Curtis C. Travis

Drinking-water standards

This paper discussed the revising of the primary and secondary drinking-water regulations by EPA in accordance with the Safe Drinking Water Act. Since consideration of risk is playing an increasing role in setting environmental standards, questions were raised regarding the adequacy of human health protection afforded by some of the existing and proposed standards. 1 table.

Positive feedback in natural systems

1. Introduction.- 1.1 Homeostasis.- 1.2 Positive Feedback.- 1.3 Ecological Systems with Positive Feedback.- 1.4 Generalization 1: Increasing Complexity.- 1.5 Generalization 2: Accelerating Change.- 1.6 Generalization 3: Threshold Effects.- 1.7 Generalization 4: Fragility of Complex Systems.- 1.8 Summary and Conclusions.- 2. The Mathematics of Positive Feedback.- 2.1 Graphical Analysis of a Simple Dynamic Positive Feedback System.- 2.2 A System of Two Mutualists.- 2.3 A System of Two Competitors.- 2.4 Mathematical Analysis of Positive Feedback.- 2.5 Summary and Conclusions.- 3. Physical Systems.- 3.1 The Life History of a Star.- 3.2 Geophysical Systems.- 3.3 Autocatalysis in Chemical Systems.- 3.4 Summary and Conclusions.- 4. Evolutionary Processes.- 4.1 Early Evolution of Life.- 4.2 Evolution at the Species Level.- 4.3 Coevolution.- 4.4 Summary and Conclusions.- 5. Organisms Physiology and Behaviour.- 5.1 Destructive Positive Feedback.- 5.2 Biochemical Processes in Cells and Organisms.- 5.3 Feeding and Drinking Behavior.- 5.4 Sleep.- 5.5 Movement and Motor-Sensory Relationships.- 5.6 Mind-Body Relationship.- 5.7 Summary and Conclusions.- 6. Resource Utilization by Organisms.- 6.1 Energy Allocation Tactics.- 6.2 Territorial Defense Strategies.- 6.3 Chemical Defense Strategies.- 6.4 Growth Rate Strategy.- 6.5 Summary and Conclusions.- 7. Social Behavior.- 7.1 Evolution of r- and K-strategies.- 7.2 Development of Social Strategies.- 7.3 Mating and Reproduction.- 7.4 Population Models Incorporating Sexual Reproduction.- 7.5 Small Group Dynamics.- 7.6 Castes In Insect Societies.- 7.7 Dominance Within Groups.- 7.8 Models of Group Formation and Size.- 7.9 The Schooling of Fish.- 7.10 Social Interactions and Game Theory.- 7.11 Summary and Conclusions.- 8. Mutualistic and Competitive Systems.- 8.1 Dynamics of Mutualistic Communities.- 8.2 Limits to Mutual Benefaction.- 8.3 Multi-Species Mutualism.- 8.4 Models of the Evolution of Mutualism.- 8.5 Isolation and Obligate Mutualism.- 8.6 Limited Competition.- 8.7 Summary and Conclusions.- 9. Age-Structured Populations.- 9.1 Age Structure.- 9.2 Leslie Matrices.- 9.3 Compensatory Leslie Matrices.- 9.4 Interacting Populations.- 9.5 Coexistence of Two Interacting Populations.- 9.6 Other Compensatory Models.- 9.7 Life-History Strategies.- 9.8 Intrinsic Rate of Increase.- 9.9 Reproductive Strategies.- 9.10 Summary and Conclusions.- 10. Spatially Heterogeneous Systems: Islands and Patchy Regions.- 10.1 Classical Theory of Island Biogeography.- 10.2 Island Clusters.- 10.3 Insular Reserves.- 10.4 Modeling the Patchy System.- 10.5 A Single Species in a Patchy Region.- 10.6 Time to Extinction on a Patch.- 10.7 Persistence of a Species in a Two-Patch Environment.- 10.8 Stability of a Single-Species, Two-Patch System.- 10.9 Persistence of a Species in an N-Patch Environment.- 10.10 Multi-Species, Multi-patch Systems with Competition and Mutalism.- 10.11 Persistence of a Species in a Two-Species, Two-Patch Environment.- 10.12 Persistence of a Species in an L-Species, iV-Patch Environment.- 10.13 Stability of a Two-Species, Two-Patch Model.- 10.14 Stability of an L-Species, iV-Patch Model.- 10.15 Relationship Between Reserve Design and Species Persistence.- 10.16 Summary and Conclusions.- 11. Spatially Heterogeneous Ecosystems: Pattern Formation.- 11.1 Spontaneous Emergence of Spatial Patterns.- 11.2 Diffusion Model.- 11.3 Pattern Formation Through Instability.- 11.4 Congregation of Colonial Organisms.- 11.5 Boundary Formation by Competition.- 11.6 Summary and Conclusions.- 12. Disease and Pest Outbreaks.- 12.1 Physiological Effects in the Host Species.- 12.2 Mutualistic Interactions of more than one Pathogenic Agent.- 12.3 Models of a Directly Communicated Disease or Parasite.- 12.4 Effects of Spatial Heterogeneity on Disease Outbreak Threshold Conditions.- 12.5 Design of Immunization Programs.- 12.6 Shape of the Contagion Rate Function.- 12.7 Comparison with other Spatially Heterogeneous Models.- 12.8 Host-Vector Models.- 12.9 Summary and Conclusions.- 13. The Ecosystem and Succession.- 13.1 The Ecosystem.- 13.2 Succession as a Positive Feedback Process.- 13.3 A Clementsian Model.- 13.4 Markov Chain Models.- 13.5 A Model of a Fire-Dependent System.- 13.6 Positive Feedback Loops in Ecosystems.- 13.7 Nutrient Cycling.- 13.8 Selection on the Community or Ecosystem Level.- 13.9 Summary and Conclusions.- Appendices.- Appendix A: Positive Linear Systems.- Appendix B: Stability of Positive Feedback Systems.- Appendix C: Stability of Discrete-Time Systems.- Appendix D: Positive Equilibria and Stability.- Appendix E: Comparative Statics of Positive Feedback Systems.- Appendix F: Similarity Transforms.- Appendix G: Bounds on the Roots of a Positive Linear System.- Appendix H: Relationship Between Positive Linear System Stability Criteria and the Routh-Hurwitz Criteria.- References.- Author Index.

Benzo-a-Pyrene: Environmental Partitioning and Human Exposure

A multimedia transport model was used to evaluate the environ mental partitioning of benzo-a-pyrene (BaP). Measured and pre dicted environmental concentrations were used to estimate the accumulation of BaP in the food chain and the subsequent ex tent of human exposure from inhalation and ingestion. Results show that BaP partitions mainly into soil (82%) and sediment (17%) and that the food chain is the dominant pathway of hu man exposure, accounting for about 97% of the total daily in take of BaP. Inhalation and consumption of contaminated water are only minor pathways of human exposure. The long-term av erage daily intake of BaP by the general population of the U. S. is estimated to be 2.2 micrograms (μg) per day. Cigarette smok ing and indoor activities do not substantially increase human ex posure to BaP relative to exposures to background levels of BaP present in the environment. Since the increased lifetime risk as sociated with human exposure to background levels of BaP is 3.5 x 10 -4, we conclude that ingestion of food items contami nated with BaP may pose a serious health threat to the U. S. population.

Cancer risk management A review of 132 federal regulatory decisions.

Various federal agencies are responsible for promulgating regulations and standards to protect the public from exposure to environmental carcinogens. Although many factors are considered in the decision to regulate a carcinogen, one important issue concerns the probability that individuals in an exposed population will develop cancer. What has not been clear, however, is the level of cancer risk that triggers regulation, or whether there is consistency within and between agencies in arriving at the risk decisions that underpin regulatory action. The authors retrospectively reviewed the use of cancer risk estimates in prevailing federal standards and in withdrawn regulatory initiatives to determine whether any simple patterns emerge to correlate risk level with regulatory action. The results show that there are definite patterns and a surprising degree of consistency in the federal regulator process.

Human exposure to 2,3,7,8-TCDD

Abstract This paper uses an environmental partitioning model to evaluate the concentration of 2,3,7,8-Tetrachlorodibenzo-p-dioxin (TCDD) in various environmental media. These concentrations are then used to estimate the amount of TCDD entering the food chain and the average daily intake of TCDD by the general population of the US. The food chain accounts for 98% of human exposure to TCDD. The model estimated the average daily intake of TCDD to be 0.05 ng/day.

Pharmacokinetics of benzene.

A physiologically based pharmacokinetic model was developed and used to describe the pharmacokinetics of benzene in three species: mice, rats, and humans. For each species, the body was divided into five anatomical compartments, consisting of liver, fat, bone marrow, and muscle, and organs such as brain, heart, kidney, and viscera, connected by the arterial and venous blood flow pathways. Metabolism of benzene followed Michaelis-Menten (nonlinear) kinetics in all species and occurred primarily in the liver compartment and, to a lesser extent, in the bone marrow. Comparison of model results with empirical data on inhalation, gavage, and intraperitoneal and subcutaneous injection in mice, rats, and humans, demonstrates the utility of a physiological pharmacokinetic model in describing the pharmacokinetics of benzene in three species across multiple routes of exposure.

Pentachlorophenol: Environmental partitioning and human exposure

This paper uses a six compartment environmental partitioning model to explore the transport and accumulation of pentachlorophenol (PCP) within and between various environmental media. Environmental concentrations were then used to estimate the amount of PCP entering the food chain and the long-term, average daily intake of PCP by the general population of the U.S. Results show that PCP partitions mainly into soil (96.5%) and that the food chain, especially fruits, vegetables, and grains, accounts for 99.9% of human exposure to PCP. The long-term, average daily intake of PCP is estimated to be 16 μg/day, which agrees well with a previous estimate of 19 μg/day (Geyeret al. 1987).

Dynamics and comparative statics of mutualistic communities

Abstract The sensitivity of mutualistic communities to perturbations from equilibrium is examined, and the factors which regulate this sensitivity are discussed in both biological and mathematical terms. The response of equilibrium population densities to changes in environmental and biological parameters is also investigated. These investigations are then extended to include communities which allow for a limited form of competition. The results are discussed in terms of the familiar two species Lotka-Volterra equations.

Interspecies extrapolation of pharmacokinetics

The purpose of this paper is to use physiologically based pharmacokinetic models to demonstrate that if toxic response is a function of the time profile in physiological time of the concentration of the toxic moiety in the target tissue, then the appropriate interspecies scaling law for toxic compounds which are metabolically deactivated is mg kg-1 per unit of physiological time (mg kg-1 pt-1). At low dose rates this metric is approximately equivalent to mg kg-0.75 day-1. For reactive metabolites which are spontaneously deactivated, an approximate interspecies scaling law is mg kg-1 day-1.

Global stability of a biological model with time delay

This paper gives necessary and sufficient conditions for global stability of certain logistic delay differential equations for all values of the delay. Biological models frequently lead to delay differential equations and to questions concerning the stability of equilibrium solutions of such models. The monographs by Cushing (6) and MacDonald (16) discuss a number of examples of such models from population dynamics, ecology, and physiology. Much of the work with such models has focused on delay equations which are reducible, through a change of variables, to systems of differential equations without delays (3,4,8,14,18,19). Another line of research is concerned with conditions under which linear retarded functional differential equations of the form L x(t) = ax(t) + £ btx(t - r,), r, > 0, /=i are asymptotically stable for all values of the delay (1,3,5,7,9,11,12,14). We propose to combine these lines of research and examine global stability of the widely used logistic model of population dynamics,