A new analysis suggests mouse and human development line up on a quarter-power curve

In Short. Researchers who study development in mice and rats need a reliable way to match rodent ages to human ones. A new, unreviewed analysis finds the best fit on a curve built from the fourth root of human age.

READ THE methods section of almost any mouse study and you will find the animals described by age. They are newborn, juvenile, adolescent or adult, and each label implies a human equivalent that a reader is expected to accept. Somebody had to decide which day of a mouse's life corresponds to which stage of a person's, and the choice matters for anyone who wants to apply the result to children. The rule for making that choice has been argued over for decades, and there is still no agreed formula for it.

A paper posted to bioRxiv, a server for research that has not yet been formally reviewed, on October 22nd proposes one. Its single author is Pablo Vázquez-Borsetti of the University of Buenos Aires and CONICET, Argentina's national research council. It has not been peer reviewed. He compared seven mathematical rules for converting human developmental age into mouse and rat age, and reports that one of them, built on the fourth root of human age, fits the data better than the logarithmic scales that researchers in the field have long relied on. The data come from a companion dataset preprint posted a week earlier by Eugenia Amici, Rafael Grimson and Dr Vázquez-Borsetti. That paper has not been peer reviewed either, and because it comes from the same group it cannot serve as an independent check on the first.

Counting the days

The matching starts with events that happen in both species. The eyes open, for example, or a particular group of brain cells is born. If such an event happens on a known day in a mouse and in a known week in a human, the two dates can be paired, and enough pairs together describe how the two timetables relate. Each such event is called a developmental milestone. The oldest large source of mouse milestones in the new dataset is a comparison published in 1954 by Otis and Brent, who recorded anatomical landmarks in mouse embryos studied under controlled conditions and set them beside published human data.

Ages in this work are counted from conception rather than from birth. A mouse and a person are born at very different stages of development, so counting from birth would compare animals at quite different stages of development. Researchers instead use days after fertilization, which starts the count for both species at the single fertilized cell.

The companion dataset gathers 783 records covering 371 unique milestones. Of those 371 milestones, 179 are shared only by humans and mice, 167 only by humans and rats, 9 only by rats and mice, and 16 by all three species. Of the 783 records, 687 (87.7%) came from previously published or externally curated sources, and the remaining 96 (12.3%) were compiled by the group for this study. Otis and Brent alone contributed 128 mouse records. The dataset's authors list this concentration among their limitations, noting that Otis and Brent used a single strain of mouse, which reduces natural variation in the data, and they advise checking whether analyses still hold when data from the most frequently cited sources are removed. They also stress a point that matters for anyone tempted by a single conversion factor. Ages cannot be translated between species as a direct equivalence, they write, because individual milestones are not perfectly aligned and the two timetables diverge more as development goes on. The dataset itself offers no single mouse-to-human ratio, and the authors argue that no fixed ratio holds across development.

Why simple scales fall short

If mice simply developed at a constant fraction of the human pace, a straight line would link the two sets of dates. They do not. Rodents pass quickly through the earliest stages, and the gap between the species widens later in development, so a plot of mouse age against human age bends. The usual remedy has been to take logarithms of the ages, which compresses large numbers more than small ones and often straightens such a curve. In earlier work on rats, published in 2024, Dr Vázquez-Borsetti's group found that logarithmic scales improved the fit but left a bend in the data. The new preprint reports the same problem in mice. Taking the logarithm of human age alone reduced the bend, and taking logarithms of both ages reduced it further, but neither removed it, particularly in early development, where most of the paired milestones sit.

The alternative he tested is a rule in which one quantity grows as a fixed power of another. Squaring and taking a square root are simple examples, and a fourth root is a power of one quarter. Such a rule is called a power law. Power laws have a long history in biology because body processes in animals of very different sizes often scale with size in a regular way. Larger animals use more energy overall but less per gram of body, and the timing of many biological processes stretches out with body size. The study of how traits change with body size is called allometry. Its best-known result, Kleiber's law, which the preprint cites, states that an animal's resting metabolic rate increases with body mass to the power of three quarters. Earlier researchers had proposed that lifespans and developmental timescales scale with body mass to roughly the one-quarter power, which gave the author a theoretical reason to try a fourth root.

Testing the curve

He fitted each of the seven candidate rules separately to the mouse data and the rat data, and judged them in two ways. The first was predictive. A good rule should predict data it has not seen, so each milestone was left out in turn, the rule was fitted to the others, and the fitted rule was asked to predict the missing one. This was repeated until every milestone had been left out once, and the rule with the smallest average prediction error ranked first. The procedure is called cross-validation. In mice, a quarter-power rule with an added constant had the smallest error of the seven. In rats, it came second, with an error 0.23% larger (3.1826 against 3.1752) than a power law whose exponent was fitted to the data rather than fixed in advance.

The second test asked whether any bend remained once human age had been transformed. A statistical check called a RESET test looks for leftover curvature that a straight-line fit fails to capture, and a low p-value signals that some curvature remains. For untransformed ages, for logarithms of human age and for logarithms of both ages, the test found significant curvature in both species, with p-values of 0.0007 or lower in mice and below 0.0001 in rats. With the fourth root of human age, it found no detectable bend in either species (mouse F = 0.90, p = 0.407, rat F = 1.83, p = 0.163). A result like that means the test could not detect a bend, which is weaker than proof that the relationship is a true straight line. The same tests found that the scatter of the data was uneven across ages under every transformation, which the analysis handled by weighting the data points.

The author is open that his choice of the fourth root was partly a judgment. He gives three reasons in the preprint. The exponent of one quarter is consistent with proposed scaling principles in biology, it needs one fewer parameter than the best rat model because the exponent is fixed rather than estimated, and fixing it made the combined mouse and rat model more stable. When the exponent was left open, the fitted values were 0.248 for rats and 0.310 for mice, and one quarter fell within the statistical uncertainty for both species. A rule built on the cube root, which some researchers favor in the long debate over how metabolism scales with size, never ranked first in either species.

The added constant

Every version of the model that worked needed an extra number added to the result. A pure power law with no constant fitted poorly, especially for the earliest milestones, and in every formulation the constant was statistically required. A pure power law implies that the two species keep the same proportional relationship from fertilization to the end of development, and the constant shows that the data do not behave that way.

Dr Vázquez-Borsetti offers an explanation drawn from evolutionary developmental biology. Every mammal begins as a single cell, and the events just after fertilization are much alike across species. As development continues, differences in growth and body size accumulate, so the species' timetables may start close together and then separate. On this reading the constant corrects for an early period in which mice and people develop in similar ways. He presents this as a hypothesis, and he also raises the possibility that the constant reflects some feature of development that has not yet been identified. The preprint contains no experiment designed to distinguish between the two explanations.

Beyond rodents

The Buenos Aires group is not the only one working on this question. The longest-running effort is Translating Time, an online resource that converts ages between humans and a range of laboratory and other animals. A 2025 review in Brain Research Bulletin by Christine Charvet, Alexandra de Sousa and Tatianna Vassilopoulos of Auburn University, a group with no authors in common with the Argentine papers, traces its history. It began when Finlay and Darlington, in 1995, estimated when different populations of nerve cells are born across many brain regions and used those dates to align ages across species. Later work led by Clancy and Finlay added other processes, including the formation of connections between nerve cells, cell death and the insulation of nerve fibers, and reached a total of 271 time points covering human ages up to 2 years and their equivalents in other species. Adding data on gene activity, anatomy and behavior later increased the dataset to 573 time points across humans and great apes.

The Auburn group also argues that the laboratory mouse has limits as a model for people. Mice were chosen because they develop quickly and breed easily in the laboratory, the review notes, but they do not naturally develop the protein plaques and tangles seen in the brains of people with Alzheimer's disease, and their short lives may not reproduce every stage of the human lifespan. A conversion rule, however well it fits, cannot fix those differences. It can only make the comparison of ages more consistent.

The quarter-power rule now needs the scrutiny that peer review and independent reanalysis provide. Its code and data are public, so other researchers can check whether the result survives when the 128 records from Otis and Brent are removed, and whether it holds for milestones gathered by other groups or for older animals. Until then, a reader of any mouse study that makes a claim about human age should look for three things in the methods: the day of the animal's life the experiment used, whether that age was counted from birth or from fertilization, and which conversion the authors relied on to pick a human equivalent. A human age attached to a mouse result is only as reliable as the conversion behind it, and the methods section should say which one was used.