Applying evolutionary concepts to wildlife disease ecology and management

Existing and emerging infectious diseases are among the most pressing global threats to biodiversity, food safety and human health. The complex interplay between host, pathogen and environment creates a challenge for conserving species, communities and ecosystem functions, while mediating the many known ecological and socio-economic negative effects of disease. Despite the clear ecological and evolutionary contexts of host-pathogen dynamics, approaches to managing wildlife disease remain predominantly reactionary, focusing on surveillance and some attempts at eradication. A few exceptional studies have heeded recent calls for better integration of ecological concepts in the study and management of wildlife disease; however, evolutionary concepts remain underused. Applied evolution consists of four principles: evolutionary history, genetic and phenotypic variation, selection and eco-evolutionary dynamics. In this article, we first update a classical framework for understanding wildlife disease to integrate better these principles. Within this framework, we explore the evolutionary implications of environment-disease interactions. Subsequently, we synthesize areas where applied evolution can be employed in wildlife disease management. Finally, we discuss some future directions and challenges. Here, we underscore that despite some evolutionary principles currently playing an important role in our understanding of disease in wild animals, considerable opportunities remain for fostering the practice of evolutionarily enlightened wildlife disease management

A Multicomplex Riemann Zeta Function

After reviewing properties of analytic functions on the multicomplex number space ℂk (a commutative generalization of the bicomplex numbers ℂ2), a multicomplex Riemann zeta function is defined through analytic continuation. Properties of this function are explored, and we are able to state a multicomplex equivalence to the Riemann hypothesis. © 2012 Springer Basel

Multicomplex Wave Functions for Linear And Nonlinear Schrödinger Equations

We consider a multicomplex Schrödinger equation with general scalar potential, a generalization of both the standard Schrödinger equation and the bicomplex Schrödinger equation of Rochon and Tremblay, for wave functions mapping onto (Formula presented.). We determine the equivalent real-valued system in recursive form, and derive the relevant continuity equations in order to demonstrate that conservation of probability (a hallmark of standard quantum mechanics) holds in the multicomplex generalization. From here, we obtain the real modulus and demonstrate the generalized multicomplex version of Born’s formula for the probability densities. We then turn our attention to possible generalizations of the multicomplex Schrödinger equation, such as the case where the scalar potential is replaced with a multicomplex-valued potential, or the case where the potential involves the real modulus of the wave function, resulting in a multicomplex nonlinear Schrödinger equation. Finally, in order to demonstrate the solution methods for such equations, we obtain several particular solutions to the multicomplex Schrödinger equation. We interpret the generalized results in the context of the standard results from quantum mechanics