The Heat Equation and Stein\u27s Identity: Connections, Applications

This article presents two expectation identities and a series of applications. One of the identities uses the heat equation, and we show that in some families of distributions the identity characterizes the normal distribution. We also show that it is essentially equivalent to Stein\u27s identity. The applications we have presented are of a broad range. They include exact formulas and bounds for moments, an improvement and a reversal of Jensen\u27s inequality, linking unbiased estimation to elliptic partial differential equations, applications to decision theory and Bayesian statistics, and an application to counting matchings in graph theory. Some examples are also given

Oxidative Stress Mediates Physiological Costs of Begging in Magpie (Pica pica) Nestlings

[Background] Theoretical models predict that a cost is necessary to guarantee honesty in begging displays given by offspring to solicit food from their parents. There is evidence for begging costs in the form of a reduced growth rate and immunocompetence. Moreover, begging implies vigorous physical activity and attentiveness, which should increase metabolism and thus the releasing of pro-oxidant substances. Consequently, we predict that soliciting offspring incur a cost in terms of oxidative stress, and growth rate and immune response (processes that generate pro-oxidants substances) are reduced in order to maintain oxidative balance. [Methodology/Principal Findings] We test whether magpie (Pica pica) nestlings incur a cost in terms of oxidative stress when experimentally forced to beg intensively, and whether oxidative balance is maintained by reducing growth rate and immune response. Our results show that begging provokes oxidative stress, and that nestlings begging for longer bouts reduce growth and immune response, thereby maintaining their oxidative status. [Conclusions/Significance] These findings help explaining the physiological link between begging and its associated growth and immunocompetence costs, which seems to be mediated by oxidative stress. Our study is a unique example of the complex relationships between the intensity of a communicative display (begging), oxidative stress, and life-history traits directly linked to viability.GM-R was supported by the Spanish Government (Ministerio de Ciencia y Tecnología, “Juan de la Cierva” program), and TR was supported by the Consejo Superior de Investigaciones Científicas (CSIC; Proyectos Intramurales Especiales)

Empirical evidence for multiple costs of begging in poison frog tadpoles

In recent decades, theoretical and empirical work has investigated the relative roles of costs and benefits in inhibiting excessive displays of begging to parents. Whether costs are important in maintaining reliability of offspring signals is still debated, in part because empirical evidence for costs is conflicting. Nearly 90% of empirical studies have focused on birds. Costs may differ between birds and other animal groups, but more information is needed about non-avian systems. In this study, we tested for evidence of costs of begging in an anuran, Oophaga pumilio, in which tadpoles vibrate vigorously against mother frogs to solicit nutritive eggs. First, we tested whether a realistic manipulation of begging effort affected tadpole growth over two weeks, and found evidence for such physiological costs. Second, we tested whether the presence of a natural predator would alter begging behavior. Tadpoles begged when hungry, but begged significantly less when both hungry and viewing a spider, suggesting that they have evolved to reduce potential costs of predation risk when begging. Thus, we demonstrate the first example of costs via both physiological expenditure and predation risk in a non-avian species. Unlike most birds which rear offspring in clutches, O. pumilio mothers rear tadpoles in individual sites, suggesting that in the absence of sibling effects, multiple costs of begging work concomitantly to prevent the expression and evolution of excessive or indiscriminate signaling. Future studies of begging from a comparative perspective will continue to augment our understanding of the mechanisms behind the evolution of parent-offspring communication.University of Miami/[]/UM/Estados UnidosAmerican Association of University Women/[]/AAUM/Estados UnidosNational Science Foundation/[OISE-1114218]/NSF/Estados UnidosUCR::Vicerrectoría de Docencia::Ciencias Básicas::Facultad de Ciencias::Escuela de Biologí