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Published equation contexts

Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}

Why this formula appears here

Every one of those covariance terms is a realized statistic computed on one historical sample path, and molecular evolution learned the hard way not to trust such statistics without a baseline: Kimura’s neutral theory showed that most measured molecular substitution is drift, not selection, and the field has required a null model ever since before crediting any pattern to adaptation. Proposition 4 supplies the economic equivalent. Assume market shares move by pure noise, uncorrelated with productivity — no firm is being selected for or against — and the expected value of the measured selection term is exactly zero. Its variance is not zero, and it has a closed form: Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}.…

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Symbol i

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ii

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Published contexts (1)

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Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}

Equation 10 · Evolutionary Economics

Selection Accounting: The Price Equation Runs the Economy

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

Every one of those covariance terms is a realized statistic computed on one historical sample path, and molecular evolution learned the hard way not to trust such statistics without a baseline: Kimura’s neutral theory showed that most measured molecular substitution is drift, not selection, and the field has required a null model ever since before crediting any pattern to adaptation. Proposition 4 supplies the economic equivalent. Assume market shares move by pure noise, uncorrelated with productivity — no firm is being selected for or against — and the expected value of the measured selection term is exactly zero. Its variance is not zero, and it has a closed form: Var⁡(Sel)=σ2∑isi2(zi−zˉ)2,Ne=1HHI\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}.…

Meanings in this article

  • NeN_e: the same headcount and wildly different.
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