Inferring mechanism from time-series data: Delay-differential equations

Ellner, Stephen P.; Kendall, Bruce E.; Wood, Simon N.; McCauley, Edward; Briggs, Cheryl J.

doi:10.1016/s0167-2789(97)00123-1

Cited by 50 publications

(27 citation statements)

References 14 publications

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“…Gradient matching methods have been proposed numerous times in applications (e.g. Bellman and Roth 1971;Swartz and Bremermann 1975;Varah 1982;Ellner et al 1997) and recently their statistical properties have been studied (Brunel 2008), proving that consistent parameter estimates can be obtained. The functionsp(t) andπ(t) were modeled using basis expansion methods,…”

Section: Descriptionmentioning

confidence: 99%

Rapid prey evolution and the dynamics of two-predator food webs

Ellner

Becks

2010

Theor Ecol

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Traits affecting ecological interactions can evolve on the same time scale as population and community dynamics, creating the potential for feedbacks between evolutionary and ecological dynamics. Theory and experiments have shown in particular that rapid evolution of traits conferring defense against predation can radically change the qualitative dynamics of a predator-prey food chain. Here, we ask whether such dramatic effects are likely to be seen in more complex food webs having two predators rather than one, or whether the greater complexity of the ecological interactions will mask any potential impacts of rapid evolution. If one prey genotype can be well-defended against both predators, the dynamics are like those of a predator-prey food chain. But if defense traits are predator-specific and incompatible, so that each genotype is vulnerable to attack by at least one predator, then rapid evolution produces distinctive behaviors at the population level: population typically oscillate in ways very different from either the food chain or a two-predator food web without rapid prey evolution. When many prey genotypes coexist, chaotic dynamics become likely. The effects of rapid evolution can still be detected by analyzing relationships between prey abundance and predator population growth rates using methods from functional data analysis

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Section: Descriptionmentioning

confidence: 99%

Rapid prey evolution and the dynamics of two-predator food webs

Ellner

Becks

2010

Theor Ecol

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“…For example, techniques have now been developed to fit both deterministic semiparametric models (e.g., Wood 2001) and stochastic semiparametric models (Ellner et al 2002). Semiparametric models have been developed that use splines that are a function of time (e.g., Wood 1994, 2001, Ohman and Wood 1996 or density of one or more state variables (e.g., Ellner et al 1997, Bjørnstad et al 1999. As a result, semiparametric models are being applied more often to ecological problems (e.g., Ohman and Wood 1995, Ellner et al 1998, Wood 1999, Ohman and Hirche 2001.…”

Section: Concepts and Synthesismentioning

confidence: 99%

Capturing Dynamics With the Correct Rates: Inverse Problems Using Semiparametric Approaches

Nelson

McCauley

Wimbert

2004

Ecology

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Ecological interactions are often difficult to observe or manipulate directly, making it a challenge to evaluate competing hypotheses in natural systems. Semiparametric models can provide a powerful inverse approach to infer population processes from observational data because they allow an ecologist to model aspects of a system that are known, but allow the data to “speak for themselves” with regard to aspects that are unknown. However, (st)age‐structured semiparametric models are plagued with demographic instabilities that can cause different combinations of interactions, including competing hypotheses, to predict the observed pattern equally well. We developed and tested two new solutions to these demographic instabilities that expand the range of life histories for which (st)age‐structured semiparametric inverse methods can be used. We begin by reviewing the range of inverse methods, from fully parametric models in which the governing functions are completely specified, to semiparametric models that replace these functions with nonparametric curves. We illustrate how the demographic instabilities emerge and indicate the requirements that any successful solution must satisfy. Existing solutions use constraints that may conflict with ecological processes and cause strong biases in the inferred rates. Our first solution uses a new statistical constraint that is less restrictive than previous methods. Our second solution is a hybrid approach that supplements the less restrictive statistical constraint with a few estimates of the interaction rates. This hybrid approach provides a way of distinguishing among dynamical mechanisms without imposing constraints on ecological relationships.

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“…As discussed in Introduction, we are interested in nonparametric estimates of B and D. The methods presented here are conceptually similar to those in Ellner et al (1997). However, those methods were statistically inefficient and relied on ad hoc visual criteria for selecting the complexity of the fitted rate equations.…”

Section: Methods: Single-species Model and Fitting Proceduresmentioning

confidence: 99%

Fitting Population Dynamic Models to Time-Series Data by Gradient Matching

Ellner

Seifu

Smith

2002

Ecology

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We describe and test a method for fitting noisy differential equation models to a time series of population counts, motivated by stage-structured models of insect and zooplankton populations. We consider semimechanistic models, in which the model structure is derived from knowledge of the life cycle, but the rate equations are estimated nonparametrically from the time-series data. The method involves smoothing the population time series x(t) in order to estimate the gradient dx/dt, and then fitting rate equations using penalized regression splines. Computer-intensive methods are used to estimate and remove the biases that result from the data being discrete time samples with sampling errors from a continuous time process. Semimechanistic modeling makes it possible to test assumptions about the mechanisms behind population fluctuations without the results being confounded by possibly arbitrary choices of parametric forms for process-rate equations. To illustrate this application, we analyze time-series data on laboratory populations of blowflies Lucilia cuprina and Lucilia sericata. The models assume that the populations are limited by competition among adults affecting their current birth and death rates. The results correspond to the actual experimental conditions. For L. cuprina (where the model's structure is appropriate) a good fit can be obtained, while for L. sericata (where the model is inappropriate), the fitted model does not reproduce some major features of the observed cycles. A documented set of R functions for all steps in the model-fitting process is provided as a supplement to this article.

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Inferring mechanism from time-series data: Delay-differential equations

Cited by 50 publications

References 14 publications

Rapid prey evolution and the dynamics of two-predator food webs

Rapid prey evolution and the dynamics of two-predator food webs

Capturing Dynamics With the Correct Rates: Inverse Problems Using Semiparametric Approaches

Fitting Population Dynamic Models to Time-Series Data by Gradient Matching

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