title: Analysis of spread and persistence for stream insects with winged adult stages.
abstract: Species such as stoneflies have complex life history details, with larval stages in the river flow and adult winged stages on or near the river bank. Winged adults often bias their dispersal in the upstream direction, and this bias provides a possible mechanism for population persistence in the face of unidirectional river flow. We use an impulsive reaction-diffusion equation with non-local impulse to describe the population dynamics of a stream-dwelling organism with a winged adult stage, such as stoneflies. We analyze this model from a variety of perspectives so as to understand the effect of upstream dispersal on population persistence. On the infinite domain we use the perspective of weak versus local persistence, and connect the concept of local persistence to positive up and downstream spreading speeds. These spreading speeds, in turn are connected to minimum travelling wave speeds for the linearized operator in upstream and downstream directions. We show that the conditions for weak and local persistence differ, and describe how weak persistence can give rise to a population whose numbers are growing but is being washed out because it cannot maintain a toe hold at any given location. On finite domains, we employ the concept of a critical domain size and dispersal success approximation to determine the ultimate fate of the populations. A simple, explicit formula for a special case allows us to quantify exactly the difference between weak and local persistence.
authors.affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada.|Department of Mathematics, Christopher Newport University, Newport News, VA, 23606, USA.
authors.forename: Olga
authors.initials: O
authors.lastname: Vasilyeva
authors.affiliation: Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, K1N 6N5, Canada. flutsche@uottawa.ca.|Department of Biology, University of Ottawa, Ottawa, ON, K1N 6N5, Canada. flutsche@uottawa.ca.
authors.forename: Frithjof
authors.initials: F
authors.lastname: Lutscher
authors.affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.|Department of Biological Sciences, University of Alberta, Edmonton, AB, T6G 2G1, Canada.
authors.forename: Mark
authors.initials: M
authors.lastname: Lewis
mesh_terms: D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D005426:Flight, Animal; D007313:Insecta / Q000254:growth & development* / Q000502:physiology; D007814:Larva / Q000254:growth & development; D016014:Linear Models; D055641:Mathematical Concepts; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D045483:Rivers; D014872:Water Movements; D014921:Wings, Animal / Q000254:growth & development / Q000502:physiology
keywords: Drift paradox; Non-local impulsive reaction–diffusion equation; Persistence condition; Spreading speed