Inverted U-shaped relationship

Figure 2.1 shows three hypothetical relationships between job tenure and accidents. Clearly, there is evidence to support the possibility of both a negative linear relationship and an inverted U-shaped relationship between job tenure and accidents. Furthermore, it is likely that organizations may experience either, or both of these relationships. The ideal situation is shown by the dotted line in Fig. 2.1, where... 

The relationship between dose and SLA was characterized by an inverted U-shaped curve for the phencyclinoids tested and dextroamphetamine. Geometric increases in cumulative IV doses produced nearly linear increases followed by decreases in SLA for each... 

Fig. 6. The Yerkes-Dodson principle based on the inverted U-shaped function describing the relationship between arousal and efficiency. A similar relationship holds for the relationship between DA activity (e.g. within the mesocortical DA system) and performance efficiency. Note that the optimal level of performance may also be a function of the nature of the task in the classical formulation, easy tasks being best performed at higher levels of arousal than hard or difficult tasks.

Figure 2 Representative examples of inverted U-shaped dose-response relationships displayed by a variety of experimental models and chemical agents. The asterisks indicate statistically significant data ( = P < 0.05, = P < 0.01, = P < 0.005). Absence of statistical significance denotes studies that did not perform statistical analyses on their data. Sources of data for (a)-(p) are References 14-29, respectively.

Figure 26.1. Hormesis may be defined as a dose-response relationship that is characterized by a biphasic (J- or inverted U-shaped) response. The quantitative features of the typical hermetic responses are similar, with the magnitude of the maximum stimulatory response typically being 30-60% greater than controls, the width of the stimulatory or hermetic zone averaging approximately 10-fold, and the interval from the zero equivalent point to the maximum stimulation averaging four- to fivefold (Calabrese and Blain 2005). [Figure adapted from Nascarella et al. (2009).]...

These and other relationships that follow from the model are summarized in Table 13.2. This empirical formula apparently works well because (dafdT) as a function of temperature for water is U-shaped, which gives to the expression for ArC° (if AC° is negative) an inverted-U shape with a maximum around 100°C, which is the same shape that the C° of many aqueous ions have (see Chapter 17). Furthermore the variation of AC° at higher pressures is also fairly faithfully modeled by the expression for AC°. 

I am sure most of you have been in situations—or predicaments—where the pressure to perform seemed overwhelming. This is the point where too much pressure can hurt performance, where stress becomes distress. The relationship between external stimulation or pressure to perform and actual performance is depicted in Figure 6.3. This inverted U-shaped function is known as the Yerkes-Dodson Law (Yerkes and Dodson, 1908). 

As well as being suppressed by VA deficiency, immune responses may be suppressed by excessive dietary VA. Sklan et al. [36] assayed a TD antibody response and antigen-specific T cell proliferation in young chicks fed diets supplemented with 0 to 13 200 pg VA/kg diet. Antibody production and T cell proliferation increased progressively with dietary VA up to 6600 pg/kg and then declined slightly. Thus, an inverted U-shaped curve may best describe the relationship of antibody production to dietary VA intake. 

The shape of the relationship between safety and competency is therefore an inverted U curve. 

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