The utility of mortality hazard rates in population analyses

Abstract Mortality is a key process in ecology and evolution, and much effort is spent on development and application of statistical and theoretical models involving mortality. Mortality takes place in continuous time, and a fundamental representation of mortality risks is the mortality hazard rate, which is the intensity of deadly events that an individual is exposed to at any point in time. In discrete-time population models, however, the mortality process is represented by survival or mortality probabilities, which are aggregate functions of the mortality hazard rates within given intervals. In this commentary, we argue that focussing on mortality hazard rates, also when using discrete-time models, aids the construction of biologically reasonable models and improves ecological inference. We discuss three topics in population ecology where hazard rates can be particularly useful for biological inference, but are nevertheless often not used: (i) modelling of covariate effects, (ii) modelling of multiple sources of mortality and competing risks, and (iii) elasticity analyses of population growth rate with respect to demographic parameters. To facilitate estimation of cause-specific mortality hazard rates, we provide extensions to the R package ‘marked’. Using mortality hazard rates sometimes makes it easier to formulate biologically reasonable models with more directly interpretable parameterizations and more explicit assumptions. In particular, interpretations about relative differences between mortality hazard rates, or effects of relative changes in mortality hazard rates on population growth (elasticities), are often more meaningful than interpretations involving relative differences in survival (or mortality) probabilities or odds. The concept of hazard rates is essential for understanding ecological and evolutionary processes and we give an intuitive explanation for this, using several examples. We provide some practical guidelines and suggestions for further methods developments.