  Uncovering the mechanisms that control size, growth, and division rates of
systems reproducing through binary division means understanding basic
principles of their life cycle. Recent work has focused on how division rates
are regulated in bacteria and yeast, but this question has not yet been
addressed in more complex, multicellular organisms. We have acquired a unique
large-scale data set on the growth and asexual reproduction of two freshwater
planarian species, Dugesia japonica and Dugesia tigrina, which reproduce by
transverse fission and succeeding regeneration of head and tail pieces into new
planarians. We show that generation-dependent memory effects in planarian
reproduction need to be taken into account to accurately capture the
experimental data. To achieve this, we developed a new additive model that
mixes multiple size control strategies based on planarian size, growth, and
time between divisions. Our model quantifies the proportions of each strategy
in the mixed dynamics, revealing the ability of the two planarian species to
utilize different strategies in a coordinated manner for size control.
Additionally, we found that head and tail offspring of both species employ
different mechanisms to monitor and trigger their reproduction cycles. Thus, we
find a diversity of strategies not only between species but also between heads
and tails within species. Our additive model provides two advantages over
existing 2D models that fit a multivariable splitting rate function to the data
for size control: Firstly, it can be fit to relatively small data sets and can
thus be applied to systems where available data is limited. Secondly, it
enables new biological insights because it explicitly shows the contributions
of different size control strategies for each offspring type.
