title: How square is the survival curve of a given species?
abstract: An investigator-independent parameter, the prolate rectangularity index kappa for describing the so-called rectangularity of biological population survival curves, is introduced, developed, and applied to realworld survival datasets. This new rectangularity parameter is constructed using an intrinsic time scaling that places the intrinsic inflection point time at a value of unity so that species populations may be compared independently of their extrinsic life span distributions. The analytical expressions for the prolate rectangularity index of the theoretical Gompertz and Weibull continuous models are obtained, as are numerical values of this index for discrete experimental population survival data sets from two dissimilar species with orders of magnitude difference in extrinsic life span range. The values of the parameter are also compared for populations of a single species having differing dietary regimens, and for human demographic populations at decade intervals in extrinsic chronological time during the current century. It is found that scaling time, using the survival inflection point, appreciably collapses extrinsic survival profile dispersion among similar populations and allows a more meaningful comparison of profiles among dissimilar populations. Using this method of scaling, demographic populations within the United States are seen to have rectangularity parameter values that have been slowly drifting during this century toward values indicating a higher degree of rectangularity. In recent decades, however, the trend appears to be stabilizing with kappa values indicating no approach towards the theoretical maximum rectangularity. This apparent submaximal stabilization of kappa supports a hypothesis of no genetically pre-determined maximum life span in human populations. Or, if such a maximum exists, we are not currently near it.
authors.affiliation: University of Texas System, Department of Applications Research and Development, Balcones Research Center, Austin 78758-4497, USA.
authors.forename: T
authors.initials: T
authors.lastname: Eakin
authors.forename: M
authors.initials: M
authors.lastname: Witten
mesh_terms: D000818:Animals; D005544:Forecasting; D006801:Humans; D008954:Models, Biological; D011159:Population Surveillance; D016019:Survival Analysis; D013995:Time