Estimating Chaos and Complex Dynamics in an Insect Population

Dennis, B. R.; Desharnais, Robert A.; Cushing, J. M.; Henson, Shandelle M.; Costantino, R. F.

doi:10.2307/2657219

Cited by 52 publications

(124 citation statements)

References 53 publications

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“…For species 2, process error was kept fixed at the intermediate level (σ 2 2 = 0.1). Such range of process error matches what is observed in the field (Dennis, Desharnais, Cushing, Henson, & Costantino, 2001;Jonzén, Pople, Grigg, & Possingham, 2005).…”

Section: Simulating Ecological Dynamicssupporting

confidence: 85%

“…At low process error level, these plots often displayed the curved relationships typical of nonlinearities unaccounted for, as exemplified in Figure 4a. As process error increased to levels commonly observed in the field (σ 2 = 0.1-0.5, Dennis, Kemp, & Taper, 1998;Dennis et al, 2001), these curved relationships became harder and harder to detect, to the point where they could very well become unnoticed (Figure 4b). Hence, even if looking at the residuals is a crucial step of the modelling process, failing to observe curved relationships is not a proof of absence of nonlinearities, especially for noisy systems.…”

Section: The Gompertz Assumption Of Linearity On a Log-scalementioning

confidence: 98%

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How do MAR(1) models cope with hidden nonlinearities in ecological dynamics?

2018

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Multivariate autoregressive (MAR) models are an increasingly popular technique to infer interaction strengths between species in a community and to predict the community response to environmental change. The most commonly employed MAR(1) models, with one time lag, can be viewed either as multispecies competition models with Gompertz density dependence or, more generally, as a linear approximation of more complex, nonlinear dynamics around stable equilibria. This latter interpretation allows for broader applicability, but may come at a cost in terms of interpretation of estimates and reliability of both short‐ and long‐term predictions. We investigate what these costs might be by fitting MAR(1) models to simulated 2‐species competition, consumer‐resource and host–parasitoid systems, as well as a larger food web influenced by the environment. We review how MAR(1) coefficients can be interpreted and evaluate how reliable are estimates of interaction strength, rank, or sign; accuracy of short‐term forecasts; as well as the ability of MAR(1) models to predict the long‐term responses of communities submitted to environmental change such as PRESS perturbations. The net effects of species j on species i are usually (90%‐95%) well recovered in terms of sign or rank, with the notable exception of overcompensatory dynamics. In actual values, net effects of species j on species i are not well recovered when the underlying dynamics are nonlinear. MAR(1) models are better at making short‐term qualitative forecasts (next point going up or down) than at predicting long‐term responses to environmental perturbations, which can be severely over‐ as well as underestimated. We conclude that when applying MAR(1) models to ecological data, inferences on net effects among species should be limited to signs, or the Gompertz assumption should be tested and discussed. This particular assumption on density‐dependence (log‐linearity) is also required for unbiased long‐term predictions. Overall, we think that MAR(1) models are highly useful tools to resolve and characterize community dynamics, but we recommend to use them in conjunction with alternative, nonlinear models resembling the ecological context in order to improve their interpretation in specific applications.

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Section: Simulating Ecological Dynamicssupporting

confidence: 85%

Section: The Gompertz Assumption Of Linearity On a Log-scalementioning

confidence: 98%

How do MAR(1) models cope with hidden nonlinearities in ecological dynamics?

2018

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“…Understanding the interaction between environmental noise and the underlying deterministic behaviour of a biological system is of considerable interest (Bjørnstad and Grenfell 2001, Dennis et al 2001, Clutton‐Brock and Coulson 2002, Lundberg et al 2002, Cazelles and Stone 2003, Greenman and Benton 2003, Ripa and Ives 2003), not least because of the increasing need to be able to predict population behaviour for conservation and management, in a changing world. In this paper we have studied this interaction for systems that can be described by structured nonlinear discrete time models, influenced by weak noise.…”

Section: Discussionmentioning

confidence: 99%

The frequency spectrum of structured discrete time population models: its properties and their ecological implications

Greenman¹,

Benton²

2005

Oikos

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2005. The frequency spectrum of structured discrete time population models: its properties and their ecological implications. Á/ Oikos 110: 369 Á/389.Much research effort has been devoted to the study of the interaction between environmental noise and discrete time nonlinear dynamical systems. A large part of this effort has involved numerical simulation of simple unstructured models for particular ranges of parameter values. While such research is important in encouraging discussion of important ecological issues it is often unclear how general are the conclusions reached. However, by restricting attention to weak noise it is possible to obtain analytical results that hold for essentially all discrete time models and still provide considerable insight into the properties of the noise-dynamics interface. We follow this approach, focusing on the autocorrelation properties of the population fluctuations using the power (frequency) spectrum matrix as the analytic framework. We study the relationship between the spectral peak structure and the dynamical behaviour of the system and the modulation of this relationship by its internal structure, acting as an ''intrinsic'' filter and by colour in the noise acting as an ''extrinsic'' filter. These filters redistribute ''power'' between frequency components in the spectrum. The analysis emphasises the importance of eigenvalues in the identification of resonance, both in the system itself and in its subsystems, and the importance of noise configuration in defining which paths are followed on the network. The analysis highlights the complexity of the inverse problem (in finding, for example, the source of long term fluctuations) and the role of factors other than colour in the persistence of populations.

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“…Costantino et al. 1997; Dennis et al. 2001; Fowler & Ruxton 2002), whereas time‐varying stochastic forms incorporate extrinsic drivers, such as variation in climate or resource abundance (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Density‐dependent models largely focus on analysing attractors including stable equilibria such as carrying capacity or unstable equilibria such as limit cycles and chaotic dynamics (e.g. Turchin 1993; Dennis et al. 2001).…”

Section: Introductionmentioning

confidence: 99%

A framework for studying transient dynamics of population projection matrix models

2011

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Empirical models are central to effective conservation and population management, and should be predictive of real-world dynamics. Available modelling methods are diverse, but analysis usually focuses on long-term dynamics that are unable to describe the complicated short-term time series that can arise even from simple models following ecological disturbances or perturbations. Recent interest in such transient dynamics has led to diverse methodologies for their quantification in density-independent, time-invariant population projection matrix (PPM) models, but the fragmented nature of this literature has stifled the widespread analysis of transients. We review the literature on transient analyses of linear PPM models and synthesise a coherent framework. We promote the use of standardised indices, and categorise indices according to their focus on either convergence times or transient population density, and on either transient bounds or case-specific transient dynamics. We use a large database of empirical PPM models to explore relationships between indices of transient dynamics. This analysis promotes the use of population inertia as a simple, versatile and informative predictor of transient population density, but criticises the utility of established indices of convergence times. Our findings should guide further development of analyses of transient population dynamics using PPMs or other empirical modelling techniques.

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Estimating Chaos and Complex Dynamics in an Insect Population

Cited by 52 publications

References 53 publications

How do MAR(1) models cope with hidden nonlinearities in ecological dynamics?

How do MAR(1) models cope with hidden nonlinearities in ecological dynamics?

The frequency spectrum of structured discrete time population models: its properties and their ecological implications

A framework for studying transient dynamics of population projection matrix models

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