Combining Multiple Tactics Over Time for Cost‐Effective Eradication Of

Ecology Letters, (2021) 24: 279–287 doi: 10.1111/ele.13640 LETTER Combining multiple tactics over time for cost-effective eradication of invading insect populations Abstract Adam Lampert1,2* and Because of the profound ecological and economic impacts of many non-native insect species, early Andrew M. Liebhold3,4 detection and eradication of newly founded, isolated populations is a high priority for preventing damages. Though successful eradication is often challenging, the effectiveness of several treatment methods/tactics is enhanced by the existence of Allee dynamics in target populations. Historically, successful eradication has often relied on the application of two or more tactics. Here, we examine how to combine three treatment tactics in the most cost-effective manner, either simultaneously or sequentially in a multiple-annum process. We show that each tactic is most efficient across a specific range of population densities. Furthermore, we show that certain tactics inhibit the efficiency of other tactics and should therefore not be used simultaneously; but since each tactic is effective at specific densities, different combinations of tactics should be applied sequentially through time when a multiple-annum eradication programme is needed. Keywords Bioeconomic, extinction, gypsy moth, insecticide, invasion, management, mating disruption, model, optimisation, sterile male. Ecology Letters (2021) 24: 279–287 pesticide application, habitat removal, mass-trapping, the ster- INTRODUCTION ile male technique and mating disruption (Suckling et al. Given the enormous ecological and economic costs of biologi- 2014; Liebhold and Kean 2019). A feature seen in several suc- cal invasions, the management of invasions is an important cessful insect eradication programmes has been the applica- priority in all world regions. Several studies have shown that tion of several of these tactics for targeting a single species preventing initial arrivals of new species is an economically during an eradication programme. For example the successful preferable approach (Leung et al. 2002; Finnoff et al. 2007). eradication of the painted apple moth, Teia anartoides, from But some invasion pathways are difficult to manage, and it Auckland, New Zealand employed three different tactics may not be possible to prevent arrivals and establishments of between 1999 and 2002; initial efforts were limited to mechan- all species (Perrings et al. 2005). Therefore, the strategy of ical removal of host plants, but then aerial spraying of micro- detecting and eradicating localised, newly founded popula- bial pesticides was implemented and finally sterile male tions is a key component of biosecurity programmes in place releases were used during the final year of the programme in various countries (Simberloff 2003; Liebhold et al. 2016). (Suckling et al. 2007). Eradication, which refers to the suppression of a population Studies have investigated how various treatment tactics to local extinction, has been recognised as a challenging goal, interact with Allee effects to achieve eradication. These studies given the difficulty of finding and eliminating every individual have focused on pesticide treatments (Liebhold and Bas- in a population (Genovesi 2008). However, many different compte 2003), host removal (Barron et al. 2020), release of types of organisms exhibit Allee effects, in which their popula- Wolbachia bacteria (Blackwood et al. 2018), mating disruption grows slower or declines at low densities, and this can be tion, mass-trapping and the sterile insect technique (Yama- exploited to facilitate eradication with reduced effort (Tobin naka and Liebhold 2009), but less is known about how these et al. 2011; Liebhold et al. 2016). In the presence of a strong treatments interact with each other. Suckling et al.(2012) Allee effect, eradication can be achieved by reducing a popu- reviewed various possible biological interactions between dif- lation below a threshold level, after which it is likely to ferent eradication tactics and speculated on how these combi- decline naturally to extinction; in some cases, the strength of nations might perform. Blackwood et al.(2012, 2018) used a an Allee effect can be manipulated to achieve extinction. modelling approach to evaluate interactions between different For insects, there has been increasing success at developing eradication tactics when applied simultaneously and to iden- and applying effective tools/tactics for eradicating invading tify economically optimal combinations of tactics for eradica- populations (Pluess et al. 2012; Tobin et al. 2014), including tion. Lampert and Hastings (2019) examined how to combine 1School of Human Evolution and Social Change, Arizona State University, 3USDA Forest Service Northern Research Station, Morgantown, WV 26505, Tempe, AZ 85287, USA USA 2Simon A. Levin Mathematical, Computational and Modeling Science Center, 4Faculty of Forestry and Wood Sciences, Czech University of Life Sciences Pra- Arizona State University, Tempe, AZ 85287, USA gue, Suchdol 165 21 Praha 6, Czech Republic *Correspondence: E-mail: [email protected] © 2020 John Wiley & Sons Ltd. 280 A. Lampert and A. M. Liebhold Letter tactics to restore ecosystems and cross the Allee threshold. Suckling et al. (2016) conducted field trials to evaluate the exis- Invading insect tence of synergistic vs. antagonistic interactions between insecti- Pescide populaon, cide and mating disruption treatments. However, these previous investigations have evaluated combinations of treatment tactics applicaon, only when these tactics are applied simultaneously, and they × × have not considered sequences of eradication tactics during a multiple annum eradication programme. These sequences are Sterile male potentially critical because eradication programmes typically release, target larger populations at the beginning, and populations are successively reduced to smaller levels. As the target population size decreases, certain tactics may become more effective than others, and consequently, managers may need to vary their tac- Mang tics during different phases (years) of the eradication project. disrupon, The objective of this study was to apply a bioeconomic pheromones model to identify optimal sequences for applying different tactics to achieve eradication. As a case study, we consider pesticide applications, mating disruption and sterile male release Figure 1 Illustration of the three tactics. Each year, the manager can use applied to eradicate isolated populations of invading insects. three different tactics to manage the invasive insect: (1) pesticide We focus on the gypsy moth, Lymantria dispar, though we application, which is typically applied at the larval stage and kills both males and females; (2) the release of sterile males that compete with the expect that our analysis is generalisable to most univoltine wild males for the females, but result in females laying non-viable eggs insects. We analyse a mechanistic model to evaluate various and (3) mating disruption, accomplished via distribution of large numbers sequences in which different tactics are applied in order to of pheromone sources that compete with females for the attraction of identify the most cost-effective strategies. males. egg mass), which develop into larvae, which pupate and METHODS develop into adults. Each year, a new generation replaces the previous generation. In turn, the probability that a female lays Mathematical model a viable egg mass is given by the probability that the female We consider an isolated population of a newly arrived non- finds a mate, P, times the probability that a female that found native insect species, where the density of adult individuals in a mate lays viable eggs, Q. Note that both P and Q depend year t is given by N(t). We consider a manager who can use on the number of feral males (depends on N) and the number various tactics to suppress populations of the species (Fig. 1) of sterile males (depends on S), and P also depends on the and can combine different tactics in different years with an probability that a given male finds a female (depends on F): ultimate intent of eradication. The objective of the manager is P ¼ PNðÞ, F, S , and Q ¼ QNðÞ, S . to minimise the total cost due to both treatment and damages In the second stage, we assume that, if the density is low over time, while promoting the eradication of the species and no pesticides are used, the number of eggs in a given egg locally in a given area. Below we describe which tactics are mass that survive and ultimately become adult females is given available to the manager in our model, how the target popula- by r. At higher densities, however, the larvae might compete tion responds to the various tactics over time and what the for tree foliage (food resources), and the number of female objective function of the manager is. adults produced by an egg mass is given by r(1 − N/K), where K is the population’s carrying capacity. Also, only a fraction Tactics of the manager exp(−γR) of larvae survives the use of pesticides, where γ is Our goal is to determine how the manager should invest in each the probability that an egg does not develop into a pupa due tactic over time (Fig. 1). Specifically, the manager can use any to each dollar invested in pesticide application. of the following three tactics, and s/he can decide how much to It follows that the following formula characterises the den- invest in each tactic each year, depending on the population sity of adult individuals during the mating season in year density in that year: (1) Insecticide application, R(t), which t + 1 as a function of the density of adults in the former gen- kills some fraction of larvae and thereby reduces the proportion eration in year t: of eggs that become adults; (2) mating disruption, F(t), which NtðÞ¼þ 1 rNðÞ1 À N=K expðÞÀγRNðÞPNðÞ, FNðÞ, SNðÞQNðÞ, SNðÞ, inhibits the ability of males to find a female, thereby increasing the chances that a female is not fertile by the end of the mating (1) season, and (3) release of sterile males, S(t), that compete with where N stands for N(t) for simplicity of the notations.

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