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

Abstract

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.