UW Aquatic & Fishery Sciences Quantitative Seminar

Jim Anderson

UW Aquatic & Fishery Sciences, Columbia Basin Research

Linking growth, survival and heterogeneity through stochastic vitality

Abstract

Abstract: Juvenile growth is an important determinant of fish survival and population regulation. However, the mechanisms that link growth to mortality occur at the individual level, so models that treat survival as a population level process, i.e. through the hazard rate, cannot capture the underlying processes that link growth and death of the individual. To address this problem, we represent the relationship between individual growth and mortality in terms of vitality - a concept proposed three decades ago as a measure of the ability of cells to restore proper function. In its current form, vitality is an abstract measure of the survival capacity of organisms and its distribution within a population is characterized by a probability density function that evolves through a Wiener process characterized by a deterministic drift rate and a stochastic spread rate. In our formulation, growth rate determines the rates of drift and spread of vitality from a population's initial distribution and death is represented by absorption of vitality into a zero boundary. We quantify the effect of growth on vitality from a laboratory treatment/challenge study in which juvenile salmon, grown at different rates, were subjected to a lethal temperature challenge. We apply the treatment/challenge framework to a study showing juvenile salmon hatchery growth rate affects on their returns as adults and conclude that fish population survival has a sigmoidal response to juvenile growth. We propose that, in general, viewing the effect of early life history conditions on later life survival in a vitality based treatment/challenge context presents a rigorous framework in which to view the effects of intrinsic and extrinsic sources of heterogeneity on population survival. Additionally, we consider the sigmoidal response in the context of basic features of population dynamics including: the effects of juvenile growth and ocean conditions on salmon recruitment, the effect of growth on overwinter survival, the contributions of physiological factors and environmental variability to year-to-year population fluctuations, and the effects of intrinsic and extrinsic sources of heterogeneity on population extinction. We also consider a putative biological basis of vitality as an ensemble measure of physiological and ecological processes that determine fish survival. In summary, we suggest that vitality offers insights into how heterogeneous forces distinguish individuals that, in turn, shape the fate of populations.

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