In the accompanying Comment1, de Beer et al. question our finding of a limit to human lifespan2. However, we feel that their criticisms are based on misinterpretation of our results, unsubstantiated assumptions and extrapolation without support from real data. The authors claim out that our findings do not necessarily suggest that no one will survive beyond age 115 in the future. We agree, and that is why we made the distinction between the level at which yearly maximum reported age at death (MRAD) has plateaued (115 years) and the absolute maximum age beyond which it is unlikely anyone will live, which we estimated to be 125 years2. de Beer et al.1 calculated that by 2070, at least one person in Japan will live to age 118 when assuming no change in mortality, which does not contradict our model. They also present models in which ages 120 and 125 are reached owing to a decrease in mortality before age 100 and a decrease in mortality at all ages, respectively. However, we do not think that these latter two scenarios are plausible in light of the evidence.
The results of the authors are substantially based on an extrapolation of death probabilities from data up to age 109 to beyond age 110 using the CoDe 2.0 model (figure 1 in ref. 1). de Beer et al.1 argue that a logistic-type model (such as CoDe 2.0), which suggests little further increase in death probability with age beyond age 110 (red line), is more appropriate for this purpose than a Gompertz model, which suggests a substantial increase in death probability with ages beyond age 110 (blue line). However, the only actual data available do not reach further than age 109, during which time the predictions from the two models are practically on top of each other. It is only after age 109 that the models diverge. Since death probabilities display an accelerating increase before this point, it seems biologically implausible to conclude, in the absence of compelling evidence, that they would then asymptotically approach a value much less than 1. Extended data figure 1 of ref. 1 is a zoomed-in view of figure 1 (ref. 1), in which the two models begin to visibly diverge around age 105. Here, the actual data appear to lie somewhere in between the two models. Looking at the changes in death probabilities (extended data figure 2 of ref. 1), the actual data is still in between the two models, especially towards older ages. In addition, the data show several fluctuations not accounted for, including a sharp drop at the end, which could be construed as support for the CoDe 2.0 model, but which is more likely to be an artefact. Therefore, there is little reason to choose the CoDe 2.0 model over the Gompertz model when modelling mortality beyond age 110. In light of this, the evidence does not support the proposition of ref. 1 that maximum human lifespan will increase to 125 years.
de Beer, J., Bardoutsos, A. & Janssen, F. Maximum human lifespan may increase to 125 years. Nature 546, http://dx.doi.org/10.1038/nature22792 (2017)
Dong, X., Milholland, B. & Vijg, J. Evidence for a limit to human lifespan. Nature 538, 257–259 (2016)