Chaotic Populations Research Articles

Chaos is not rare in natural ecosystems.

Chaotic dynamics are thought to be rare in natural populations but this may be due to methodological and data limitations, rather than the inherent stability of ecosystems. Following extensive simulation testing, we applied multiple chaos detection methods to a global database of 172 population time series and found evidence for chaos in >30%. In contrast, fitting traditional one-dimensional models identified <10% as chaotic. Chaos was most prevalent among plankton and insects and least among birds and mammals. Lyapunov exponents declined with generation time and scaled as the -1/6 power of body mass among chaotic populations. These results demonstrate that chaos is not rare in natural populations, indicating that there may be intrinsic limits to ecological forecasting and cautioning against the use of steady-state approaches to conservation and management.

A binary dandelion algorithm using seeding and chaos population strategies for feature selection

Feature selection (FS) is an important pre-processing step in data mining and pattern recognition. It can effectively compress the dimensionality of the feature space to reduce computation time and improve classification performance. The meta-heuristic algorithm-based feature selection method by finding the optimal set of features in the solution space has been widely used. However, this method is prone to trap into local optimality in a sufficiently large solution space. In this paper, we first propose a binary dandelion algorithm (BDA) to improve classification accuracy. In addition, to improve the performance of the algorithm, a binary dandelion algorithm using an improved seeding strategy and chaotic populations (SBDA) is proposed in this paper. Firstly, the strategy of optimizing the seeding radius by using the vibrational function and the historical optimal population increases the complexity of the search process and improves the search performance of the algorithm in the solution space. Secondly, when generating seeds, chaotic populations are generated using chaotic operators, which improves the ability of the algorithm to jump out of the local optimum and improves the stability of the algorithm. In this paper, 15 well-established datasets collected from the UCI machine learning database were adopted to compare four variants of BDA using only chaotic population improvement and in the next experiments, both mechanisms are verified to be effective in improving the performance of the algorithm. In addition, this paper compares the proposed BDA algorithm and SBDA algorithm with eight other classical algorithms. The experimental results show that SBDA can obtain fewer features with higher classification accuracy in most cases.

Allometric scaling of Lyapunov exponents in chaotic populations

AbstractChaos has been a central topic of research in ecology for decades, in part because of its implications for the predictability of population dynamics. Chaotic systems are characterized by low predictability at long timescales, as slight differences in initial conditions (e.g., the actual vs. the measured initial conditions) yield trajectories (e.g., the actual vs. the predicted trajectory) that diverge exponentially at a rate determined by the global Lyapunov Exponent (LE). The LE is therefore a critical descriptor of chaotic systems that sets the time horizon for predictability. Recent observations of chaos in populations or communities have shown that LEs vary by at least two orders of magnitude, yet the factors underlying this variability remain unclear. Here, we examine the drivers of heterogeneity in LEs among chaotic populations and communities. We show that LEs decline with increasing body size as a shallow power law (exponent −0.21), suggesting that LEs are inversely proportional to the populations' generation time (GT). However, this allometric scaling relationship holds only when considering the larger, slower growing populations in multispecies communities (the primary and secondary consumers), indicating that these populations constrain or determine LEs for the community. These results suggest that the rate at which the predictability of a chaotic time series declines over time generally reflects either the populations' GT, or that of a slower growing population in the community.

Expanding the methodological repertoire of participatory research into homelessness: The utility of the mobile phone diary

Participatory research methodologies have expanded the opportunities for critical, emancipatory and democratic health and social work research. However, their practical application in research with vulnerable participants has historically been challenging due to ethical, practical and theoretical concerns. Individuals who are homeless are typically seen as ‘hard-to-reach’, transient, ‘hidden’ and even chaotic participant populations. Unsurprisingly, examples of the use of innovative participatory research techniques with those groups have been relatively scarce. This paper aimed to address this gap by discussing the application of one such technique – the mobile phone diary in research with multiply disadvantaged homeless adults. Diary methods are situated within the qualitative research on health, illness and social marginality, and the enhanced capabilities of the mobile phone diary are highlighted. The author illustrates the application of the mobile phone diary in his participatory research on the everyday life narratives of adults with serious mental illness (SMI) who were homeless. The process of designing the mobile phone diary is detailed. Following this, participant testimonies of their use of the mobile phone diary are presented. They demonstrate the participatory and inclusive nature, as well as the cathartic and empowering potential, of this technique. The methodological contributions and challenges and the theoretical generativity of the mobile phone diary method are discussed. The mobile phone diary is a feasible approach for eliciting evocative, contextualised and nuanced accounts of the lived experience of homelessness, social isolation, coping and recovery.

Where and how do localized perturbations affect stream and coastal ocean populations with nonlinear growth dynamics?

Chaotic systems are sensitive to small changes in parameters and initial conditions, but are spatially distributed chaotic populations sensitive to the location of perturbations within their domain? Here, we examine the transient responses to perturbation in a density-dependent population model with asymmetrical dispersal, where offspring are moved some distance downstream of the parent population and diffusively spread, an appropriate approximation for species in streams, rivers, and ocean currents. We find that over a portion of the studied parameter space, our system displays extreme convective instability; that is, an arbitrarily small point-source perturbation to the upstream region grows and propagates downstream (in our finite one-dimensional domain, the current moves offspring preferentially in the downstream direction). We can then divide our domain into distinct upstream and downstream regions based on the response to perturbation. A perturbation to the upstream region will create transient downstream instability, and a perturbation to the downstream region has no qualitative effect on the population. We investigate the factors affecting the existence/size of the sensitive upstream region, discuss the ecologically relevant time scales of the transient dynamics following a perturbation, and consider the ecological implications of managing and predicting a population with transient amplification of perturbations.

Emergence of extreme events in networks of parametrically coupled chaotic populations.

We consider a collection of populations modelled by the prototypical chaotic Ricker map, relevant to the population growth of species with non-overlapping generations. The growth parameter of each population patch is influenced by the local mean field of its neighbourhood, and we explore the emergent patterns in such a parametrically coupled network. In particular, we examine the dynamics and distribution of the local populations, as well as the total biomass. Our significant finding is the following: When the range of coupling is sufficiently large, namely, when enough neighbouring populations influence the growth rate of a population, the system yields remarkably large biomass values that are very far from the mean. These extreme events are relatively rare and uncorrelated in time. We also find that at any point in time, exceedingly large population densities emerge in a few patches, analogous to an extreme event in space. Thus, we suggest a new mechanism in coupled chaotic systems that naturally yield extreme events in both time and space.

A downstream drift into chaos: Asymmetric dispersal in a classic density dependent population model

In the ocean, propagules with a planktonic stage are typically dispersed some distance downstream of the parent generation, introducing an asymmetry to the dispersal. Ocean-dwelling species have also been shown to exhibit chaotic population dynamics. Therefore, we must better understand chaotic population dynamics under the influence of asymmetrical dispersal. Here, we examine a density-dependent population in a current, where the current has both a mean and stochastic component. In our finite domain, the current moves offspring in the downstream direction. This system displays a rich variety of dynamics from chaotic to steady-state, depending on the mean distance the offspring are moved downstream, the diffusive spread of the offspring, and the domain size. We find that asymmetric dispersal can act as a stabilizing or destabilizing mechanism, depending on the size of the mean dispersal distance relative to the other system parameters. As the strength of the current increases, the system can experience period-halving bifurcation cascades. Thus, we show that stability of chaotic aquatic populations is directly tied to the strength of the ocean current in their environment, and our model predicts increased prevalence of chaos with decreasing dispersal distance. Climate change is likely to alter the dispersal patterns of many species, and so our results have implications for conservation and management of said species. We discuss the management implications, particularly of exploited species.

Threshold-activated transport stabilizes chaotic populations to steady states.

We explore Random Scale-Free networks of populations, modelled by chaotic Ricker maps, connected by transport that is triggered when population density in a patch is in excess of a critical threshold level. Our central result is that threshold-activated dispersal leads to stable fixed populations, for a wide range of threshold levels. Further, suppression of chaos is facilitated when the threshold-activated migration is more rapid than the intrinsic population dynamics of a patch. Additionally, networks with large number of nodes open to the environment, readily yield stable steady states. Lastly we demonstrate that in networks with very few open nodes, the degree and betweeness centrality of the node open to the environment has a pronounced influence on control. All qualitative trends are corroborated by quantitative measures, reflecting the efficiency of control, and the width of the steady state window.

Effect of Psychoactive Drugs on Demographic Parameters of the Blow Fly Chrysomya albiceps (Wiedemann) (Diptera: Calliphoridae)

Knowledge of the factors influencing the ecology of blow flies, especially the dynamic population equilibrium, is essential in forensic entomology. However, lack of knowledge of the action of psychoactive drugs on the population dynamics of these flies may affect the inferences that experts must make in medico-legal reports. This study evaluated the effects of amphetamine and phenobarbital on the population dynamics of Chrysomya albiceps (Wiedemann), by combining laboratory experimentation and mathematical modelling. Only amphetamine and its control, methanol, influenced the qualitative dynamic behaviour of Chrysomya albiceps, stabilising chaotic populations. The results are discussed in an ecological and forensic context.

Chaotic populations in genetic algorithms

We set two objectives for this study: one is to emulate chaotic natural populations in GA (Genetic Algorithms) populations by utilizing the Logistic Chaos map model, and the other is to analyze the population fitness distribution by utilizing insect spatial distribution theory. Natural populations are so dynamic that one of the first experimental evidences of Chaos in nature was discovered by a theoretical ecologist, May (1976, Nature, 261,459–467)[30], in his analysis of insect population dynamics. In evolutionary computing, perhaps influenced by the stable or infinite population concepts in population genetics, the status quo of population settings has dominantly been the fixed-size populations. In this paper, we propose to introduce dynamic populations controlled by the Logistic Chaos map model to Genetic Algorithms (GA), and test the hypothesis – whether or not the dynamic populations that emulate chaotic populations in nature will have an advantage over traditional fixed-size populations.The Logistic Chaos map model, arguably the simplest nonlinear dynamics model, has surprisingly rich dynamic behaviors, ranging from exponential, sigmoid growth, periodic oscillations, and aperiodic oscillations, to complete Chaos. What is even more favorable is that, unlike many other population dynamics models, this model can be expressed as a single parameter recursion equation, which makes it very convenient to control the dynamic behaviors and therefore easy to apply to evolutionary computing. The experiments show result values in terms of the fitness evaluations and memory storage requirements. We further conjecture that Chaos may be helpful in breaking neutral space in the fitness landscape, similar to the argument in ecology that Chaos may help the exploration and/or exploitation of environment heterogeneity and therefore enhance a species’ survival or fitness.

Preventing Extinction and Outbreaks in Chaotic Populations

Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage-structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.

Spatial synchrony in host–parasitoid populations

The ubiquity of spatial synchrony and its influences and causes have attracted the interest of ecologists. Spatially correlated environmental noises, dispersal, and trophic interactions have been considered as the causes of spatial synchrony. In this study, we developed a spatially implicit host–parasitoid model. Beside the above three mechanisms, correlation of environmental noise on different trophic levels was also included. Patterns of spatial synchrony was considered for stable, quasi-periodic, periodic, and chaotic population dynamics, respectively. In the stable region, a theoretical exploration based on a linearized 2-patch model was firstly done. Theoretical prediction shows that trophic correlation of environmental noises is another mechanism causing spatial synchrony. Numerical simulations of 2-patch and multi-patch models also verified the prediction. More simulations in other region show that periodic and quasi-periodic populations could be synchronized, while chaotic populations are hard to synchronize. The importance of our research is enriching the theory of potential causes of spatial synchrony.

Preventing Extinction and Outbreaks in Chaotic Populations

Interactions in ecological communities are inherently nonlinear and can lead to complex population dynamics including irregular fluctuations induced by chaos. Chaotic population dynamics can exhibit violent oscillations with extremely small or large population abundances that might cause extinction and recurrent outbreaks, respectively. We present a simple method that can guide management efforts to prevent crashes, peaks, or any other undesirable state. At the same time, the irregularity of the dynamics can be preserved when chaos is desirable for the population. The control scheme is easy to implement because it relies on time series information only. The method is illustrated by two examples: control of crashes in the Ricker map and control of outbreaks in a stage‐structured model of the flour beetle Tribolium. It turns out to be effective even with few available data and in the presence of noise, as is typical for ecological settings.

A prolegomenon to nonlinear empiricism in the human behavioral sciences

We propose a general framework for integrating theory and empiricism in human evolutionary ecology. We specifically emphasize the joint use of stochastic nonlinear dynamics and information theory. To illustrate critical ideas associated with historical contingency and complex dynamics, we review recent research on social preferences and social learning from behavioral economics. We additionally examine recent work on ecological approaches in history, the modeling of chaotic populations, and statistical application of information theory.

Anatomy of a chaotic attractor: subtle model-predicted patterns revealed in population data.

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn from chaotic insect populations, we show quantitatively that chaos manifests itself as a tapestry of identifiable and predictable patterns woven together by stochasticity. We show too that the mixture of patterns an experimentalist can expect to see depends on the scale of the system under study.

Fuzzy Chaos: Reduced Chaos in the Combined Dynamics of Several Independently Chaotic Populations

Nonlinear modeling, which showed the occurrence of deterministic chaos, has had a pivotal and stimulating effect on our understanding of diverse processes. May (1974, 1975, 1976, 1981a, 1981b, 1986, 1995) introduced nonlinear modeling into population ecology. He showed that the apparently simple equation (where x p rx (1 x ) t 1 t t of population of generation t, of x p size x p size t t 1 population of generation , and rate of t 1 r p intrinsic population growth) describes amazingly complex processes. At , populations are in equilibrium with 1 ! r ! 3 single values for xt. At , there are two values for xt; r 1 3 that is, populations alternate between high and low densities. At even higher values of r, there are 4, 8, and 16 values of xt, until at about , fluctuations in popr p 3.57 ulation size become chaotic, that is, apparently random but in fact strictly deterministic. To complicate matters even further, bifurcations characteristic of also 3 ! r ! 3.57 occur in the chaotic field. Moreover, fluctuations in population size are extremely sensitive to initial conditions; minute differences in initial x values (x 0) lead to very large differences in future population fluctuations, which makes predictions impossible. Many subsequent authors have applied nonlinear modeling to single-species populations and multispecies communities (e.g., Allen et al. 1993; Hastings et al. 1993; Harris 1994; Bond et al. 1995; Brown et al. 1995; Constantino et al. 1995; Rohani and Miramontes 1996; Stone and Ezrati 1996; Dennis et al. 1997; Earn et

Fuzzy Chaos: Reduced Chaos in the Combined Dynamics of Several Independently Chaotic Populations

Previous article No AccessNotes and CommentsFuzzy Chaos: Reduced Chaos in the Combined Dynamics of Several Independently Chaotic PopulationsKlaus Rohde, Peter P. Rohde, and Associate Editor: Lenore FahrigKlaus RohdeSchool of Biological Sciences, University of New England, Armidale, New South Wales 2351, Australia*Corresponding author; e‐mail: [email protected]. Search for more articles by this author , Peter P. RohdeSchool of Biological Sciences, University of New England, Armidale, New South Wales 2351, Australia Search for more articles by this author , and Associate Editor: Lenore Fahrig Search for more articles by this author School of Biological Sciences, University of New England, Armidale, New South Wales 2351, AustraliaPDFPDF PLUSFull TextSupplemental Material Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by The American Naturalist Volume 158, Number 5November 2001 Published for The American Society of Naturalists Article DOIhttps://doi.org/10.1086/323120 Views: 23Total views on this site Citations: 5Citations are reported from Crossref HistoryReceived October 6, 2000Accepted June 4, 2001 Keywordsfuzzy chaoschaosnonlinear dynamicsmetapopulationspopulation ecology© 2001 by The University of Chicago. PDF download Crossref reports the following articles citing this article:Puneet Sharma, Anima Nagar Topological dynamics on hyperspaces, Applied General Topology 11, no.11 (Apr 2010): 1–19.https://doi.org/10.4995/agt.2010.1724 Jack Teng and Kevin S. McCann Dynamics of Compartmented and Reticulate Food Webs in Relation to Energetic Flows. J. Teng and K. S. McCann, The American Naturalist 164, no.11 (Jul 2015): 85–100.https://doi.org/10.1086/421723Karine F. Magnago, Rodney C. Bassanezi Metapopulations Study with Subjective Biotic and Abiotic Processes, (Jan 2004): 733–740.https://doi.org/10.1007/978-3-540-44465-7_91J. M. J. Travis Neighbourhood size, dispersal distance and the complex dynamics of the spatial Ricker model, Population Ecology 45, no.33 (Dec 2003): 227–237.https://doi.org/10.1007/s10144-003-0161-9Klaus Rohde Ecology and biogeography of marine parasites, (Jan 2002): 1–83.https://doi.org/10.1016/S0065-2881(02)43002-7

Control, synchrony and the persistence of chaotic populations

The existence of deterministic chaos has been reported to date for a small number of real ecosystems. However, advances in the quest for chaos may include the application of chaos control techniques. In this paper, we study a model system, that of vegetation–hares–lynx interactions, in order to show the effects that control may exert on the structure and dynamics of the populations at play. Control techniques work effectively not only under the deterministic description, but also under assumptions of demographic and environmental stochasticity and even using spatially oriented approaches. Finally, some outlines are drawn with respect to the ecological consequences of applying chaos control in real ecosystems.

Self-segregation of competitive chaotic populations

The dynamical behavior of species competing for a common resource is studied with a reaction-diffusion system based on cubic autocatalysis. Randomly seeded populations self-segregate to form a complex network of domains separated by distinct interfaces. For chaotic populations in one-dimensional media, the interfaces exhibit irregular motions on long time scales. In two-dimensional media, the interface motions are governed by curvature-induced drift.

Mortality can produce predictable dynamics in chaotic populations

AbstractRecent theoretical studies have pointed out that a relatively small degree of dispersion between chaotic subpopulations produces predictable, simple dynamics and severely reduces the frequency of the occurrene of chaos. In this paper, we show that the introduction of mortality to models which are initially chaotic, alone or combined with dispersal, can produce similar effects.