Population Dynamics and the Tribolium Model: Genetics and Demography

by Robert F. Costantino, Robert A. Desharnais

Overview

The study of populations is becoming increasingly focused on dynamics. We believe there are two reasons for this trend. The ftrst is the impactof nonlinear dynamics with its exciting ideas and colorful language: bifurcations, domains of attraction, chaos, fractals, strange attractors. Complexity, which is so very much a part of biology, now seems to be also a part of mathematics. A second trend is the accessibility of the new concepts. Thebarriers ommunicationbetween theorist and experiment a list seemless impenetrable. The active participationof the experimentalist means that the theory will obtain substance. Our role is the application of the theory of dynamics to the analysis ofbiological populations. We began our work early in 1979 by writing an ordinary differential equation for the rateofchange in adult numbers which was based on an equilibrium model proposed adecadeearlier. Duringthenextfewmonths we filled our notebooks with straight forward deductions from the model and its associated biological implications. Slowly, some of the biological observations were explained and papers followed on a variety of topics: genetic and demographic stability, stationary probability distributions for population size,population growth asabirth-deathprocess, natural selectionanddensity-dependent population growth, genetic disequilibrium, and the stationary shastic dynamics of adult numbers.

Product Details

ISBN-13:	9781461278238
Publisher:	Springer New York
Publication date:	09/17/2011
Series:	Monographs on Theoretical and Applied Genetics , #13
Edition description:	Softcover reprint of the original 1st ed. 1991
Pages:	258
Product dimensions:	6.69(w) x 9.61(h) x 0.02(d)

Table of Contents

1 Introduction.- 1.1 A Brief History of the Mathematics of Tribolium.- 2 Biology and Dynamics of Age Structure.- 2.1 Models for Age-Structured Populations.- 2.2 Life Stage Interactions.- 2.3 Parameterization.- 2.4 Experimental Data and Computer Simulations.- 2.5 Summary and Conclusions.- 2.6 Appendix.- 3 Demographic Oscillations.- 3.1 Egg-Larval Submodel.- 3.2 Analytical Results.- 3.3 Numerical Results.- 3.4 Biological Relevance.- 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.- 4.3 Statistical Procedures.- 4.4 Applications.- 4.5 Stationary Time Series.- 4.6 Time-Dependent Gamma Distribution.- 4.7 Summary and Conclusions.- 5 Discrete Shastic Models.- 5.1 Population Growth as a Birth-Death Process.- 5.2 Nonlinear Birth-Death Process for Tribolium.- 5.3 Linear Birth-Death Approximation.- 5.4 Application to Tribolium brevicornis.- 5.5 Summary and Conclusions.- 5.6 Appendix.- 6 Natural Selection.- 6.1 Ecological-Genetic Perspective.- 6.2 Density-Regulated Natural Selection.- 6.3 Experimental Results on the Corn Oil Sensitive Mutant.- 6.4 Summary and Conclusions.- 7 Genetic Disequilibrium.- 7.1 An Entropy Measure of Genetic Disequilibrium.- 7.2 Rate of Genetic Adaptation.- 7.3 Density-Independent Population Growth.- 7.4 Density-Dependent Population Growth.- 7.5 Extensions to the Theory.- 7.6 Summary and Conclusions.- 8 Two Interacting Species.- 8.1 Competition as an Adult-Immature Interaction.- 8.2 Two Cannibalistic Species.- 8.3 An Inhibiting Species with a Cannibalistic Species.- 8.4 Two Inhibiting Species.- 8.5 Summary and Conclusions.- 9 Dynamics and the Tribolium Model.- 9.1 Demography.- 9.2 Shasticity.- 9.3 Natural Selection.- 9.3.1 Natural Selection and Age Structure.- 9.4 Species Interactions.- 9.5 Summary and Conclusions.- References.- Author Index.

Editorial Reviews

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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