The panzootic white-nose syndrome: an environmentally constrained disease?

White-nose syndrome (WNS) is an emerging disease of hibernating bats probably caused by a pathogenic fungus, Geomyces destructans. The fungus has dispersed rapidly in the Northeastern United States and Canada and is presently a serious risk to hibernating bats of the mid-southern United States. Our objectives were to investigate how the environmental factors of temperature and resources impact the physiology of bats and apply this to explore possible effects of the fungus G. destructans on bats. Using a dynamic, physiologically based model parameterized for little brown bats (Myotis lucifugus), we found that the survival region defined in terms of minimal and maximal cave temperatures and bat lipid reserve levels exhibits plasticity as a function of cave temperature. During the pre-hibernation period, constellations of increased availability of fall and winter prey, reduced energy expenditure and lipogenic factors provide fat deposition in hibernator species that engender survival throughout the hibernation period. The model-derived survival region is used to demonstrate that small increases in lipid reserves allow survival under increasing maximum temperatures, which provides flexibility of bat persistence at the higher cave temperature ranges that may occur in the Southern United States. Antipodally, the lower-temperature survival range is bounded with minimum temperatures. Our results suggest that there is an environmental distinction between survival of bats in Southern and Northern US states, a relationship that could prove very important in managing WNS and its dispersal.

Iteroparous reproduction strategies and population dynamics

Asymptotic relationships between a class of continuous partial differential equation population models and a class of discrete matrix equations are derived for iteroparous populations. First, the governing equations are presented for the dynamics of an individual with juvenile and adult life stages. The organisms reproduce after maturation, as determined by the juvenile period, and at specific equidistant ages, which are determined by the iteroparous reproductive period. A discrete population matrix model is constructed that utilizes the reproductive information and a density-dependent mortality function. Mortality in the period between two reproductive events is assumed to be a continuous process where the death rate for the adults is a function of the number of adults and environmental conditions. The asymptotic dynamic behaviour of the discrete population model is related to the steady-state solution of the continuous-time formulation. Conclusions include that there can be a lack of convergence to the steady-state age distribution in discrete event reproduction models. The iteroparous vital ratio (the ratio between the maximal age and the reproductive period) is fundamental to determining this convergence. When the vital ratio is rational, an equivalent discrete-time model for the population can be derived whose asymptotic dynamics are periodic and when there are a finite number of founder cohorts, the number of cohorts remains finite. When the ratio is an irrational number, effectively there is convergence to the steady-state age distribution. With a finite number of founder cohorts, the number of cohorts becomes countably infinite. The matrix model is useful to clarify numerical results for population models with continuous densities as well as delta measure age distribution. The applicability in ecotoxicology of the population matrix model formulation for iteroparous populations is discussed.

The application of mass and energy conservation laws in physiologically structured population models of heterotrophic organisms

Rules for energy uptake, and subsequent utilization, form the basis of population dynamics and, therefore, explain the dynamics of the ecosystem structure in terms of changes in standing crops and size distributions of individuals. Mass fluxes are concomitant with energy flows and delineate functional aspects of ecosystems by defining the roles of individuals and populations. The assumption of homeostasis of body components, and an assumption about the general structure of energy budgets, imply that mass fluxes can be written as weighted sums of three organizing energy fluxes with the weight coefficients determined by the conservation law of mass. These energy fluxes are assimilation, maintenance and growth, and provide a theoretical underpinning of the widely applied empirical method of indirect calorimetry, which relates dissipating heat linearly to three mass fluxes: carbon dioxide production, oxygen consumption and N-waste production. A generic approach to the stoichiometry of population energetics from the perspective of the individual organism is proposed and illustrated for heterotrophic organisms. This approach indicates that mass transformations can be identified by accounting for maintenance requirements and overhead costs for the various metabolic processes at the population level. The theoretical background for coupling the dynamics of the structure of communities to nutrient cycles, including the water balance, as well as explicit expressions for the dissipating heat at the population level are obtained based on the conservation law of energy. Specifications of the general theory employ the Dynamic Energy Budget model for individuals. Copyright 1999 Academic Press.

A community model of ciliate Tetrahymena and bacteria E coli: Part II. interactions in a batch system

Premised on relatively simple assumptions, mathematical models like those of Monod, Pirt or Droop inadequately explain the complex transient behavior of microbial populations. In particular, these models fail to explain many aspects of the dynamics of a Tetrahymena pyriformis-Escherichia coli community. In this study an alternative approach, an individual-based model, is employed to investigate the growth and interactions of Tetrahymena pyriformis and E. coli in a batch culture. Due to improved representation of physiological processes, the model provides a better agreement with experimental data of bacterial density and ciliate biomass than previous modeling studies. It predicts a much larger coexistence domain than rudimentary models, dependence of biomass dynamics on initial conditions (bacteria to ciliate biomasses ratio) and appropriate timing of minimal bacteria density. Moreover, it is found that accumulation of E. coli sized particles and E. coli toxic metabolites has a stabilizing effect on the system.

A community model of ciliate Tetrahymena and bacteria E. coli: Part I. individual-based models of tetrahymena and E. coli populations

The dynamics of a microbial community consisting of a eucaryotic ciliate Tetrahymena pyriformis and procaryotic Escherichia coli in a batch culture is explored by employing an individual-based approach. In this portion of the article, Part I, population models are presented. Because both models are individual-based, models of individual organisms are developed prior to construction of the population models. The individual models use an energy budget method in which growth depends on energy gain from feeding and energy sinks such as maintenance and reproduction. These models are not limited by simplifying assumptions about constant yield, constant energy sinks and Monod growth kinetics as are traditional models of microbal organisms. Population models are generated from individual models by creating distinct individual types and assigning to each type the number of real individuals they represent. A population is a compilation of individual types that vary in a phase of cell cycle and physiological parameters such as filtering rate for ciliates and maximum anabolic rate for bacteria. An advantage of the developed models is that they realistically describe the growth of the individual cells feeding on resource which varies in density and composition. Part II, the core of the project, integrates models into a dynamic microbial community and provides model analysis based upon available data.

Compensation and stability in nonlinear matrix models

Stability, bifurcation, and dynamic behavior, investigated here in discrete, nonlinear, age-structured models, can be complex; however, restrictions imposed by compensatory mechanisms can limit the behavioral spectrum of a dynamic system. These limitations in transitional behavior of compensatory models are a focal point of this article. Although there is a tendency for compensatory models to be stable, we demonstrate that stability in compensatory systems does not always occur; for example, equilibria arising through a bifurcation can be initially unstable. Results concerning existence and uniqueness of equilibria, stability of the equilibria, and boundedness of solutions suggest that "compensatory" systems might not be compensatory in the literal sense.

On the dynamics of a toxicant-individual system

The dynamics of a toxicant-individual model where the individual is represented by von Bertalanffy dynamics and the uptake model component is one developed by Barber, Suarez & Lassiter is discussed. A sufficient condition for the death of an individual subjected to chemical stress is found. Another possible behavior of the system is an oscillatory mode of individual size and internal chemical concentration determined by a limit cycle. These fluctuations are a consequence of formulations of growth, maintenance, and the dose-response functions in the model system.

The threshold of survival for systems in a fluctuating environment

Thresholds for survival and extinction are important for assessing the risk of mortality in systems exposed to exogenous stress. For generic, rudimentary population models and the classical resource-consumer models of Leslie and Gallopin, we demonstrate the existence of a survival threshold for situations where demographic parameters are fluctuating, generally, in a nonperiodic manner. The fluctuations are assumed to be generated by exogenous, anthropogenic stresses such as toxic chemical exposures. In general, the survival threshold is determined by a relationship between mean stress measure in organisms to the ratio of the population intrinsic growth rate and stress response rate.

On density and extinction in continuous population models

Survival analyses, investigations of extinction and persistence, are executed for populations represented by a nonautonomous differential equation model. The population is assumed governed by density dependent and time varying density independent demographic parameters. While traditional approaches to extinction postulate extinction on an infinite time horizon and at zero abundance level, survival analysis is developed not only for this traditional setting but also on a finite time horizon and at a nonzero threshold level. A main conclusion is that extinction of a temporally stressed population is determined by a totality of density independent and density dependent factors.

Demographic variation and survival in discrete population models

Persistence and extinction attributes of a discrete population model are explored on both a finite and an infinite time horizon. For a first-order autonomous nonlinear difference equation, a classification is found of when, for each positive integer N, trajectories go to extinction at time N. The dynamic complexity that is known to permeate difference-equation models is also present in the survival analyses developed here. Also found is an interesting decomposition of the continuum of initial population sizes into intervals where populations are persistent at time N and intervals leading to extinction at time n less than or equal to N.

Persistence in population models with demographic fluctuations

A persistence and extinction theory is developed through analytical studies of deterministic population models. Under hypotheses that require demographic parameters to fluctuate temporally, the populations may or may not oscillate. Extinction, when it occurs, is asymptotic. An hierarchy of persistence criteria, based upon fluctuations measured by time average means, is derived. In some situations a threshold value is found to separate persistent population models from those that tend to extinction. Application of the persistence-extinction theory is to the problem of assessing effects of a toxic substance on a population when toxicant inputs to the environment and to resources are oscillatory.

Effects of toxicants on populations: a qualitative approach II. First order kinetics

System level effects exhibited by a population subjected to a chronic or an acute dose of toxicant are the emphasis of this study. A three dimensional model of a toxicant and a population, with state variables (the population biomass, the concentration of toxicant in an organism, and the concentration of toxicant in the environment) coupled by a linear dose-response function, is analyzed analytically. One of the main results presents sufficient conditions, in terms of a system level parameter, for the persistence, and for the extinction, of a population exposed to a chronic dose of toxicant. When depuration and degradation are negligible processes, the effects of toxicant accumulation associated with an acute exposure of a population are analyzed in some detail. Both persistence and extinction are shown to be viable behavior modes of a population in this biochemical setting.