Author

# Robert A. Desharnais

Other affiliations: California State University, University of Idaho, California Institute of Technology

Bio: Robert A. Desharnais is an academic researcher from California State University, Los Angeles. The author has contributed to research in topics: Population & Attractor. The author has an hindex of 29, co-authored 55 publications receiving 3041 citations. Previous affiliations of Robert A. Desharnais include California State University & University of Idaho.

##### Papers published on a yearly basis

##### Papers

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TL;DR: A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior.

Abstract: A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior. With the adult mortality rate experimentally set high, the dynamics of animal abundance changed from equilibrium to quasiperiodic cycles to chaos as adult-stage recruitment rates were experimentally manipulated. These transitions in dynamics corresponded to those predicted by the mathematical model. Phase-space graphs of the data together with the deterministic model attractors provide convincing evidence of transitions to chaos.

395 citations

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TL;DR: In this article, it was shown that the sensitivity of a stochastic Lyapunov exponent (SLE) to the initial conditions of a deterministic model is not a sign of chaos.

Abstract: An important component of the mathematical definition of chaos is sensitivity to initial conditions. Sensitivity to initial conditions is usually measured in a deterministic model by the dominant Lyapunov exponent (LE), with chaos indicated by a positive LE. The sensitivity measure has been extended to stochastic models; however, it is possible for the stochastic Lyapunov exponent (SLE) to be positive when the LE of the underlying deterministic model is negative, and vice versa. This occurs because the LE is a long-term average over the deterministic attractor while the SLE is the long-term average over the stationary probability distribution. The property of sensitivity to initial conditions, uniquely associated with chaotic dynamics in deterministic systems, is widespread in stochastic systems because of time spent near repelling invariant sets (such as unstable equilibria and unstable cycles). Such sensitivity is due to a mechanism fundamentally different from deterministic chaos. Positive SLE's should therefore not be viewed as a hallmark of chaos. We develop examples of ecological population models in which contradictory LE and SLE values lead to confusion about whether or not the population fluctuations are primarily the result of chaotic dynamics. We suggest that “chaos” should retain its deterministic definition in light of the origins and spirit of the topic in ecology. While a stochastic system cannot then strictly be chaotic, chaotic dynamics can be revealed in stochastic systems through the strong influence of underlying deterministic chaotic invariant sets.

264 citations

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TL;DR: This study documents the nonlinear prediction of periodic 2-cycles in laboratory cultures of Tribolium and represents a new interdisciplinary approach to un- derstanding nonlinear ecological dynamics.

Abstract: Our approach to testing nonlinear population theory is to connect rigorously mathematical models with data by means of statistical methods for nonlinear time series. We begin by deriving a biologically based demographic model. The mathematical analysis identifies boundaries in parameter space where stable equilibria bifurcate to periodic 2-cy- cles and aperiodic motion on invariant loops. The statistical analysis, based on a stochastic version of the demographic model, provides procedures for parameter estimation, hypothesis testing, and model evaluation. Experiments using the flour beetle Tribolium yield the time series data. A three-dimensional map of larval, pupal, and adult numbers forecasts four possible population behaviors: extinction, equilibria, periodicities, and aperiodic motion including chaos. This study documents the nonlinear prediction of periodic 2-cycles in laboratory cultures of Tribolium and represents a new interdisciplinary approach to un- derstanding nonlinear ecological dynamics.

229 citations

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TL;DR: A simple model describing population growth in the flour beetle Tribolium was developed and it was predicted that changes in adult mortality would produce substantial shifts in population dynamic behaviour, and changes in the dynamics from stable fixed points to periodic cycles to aperiodic oscillations were observed.

Abstract: SIMPLE nonlinear models can generate fixed points, periodic cycles and aperiodic oscillations in population abundance without any external environmental variation Another familiar theoretical result is that shifts in demographic parameters (such as survival or fecundity) can move a population from one of these behaviours to another1–4 Unfortunately, empirical evidence to support these theoretical possibilities is scarce5–15 We report here a joint theoretical and experimental study to test the hypothesis that changes in demographic parameters cause predictable changes in the nature of population fluctuations Specifically, we developed a simple model describing population growth in the flour beetle Tribolium16 We then predicted, using standard mathematical techniques to analyse the model, that changes in adult mortality would produce substantial shifts in population dynamic behaviour Finally, by experimentally manipulating the adult mortality rate we observed changes in the dynamics from stable fixed points to periodic cycles to aperiodic oscillations that corresponded to the transitions forecast by the mathematical model

205 citations

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TL;DR: In this article, a model- predicted sequence of transitions (bifurcations) in the dynamic behavior of a population from stable equilibria to quasiperiodic and periodic cycles to chaos to three-cycles using cultures of the flour beetle Tribolium.

Abstract: A defining hypothesis of theoretical ecology during the past century has been that population fluctuations might largely be explained by relatively low-dimensional, non- linear ecological interactions, provided such interactions could be correctly identified and modeled. The realization in recent decades that such nonlinear interactions might result in chaos and other exotic dynamic behaviors has been exciting but tantalizing, in that attri- buting the fluctuations of a particular real population to the complex dynamics of a particular mathematical model has proved to be an elusive goal. We experimentally tested a model- predicted sequence of transitions (bifurcations) in the dynamic behavior of a population from stable equilibria to quasiperiodic and periodic cycles to chaos to three-cycles using cultures of the flour beetle Tribolium. The predictions arose from a system of difference equations (the LPA model) describing the nonlinear life-stage interactions, predominantly cannibalism. We built a stochastic version of the model incorporating demographic vari- ability and obtained conditional least-squares estimates for the model parameters. We gen- erated 2000 ''bootstrapped data sets'' with a time-series bootstrap technique, and for each set we reestimated the model parameters. The resulting 2000 bootstrapped parameter vectors were used to obtain confidence intervals for the model parameters and estimated distri- butions of the Liapunov exponents for the deterministic portion (the skeleton) of the model as well as for the full stochastic model. Frequency distributions of estimated dynamic behaviors of the skeleton at each experimental treatment were produced. For one treatment, over 83% of the bootstrapped parameter estimates corresponded to chaotic attractors, and the remainder of the estimates yielded high-period cycles. The low-dimensional skeleton accounted for at least 90% of the variability in the population abundances and accurately described the responses of populations to experimental demographic manipulations, in- cluding treatments for which the predicted dynamic behavior was chaos. Demographic stochasticity described the remaining noise quite well. We conclude that the fluctuations of experimental flour beetle populations are explained largely by known nonlinear forces involving cannibalistic-stage interactions. Claims of dynamic behavior such as periodic cycles or chaos must be accompanied by a consideration of the reliability of the estimated parameters and a realization that the population fluctuations are a blend of deterministic forces and stochastic events.

192 citations

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TL;DR: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols used xiii 1.

Abstract: Preface to the Princeton Landmarks in Biology Edition vii Preface xi Symbols Used xiii 1. The Importance of Islands 3 2. Area and Number of Speicies 8 3. Further Explanations of the Area-Diversity Pattern 19 4. The Strategy of Colonization 68 5. Invasibility and the Variable Niche 94 6. Stepping Stones and Biotic Exchange 123 7. Evolutionary Changes Following Colonization 145 8. Prospect 181 Glossary 185 References 193 Index 201

14,171 citations

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TL;DR: It is suggested that maternal behavior serves to "program" hypothalamic-pituitary-adrenal responses to stress in the offspring.

Abstract: Variations in maternal care affect the development of individual differences in neuroendocrine responses to stress in rats. As adults, the offspring of mothers that exhibited more licking and grooming of pups during the first 10 days of life showed reduced plasma adrenocorticotropic hormone and corticosterone responses to acute stress, increased hippocampal glucocorticoid receptor messenger RNA expression, enhanced glucocorticoid feedback sensitivity, and decreased levels of hypothalamic corticotropin-releasing hormone messenger RNA. Each measure was significantly correlated with the frequency of maternal licking and grooming (all r 9s > −0.6). These findings suggest that maternal behavior serves to “program” hypothalamic-pituitary-adrenal responses to stress in the offspring.

3,020 citations

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07 Nov 1996

TL;DR: One-dimensional maps, two-dimensional map, fractals, and chaotic attraction attractors have been studied in this article for state reconstruction from data, including the state of Washington.

Abstract: One-Dimensional Maps.- Two-Dimensional Maps.- Chaos.- Fractals.- Chaos in Two-Dimensional Maps.- Chaotic Attractors.- Differential Equations.- Periodic Orbits and Limit Sets.- Chaos in Differential Equations.- Stable Manifolds and Crises.- Bifurcations.- Cascades.- State Reconstruction from Data.

1,924 citations

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21 Jul 2008

TL;DR: In step-by-step detail, Benjamin Bolker teaches ecology graduate students and researchers everything they need to know in order to use maximum likelihood, information-theoretic, and Bayesian techniques to analyze their own data using the programming language R.

Abstract: Ecological Models and Data in R is the first truly practical introduction to modern statistical methods for ecology. In step-by-step detail, the book teaches ecology graduate students and researchers everything they need to know in order to use maximum likelihood, information-theoretic, and Bayesian techniques to analyze their own data using the programming language R. Drawing on extensive experience teaching these techniques to graduate students in ecology, Benjamin Bolker shows how to choose among and construct statistical models for data, estimate their parameters and confidence limits, and interpret the results. The book also covers statistical frameworks, the philosophy of statistical modeling, and critical mathematical functions and probability distributions. It requires no programming background--only basic calculus and statistics.

1,626 citations

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01 Jan 2005TL;DR: In this paper, the authors present a spatial analysis of complete point location data, including points, lines, and graphs, and a multiscale analysis of the data set, including spatial diversity analysis and spatial autocorrelation.

Abstract: Preface 1. Spatial concepts and notions 2. Ecological and spatial processes 3. Points, lines and graphs 4. Spatial analysis of complete point location data 5. Contiguous units analysis 6. Spatial analysis of sample data 7. Spatial relationship and multiscale analysis 8. Spatial autocorrelation and inferential tests 9. Spatial partitioning: spatial clusters and boundary detection 10. Spatial diversity analysis 11. Spatio-temporal analysis 12. Closing comments and future directions References Index.

1,250 citations