a, The solid black line shows the average observed death probabilities for the years 2012–2014 for ages 70–109. The dashed blue line shows the fit of the Gompertz model for ages 70–100. Using the estimated parameters of the Gompertz model, the death probabilities are projected for ages 101–109. The dashed red line shows the fit and projection of the logistic-type function used in the CoDe 2.0 model. b, The solid black line shows the changes in the average observed values of the death probabilities between successive ages. The dashed blue line shows that the Gompertz model projects an acceleration of the increase in the death probabilities. The dashed red line shows that the logistic-type model used in the CoDe 2.0 model describes the levelling off of the increase in the death probabilities at ages 90 and over. c, The solid line shows the logarithm of the observed death probabilities in 2014. The dashed line shows the fit of the CoDe 2.0 model if the slope parameter of the logistic model b would not change with age. d, The blue line shows the probability that at least one woman aged 115 will reach age 116, and the red line shows the probability that at least one woman will reach age 120. These probabilities depend on both the size of the population at risk and the level of death probabilities.