The Fathers rejected the theory of the transmigration of souls, ie the theory that the souls of fallen men could come back into animal bodies. To support the theory of evolution is to say that human souls were at one time dwelling in animal bodies. (Either this or we must say that at some point a human being, soul and body, was born from and raised by an animal and while Genesis may not be literal, I see absolutely no evidence anywhere in the Bible or Christian writings of any kind that say man was born from animals. What I see is that God made man and raised him and took care of him as his parent. )
Also, as far as I know, (and maybe those who know better can comment) it is taught that human souls are not considered to be created individually by God in the same way that Adam was. Rather, a child is begotten, soul and body together as the offspring of their parents' souls and bodies -- not just the body is the offspring of those parents. Otherwise God would have to breathe his breath into each new body that was formed. But rather we are told that we were all (as human persons, not just as bodies) contained within the first man and spawned from him. So if souls beget like souls, and we postulated that a human body was at some point in history born from an ape, one would then have the ridiculous problem of the soul of an ape existing in a human body. One can see then how important the integrity of each nature within itself is. God made each kind of soul compatible with and intimately connected to each type of body.
from City of God bk 12 ch 25
For whereas there is one form which is given from without to every bodily substance,- such as the form which is constructed by potters and smiths, and that class of artists who paint and fashion forms like the body of animals,- but another and internal form which is not itself constructed, but, as the efficient cause, produces not only the natural bodily forms, but even the life itself of the living creatures, and which proceeds from the secret and hidden choice of an intelligent and living nature,- let that first-mentioned form be attributed to every artificer, but this latter to one only, God,
. Whatever bodily or seminal causes, then, may be used for the production of things, either by the cooperation of angels, men, or the lower animals, or by sexual generation; and whatever power the desires and mental emotions of the mother have to produce in the tender and plastic fotus corresponding lineaments and colors; yet the natures themselves, which are thus variously affected, are the production of none but the most high God.
Augustine's point here, which is repeated elsewhere in the Patristic witness, is that it is this 'internal form' or 'inner essence' of things that makes them what they are, and it is this inner essence that produces both the bodily form and the type of life of any given creature, not the genetic material. Rather, the genetic material itself is a product of and takes its form from the inner essence.
As far as I understand it, this is what is meant when we speak of what makes each nature unique- this inner power/energy (undetectable by scientific instruments) giving form and unity to that nature. Considering the second part of the quote, I would say that variations in the genetic material would be considered a secondary cause that merely allows variation in the basic forms already determined, just as do other material and environmental factors.
The major contention between modern scientific theory and the Christian witness is what the efficient causes are. Modern evolutionary theory recognizes no efficient causes except the material ones. They don't believe in any other power. The Patristic writers not only teach God as the efficient cause of natures, but also recognize that this nature itself is a power that is, as Fr Raphael says above, cohesive and unifying.
It's a matter in both cases of working form observable phenomena. The scientists working from observation of the material world. The Christian spiritual teachers working from their observations of the spiritual world and it's interactions with the material. These spiritual observations then have become part of the Patristic tradition of how the world works. The Philokalia, St Maximos the Confessor, St Gregory of Palmas and many of the other writers in the Christian ascetic tradition mention these things.