ASK THE 4 QUESTIONS

Ask the 4 questions

Ask the 4 questions

Answer 1

The analysis of experimental lifespan data is fraught with statistical difficulties. The difficulties are multiplied when we examine mortality rates for the 'oldest old', when sample sizes have dwindled. Wang et al. (1998) have argued, for example, that inappropriate parametric estimators, combined with an inadequate treatment of data-censoring, led Brooks et al. (1994) to favor an unwarranted fixed-frailty interpretation of mortality deceleration in nematodes. (For an account of general biodemographic issues related to mortality deceleration, see ([Vaupel et al., 1998] and [Pletcher and Curtsinger, 1998])).

Drapeau et al. (2000) present the results of an experiment on Drosophila melanogaster, which, they claim, are inconsistent with the heterogeneity theory of mortality plateaus. A more nuanced analysis of the data, we contend, points in the opposite direction. Not only does this force us to reevaluate the conclusions of this experiment, it may serve as a paradigm for some pitfalls in survival-data analysis.

Answer 2

The authors aim to test the prediction that 'populations that are greatly differentiated for stress resistance should show great differences in their late-life mortality schedules,' without stating explicitly what those differences should be. There is, in any case, no single consensus 'heterogeneity model'—some mathematical treatments of heterogeneity models may be found in (Vaupel et al., 1998), (Vaupel et al., 1979), (Vaupel and Carey, 1993) and (Service et al., 2000). Since heterogeneity produces its plateau gradually and indirectly—and transiently, if the variation is only in the initial mortality, and is bounded—the definition of the plateau will inevitably be ambiguous.

Answer 3

Service et al. (2000), in a critique of this same work, has argued that reasonable versions of the heterogeneity model could produce plateaus that are fairly insensitive to selection. In a more extensive work Service (2000), the same author has shown that a population with Gaussian-form heterogeneity should see the plateau levels rise under selection for increased robustness. On the other hand, consider a population composed of just two strains, each with mortality rate k e0.05x, with one having k=10-4, the other k=10-6. The heterogeneity of k will produce a transient plateau, and it is easy to see that increasing the proportion of robust flies will lower the plateau. In other words, any change in plateau level, or no change at all, is still consistent with the heterogeneity explanation.

Even on the standard set by Drapeau et al. though, the heterogeneity theory acquits itself well. ...