Mortality as a bivariate function of age and size in indeterminate growers

Abstract

Citation: Colchero, F., and R. Schaible. 2014. Mortality as a bivariate function of age and size in indeterminate growers.Ecosphere 5(12):161. http://dx.doi.org/10.1890/ES14-00306.1Abstract. Mortality in organisms that grow indefinitely, known as indeterminate growers, is thought to be driven primarily by size. However, a number of ageing mechanisms also act as functions of age. Thus, to explain mortality in these species, both size and age need to be explicitly modeled. Here we developed a model that treats age-and size-specific mortality as a bivariate process. This method facilitates the exploration of the underlying (unobserved) contributions of age and size to mortality. We show that, in theory, a population can show declining mortality with age and size while the underlying contribution of age, as a proxy for chronological deterioration, is of typical senescence; while a seemingly senescent population can have underlying age-related negative senescence, which is, however, overcome by negative underlying size effects (i.e., increasing size-specific mortality). We show how inference about these unobserved processes can be made using a simple Bayesian model, and how all of the mortality parameters are accurately retrieved. We then apply the methods to published datasets on water pythons and freshwater mussels and test different hypotheses regarding the effects of age and size on mortality. In both cases we found age-dependent senescent mortality, with size having only negligible effects. The methods we present here can help to improve the demographic models commonly applied to a vast number of species of commercial and conservation importance such as fish, trees or bivalves, among many other, for which both age and size are relevant. In addition, the application of these methods can help to shed light on the existence of processes such as negative senescence, and contribute to our understanding of the evolutionary mechanisms of senescence in species that do not fit the established theories.

Senescence is not inevitable

“…Researchers are now striving to broaden this view by assembling demographic data sets for diverse taxa across the plant and animal kingdoms (e.g. Salguero-Gómez et al 2014), developing measures to better quantify mortality trajectories (Baudisch 2011), and developing models that can examine the bivariate effect of age and size on mortality (Colchero and Schaible 2014). The biodemographic community is thus making great progress towards understanding the puzzle of senescence but significant challenges nevertheless remain: A crucial one is to resolve how best to deal with eusocial, clonal or modular species where we are unsure how to identify an “individual”, the standard unit of demography and where growth may sometimes be considered a form of reproduction (and vice versa ).…”

Evidence for reproductive senescence across ray-finned fishes: A review

“…This makes them candidates for negligible and negative senescence because large (and hence old) individuals are generally favored by natural selection (Bidder, 1932;Vaupel et al, 2004;Jones and Vaupel, 2017). This is because mortality (actuarial senescence) increases as a function of age but declines with body size (Caswell and Salguero-Gómez, 2013;Colchero and Schaible, 2014;Jones and Vaupel, 2017). In fact, body size explained variations in fish reproductive traits better than age in 75% of cases in our database.…”

Senescence: why and where selection gradients might not decline with age

“…Caswell & Salguero-Gómez [67] showed how within a stage, age-specific selection gradients can actually increase with age, a pattern that might commonly be found in plants [32]. Spanning across taxa, many stage-categorized species have the capacity to grow indefinitely [26,68]. Extremely common in plants [69], indeterminate growth is also found in insects [70], fish [71], reptiles [72] and corals [73].…”