Joanna A. Bieri

Modeling complex human–environment interactions: the Grand Canyon river trip simulator

Abstract Understanding the impacts of human recreation on natural resources is of critical importance in constructing effective management strategies. The Grand Canyon River Trip Simulator is a computer program that models complex, dynamic human–environment interactions in the river corridor of the Grand Canyon National Park. The system consists of a database and simulator engine. The database contains 487 trip diaries that report all stops for activities and camping along the 447 km Colorado River corridor within the purview of the National Park Service. The computer simulation employs statistics and artificial intelligence in creating an individual-based modeling system. This simulation system successfully models the recreational rafting behavior and captures the decision making of rafting parties as they responsively seek to optimize their experience. The model allows the Park managers to assess the likely impact of various alternative management scenarios for rafting trips on the Colorado River. The Grand Canyon River Trip Simulator advances our abilities to model complex systems in the context of human–environment interactions. It may serve as a suitable template for modeling a suite of other complex adaptive systems including ecosystems.

Edge flames stabilized in a non-premixed microcombustor

The dynamics of an edge flame confined in a non-premixed microcombustor model is studied numerically within the context of a diffusive-thermal model. Fuel and oxidizer, separated upstream by a thin plate, flow through a channel with a prescribed velocity. At the tip of the plate, the fuel and oxidizer mix and, when ignited, an edge flame is sustained at some distance from the plate. The objective in this work is to consider the effects of confinement, differential diffusion, and heat loss on the dynamics of an edge flame in a narrow channel. We consider a wide range of channel widths and allow for changing Lewis numbers, and both adiabatic conditions and heat losses along the channel walls. The results illustrate how the flame shape and standoff distance are affected by the channel width, by mixture composition through variations in Lewis numbers and by heat losses. Conditions for flame stabilization, flame oscillations and flame extinction or blowoff are predicted.

Defining and classifying migratory habitats as sources and sinks: The migratory pathway approach

Understanding and conserving migratory species requires a method for characterizing the seasonal flow of animals among habitats. Source-sink theory describes the metapopulation dynamics of species by classifying habitats as population sources (i.e. net contributors) or sinks (i.e. net substractors). Migratory species may have non-breeding habitats important to the species (e.g. overwintering or stopover habitats) that traditional source-sink theory would classify as sinks because these habitats produce no individuals. Conversely, existing migratory network models can evaluate the relative contribution of non-breeding nodes, but these models make an equilibrium assumption that is difficult to meet when examining real migratory populations. We extend a pathway-based metric allowing breeding habitats, non-breeding habitats and migratory pathways connecting these habitats to be classified as sources or sinks. Rather than being based on whether place- or season-specific births exceed deaths, our approach quantifies the total demographic contribution from a node or migratory pathway over a flexibly defined yet limited time period across an organisms life cycle. As such, it provides a snapshot of a migratory system and therefore does not require assumptions associated with equilibrium dynamics. We first develop a generalizable mathematical notation and then demonstrate how the metric may be used with two case studies: the common loon (Gavia immer) and Yellowstone cutthroat trout (Oncorhynchus clarkii bouvieri). These examples highlight how stressors can impact stopover and wintering habitats (loons) and habitat management targeting migratory pathways can improve population status (trout). Synthesis and applications. Each of the two case studies presented describes how effects at one location are felt by populations in another through the seasonal flow of individuals. The contribution metric we present should be helpful in allocating regulatory and management attention to times and locations most critical to migratory species persistence.

A general modeling framework for describing spatially structured population dynamics

Abstract Variation in movement across time and space fundamentally shapes the abundance and distribution of populations. Although a variety of approaches model structured population dynamics, they are limited to specific types of spatially structured populations and lack a unifying framework. Here, we propose a unified network‐based framework sufficiently novel in its flexibility to capture a wide variety of spatiotemporal processes including metapopulations and a range of migratory patterns. It can accommodate different kinds of age structures, forms of population growth, dispersal, nomadism and migration, and alternative life‐history strategies. Our objective was to link three general elements common to all spatially structured populations (space, time and movement) under a single mathematical framework. To do this, we adopt a network modeling approach. The spatial structure of a population is represented by a weighted and directed network. Each node and each edge has a set of attributes which vary through time. The dynamics of our network‐based population is modeled with discrete time steps. Using both theoretical and real‐world examples, we show how common elements recur across species with disparate movement strategies and how they can be combined under a unified mathematical framework. We illustrate how metapopulations, various migratory patterns, and nomadism can be represented with this modeling approach. We also apply our network‐based framework to four organisms spanning a wide range of life histories, movement patterns, and carrying capacities. General computer code to implement our framework is provided, which can be applied to almost any spatially structured population. This framework contributes to our theoretical understanding of population dynamics and has practical management applications, including understanding the impact of perturbations on population size, distribution, and movement patterns. By working within a common framework, there is less chance that comparative analyses are colored by model details rather than general principles.

Edge flames in confined mixing layers

The of dynamics of an edge ame con ned in a narrow channel is studied numerically within the context of a di usive-thermal model. Fuel and oxidizer, separated upstream by a thin plate, ow through a channel with a prescribed velocity. At the tip of the plate, the fuel and oxidizer mix and, when ignited, an edge ame is sustained at some distance from the plate. The objective in this work is to determine the e ect of lateral con nement on the stando distance, the ame shape, and the ame stability. We consider a wide range of widths, allow for di erential di usion and examine the e ect heat loss to the channel wall.

Ecosystem service flows from a migratory species: Spatial subsidies of the northern pintail.

Migratory species provide important benefits to society, but their cross-border conservation poses serious challenges. By quantifying the economic value of ecosystem services (ESs) provided across a species’ range and ecological data on a species’ habitat dependence, we estimate spatial subsidies—how different regions support ESs provided by a species across its range. We illustrate this method for migratory northern pintail ducks in North America. Pintails support over

The effect of gas expansion on edge flames stabilized in narrow channels

101 million USD annually in recreational hunting and viewing and subsistence hunting in the U.S. and Canada. Pintail breeding regions provide nearly

A general modeling framework for describing spatio-temporal population dynamics

30 million in subsidies to wintering regions, with the “Prairie Pothole” region supplying over

Mathematical Models for Habitat Contributions of Migrating Species on a Network, Part I

24 million in annual benefits to other regions. This information can be used to inform conservation funding allocation among migratory regions and nations on which the pintail depends. We thus illustrate a transferrable method to quantify migratory species-derived ESs and provide information to aid in their transboundary conservation.