I can kind of agree with the last part. I've gotten as low as 3 generations all made with the same male, who is likely already related to the first females somehow. After this, I've noticed my chicks more often than not don't make it. I got a good few batches this year, bit many more failed before they reached sexing.ageOn another note for knowing if your eggs are fertile, you may notice when you crack open an egg to eat, there is a white spot on the yolk. If this spot also has a white ring around it - like a bullseye, it was fertilized.
You can track your rooster's fertility this way as you eat your eggs. Also, if you incubate, you should always crack open early quitters and 'clears' - with the latter, you may find they were never fertile to begin with. If you're getting too many clears, your rooster may have too many hens, or be experiencing fertility issues.
If you are hatching into your flock, be mindful of your flock genetics. Ideally, you want a roo from a different source, or have sourced your birds from someone who has put in a fresh roo that season.
Chickens can safely be inbred for one generation without worrying about too many negative health effects. (Brother sister, mother son, or father daughter). After doing this for one generation though, it's time to get a new roo in to ensure your flock remains healthy and robust in the long run.