The study of post-reproductive lifespan has been of interest primarily with regard to the extended post-menopausal lifespan seen in humans. This unusual feature of human demography has been hypothesized to have evolved because of the “grandmother” effect, or the contributions that post-reproductive females make to the fitness of their children and grandchildren. While some correlative analyses of human populations support this hypothesis, few formal, experimental studies have addressed the evolution of post-reproductive lifespan. As part of an ongoing study of life history evolution in guppies, we compared lifespans of individual guppies derived from populations that differ in their extrinsic mortality rates. Some of these populations co-occur with predators that increase mortality rate, whereas other nearby populations above barrier waterfalls are relatively free from predation. Theory predicts that such differences in extrinsic mortality will select for differences in the age at maturity, allocation of resources to reproduction, and patterns of senescence, including reproductive declines. As part of our evaluation of these predictions, we quantified differences among populations in post-reproductive lifespan. We present here the first formal, comparative study of the evolution of post-reproductive lifespan as a component of the evolution of the entire life history.Guppies that evolved with predators and that experienced high extrinsic mortality mature at an earlier age but also have longer lifespans. We divided the lifespan into three non-overlapping components: birth to age at first reproduction, age at first reproduction to age at last reproduction (reproductive lifespan), and age at last reproduction to age at death (post-reproductive lifespan). Guppies from high-predation environments live longer because they have a longer reproductive lifespan, which is the component of the life history that can make a direct contribution to individual fitness. We found no differences among populations in post-reproductive lifespan, which is as predicted since there can be no contribution of this segment of the life history to an individual's fitness.Prior work on the evolution of post-reproductive lifespan has been dominated by speculation and correlative analyses. We show here that this component of the life history is accessible to formal study as part of experiments that quantify the different segments of an individual's life history. Populations of guppies subject to different mortality pressures from predation evolved differences in total lifespan, but not in post-reproductive lifespan. Rather than showing the direct effects of selection characterizing other life-history traits, post-reproductive lifespan in these fish appears to be a random add-on at the end of the life history. These findings support the hypothesis that differences in lifespan evolving in response to selection are confined to the reproductive lifespan, or those segments of the life history that make a direct contribution to fitness. We also show, f...

Membrane inflation tests were performed on fresh, intact human corneas using a fiber optic displacement probe to measure the apical displacements. Finite element models of each test were used to identify the material properties for four different constitutive laws commonly used to model corneal refractive surgery. Finite element models of radial keratotomy using the different best-fit constitutive laws were then compared. The results suggest that the nonlinearity in the response of the cornea is material rather than geometric, and that material nonlinearity is important for modeling refractive surgery. It was also found that linear transverse isotropy is incapable of representing the anisotropy that has been experimentally measured by others, and that a hyperelastic law is not suitable for modeling the stiffening response of the cornea.

No abstract