A VITALITY‐BASED MODEL RELATING STRESSORS AND ENVIRONMENTAL PROPERTIES TO ORGANISM SURVIVAL

A survivorship curve is shaped by the differential survivability of the or- ganisms 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 stress- ors. 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 stress- ors, 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 envi- ronment; by characterizing how stressors alter the vitality probability distribution, it can quantify the degree to which a stressor differentiates members of a population.

[1]  J. H Pollard,et al.  Mathematical Models for the Growth of Human Populations , 1973 .

[2]  T. Witten,et al.  Multiphasic models of survival: Analysis of mortality rate change regions and the issue of finite species lifespan , 1997, Experimental Gerontology.

[3]  R. Hosono,et al.  Life span of the wild and mutant nematode Caenorhabditis elegans Effects of Sex, Sterilization, and Temperature , 1982, Experimental Gerontology.

[4]  N. Goel,et al.  Stochastic models in biology , 1975 .

[5]  J. Schnute,et al.  Assessing Juvenile Salmonid Response to Gas Supersaturation Using a General Multivariate Dose–Response Model , 1986 .

[6]  J. Leroy Folks,et al.  The Inverse Gaussian Distribution , 1989 .

[7]  D. R. Jones,et al.  7 - The Respiratory and Circulatory Systems During Exercise , 1978 .

[8]  G. Branch.  Intraspecific Competition in Petella cochlear Born , 1975 .

[9]  W. Calder.  The relationship of the Gompertz constant and maximum potential lifespan to body mass , 1982, Experimental Gerontology.

[10]  P. H. Leslie.  The mortality, fertility and rate of natural increase of the vole(Microtus agrestis), as observed in the laboratory. , 1940 .

[11]  James J. Anderson.  A Vitality-Based Stochastic Model for Organism Survival , 1992 .

[12]  C. J. Leeuwen,et al.  Aquatic toxicological aspects of dithiocarbamates and related compounds. III. Embryolarval studies with rainbow trout (Salmo gairdneri) , 1986 .

[13]  A. Łomnicki.  Population ecology of individuals. , 1988, Monographs in population biology.

[14]  Benjamin Gompertz,et al.  XXIV. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. F. R. S. &c , 1825, Philosophical Transactions of the Royal Society of London.

[15]  N. Ishii,et al.  Properties of a strain of free-living nematode, Rhabditidae sp.: Life cycle and age-related mortality , 1978, Experimental Gerontology.

[16]  E. Garside,et al.  Lethal effects of vanadium to two life stages of brook trout Salvelinus fontinalis (Mitchill) , 1987 .

[17]  G. Hutchinson,et al.  An Introduction to Population Ecology , 1978 .

[18]  D. Martinez,et al.  Mortality Patterns Suggest Lack of Senescence in Hydra , 1998, Experimental Gerontology.

[19]  Earl M. Dawley,et al.  EFFECTS OF VARIOUS CONCENTRATIONS OF DISSOLVED ATMOSPHERIC GAS ON JUVENILE CHINOOK SALMON AND STEELHEAD TROUT , 1975 .

[20]  B. Gompertz,et al.  On the Nature of the Function Expressive of the Law of Human Mortality , 1825 .

[21]  P. Frank,et al.  Vital Statistics of Laboratory Cultures of Daphnia pulex DeGeer as Related to Density , 1957, Physiological Zoology.

[22]  Granino A. Korn,et al.  Mathematical handbook for scientists and engineers , 1961 .

[23]  T. Crovello,et al.  EVOLUTIONARY STRATEGIES IN LIFE TABLE CHARACTERISTICS AMONG FERAL AND URBAN STRAINS OF AEDES AEGYPTI (L.) , 1972, Evolution; international journal of organic evolution.

[24]  G. Caughley.  Mortality Patterns in Mammals , 1966 .

[25]  A. M. de Roos,et al.  The role of physiologically structured population models within a general individual-based modelling perspective , 1992 .

[26]  C. Dye.  Population ecology of individuals (monographs in population biology 25): by Adam Łomnicki, Princeton University Press, 1988. £25.20 hbk, £7 90 pbk (x+223 pages) ISBN 0 691 08462 9 , 1988 .

[27]  C. R. Taylor,et al.  Design of the mammalian respiratory system. I. Problem and strategy. , 1981, Respiration physiology.

[28]  W. T. Edmondson.  Ecological Studies of Sessile Rotatoria, Part II: Dynamics of Populations and Social Structures , 1945 .

[29]  C. W. Gardiner,et al.  Handbook of stochastic methods - for physics, chemistry and the natural sciences, Second Edition , 1986, Springer series in synergetics.

[30]  C. Verdone-Smith,et al.  The effect of temperature and of dietary restriction on lifespan and reproduction in the rotifer Asplanchna brightwelli , 1982, Experimental Gerontology.

[31]  G. Sacher.  Evolution of Longevity and Survival Characteristics in Mammals , 1978 .

[32]  J. David,et al.  Reduction of longevity in Drosophila by chronic ingestion of a bacterial toxin , 1970 .

[33]  W. Calder.  Size, Function, and Life History , 1988 .

[34]  G. M. Hughes.  1 General Anatomy of the Gills , 1984 .

[35]  J. Klein,et al.  Survival Analysis: Techniques for Censored and Truncated Data , 1997 .

[36]  J. Harper,et al.  Studies on plant demography Ranunculus repens L., R. bulbosus L. and R. acris L. I. Population flux and survivorship , 1973 .

[37]  G. H. Heinz,et al.  Lethal and behavioral effects of chlordimeform in bobwhite. , 1985, Toxicology.

[38]  W. Calder,et al.  An allometric approach to population cycles of mammals , 1983 .

[39]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .