  Fundamental mechanisms governing cell size control and homeostasis are still
poorly understood. The relationship between sizes at division and birth in
single cells is used as a metric to categorize the basis of size homeostasis
[1-3]. Cells dividing at a fixed size regardless of birth size (sizer) are
expected to show a division-birth slope of 0, whereas cells dividing after
growing for a fixed size increment (adder) have an expected slope of +1 [4].
These two theoretical values are, however, rarely experimentally observed. For
example, rod-shaped fission yeast $\it{Schizosaccharomyces}$ $\it{pombe}$
cells, which divide at a fixed surface area [5, 6], exhibit a division-birth
slope for cell lengths of 0.25$\pm$0.02, significantly different from the
expected sizer value of zero. Here we investigate possible reasons for this
discrepancy by developing a mathematical model of sizer control including the
relevant sources of variation. Our results support $\it{pure}$ sizer control
and show that deviation from zero slope is exaggerated by measurement of an
inappropriate geometrical quantity (e.g., length instead of area), combined
with cell-to-cell radius variability. The model predicts that mutants with
greater errors in size sensing or septum positioning paradoxically appear to
behave as better sizers. Furthermore, accounting for cell width variability, we
show that pure sizer control can in some circumstances reproduce the apparent
adder behaviour observed in $\it{E. coli}$. These findings demonstrate that
analysis of geometric variation can lead to new insights into cell size
control.
