Editing Quantitative genetics (section)

===== Dispersion via σ<sup>2</sup><sub>p,q</sub>=====
Earlier this variance (σ <sup>2</sup><sub>p,q</sub><ref name="varpq"/>) was seen to be:-
<math display="block"> \begin{align} \sigma ^2_{p,q} & = p_g q_g \ / \ 2N \\ & = p_g q_g \left( \frac{1}{2N} \right) \\ & = p_g q_g \ f \\ & = p_g q_g \ \Delta f  \ \scriptstyle \text{when used in recursive equations} \end{align} </math>

With the extension over time, this is also the result of the ''first'' cycle, and so is <math display="inline"> \sigma^2_1 </math> (for brevity). At cycle 2, this variance is generated yet again—this time becoming the ''de novo'' variance (<math display="inline"> \Delta \sigma^2 </math>)—and accumulates to what was present already—the "carry-over" variance. The ''second'' cycle variance ('''<math display="inline"> \sigma^2_2 </math>''') is the weighted sum of these two components, the weights being <math display="inline"> 1 </math> for the ''de novo'' and  <math display="inline"> \left( 1 - \tfrac{1}{2N} \right) </math> = <math display="inline"> \left( 1 - \Delta f \right) </math> for the"carry-over". 
Thus, {{NumBlk|:| <math> \sigma^2_2 = \left( 1 \right) \ \Delta \sigma^2 + \left( 1- \Delta f \right) \sigma^2_1 </math>| {{EquationRef|1}}}}

The extension to generalize to any time ''t'', after considerable simplification, becomes:<ref name="Crow & Kimura"/>{{rp|328}}-  
{{NumBlk|:| <math> \sigma^2_t = p_g q_g \left[ 1 - \left( 1 - \Delta f \right)^t \right] </math>| {{EquationRef|2}}}}

Because it was this variation in allele frequencies that caused the "spreading apart" of the progenies' means (''dispersion''), the change in''' σ<sup>2</sup><sub>t</sub>''' over the generations indicates the change in the level of the ''dispersion''.