved human nature.