In this paper we analyze survival data of populations of sterilized nematodes, Caenorhabditis elegans, exposed to heat shocks of different duration at the beginning of their adult lives. There are clear hormesis effects after short exposure to heat and clear debilitation effects after long exposure. Intermediate durations result in a mixture of these two effects. In this latter case, the survival curves for the control and experimental populations intersect. We show that observed effects may be explained by using a model of discrete heterogeneity. According to this model, each population of worms in the experiment is a mixture of subcohorts of frail, normal, and robust individuals; exposure to heat changes the initial proportion of worms in the subcohorts (heterogeneity distribution); and these changes depend on the duration of exposure. In other words, exposure to heat does not influence mortality rates (survival functions) in the subcohorts but does cause individuals to move from one subcohort to another. In a biological interpretation of this finding we hypothesize that, when coping with stress, the organisms of worms use several lines of defense. Switching these lines on and off in response to stress in individual organisms generates the spectrum of observed survival effects at the population level. We discuss possible molecular biological mechanisms of stress response and directions for further research.
BackgroundVectorial capacity and the basic reproductive number (R0) have been instrumental in structuring thinking about vector-borne pathogen transmission and how best to prevent the diseases they cause. One of the more important simplifying assumptions of these models is age-independent vector mortality. A growing body of evidence indicates that insect vectors exhibit age-dependent mortality, which can have strong and varied affects on pathogen transmission dynamics and strategies for disease prevention.Methodology/Principal FindingsBased on survival analysis we derived new equations for vectorial capacity and R0 that are valid for any pattern of age-dependent (or age–independent) vector mortality and explore the behavior of the models across various mortality patterns. The framework we present (1) lays the groundwork for an extension and refinement of the vectorial capacity paradigm by introducing an age-structured extension to the model, (2) encourages further research on the actuarial dynamics of vectors in particular and the relationship of vector mortality to pathogen transmission in general, and (3) provides a detailed quantitative basis for understanding the relative impact of reductions in vector longevity compared to other vector-borne disease prevention strategies.Conclusions/SignificanceAccounting for age-dependent vector mortality in estimates of vectorial capacity and R0 was most important when (1) vector densities are relatively low and the pattern of mortality can determine whether pathogen transmission will persist; i.e., determines whether R0 is above or below 1, (2) vector population growth rate is relatively low and there are complex interactions between birth and death that differ fundamentally from birth-death relationships with age-independent mortality, and (3) the vector exhibits complex patterns of age-dependent mortality and R0∼1. A limiting factor in the construction and evaluation of new age-dependent mortality models is the paucity of data characterizing vector mortality patterns, particularly for free ranging vectors in the field.
Survival data from Caenorhabditis elegans strain TJ1060 (spe-9; fer-15) following brief exposure to 35 degrees C have been investigated. Three experiments with 3-day-old worms were conducted with heat duration ranging between 0 and 12 hours. A statistically significant increase in life expectancy was observed in the groups heated for less than 2 hours, as compared to the unheated control groups. In different experiments P-values for the observed life spans under the hypothesis that heating has no influence on longevity were P < 0.004 after 0.5 hour heat, P < 0.012 after 1 hour heat and P < 0.055 after 2 hours of heating. A biphasic survival model with Gamma distributed frailty has been constructed to describe the survival of worms after heating. The increase in the remaining life expectancy is determined by more effective protection by heat-induced substances in the ages yanger than 27 days. The unheated control group demonstrated acquired heterogeneity of frailty with chronological age while the heat-induced substances defend the worms in a universal way and protect against the development of frailty.
Background and AimOccasionally, there is a need to split aggregated fertility data into a fine grid of ages. For this purpose, several disaggregation methods have been developed. Yet these methods have some limitations. We seek to identify a method that satisfies the following criteria: 1) shape -the estimated fertility curves should be plausible and smooth; 2) fit -the predicted values should closely trace the observed values; 3) non-negativity -only positive values should be returned; 4) balance -the estimated five-year age group totals should match the input data;and in case of birth order data 5) parity -the balance by parity has to be maintained. To our knowledge, none of the existing methods fully meets the first four criteria. Moreover, no attempt has been made to extend the restrictions to criterion (5). To address the disadvantages of the existing methods, we introduce two alternative approaches for splitting abridged fertility data: namely, the quadratic optimization (QO) method and the neural network (NN) method. Data and Methods We mainly rely on high-quality fertility data from the Human Fertility Database (HFD), Additionally, we use a large and heterogeneous dataset from the Human Fertility Collection (HFC). The performance of the proposed methods is evaluated both visually (by examining of the obtained fertility schedules), and statistically using several metrics of fit. The QO and NN methods are tested against the current HFD splitting protocol (HFD method) and the calibrated spline (CS) method. Results The results of thorough testing suggest that both methods perform well. The main advantage -and a distinguishing feature -of the QO approach is that it meets all of the requirements listed above. However, it does not provide a fit as good as that of the NN and CS methods. In addition, when it is applied to birth order data, it can sometimes produce implausible shapes for parity 1. To account for such cases, we have developed individual solutions, which can easily be adapted to account for other cases that might occur. While the NN method does not satisfy the balance and parity criteria, it returns better results in terms of fit than the other methods. Conclusions The QO method satisfies the needs of large databases such as the HFD and the HFC. While this method has very strict requirements, it returns plausible fertility estimates regardless of the nature of the input data. The NN method appears to be a suitable alternative for use in individual cases in which the priority is given to the fit criterion.
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