This book introduces various mathematical models used in ecological risk assessment, primarily discussing models used in hazard assessment. The book aims to link ecology and conservation biology with risk assessments, bringing together the knowledge of ecotoxicology and ecology for effective risk assessment.
The first part describes population-level assessment in ecological risk assessment. The chapters cover current methodologies for ecological risk assessment, individual-level assessment, population dynamics models for population-level assessment, case studies, mathematical models for population extinctions, the derivation of mean time to extinction (MTE) and their case studies. The second part of the book discusses the mathematical models involved in hazard assessments. It introduces the method of risk assessment using species sensitivity distributions (SSDs), hazard assessment of metals, chemical mixtures using the Michaelis-Menten equation, basic elements of statistics and related topics.
Expected readers are risk assessors in governments and public sectors, students and young researchers interested in environmental science. The book is made accessible and easy to follow by beginners in mathematical biology and theoretical ecology.
Author(s): Masashi Kamo
Series: Theoretical Biology
Publisher: Springer
Year: 2023
Language: English
Pages: 211
City: Singapore
Preface
Acknowledgments
Contents
Part I Linking Ecology and Ecotoxicology
1 Basic Concepts of Ecological Risk Assessment
1.1 What Is Risk?
1.2 What Is Risk Assessment?
1.3 Ecological Risk Assessment
1.4 Are Different NOEC Values Comparable Indices for Ecological Risk Assessment?
References
2 Population-level Assessment
2.1 Introduction
2.2 Differential Equation Model
2.2.1 Logistic Growth
2.2.2 Equilibrium and Stability
2.2.3 Multiple Species
2.2.4 Including Toxic Effects
2.3 Difference Equation Model
2.3.1 Increase or Decrease
2.3.2 Sensitivity Analysis
2.4 Case Studies
2.4.1 The Effect of Zinc on an Algal Population
Zinc Toxicity on Fathead Minnow
The Life-History Parameters of the Fathead Minnow and Sensitivities
Combining the Toxic Effect and Life-History Matrix
2.4.2 Population-level Species Sensitivity Distribution
2.4.3 Comparison of the NOEC and PTC
2.5 Toxic Effects on r- vs. K-Selected Species
2.5.1 r vs. K Selection
2.5.2 Model
2.5.3 Optimum Allocation Rates in a Crowded Population
2.5.4 Optimum Allocation Rates in a Sparse Population
2.5.5 Toxic Effects: r vs. K
References
3 Population Models of Extinction
3.1 Introduction
3.2 A Model of the Birth and Death Process
3.3 Models of Stochastic Processes: Necessary Elements
3.3.1 The Random Walk
3.3.2 Mean and Variance in Location
3.3.3 The Forward (Fokker–Planck) Equation
3.3.4 Backward Equation
Solving the Backward Equation: Obtaining MTE
3.4 A Model for Exponential Growth and EnvironmentalStochasticity
3.5 Logistic Equation with Environmental and Demographic Stochasticity
3.5.1 Mean Time to Extinction
The Numerical Solution for Eq.3.47
3.5.2 Time Evolution of the Probability Density and the Probability of Extinction
References
4 Population-Level Assessment Using the Canonical Model
4.1 The Canonical Model and the Adverse Effect of Chemicals
4.2 Parameter Estimation
4.2.1 Intrinsic Rate of Reproduction
4.2.2 Carrying Capacity and Environmental StochasticityIntensity
4.3 The Effect of DDT Exposure on a Herring Gull Population
4.3.1 Parameters for Natural (DDT-Free) Population
4.3.2 The Effects of DDT on a Herring Gull Population
4.3.3 Mean Time to Extinction (MTE)
4.3.4 Effect of DDT on MTE
4.4 Risk Equivalence
4.4.1 DDT Exposure vs. Habitat Loss
4.4.2 DDT Exposure vs. Environmental Stochasticity
4.4.3 How Long Do We Have for Habitat Restoration?
4.5 Effect of Nonylphenol Exposure on Medaka Fish
4.5.1 Medaka Life History
4.5.2 NP Toxicity for the Medaka Fish
4.6 Conclusion
References
Part II Models for Ecotoxicology
5 Species Sensitivity Distribution in Ecological Risk Assessment
5.1 Introduction
5.2 Basic SSD Elements
5.3 Criticisms of SSDs
5.4 The Probability that We Achieve the Protection Goal
5.4.1 The Minimum NOEC Approach
5.4.2 The SSD Approach
5.4.3 The t-Distribution
5.4.4 The Noncentral t-Distribution and the ExtrapolationFactor
5.4.5 The Distribution of the Estimated HC5
5.5 The Relationship Between , Sample Size, and the AF
5.5.1 Reduction of the Protection Goal
5.5.2 How Far from HC5
References
6 BLM: A Model for Predicting Metal Toxicities
6.1 Introduction
6.2 Estimation of Metal Toxicities Using the BLM
6.2.1 Metal Speciation: From Total Concentration to Bioavailability (i.e., Free-Ion Concentration)
6.2.2 The Concentration of Free Ions that Bind to the Biotic Ligands
6.3 Relationship Among Metals
6.4 The Toxic Effect of Metal Mixtures
References
7 Mathematical Models for Chemical Mixtures
7.1 Introduction
7.2 Two Classical Models for Predicting the Effects of Chemical Mixtures
7.2.1 Bliss's Independent Action
7.2.2 Loewe's Additivity Model
7.3 Statistical Test for Additivity
7.4 The Conditions for Additivity and Non-additivity
7.4.1 Case 1: Single Enzyme-Substrate Reaction
7.4.2 Case 2: Sequential Enzyme-Substrates Reactions
7.5 The Funnel Hypothesis
7.6 Metal Mixture
7.6.1 The Outline for the Model Predicting the Toxicity of Metal Mixture
7.6.2 The Total Metal Concentration Resulting in 50% Effect
7.6.3 Binary Mixture of Two Metals
7.6.4 The Reason for Non-additivity with Identical Toxic Mechanisms
References
8 Statistics and Related Topics
8.1 Introduction
8.2 Hypothesis Testing
8.3 Regression Analysis
8.3.1 Regression Analysis Based on the Maximum Likelihood
8.4 The Confidence Interval
8.5 AIC and Model Selection
8.6 SSDs, Hypothesis Testing, and Model Selection
References
