Two different contributions to the intra-embryonic variance in the boundary position.

The total variance of the gap gene expression boundary position due to intra-embryonic fluctuations, , can be decomposed into two contributions: , the variance in time of the circumferential mean of , and , the time-average of the variance of along the circumference of the embryo. The sketch illustrates two extremal cases: If the boundary is very smooth along the circumference at any moment in time, concerted movements of the boundary will dominate the total variance, i.e. (left side). If, in contrast, the boundary is rough but its mean position does not fluctuate much in time, then (right side). Naturally, a combination of the two types of fluctuations is possible.