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Introduction to Genomic Assisted Breeding, Breeder equation, :question: -…

- - - - Selection Differential [Within-generation change ]
        
        This is the shift you cause by choosing who gets to reproduce, before any offspring exist.
        
        You start with the full parental population and its trait distribution (mean = μₚ).
        
        You apply your selection criterion (e.g., "only the top-yielding 20% become parents").
        
        The subset you actually chose has a new, higher mean (μₛ).
        
        This entire change happens within one generation — nothing has been inherited yet. You've simply looked at a population that already exists and picked a biased subset of it.
        
        Think of it as measuring how good your selection decision was, purely as a snapshot comparison: "the parents I chose vs. the population I chose them from."
        
        S =µs−µp
      - Response to selection [Between-generation change ]
        
        This is the shift you actually see in the offspring, one full generation later — compared back to the original, unselected parental population (not compared to the selected parents).
        
        You wait a generation, let the selected parents reproduce, and measure the offspring's trait mean (μ₀).
        
        R = μ₀ − μₚ — again note this is against the original population mean, not μₛ.
        
        This is the number that actually matters to a breeder, because it's the part that transmits genetically and shows up as a lasting change in the population.
        
        R =µo−µp