What does this equation mean?

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: $\operatorname{Var}(\mathrm{Sel}) = \sigma^2 \sum_i s_i^2 (z_i - \bar z)^2, \qquad N_e = \frac{1}{\mathrm{HHI}}$. Under the empirically common case where productivity dispersion does not systematically favor large or small firms, that variance collapses to a clean statement: the noise in the selection term scales with the Herfindahl-Hirschman concentration index, an antitrust yardstick every industrial economist already computes as the sum of squared market shares, and the index’s reciprocal is the economy’s effective population size in exactly Wright’s population-genetic sense — the size of an idealized equal-share population that would generate the same drift. A hundred equal firms and one firm with half the market plus two hundred sharing the rest can have the same headcount and wildly different $N_e$ .