Population Dynamics and the Tribolium Model: Genetics and Demography

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Integrates biological observations of flour beetles of the genus Tribolium with such themes of nonlinear population research as bifurcations, multiple attractors, limit cycles, and stationary probability distributions. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9781461278238
  • Publisher: Springer New York
  • Publication date: 7/31/2012
  • Series: Monographs on Theoretical and Applied Genetics Series , #13
  • Edition description: Softcover reprint of the original 1st ed. 1991
  • Edition number: 1
  • Pages: 258
  • Product dimensions: 6.69 (w) x 9.61 (h) x 0.58 (d)

Table of Contents

1 Introduction.- 1.1 A Brief History of the Mathematics of Tribolium.- 1.1.1 The Beginning.- 1.1.2 Models of Adult Numbers.- 1.1.3 Models of Age Structure.- 1.1.4 Beetle Movement, Food Preference and Tunnels.- 1.1.5 Species Interactions.- 1.1.6 Population Genetics.- 1.2 Topics in the Monograph.- 1.2.1 Life Stage Interactions.- 1.2.2 Shastic Population Growth.- 1.2.3 Natural Selection.- 1.2.4 Species Interactions.- 2 Biology and Dynamics of Age Structure.- 2.1 Models for Age-Structured Populations.- 2.1.1 McKendrick-von Foerster Equation.- 2.1.2 The Leslie Matrix Model.- 2.2 Life Stage Interactions.- 2.2.1 Life Cycle.- 2.2.2 Mortality.- 2.2.3 Fecundity.- 2.2.4 Equilibrium.- 2.3 Parameterization.- 2.3.1 Life Cycle.- 2.3.2 Fecundity.- 2.3.3 Natural Mortality.- 2.3.4 Cannibalism.- 2.4 Experimental Data and Computer Simulations.- 2.4.1 Experimental Design.- 2.4.2 Discretization.- 2.4.3 Equilibrium and Stability.- 2.4.4 Demographic Data and Simulations.- 2.4.5 Perturbations.- 2.4.6 Stable Limit Cycle.- 2.4.7 Bifurcation Points.- 2.5 Summary and Conclusions.- 2.6 Appendix.- 3 Demographic Oscillations.- 3.1 Egg-Larval Submodel.- 3.1.1 Fast and Slow Time Scales.- 3.1.2 Some Simplifying Assumptions.- 3.1.3 Integral Equations.- 3.2 Analytical Results.- 3.2.1 Equilibrium.- 3.2.2 Local Stability.- 3.2.3 Nonlinear Analysis.- 3.3 Numerical Results.- 3.3.1 Difference Equations.- 3.3.2 Multiple Attractors.- 3.3.3 Bifurcation Portrait.- 3.4 Biological Relevance.- 3.4.1 Age-Dependent Cannibalism.- 3.4.2 Complete Life Cycle.- 3.4.3 Populations in Parameter Space.- 3.4.4 Experimental Possibilities.- 3.4.5 Theoretical Questions and Extensions.- 3.5 Summary and Conclusions.- 3.6 Appendix.- 4 Continuous Shastic Models.- 4.1 Deterministic Model for Adult Numbers.- 4.2 Shastic Model for Adult Numbers.- 4.2.1 Shastic Differential Equation.- 4.2.2 Stationary Distribution.- 4.2.3 Properties of the Stationary Distribution.- 4.3 Statistical Procedures.- 4.3.1 Data Organization.- 4.3.2 Parameter Estimation.- 4.3.3 Testing the Gamma Hypothesis.- 4.3.4 Comparing Two Distributions.- 4.3.5 The Problem of Time-Dependence.- 4.4 Applications.- 4.4.1 Different Environments.- 4.4.2 Genetic Strains.- 4.4.3 Geographical Strains.- 4.4.4 Populations at Different Times.- 4.4.5 Population Outbreaks and Crashes.- 4.5 Stationary Time Series.- 4.5.1 Linear Approximation for the Shastic Model.- 4.5.2 Auorrelation Function.- 4.6 Time-Dependent Gamma Distribution.- 4.7 Summary and Conclusions.- 5 Discrete Shastic Models.- 5.1 Population Growth as a Birth-Death Process.- 5.1.1 Kolmogorov Forward Equations.- 5.1.2 Stationary Probabilities.- 5.1.3 Extinction Times and the Quasi-Steady State.- 5.2 Nonlinear Birth-Death Process for Tribolium.- 5.2.1 Recruitment and Mortality Rates.- 5.2.2 Extinction Times and the Quasi-Steady State.- 5.2.3 Approximations Based on the Normal Distribution.- 5.2.4 Cannibalism Rates and Extinction Times for Eight Genetic Strains.- 5.3 Linear Birth-Death Approximation.- 5.3.1 Linearized Recruitment Rate.- 5.3.2 Time-Dependent Mean and Variance.- 5.3.3 Transient and Stationary Probability Distribution.- 5.4 Application to Tribolium brevicornis.- 5.5 Summary and Conclusions.- 5.5.1 Deterministic versus Shastic Models.- 5.5.2 Continuous versus Discrete Shastic Models.- 5.5.3 Environmental versus Demographic Shasticity.- 5.6 Appendix.- 6 Natural Selection.- 6.1 Ecological-Genetic Perspective.- 6.2 Density-Regulated Natural Selection.- 6.2.1 Density-Dependent Fitness.- 6.2.2 Selection on Recruitment.- 6.2.3 Selection on Mortality.- 6.2.4 Selection on Both Recruitment and Mortality.- 6.3 Experimental Results on the Corn Oil Sensitive Mutant.- 6.3.1 Predictions.- 6.3.2 Genetic Polymorphism Experiment.- 6.3.3 Genetic Perturbation Experiment.- 6.3.4 Stationary Distributions of Population Numbers.- 6.3.5 Auorrelation of Population Numbers.- 6.3.6 Maximization of Population Numbers.- 6.4 Summary and Conclusions.- 7 Genetic Disequilibrium.- 7.1 An Entropy Measure of Genetic Disequilibrium.- 7.1.1 Ginzburg’s “Fitness Entropy”.- 7.1.2 Haldane’s “Cost of Natural Selection”.- 7.2 Rate of Genetic Adaptation.- 7.2.1 Entropy and the Cost of Selection.- 7.2.2 Entropy and the Adaptation Rate.- 7.2.3 An Experimental Test.- 7.3 Density-Independent Population Growth.- 7.3.1 The Reference Population.- 7.3.2 Entropy and Selective Delay.- 7.3.3 An Experimental Test.- 7.4 Density-Dependent Population Growth.- 7.4.1 Logistic Population Growth.- 7.4.2 Entropy and Life Not Lived.- 7.4.3 Properties of Life Not Lived.- 7.4.4 An Experimental Test.- 7.5 Extensions to the Theory.- 7.5.1 A Generalization for Weak Selection.- 7.5.2 Several Interacting Species.- 7.5.3 Asexual Age-Structured Populations.- 7.6 Summary and Conclusions.- 8 Two Interacting Species.- 8.1 Competition as an Adult-Immature Interaction.- 8.1.1 Two Species Equations.- 8.1.2 Analysis of the Model.- 8.2 Two Cannibalistic Species.- 8.2.1 T. castaneum versus T. confusum.- 8.2.2 The Fan-Shaped Outcome Pattern.- 8.2.3 Indiscriminate Cannibalism.- 8.2.4 Discriminate Cannibalism.- 8.2.5 Shastic Effects: Demographic or Genetic?.- 8.3 An Inhibiting Species with a Cannibalistic Species.- 8.3.1 T. castaneum versus T. brevicornis.- 8.3.2 Parameter Estimates and Model Predictions.- 8.4 Two Inhibiting Species.- 8.4.1 T. madens versus T. brevicornis.- 8.4.2 A Hypothesis.- 8.4.3 Developmental Inhibition.- 8.5 Summary and Conclusions.- 9 Dynamics and the Tribolium Model.- 9.1 Demography.- 9.1.1 Exploring Parameter Space.- 9.1.2 Strange Attractors and Chaos.- 9.1.3 Fast versus Slow Time Scales.- 9.2 Shasticity.- 9.2.1 Parameters of the Gamma Distribution.- 9.2.2 Shasticity and Age-structure.- 9.2.3 Extinction.- 9.2.4 Scale of Shastic Forces.- 9.2.5 Shastic Disequilibrium.- 9.3 Natural Selection.- 9.3.1 Natural Selection and Age Structure.- 9.3.2 Joint Distributions of Population Numbers and Allele Frequencies.- 9.3.3 Estimating the Life Not Lived.- 9.4 Species Interactions.- 9.4.1 Complex Demographic Models.- 9.4.2 Shastic Dynamics of Coexistence.- 9.5 Summary and Conclusions.- References.- Author Index.

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