Price Equation - Simple Price Equation

Simple Price Equation

When the characters z_i do not change from the parent to the child generation, the second term in the Price equation becomes zero resulting in a simplified version of the Price equation:

$w\,\Delta z = \operatorname{cov}\left(w_i,z_i\right)$

which can be restated as:

$\Delta z = \operatorname{cov}\left(v_i,z_i\right)$

where v_i is the fractional fitness: v_i= w_i/w. This simple Price equation can be proven using the definition in Equation (2) above. It makes this fundamental statement about evolution: "If a certain inheritable characteristic is correlated with an increase in fractional fitness, the average value of that characteristic in the child population will be increased over that in the parent population."

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