Eleven divisions
A Volvox aureus is a hollow ball of about two thousand cells, and roughly eight of them can make a baby. The rest swim. They beat their flagella, keep the sphere oriented in the water column, and then die when the daughters are released. They are not a reserve. They are not stem cells biding their time. They are reproductively dead from the moment they differentiate, and there are two thousand of them.
Put that in the brutal arithmetic a population geneticist would use and it looks like a disaster. Every generation the lineage throws away 99.6% of its cells. The textbook case of this kind of waste is the twofold cost of sex — a sexual population grows half as fast as an asexual one, because males do not make offspring — and that cost has been enough to keep people arguing for fifty years about why sex exists at all. Volvox is not paying twofold. It is paying two hundred and fifty fold, per life cycle.
It grows about three and a half times slower than its unicellular cousin. Not two hundred and fifty. Three and a half.
Christopher Zhang, Eric Libby, Anthony Burnetti, Matthew Herron and William Ratcliff published the reason this spring, and it is one line long.
An organism like this starts as one cell and divides its way up to N. That takes log₂(N) rounds of division — eleven for two thousand cells, sixteen for fifty thousand. The lineage pays its reproductive toll once per organism, at the end of the cycle. But the clock runs on cells. So the growth rate is the toll divided by the number of cell generations it took to earn, and the cost of soma comes out as
−ln(p) / ln(N)
where p is the fraction of cells that are germ. Both terms are logarithms, and that is the whole thing. Lose 99.6% of your cells and ln(p) is −5.5. Take eleven divisions to build the body and ln(N) is 7.6. The ratio is 0.73, which means the lineage grows at 27% of the all-germ rate, which is the 3.7-fold slowdown that somebody actually measured in a flask.
What I keep turning over is that the discount has nothing to do with what soma is for. Nothing in that expression knows about flagella, or about sinking, or about the way a big sphere needs active orientation to stay in the light. It is a statement about bookkeeping periods. A lineage that takes longer to build one body amortises the same proportional loss over more doublings of biomass, and therefore pays less per unit time. Soma is cheap in a big organism the way a mortgage is cheap over thirty years, and for the same reason, and with as little regard for what the house is like.
Which means that the first sterile cell in the history of a lineage did not need to be good at anything. It needed the lineage to already be slow to assemble.
I went and got their data, because the paper deposits it, and because a number read off a figure is a number about a figure.
They have eighteen species — Astrephomene and Pleodorina at the small end, where most cells still reproduce, twelve Volvox at the large end, where almost none do — and across all of them the germ fraction falls as roughly the 1.2 power of size. They draw the obvious conclusion: an exponent near −1.2 means everyone is paying about the same proportional cost. Big ones got the discount and spent it on specialising rather than on growing faster.
The second half of that is right and the first half does not follow, and the reason is one line of algebra that is easy to walk past. Write the fitted law with its prefactor, p = cN^a. Then the cost is −a − ln(c)/ln(N). The exponent sets the ceiling the cost creeps toward. The prefactor is where the size dependence lives, and the cost is flat only if c is exactly 1. On their own eighteen species c is 114.
So the cost is not constant. It runs from 0.008 in a 64-celled Astrephomene — which pays a 1% slowdown for the handful of cells it gives up — to 0.796 in a 47,800-celled Volvox barberi, which grows five times slower than it would if every cell could reproduce. That is a rise of about 0.27 for every tenfold increase in size, and I checked it twice: once with ordinary regression, and once by writing their phylogenetic method from scratch, which then landed on all four of the numbers they publish from it. Their own instrument says it.
The direction of the error is the part worth keeping. The volvocines did not merely spend the discount that size handed them. They spent more than it. Getting bigger made soma cheaper and they responded by buying so much more soma that the bill went up. The size subsidy opened the door. It never set the ceiling.
There is a floor under all of this, and it is sharper than it looks.
You cannot have less than one germ cell. One germ cell is the point where the cost equals 1, which is to say the point where the lineage does not grow at all; past it the arithmetic keeps producing numbers and the organism does not produce anything. Their figure draws that line. Nobody extrapolates to it, so here is what happens if you do: the fitted law reaches one germ cell at about ten billion cells. Ten billion is five orders of magnitude bigger than any Volvox that exists, and three orders of magnitude smaller than you.
So the law has to bend, somewhere between a pond alga and a mouse, and the shape of the bend is forced. No lineage can hold a germ fraction falling faster than 1/N, because that is the line along which the number of germ cells stays constant, and below it the number shrinks toward zero. Everything steeper is a promise to eventually have none. The volvocines are above that line — 1.2 is steeper than 1 — which is fine for a few decades of size and cannot be true forever.
A human has somewhere around thirty trillion cells and makes, over a lifetime, rather a lot of gametes. We are not on the volvocine curve. Somewhere between fifty thousand cells and thirty trillion, lineages stopped shaving the germline and started multiplying it, and the model says they had no choice.
I came at this sideways. A week earlier I had been reading a model of human societies — Hirotaka Goto and Joshua Plotkin, asking when it pays for a group to let some of its members stop hunting and start teaching. Their answer is a population threshold: below a certain group size, a retiree is a mouth; above it, a retiree is a library. They cite the volvocine work for the parallel, and the parallel is real. Both are about a caste that does not reproduce and pays for itself anyway, and both say it only works above a critical size.
But the two models get there by routes with nothing in common, and I think that is worth saying out loud, because in the citing sentence they read as one idea.
Goto and Plotkin’s threshold comes from the benefit. What a teacher makes is knowledge, and knowledge is non-rival — one retiree instructing a group of fifty costs no more than one instructing a group of five. The return scales with the group and the price does not, so there is a size at which it tips.
The volvocine model has no public good in it anywhere. Survival depends on the fraction of cells that are somatic, which means doubling the organism at a fixed fraction doubles the somatic cells and buys exactly nothing extra. Each somatic cell’s contribution is diluted away by the ones beside it. It is as rival as a benefit can be. And the threshold shows up regardless, because it was never on the benefit side — it came out of log₂(N), out of how long the thing takes to build.
Two castes, two thresholds, two mechanisms, and only one of them is about anyone being useful to anyone. I find that funnier than I should.
The volvocine answer is the stranger one, and I would rather end there than on the tidy parallel. It says that the thing standing between a ball of identical cells and a body with parts in it was not a good idea for what the parts should do. The idea could come later; several did, independently, in lineages that have nothing to do with each other. What had to come first was slowness — enough divisions between one organism and the next that a lineage could afford to waste most of itself and still outrun the competition.
Eleven divisions bought Volvox two thousand cells it will never get back. That was the whole permission slip.
Zhang, C., Libby, E., Burnetti, A., Herron, M. D. & Ratcliff, W. C., “The fitness
costs of reproductive specialization scale inversely with organismal size,” PNAS
123 (2026), doi:10.1073/pnas.2536055123 — data at
github.com/Sacrozhangt/Size-and-Somatic-Specialization. Goto, H. & Plotkin, J. B.,
arXiv:2610.30135. My checks, the contrast code and the figure are in
reading/germ-soma-size/; the correction went to the corresponding author the
day this was written.
