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Trade-offs between functional traits are ubiquitous in nature and can promote species coexistence depending on their shape. Classic theory predicts that convex trade-offs facilitate coexistence of specialized species with extreme trait values (extreme species) while concave trade-offs promote species with intermediate trait values (intermediate species). We show here that this prediction becomes insufficient when the traits translate non-linearly into fitness which frequently occurs in nature, e.g., an increasing length of spines reduces grazing losses only up to a certain threshold resulting in a saturating or sigmoid trait-fitness function. We present a novel, general approach to evaluate the effect of different trade-off shapes on species coexistence. We compare the trade-off curve to the invasion boundary of an intermediate species invading the two extreme species. At this boundary, the invasion fitness is zero. Thus, it separates trait combinations where invasion is or is not possible. The invasion boundary is calculated based on measurable trait-fitness relationships. If at least one of these relationships is not linear, the invasion boundary becomes non-linear, implying that convex and concave trade-offs not necessarily lead to different coexistence patterns. Therefore, we suggest a new ecological classification of trade-offs into extreme-favoring and intermediate-favoring which differs from a purely mathematical description of their shape. We apply our approach to a well-established model of an empirical predator-prey system with competing prey types facing a trade-off between edibility and half-saturation constant for nutrient uptake. We show that the survival of the intermediate prey depends on the convexity of the trade-off. Overall, our approach provides a general tool to make a priori predictions on the outcome of competition among species facing a common trade-off in dependence of the shape of the trade-off and the shape of the trait-fitness relationships.
Doping use in recreational sports is an emerging issue that has received limited attention so far in the psychological literature. The present study assessed the lifetime prevalence of controlled performance and appearance enhancing substances ( PAES), and used behavioral reasoning theory to identify the reasons for using and for avoiding using controlled PAES in young exercisers across five European countries, in the context of the "SAFE YOU" Project. Participants were 915 young amateur athletes and exercisers (M = 21.62; SD = 2.62) from Cyprus, Germany, Greece, Italy, and UK who completed an anonymous questionnaire that included measures of self-reported use of controlled PAES, as well as reasons for using and not using controlled PAES. The results of the descriptive analyses demonstrated that almost one out five exercisers in the sample had a previous experience with controlled PAES. Higher prevalence rates were found in Greece and Cyprus and lower in Italy. The most frequently reported reasons for using controlled PAES included achieving the desired results faster; pushing the self to the (physical) limits; and recovering faster after exercise/training. Furthermore, the most frequently reported reasons for not using controlled PAES involved worry about any possible adverse health effects; not feeling the need for using them; and wanting to see what can be achieved naturally without using any controlled PAES. The findings of the present study indicate that the use of controlled PAES is fast becoming a crisis in amateur sports and exercise settings and highlight the need for preventive action and concerted anti-doping education efforts.