In recent and somewhat successful human efforts at preservation and re-introduction to the wild of endangered species the issue of the necessity for gene diversity and the detriments from a lack of it are well documented. Wolves that share a closed gene pool tend toward diminished vitality and fertility after just a handful of generations. It is the same for birds, especially large birds of prey.  From my reading it seems to be generally accepted that a limited gene pool tends to weaken over a few generations and undermines species survival, even when environment is conducive to sustainability.

The urge to procreate and succeed in establishing successful progeny in highly competitive environments is well supported by the dominant male line breeding with grandmothers, mothers, and daughters; but NOT with sisters. So, if taking nature as a success role model for a breeding  program makes sense one should select the best dominant males and line breed them while strictly segregating ALL its sons and brothers onto separate Families (or "lines" as often referred). And a critical, in nature and in our aviary, transition is the decisive REPLACEMENT of that dominant patriarch with the NEXT patriarch. In nature it may be a vigorous SON or an unrelated newcomer. But either way it is a superb, and often superior, individual who achieves it.  And generally holds the position for a few breeding seasons.  When it is a SON then mating to a sister may/does occur but this is not oft repeated.

I subscribe to this approach because it makes sense and because nature shows us that historically it works quite well.

It is then a method that has certain key points:

1. As said, critical selection of the most superior male patriarchs
   
2. Choosing carefully the females that excel in desired qualities
   

As you may think from the above viewpoints I disagree strongly with   breeding by heavy use of Fostering, overuse of antibiotics, and man made nesting, etc. All these lead to flocks that can not sustain  themselves when the bird keeper is absent!

I endorse frequent "testing", by taking a sampling of a Family (Line) and placing them in a competitive minimalist flight and seeing how well they perform, survive, and procreate. If it is a successful, vital family they do quite well, and you can "Harvest" some nice birds, if it isn't you know it fairly quickly. By minimal I mean adequate, diverse, food & water but NO supplements, medicines, or man(ual) interference, and plenty of competition for that food, water, territory and nesting sites. (Finches, Sparrows, etc...)

IN summary, the Question is one that spans more than just ONE Pairing. It is one that includes THAT pairing and several previous and subsequent ones. And Conditions, Observations, and Decisions.

Hope you find this of interest, or at least NOT boring or long winded...
Cheers, Jaybird