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Theoretically speaking, natural selection causes a decrease in genetic variance and because the environmental variance should remain unchanged, natural selection causes a decrease of heritability.

$$h_B = \frac{V_G}{V_P} = \frac{V_G}{V_G + V_E + \text{Cov}(V_G, V_E)}$$

To my understanding, $V_E$ is not expected to change in response to natural selection.

Question

  • Do empirical studies show any change in the environment variance $V_E$ in respond to natural selection? Does it really remain unchanged?

  • How does the $\text{Cov}(V_G, V_E)$ term changes in respond to natural selection (both empirically and theoretically)?

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