Use of ROOT to build a software optimized for parameter estimation and simulations with Distributed Delay Model

Highlights

• A new application of the ROOT open source software in Integrated Pest Management

• A complete description of how the study will help entomologists in simulation processes with Distributed Delay Models

• An application of the ROOT open source software as a Decision Support System tool

Abstract

ROOT is a software package developed by a CERN project started in 1994 by René Brun for statistical analysis in high-energy physics. This software package can also be used in the field of protecting plants against pest insects. Indeed, for a long time there has been a significant use of the Distributed-Delay Model, but there is no specific software available to date that is useful for following the research from the first step to simulations and field validations.

This work, through ROOT's libraries, builds a series of macros that consent to do non-linear fits with functions such as Erlang PDF, linear-rate, Logan, Briére, Sharpe and De Michele, thereby giving support to the parameters-estimate step in laboratory sessions and then numerically solving the Distributed-Delay Model equations. This study supplies results both graphically and numerically.

Introduction

In Agricultural, Forest and Environmental Sciences, and especially in the context of risk management, modelling has become an important tool. In particular, entomologists started using several models to forecast pest insects' life cycles for two primary reasons: safeguarding human and environmental health, and because of the restrictive laws regarding pesticide use. The difference between a monitoring system and a forecasting system results from the possibility of having an idea of the risk situation of an agricultural field or an urban and peri-urban area (Speranza et al. 2007). There is a need to develop a control strategy different from the conventional one. Despite monitoring and forecast systems seeming similar, in reality there is a conspicuous difference between them. In the first case, data collected with traps placed in fields provides empirical information on insect presence. Capinera defines the term “monitoring” as “careful observation of pest abundance and damage” (Capinera 2001). The inconvenience is that monitoring provides no information about the future trends of the monitored population. On the other hand, a simulation could not report the exact field situation, but it is helpful to know the future development of the population. In other words, forecasting is “the process of making predictions based on past and present data”. These predictions can support a series of research projects that involve using natural enemies such as predators, parasitoids, entomopathogenic fungi and bacteria for the control of insect pests. Indeed, natural enemy complex plays a preeminent role in controlling invasive and autochthonous species in different environmental contexts. For example, the entomopathogenic fungus Entomophaga maimaiga in areas where it has been introduced is effective against the gipsy moth Lymantria dispar (Lepidoptera: Erebidae) populations (Pilarska et al., 2006), encouraging further experimentation aimed at diffusing this pathogen in new areas across the world (Contarini et al. 2016). In the agronomic context, the biological control applications of the entomopathogenic bacteria Bacillus thuringiensis (Alsaedi et al. 2017; González-Cabrera et al. 2011) or the predator Zelus obscuridorsis (Hemiptera: Heteroptera: Reduviidae) (Speranza et al. 2014) in the tomato leaf miner, Tuta absoluta (Lepidoptera: Gelechiidae) might be mentioned. The inconvenience of this type of control is that it requires highly qualified technicians, quick response and accurate knowledge of the most susceptible life stage of the insect pest if one is to maximize the efficacy of the use of biological control. On the other hand, if it is impossible to apply a biological control strategy, to know the pests' population trends helps one perform chemical control to reduce the quantity of the pesticide in question. One of the widely used models is the Distributed Delay Model (DDM).

Beginning with its introduction by Manetsch (1976), the DDM has garnished interest from entomologists and environmental scientists to describe the life cycle of poikilothermic organisms. One of the strengths concerns the possibility of linking environmental and species' parameters to the description of a population dynamics. Several applications have shown the DDM's adaptability to different pest insect species (Alilla et al. 2007; Blythe et al. 1985; Galeano-Vasco et al. 2013; Limonta et al. 2009; Pucci and Spanedda 2006; Schaalje and van der Vaart 1989; Severini 2004; Speranza et al. 2007; Wang et al. 1977). A typical application of the DDM for a species with a poorly known biological cycle starts with a series of constant-temperature laboratory rearing. This is the first phase or “laboratory session”: entomologists build cohorts of insects (all laid on the same day) and put them in climatic cells. Researchers follow each cohort's individual day by day during its life cycle, collecting data of the duration of each stage. There were similar observations for other insect pests belonging to different orders, including the beetles (Coleoptera) Rhynchophorus ferrugineus (Dryophthoridae) and Anthonomus eugenii (Curculionidae) (Li et al. 2010; Toapanta et al. 2005), the butterflies (Lepidoptera) Lobesia botrana (Tortricidae), Corcyra cephalonica (Pyralidae), and Tuta absoluta (Gelechiidae) (Moshtaghi Maleki et al. 2016; Osman et al. 1984; Özgökçe et al. 2016), the wasp (Hymenoptera) Diadegma anurum (Ichneumonidae) (Golizadeh et al. 2008), and the true bug (Hemiptera) Halyomorpha halys (Pentatomidae) (Nielsen et al. 2008).

Life tables are important because of the description of the relationship between the temperature (the main environmental driving variable for poikilothermic organisms) and the average developmental time, D[T], for each stage composing the life cycle. It is common in practical cases to convert the mean developmental time D[T] in mean development rate R[T], (specific for each temperature), by the expression (Liu et al. 1995; Severini and Gilioli 2002).

$$R\left[T\right]=\frac{1}{D\left[T\right]}$$

The reason behind this choice is the trend reported in a plot rate-temperature. In fact, with this conversion, one can obtain an increasing-decreasing profile which highlights the thermal optimum for the species as well as its lower and upper thermal thresholds. The second phase of a simulation process concerns the simulation: all the estimated parameters are inserted in a model together with the measured average daily temperature. This obtains the forecasted population dynamics. Subsequently, a validation is made comparing the results of a simulation, with data collected via in-field monitoring. Despite wide application, one of the main problems reported by the insiders is the lack of a specific software that allows researchers to collect data during each step of the project. This current work introduces a new application of the ROOT software as a base to build a helpful tool for all simulation processes with DDM. More specifically, ROOT is “a modular scientific software framework. It provides all the functionalities needed to deal with big data processing, statistical analysis, visualization and storage. It is mainly written in C++ but integrated with other languages such as Python and R.” (http://root.cern.ch) (Brun and Rademakers 1997). The following sections describe the specifics of each operation and the corresponding ROOT's macro developed to manage all the required calculations.