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A stepwise algorithm to detect significant time lags in ecological time series in terms of autocorrelation functions and ARMA model optimisation of pest population seasonal outbreaks

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Abstract

A central issue in population ecology is to determine the structure of negative feedback-density depend process which regulates population dynamics and seasonal fluctuations. In this work the incidence of population density dependences and seasonality was examined in fruit orchards of three closely related pest species (Adoxophyes orana, Anarsia lineatella and (Grapholita) Grapholitha molesta). Analysis included 13 moth population time series during 2003–2011. Additionally, considering that time lags and seasonality are fundamental characteristics of ecological organisation and pest management, the work aimed to introduce a step wise algorithm to detect significant population feedbacks, moth seasonality and population synchronisation of nearby locations. In the proposed procedure, each population-time series was first analysed on the basis of autocorrelation and partial autocorrelation. Moreover, assuming that each of the ecological variable, observed at successive time points, consist of a stochastic process, autoregressive moving average ARMA(p,q) models and seasonal autoregressive moving average models SARMA(p,q)x(P,Q) S were fitted on data. The Akaike information criteria was further used by the stepwise algorithm for parameter optimization and model improvement. Model construction is accompanied by a presentation of the fitting results and a discussion of the heuristic benchmarks used to assess the forecasting performance of the models. Life cycles of populations belonging to same species appeared to synchronise by terms of their autocorrelation functions. Delayed density dependence and order was in most cases of lag:1 and 2, while lag >3 was not found more frequently as expected by chance. In A. orana and A. lineatella moth species lag = 1 delayed density dependence was significantly more frequent and in particular in nearby locations. However, the structure of the fitted models varied with respect to species and observation region. In some cases, seasonal models were considered to be more accurate in simulating moth population dynamics. Finally, to provide means in forecasting moth emergence and abundance, utile in pest management, the models were trained using 2003–2009 data sets and their forecasting performance were validated for each case using data sets of 2010–2011. In most cases, the constructed stochastic linear autoregressive models simulated the population outbreaks very well. Describing and forecasting stochastic population fluctuations is a basic tenet of theoretical and applied ecology, while detecting the relative roles of exogenous and endogenous mechanisms can partly describe the phenomenological behavior of pest population time series data and improve pest management.

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Acknowledgments

The author acknowledges the help provided by the Agronomists of the public confederation ALMME®, in collecting part of the data that were used to generate some representative models. The author would like to thank also an anonymous reviewer, which provided his suggestions on an early draft of the MS as well the associate editor for providing some very valuable indications.

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  1. Mathematics Department, Faculty of Sciences, Aristotle University of Thessaloniki, 59100, Veroia, Greece

    Petros Damos

  2. Department of Environmental Conservation and Management, Faculty of Pure and Applied Sciences, Open University of Cyprus, Latsia, Cyprus

    Petros Damos

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Correspondence to Petros Damos.

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Damos, P. A stepwise algorithm to detect significant time lags in ecological time series in terms of autocorrelation functions and ARMA model optimisation of pest population seasonal outbreaks. Stoch Environ Res Risk Assess 30, 1961–1980 (2016). https://doi.org/10.1007/s00477-015-1150-1

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