Detecting nonlinear dynamics in spatio-temporal systems, examples from ecological models

Little, Sarah A.; Ellner, Stephen P.; Pascual, Mercedes; Neubert, Michael G.; Kaplan, Daniel T.; Sauer, Tim; Caswell, Hal; Solow, Andy

doi:10.1016/0167-2789(96)00030-9

Cited by 20 publications

(15 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Both Keeling et al (1997) and Pascual and Levin (1999) use attractor reconstruction from nonlinear time series analysis as the means of prediction (Takens 1981, Kaplan and Glass 1995, Little et al 1996. Assuming there is a deterministic system underlying the dynamics, observations of a single variable in the system over time are used as a proxy from which to predict the dynamics of the whole system.…”

Section: Existing Methods For Estimating Clss Of Dynamic Oscillating mentioning

confidence: 99%

“…Most approaches have assumed either that ecological systems are stationary in space and time, that fluctuations are random around a stationary global average (e.g., Rand and Wilson 1995), or that any trends detected are linear (see Turner et al 1991). These kinds of approaches fail to take into account the dynamical nature of ecological systems in space and time, which is arguably characterized by nonlinear oscillatory behaviors (e.g., Hastings et al 1993, Ellner and Turchin 1995, Sole and Bascompte 1995, Little et al 1996, Pascual and Ellner 2000.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Determining Natural Scales of Ecological Systems

Habeeb¹,

Trebilco²,

Wotherspoon³

et al. 2005

Ecological Monographs

View full text Add to dashboard Cite

Abstract. A key issue in ecology is to identify the appropriate scale(s) at which to observe trends in ecosystem behavior. The characteristic length scale (CLS) is a natural scale of a system at which the underlying deterministic dynamics are most clearly observed. Any approach to estimating CLSs of a natural system must be able to accommodate complex nonlinear dynamics and must have realistic requirements for data. Here, we compare the robustness of two methods to estimate CLSs of dynamical systems, both of which use attractor reconstruction to account for the complex oscillatory dynamics of ecological systems. We apply these techniques to estimate CLSs of spatial multispecies systems of varying complexity, and show that both methods are robust for the simplest system, but as model complexity increases, the Pascual and Levin metric is more robust than that of Keeling et al. Both methods demonstrate some sensitivity to the choice of species used in the analysis, with closely connected species producing more similar CLSs than loosely connected species. In this context, connectivity is determined both by the topology of the interaction network and spatial organization in the system. Notably, systems showing complex spatial self-organization can yield multiple CLSs, with larger length scales indicating the emergent dynamics of interactions between patches. While the prediction r 2 metric of Pascual and Levin is suitable to estimate CLSs of complex systems, their method is not suitable to apply to most real ecosystems because of the requirement of long time series for attractor reconstruction. We offer two alternatives, both based on prediction r 2 , but where repetition in space is largely (the ''short time series'' method) or wholly (the ''sliding window'' method) substituted for repetition in time in attractor reconstruction. Both methods, and in particular the short time series based on only three or four sequential observations of a system, are robust in detecting the primary length scale of complex systems. We conclude that the modified techniques are suitable for application to natural systems. Thus they offer, for the first time, an opportunity to estimate natural scales of real ecosystems, providing objectivity in important decisions about scaling in ecology.

show abstract

Section: Existing Methods For Estimating Clss Of Dynamic Oscillating mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Determining Natural Scales of Ecological Systems

Habeeb¹,

Trebilco²,

Wotherspoon³

et al. 2005

Ecological Monographs

View full text Add to dashboard Cite

show abstract

“…The model was introduced by Pascual (1993) and explored further by Little et al (1996), and describes the evolution of the prey q and predator h in both time t and space x according to…”

Section: Numerical Modelmentioning

confidence: 99%

“…Thus, they used methods based on attractor reconstruction for nonlinear systems to assess the strength and asymmetry of dispersal-based coupling between spatially separated components of a predator-prey model with diffusive movement (Pascual 1993;Little et al 1996). Specifically, they investigated dynamic interdependence (generalized synchrony) by drawing inferences about the nature of functions relating reconstructed attractors.…”

Section: Introductionmentioning

confidence: 99%

Inferences about information flow and dispersal for spatially extended population systems using time-series data

Nichols¹

2005

Proc. R. Soc. B.

View full text Add to dashboard Cite

This work explores an information-theoretic approach to drawing inferences about coupling of spatially extended ecological populations based solely on time-series of abundances. The efficacy of the approach, time-delayed mutual information, was explored using a spatially extended predator-prey model system in which populations at different patches were coupled via diffusive movement. The approach identified the relative magnitude and direction of information flow resulting from animal movement between populations, the change in information flow as a function of distance separating populations, and the diffusive nature of the information flow. In addition, when the diffusive movement was eliminated from the model, mutual information correctly provided no evidence of information flow, even when population synchrony was generated by a common environmental driving function. Thus, for this model system, timedelayed mutual information was useful in discriminating between the Moran effect and animal movement as causes of population synchrony, as well as in characterizing dispersal in terms of direction, relative speed and diffusive nature.

show abstract

“…[6,10]) and ecological (e.g. [11,12]) studies. In the ecological literature, they are also known as dispersal kernels [3,13], redistribution kernels [14,15], dispersal curves [16] and displacement kernels [17,18], and in epidemiological publications they are sometimes called contact kernels [7,19].…”

Section: Introductionmentioning

confidence: 99%

The shape of the spatial kernel and its implications for biological invasions in patchy environments

2010

View full text Add to dashboard Cite

Ecological and epidemiological invasions occur in a spatial context. We investigated how these processes correlate to the distance dependence of spread or dispersal between spatial entities such as habitat patches or epidemiological units. Distance dependence is described by a spatial kernel, characterized by its shape (kurtosis) and width (variance). We also developed a novel method to analyse and generate point-pattern landscapes based on spectral representation. This involves two measures: continuity, which is related to autocorrelation and contrast, which refers to variation in patch density. We also analysed some empirical data where our results are expected to have implications, namely distributions of trees (Quercus and Ulmus) and farms in Sweden. Through a simulation study, we found that kernel shape was not important for predicting the invasion speed in randomly distributed patches. However, the shape may be essential when the distribution of patches deviates from randomness, particularly when the contrast is high. We conclude that the speed of invasions depends on the spatial context and the effect of the spatial kernel is intertwined with the spatial structure. This implies substantial demands on the empirical data, because it requires knowledge of shape and width of the spatial kernel, and spatial structure.

show abstract

Detecting nonlinear dynamics in spatio-temporal systems, examples from ecological models

Cited by 20 publications

References 17 publications

Determining Natural Scales of Ecological Systems

Determining Natural Scales of Ecological Systems

Inferences about information flow and dispersal for spatially extended population systems using time-series data

The shape of the spatial kernel and its implications for biological invasions in patchy environments

Contact Info

Product

Resources

About