This is a slight departure, being a sort of review of (grumble about) a paper that appeared in Nature recently (Evidence for a limit to human lifespan) but is not at all related to weather or climate. It’s about how long people can live and the authors claim that their results “strongly suggest that the maximum lifespan of humans is fixed and subject to natural constraints”.

The reason I’m interested in it is that (a) that’s a really provocative title and (b) there seem to be a bunch of undocumented analysis choices which add up to a great deal of frustration for the reader. There are basic things in this paper that should have been justified or documented but weren’t. Nature is notorious for the forced brevity of its articles and the consequent hyper-compression of the methods section, but this paper is especially terse. Note, please, that this isn’t my area of expertise (even as I flatter myself as actually having any expertise to speak of) so take everything I say with an appropriate dose of scepticism. Correct me if you feel so moved.

First off, the authors are dealing with data that is very clearly heterogeneous. There are all sorts of things that affect human longevity and many other things that affect the accurate reporting of mortality. These aren’t mentioned in the analysis.

Is this a problem? Maybe*.



Figure 2: Reported age at death of supercentenarians. All data were collected from the IDL database (France, Japan, UK and US, 1968-2006). a. the yearly maximum reported age at death (MRAD). The lines represent the functions of linear regressions. b. The annual 1st to 5th highest reported ages at death (RAD). The dashed lines are estimates of the RAD using cubic smoothing splines. The red dots represent the MRAD. c. Annual average age at death of supercentenarians (110 years plus, n=534). The solid line is the estimate of the annual average age at death of supercentenarians, using a cubic smoothing spline.


Figure 2a (above) shows a regression analysis performed on data that represent the age of the oldest person who died in each year. Early versions of that database only recorded that information if the maximum age exceeded 109 years. The diagram shows data for 1968-2006 which is 39 years, but there are only 33 data points. This implies – but is not clearly stated – that the missing values were less than or equal to 109. I’m not a statistical expert, but there might be consequences to performing linear regressions on a data set where low values are systematically absent. This also affects how one should interpret Figure 1c, which shows the average age of “supercentenarians” i.e. people who died at 110 years of age or older.

Similar questions over the homogeneity of the data are raised when looking through the “Extended Data”. The first figure in the paper is based on data from France, which are used to illustrate a number of points. France is “a country with high-quality mortality data”. Results from other countries are said to be “similar”. Similar is subjective and even within the elastic boundaries of subjectivity, this might qualify as “pushing it”. Having shown us French data in Figure 1d, the authors say “A similar pattern was seen in 88% of the 41 countires in the database (Extended Data Fig. 5)”

My initial impression of Extended Data Fig 5. was that it was all over the place. The criterion for similarity is given in the caption of the Figure. The point of similarity was whether the data had a “plateau”. Data were considered to “plateau” if:

“the second half of the data had a negative slope; the first half of the data had a negative slope (as an increase in the second half would likely reflect a return to some equilibrium after being negatively perturbed); the first half of the data had a slope greater than that of the second half of the data; or the final 10% of the data had a slope less than that of the preceding 40%.”

It is left as an exercise for the reader to sketch out clearly-plateauless series that have a plateau by this definition.

The periods of time covered by the data sets from other countries are also quite different some go back to the 19th Century, others start in 1970. This isn’t clear from the Figures, because the captions are barely legible and it isn’t mentioned in the text.

Then there is the data analysis. Figure 2a (again) shows a plot of year on the x-axis and MRAD (Maximum Reported Age at Death) on the y-axis. The cloud of points has been split into two groups: 1968-1994 and 1995-2006. They have been helpfully rendered in contrasting yet harmonious colours and a line has been drawn through each of the two groups. The first line, covering 1968-1994 goes up (p=0.0007) and the second, from 1995-2006 goes down (p=0.27). There is no clear rationale for choosing 1994/1995 as the transition. The authors interpret this like so

These results indicate that although the MRAD increased until the 1990s, no further increases were observed after that time; human yearly MRAD has plateaued at 114.9 years.”

The downward slant of the line in the later period is probably influenced by two very high values near the start of the period. The earlier and higher of these is the death of Jeanne Calment in France at the record-setting age of 122 years. The authors repeat the analysis on a second database (which starts in the 1950s seems to be missing a chunk of data from the first half of the 1990s and continues to 2015, despite a caption that says 1972-2015) and starts the later period in the year of that all-time maximum, which will, again, skew the estimated line drawn through the later pack of data.

A second thing to note is that, the trend in a short period of data will nearly always be of low significance; short periods of data rarely provide good estimates of long-term trends particularly if all you are basing your analysis on is those trends. This lack of significance should not be taken to mean that the data are not rising or will not rise or cannot rise. All it means is that you’ve analysed too few data to achieve significance.

Third, what would happen if you stuck a line through all the data in one go from 1968 to 2006 and restored the missing values? My guess would be you’d see a “significant” upward trend through the entire period. I put “significant” in scare quotes because (a) it’s not clear how they calculated it (b) it’s not clear they did it right given the properties of the date and (c) trend significance doesn’t really mean that much anyway.

The rather superficial trend analysis does have a caveat. The authors note: “One potential confounder of our results is the fairly small number of reported MRAD cases, which could explain these results simply as fluctuations”. Leaving aside the fact that MRAD (annual Maximum Reported Age at Death) is by definition limited in number to one per year and that values like these which are culled from the very edge of the distribution are necessarily “fluctuations”, the analysis they use to unconfound this is rather weak.

Figure 2b shows smoothed series of the MRAD (maximum etc.) along with smoothed series of the SRAD (second-higest reported age at death), TRAD (third), FRAD etc. They find a similar pattern in each of these: rise, peak, fall. The question is whether this really provides additional evidence or whether it is simply what one would expect from any randomly distributed data. I suspect it is the latter.

If one repeatedly draws numbers from a random distribution (I tried normal and uniform distributions though there’s no reason to think that human age is distributed in those ways), and sorts them into order from lowest to highest then the series of 2nd highest numbers is correlated with the series of highest numbers. The 3rd highest is also correlated, but less so. In other words, the “pattern” shown in Figure 2b is consistent with a much less exciting hypothesis that this is just how distributions of random numbers behave when you do that to them.

Other questions arise when one thinks in detail about what must be done to perform the calculations shown in the figures. Figure 1c shows the rate of change of the logarithm of the number of survivors per 100,000 people since 1900 at different ages. Let that sink in for a while, then ask yourself what happens when there are no people per 100,000 at a particular time who reach a particular age. How many supercentenarians were there exactly in 1900 in Finland? What did they do in those cases? How does that affect their regression? It doesn’t say. If they exclude such values then their regressions are likely to be biased low particularly at those points in the distribution which are of most interest to the analysis. i.e. for ages over 100.

Aside from these questions about the data analysis, there’s also the question of how one translates the (mis)crunching of data into statements like

our data strongly suggest that the duration of human life is limited


Our results strongly suggest that the maximum lifespan of humans is fixed and subject to natural constraints


the observed trajectories in Fig 2 are compelling and our results strongly suggest that human lifespan has a natural limit.”

This is always the tricky bit of any analysis and it generally requires a good background knowledge in the field to provide the framework in which the new pieces of information from an analysis can be understood.

This I don’t have. I can, however, make some observations as the general scientific reader that letters and articles in Nature are pitched at.

First the conclusions strike me as essentially a description of the data, guided by summary statistics from the analysis then padded out with some discussion/speculation. No specific predictions are made and tested against new data. The discussion provides a particular gloss on what has happened dressed up to look like a prediction for what can happen and cannot happen. Second, it is not clear whether in such matters the past is any sure guide to the future. The analysis presented in this paper cannot rule out some improvement in medicine or technology that extends human life, although it sort of claims it can:

Although there is no scientific reason why such efforts could not be successful, the possibility is essentially constrained by the myriad of genetic variants that collectively determine species-specific lifespan.

Nowhere in this paper is any mention made of these myriad genetic variants. It’s a sciencey explanation that has no support from their analysis. (The longer I stare at their last sentence, the less meaningful it becomes)

So, in summary… I don’t believe the analysis presented is “evidence for a limit to human lifespan” at least not good evidence. Even on the far weaker claim that there have been plateaus in MRAD and survival gains, I have doubts. Too many details of the analysis are missing and the details that are there suggest a weak analysis.

* I learnt this rhetorical trick from Zootropolis. Highly recommended.