Natural Theology is the branch of theology concerned with deriving the nature and attributes of God from the facts of the natural universe, without the assistance of revelation. It must thus reconcile the (presumed) morality and goodness of God with many details of nature that appear to indicate amorality and cruelty.
Natural theology was quite popular among early scientists, who assumed that the orderly function of the natural world reflected, and indeed entailed, a divine moral order. The most famous example of such arguments is the "Watchmaker analogy" developed in William Paley's Natural Theology, or Evidences of the Existence and Attributes of the Deity collected from the Appearances of Nature (1802). Several decades later, this attempt was continued in a more systematic way by the eight Bridgewater Treatises (1833-1840), which took up such topics as the design of the human hand and the "function of digestion."
When it came time to move from design to moral purpose, however, natural theology ran into major problems. Nature, after all, is "red in tooth and claw," and the seemingly innocent often suffer gruesome ends. Natural theologians grappled with this problem in various ways. One was to say that individual instances of misery in the natural world were means to the greater good. William Buckland, author of one of the Bridgewater Treatises, wrote
The appointment of death by the agency of carnivora as the ordinary termination of animal existence, appears therefore in its main results to be a dispensation of benevolence; it deducts much from the aggregate amount of the pain of universal death; it abridges...the misery of disease, and accidental injuries, and lingering decay; and impose such salutary restraint upon excessive increase of numbers, that the supply of food maintains perpetually a due ratio to the demand. (from Gould op. cit.)
Thus, predation was "good" because of its final effect, a doctrine with obvious dangers.
The whole problem was created because Natural Theology assumed the morality of a good God is exemplified and supported by the workings of nature. This assumption creates a trap that it is difficult to evade. It is possible, as above, to say that morality is still upheld in the mass, though cruelty is manifest in individual cases. Another approach is selective -- gruesome examples where predators ate prey alive are extolled as examples of mother love on the part of the predator, or even the intelligent use of resources by the parasite. A third extrapolates from the racist assumption that "primitive" people suffer less to assume that animals can not suffer at all. None of these approaches proved satisfactory, and they backfired, producing arguments that the cruelty of the universe creates a natural morality in our rejection of such cruelty (Julian Huxley) or even that immoral, self-serving behavior is "natural" and thus "moral" (so-called "social Darwinism") because it results in the "survival of the fittest."
As Stephen Jay Gould points out, all these problems stem from the basic error of natural theology, the attempt to derive the nature of God and morality from the details of the natural world. Thus, what natural theology had to say about morality was that human morality is fully reflected in and supported by the natural order ordained by God, but this is no longer a convincing argument.