Complementary Gompertz Survival Models: Decreasing Alive Versus Increasing Dead

The survival patterns of many animals can be classified into one of two asymmetric sigmoid forms: One group can be predicted from the standard, classical Gompertz assumption that, with age, the number of individuals alive in the population decreases exponentially at an exponentially increasing rate. The other can be predicted from the alternative Gompertz assumption that, with age, the number of individuals that have died increases exponentially at an exponentially decreasing rate. The two models have similar mathematical forms, but the curves are not the same. In contrast to the standard, the alternative form has an early rapid fall and terminates in a gradual decay of the number of live individuals. It fits "non-Gompertzian" survival plots that are not predicted by the number-alive assumption. Analyses of published data show one or the other survival mode in various animal populations, depending on sex, genetic strain, nutrition, or activity.