A Vitality-Based Model Relating Stressors and Environmental Properties to Organism Survival

Abstract

A survivorship curve is shaped by the differential survivability of the organisms within the population, and a change in a survivorship curve with a stressor reflects the differential response of the organisms to the stressor. Quantifying this linkage in a simple, rigorous way is valuable for characterizing the response of populations to stressors and ultimately for understanding the evolutionary selection of individuals exposed to stressors. To quantify this stressor–individual–population linkage with as few parameters as possible, I present a simple mechanistic model describing organism survival in terms of age-dependent and age-independent mortality rates. The age-independent rate is represented by a Poisson process. For the age-dependent rate, a concept of vitality is defined, and mortality occurs when an organism's vitality is exhausted. The loss of vitality over age is represented by a continuous Brownian-motion process, the Weiner process; vitality-related mortality occurs when the random process reaches the boundary of zero vitality. The age at which vitality-related mortality occurs is represented by the Weiner-process probability distribution for first-arrival time. The basic model has three rate parameters: the rate of accidental mortality, the mean rate of vitality loss, and the variability in the rate of vitality loss. These rates are related to body mass, environmental conditions, and xenobiotic stressors, resulting in a model that characterizes intrinsic and extrinsic factors that control a population's survival and the distribution of vitality of its individuals. The model assumes that these factors contribute to the rate parameters additively and linearly. The model is evaluated with case studies across a range of species exposed to natural and xenobiotic stressors. The mean rate of vitality loss generally is the dominant factor in determining the shape of survival curves under optimal conditions. Xenobiotic stressors add to the mean rate in proportion to the strength of the stressor. The base, or intrinsic, vitality loss rate is proportional to the −1/3 power of adult body mass across a range of iteroparous species. The increase in vitality loss rate with a xenobiotic stressor can be a function of body mass according to the allometric relationship of the organism structures affected by the stressor. The model's applicability to dose–response studies is illustrated with case studies including natural stressors (temperature, feeding interval, and population density) and xenobiotic stressors (organic and inorganic toxicants). The model provides a way to extrapolate the impact of stressors measured in one environment to another environment; by characterizing how stressors alter the vitality probability distribution, it can quantify the degree to which a stressor differentiates members of a population.