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Here is some hypothetical input:

  1. I have a set of eggs.
  2. I hatch these eggs and get chicken from them. Say, 100 hen that can lay eggs.
  3. I have a hypothetical technology to track some parameters of each hen during their life - one of them is the moment a hen lays an egg.
  4. I collect the data and find out which hen laid the largest amount of eggs during her productive period. I mark this one as the most productive.
  5. I collect the eggs from the most productive hen in the generation.
  6. GOTO 1.

Now, if I repeat this loop of death and life, say for 20 generations, hatching only eggs from the most productive hen, will it make next generations more productive and with each iteration or is it an oversimplified picture I have?

By performing this mental experiment I want to figure out if I can use it as a clear predictable factor influencing productivity of future generations.

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In theory yes, so long as you maintain genetic variation within your flock of hens (e.g. by bringing in outsider males to prevent inherited diseases spreading), artificial selection will lead to a more productive flock.

However I don't think it would be predictable and not necessarily an improvement every generation, surely productivity would be influenced by lifespan? e.g. is it better to have a hen that lays 100 eggs/month for 24 months, or a hen that lays 120 eggs/month for 12 months? Not necessarily that important, but worth considering.

You would also want to keep more than one hen per generation, maybe 2 chick hens from each of the 3 most productive hens per generation, just in case you selected one that hadn't inherited the productivity traits.

I assume you've read about milk yields. And this looks like it covers the maths of heritability of egg production.

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