In the evolutionary biology of aging, a simple picture long held sway: after sexual maturity, mortality rises and fertility falls. But data from recent decades show that in many species with unlimited growth, such as the Greenland shark or the ocean quahog Arctica islandica, mortality can fall with age while fertility rises. This phenomenon is called negative senescence. Classic models, including the disposable soma theory, focus on explaining aging itself and barely consider the conditions under which life-history traits improve with age. The work sits off to the side: nearby in the archive are studies of tumor genealogy, aging as loss of regulation, and cellular methylation landscapes, but there are almost no direct neighbors on the topic. It fills the gap between theories of growth and theories of aging, which until now have developed separately.
The authors build a mathematical life-cycle model in which an individual at every moment distributes energy among three budget lines: reproduction, body growth, and repair of accumulated damage. Damage accumulates over time and raises mortality, while body growth, by contrast, lowers it. The evolutionary fate of a strategy is determined through analysis of invasion by a rare mutant into a population of residents: if the mutant cannot displace the resident, the resident's strategy is considered unbeatable. To find the optimal energy allocation, they use Pontryagin's maximum principle, and numerical solutions are obtained with the GPOPS-II package. The key parameter of the model is the shape of the return curves on investment: linear returns mean that each additional unit of energy yields the same gain, while diminishing returns mean that the gain slows down.
The model reproduces two contrasting scenarios. If returns on investment in growth and reproduction are linear, the individual first puts everything into growth, then switches to reproduction after maturity. Mortality in this case has a U-shape with a minimum at maturity, which corresponds to classic aging. If, however, returns on investment in growth or reproduction diminish, evolution picks a strategy of unlimited growth: the individual keeps growing after maturity, and mortality first falls with age. This period of negative senescence arises because growth lowers mortality faster than the accumulation of damage raises it. Diminishing returns on reproduction prolong the period of negative senescence by keeping investment in growth at a high level. Body repair appears in the optimal strategy only if its returns diminish, or if returns on growth and reproduction diminish at the same time. In the numerical examples, mortality during the period of negative senescence falls by roughly 20–30% from its maximum value.
The work shows that negative senescence is not an exotic exception but arises naturally from the evolutionary trade-off between growth, reproduction, and body repair. Unlike neighboring studies that treat aging as loss of regulation or accumulation of epigenetic errors, this model puts the energy budget and the shape of the return curves front and center. It links two previously disconnected phenomena: unlimited growth and improvement of life-history traits with age. The main difference from the classic disposable soma theory is that body repair here is not the only way to fight aging: growth itself can lower mortality if larger individuals have an advantage.
The model can be extended to sexual reproduction and to differences in energy allocation between the sexes. Another direction is to account for seasonality and environmental variability, which affect optimal growth. It would also be interesting to check how the predictions change if mortality depends not only on size but also on growth rate. In the long run, the model could be parameterized with data from long-term observations of specific species with unlimited growth, in order to predict the shape of mortality curves quantitatively.
The results matter for the evolutionary biology of aging, demography, and comparative life-history biology. They provide a theoretical basis for interpreting data on species with negative senescence and for finding new such species.
The immediate step is to gather data on the shape of the return curves on investment in growth and reproduction in species with unlimited growth. Then one can test whether species with more pronounced diminishing returns really do show a longer period of negative senescence.
The work is directly tied to an unsolved problem in evolutionary biology: why some species age and others do not. It proposes a mechanism that could explain the observed diversity of aging patterns in nature. What remains open is how universal the link between the shape of the return curves and the type of aging is beyond the conditions considered in the model.
The Greenland shark can live more than 400 years, and its mortality apparently does not rise with age. The model predicts that in such species, returns on investment in growth or reproduction should diminish more strongly than in species with classic aging.
Not published on arXiv. Here are its page, the PDF and the formalization: you can check it yourself, not only read our account.