# Predicting biological control performance under global change using model-based exploration of predator-prey dynamics: Application to the Nesidiocoris tenuis - Tuta absoluta system

Isabelle Grechi, Mame Diarra Bousso Ba, Philippe Correa, Massamba Diakhaté, Thibault Nordey, Serigne Sylla, Thierry Brevault, Anaïs Chailleux

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Isabelle Grechi, Mame Diarra Bousso Ba, Philippe Correa, Massamba Diakhaté, Thibault Nordey, et al.. Predicting biological control performance under global change using model-based exploration of predator-prey dynamics: Application to the Nesidiocoris tenuis - Tuta absoluta system. Ecological Modelling, 2025, 507, pp.111186. 10.1016/j.ecolmodel.2025.111186. hal-05183265

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# Predicting biological control performance under global change using model-based exploration of predator-prey dynamics: application to the *Nesidiocoris tenuis - Tuta absoluta* system

Isabelle Grechi<sup>a,b,*</sup> <sup>ID</sup>, Mame Diarra Bousso Ba<sup>a,c</sup> <sup>ID</sup>, Philippe Correa<sup>a,c</sup>, Massamba Diakhaté<sup>a,c</sup>, Thibault Nordey<sup>a,b,1</sup>, Serigne Sylla<sup>c</sup>, Thierry Brévault<sup>d,e</sup>, Anaïs Chailleux<sup>b,f ID</sup>

## ARTICLE INFO

### Keywords:

- Climate change

- Invasive pest

- Mirid bug

- Temperature

- Tomato leaf miner

- Trophic interactions

## ABSTRACT

Global change is disrupting our knowledge of ecosystem functioning through climate warming and pest invasion, affecting predator-prey population dynamics. We hypothesized that the control of invasive pests by native predators would decrease with increasing temperatures. We investigated the effects of high temperatures jointly with other factors related to biological control conditions (i.e., habitat complexity reflected by predator searching efficiency, predator-to-prey ratio, and relative timing of species establishment) on predator-prey population dynamics for the zoophytophagous and generalist mirid bug, *Nesidiocoris tenuis*, and the tomato leaf miner, *Tuta absoluta*, a native insect predator and an invasive insect pest, respectively, in Senegal. We carried out life history trait measurements in the laboratory at different temperatures (i.e., constant temperatures of 25, 30, 35, 40, and 45 °C and temperatures of 40:35 °C alternating following the light and dark cycle). We developed a stochastic individual-based model to simulate predator and prey population dynamics. Both species were able to complete their life cycle until 35 °C and until 40 °C when the night temperature decreased to 35 °C, while populations persisted over time only at 25 and 30 °C. Contrary to our expectations, pest control increased with temperature due to a higher predation efficiency and asymmetries between insect fitness responses to temperature in favor of the predator. Our study showed that populations of *T. absoluta* would not increase at high temperatures, either due to successful control by *N. tenuis* at 30 °C or due to a population collapse at 35 °C and beyond, as *T. absoluta* approaches its critical thermal maximum. At a temperature less favorable for pest control (25 °C), the timing of predator and pest establishment was the main factor determining the performance of pest control. Control was ensured when the predator established before or close to pest infestation. This can occur with generalist predators that can survive by feeding on alternative resources.

## 1. Introduction

Synergies between global change and biological invasion have recently been identified as a significant threat to global biodiversity and human welfare (Millennium Ecosystem Assessment, 2005). On the one hand, climate warming can affect ecological communities through the thermal sensitivity of predator-prey interactions (Grigaltchik et al.,

2012; Traill et al., 2010), especially for poikilothermic animals (including insects). On the other hand, while ecosystem invasions by exotic species increase due to increased international trade (Chapman et al., 2017; Dukes and Mooney, 1999), climate warming is also hypothesized to favor biological invasions (Huang et al., 2011). This calls for a better understanding of the effect of temperature on species interactions, both for biological conservation and ecosystem services

<footnote><sup>a</sup> CIRAD, UPR HortSys, F-34398 Montpellier, France</footnote>

<footnote><sup>b</sup> HortSys, Univ Montpellier, CIRAD, Montpellier, France</footnote>

<footnote><sup>c</sup> UCAD, Dakar, Senegal</footnote>

<footnote><sup>d</sup> CIRAD, UPR AIDA, Biopass, Centre de recherche ISRA-IRD, Dakar, Senegal</footnote>

<footnote><sup>e</sup> AIDA, Univ Montpellier, CIRAD, Montpellier, France</footnote>

<footnote><sup>f</sup> CIRAD, UPR HortSys, F-97455 Saint-Pierre, Réunion, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: isabelle.grechi@cirad.fr (I. Grechi).</footnote>

<footnote n="1">¹ Present address: Terre d'Essais, Le Glazic, F-22740 Pleumeur-Gautier, France</footnote>
management (Chailleux et al., 2020; Traill et al., 2010).

In arthropod food webs, temperature affects the dynamics of her-
bivorous populations directly by affecting their fitness but also indi-
rectly by affecting their predator fitness and predatory activity. Indeed,
insect fitness responds to temperature following a unimodal and left-
skewed curve with an optimum temperature and critical lower and
upper thresholds (Deutch et al., 2008; Martinez-Garcia et al., 2016).
Warming is expected to shift temperatures from optimal to unfavorable.
The effect on predator-prey population dynamics depends on the
asymmetries in the thermal response of the interacting species (Dell
et al., 2014). In addition, evidence has suggested that i) higher trophic
levels are more sensitive to warming than lower trophic levels (Preisser
and Strong, 2004; Voigt et al., 2003), which might give the prey an
advantage over the predator, and ii) invasive species have a higher
plasticity than native species, which might help them better facing
warmer climate (Chown et al., 2007). This is alarming about the future
control of invasive pests by native predators. In addition to species
fitness, temperature affects arthropod predators' feeding rate. The
functional response of the predator to the density of prey depends
mainly on the search rate (i.e., the searching efficiency of the predator,
also called the encounter or attack rate) and the handling time (i.e., the
time to kill and eat a prey), both of which are related to temperature
(Madbouni et al., 2017; Sentis et al., 2012). According to Sentis et al.
(2012), predator feeding rate is primarily determined by searching ac-
tivities and second by prey handling. On a ladybeetle-aphid system, they
found that the search rate exhibits a hump-shaped relationship with
temperature, whereas the handling time exponentially decreases with
temperature. Other studies showed that predation increases with tem-
perature (Frances and McCauley, 2018; Frank and Bramböck, 2016),
even though the prey's vulnerability window was reduced due to their
faster development (Pepi et al., 2018). Therefore, climate warming
could affect predator-prey interactions in several ways: through asym-
metries in species' thermal performance, through changes in predator
feeding rate, and also through shifts in species' geographical distribu-
tions, bringing previously non-interacting species into contact (Dell
et al., 2014). Consequently, the outcome of predator-prey population
dynamics in the face of climate warming is difficult to predict.

Within the changing context that affects ecosystems, the current willingness to reach human- and environment-safe agriculture is leading to increased mobilization of nature-based pest control methods. Biological control is a promising lever mediated by predator-prey interactions. This raises the question of how biological control programs would be affected by climate warming. McEvoy (2018) comprehensively summarized how the theory surrounding biological control (sensu Kar-eiva (1996)) can help to understand, optimize, and upscale biological control. Most model-based theoretical studies have investigated a very restricted range of contexts, focusing on (i) classical biological control (i. e., control of an exotic pest using exotic natural enemies), (ii) parasitoid-host interactions, or (iii) green-house or perennial systems, to name but a few restrictions. This makes current attempts to develop conservation or augmentative biological control in annual field crops completely orphan of theorizing. Including generalist predators in theorizing is another issue, as they increasingly appear more promising than specialists (Stiling and Cornelissen, 2005), especially in the tropics (Hawkins et al., 1997). Unlike specialists, generalists' population dynamic is less dependent on the target pest, as they can feed on other prey or plant-provided resources, allowing the predator to be present before the pest infestation. The pre-infestation presence of some predators, especially mirids, has been empirically shown to improve biological control greatly (Calvo et al., 2012; Messelink et al., 2015; Pijnakker et al., 2020; Sanchez et al., 2021), but no evidence theoretically by modeling.

In this study, we tackle theorizing the effect of climate warming on
the biological control of an invasive insect pest by a native and gener-
alist insect predator, with application to the tomato leaf miner, *Tuta
absoluta* Meyrick (Lepidoptera: Gelechiidae), and the zoophytophagous

mirid bug, *Nesidiocoris tenuis* Reuter (Hemiptera: Miridae), in Senegal. African agriculture is strongly endangered by global warming (Müller et al., 2011) and is particularly susceptible to invasions (Paini et al., 2016), making local case studies particularly relevant. *T. absoluta* invaded Senegal in 2012 (Brévault et al., 2014; Pfeiffer et al., 2013) and spread rapidly throughout the country (Sylla et al., 2017). It devastates tomato crops in this country and throughout Africa (Mansour et al., 2018; Desneux et al., 2022). *N. tenuis* was shown to occur in Senegal naturally and prey on *T. absoluta* in open fields (Chailleux et al., 2022; Sylla et al., 2016).

The biological control of *T. absoluta* by *N. tenuis* was investigated using a two-step approach: (i) by producing laboratory data to test the effect of temperature on life history traits (i.e., juvenile developmental time and mortality, adult longevity, and female fecundity) of the Senegalese populations of both species, and the *per capita* kill rate of *N. tenuis* (defined as the number of prey killed per predator per unit of time), and (ii) by developing a model that integrates these data to investigate the effect of temperature on predator-prey population dynamics and pest control outcomes. The temperature effect was investigated jointly with other factors related to biological control conditions (i.e., habitat complexity, predator-to-prey ratio, and relative timing of species establishment). Habitat complexity (Gotceitas and Colgan, 1989; Schmidt and Rypstra, 2010), plant architecture (Grevstad and Klepetka, 1992), and plant diversity and size (Gols et al., 2005) influence predator foraging efficiency. The initial predator-to-prey ratio is another factor driving predator-prey population dynamics (Strong and Croft, 1995), with varying outcomes depending on the environment (Lesna et al., 2000) and on the release frequency in impulsive biological control (Nundloll et al., 2010). The relative timing of predator establishment or release is considered in the pre- versus post-infestation strategy. Based on model simulations, we first explored the effect of temperature on the dynamics of isolated populations. Then, we investigated the effect of temperature on interacting predator-prey populations, as well as the effect of the factors mentioned above to determine whether pest control outcomes were conditioned differently by specific biological control conditions depending on the temperature.

## 2. Materials and methods

### 2.1. Laboratory data

#### 2.1.1. Biological materiel

A colony of *T. absoluta* was established four months upstream of laboratory experiments, using 300 larvae collected in tomato fields in the Niayes area in Senegal. The individuals were reared in net cages (120×70×125 cm) containing four to six tomato plants (variety Mongal F1) at the four to eight leaves stage and placed in a net house. The larvae were fed tomato plants, while the adults received 10 % sugared water (crystal sugar, Compagnie Sucrière du Sénégal) ad libitum. Two new plants were added to the routine cages for plant turnover weekly. Age segregation cages were created weekly by releasing 50 adults for one week to obtain individuals of the same ages ± 3.5 days. A colony of *N. tenuis* was reared in conditions similar to *T. absoluta* from 50 adults collected in tomato fields in the Niayes area in Senegal. Adults were fed 10 % sugared water, crushed bee pollen pellets (Lune de Miel®), and *Ephestia kuheniella* Zeller (Lepidoptera: Phycitidae) sterilized eggs (Bioline AgroSciences Ltd.) ad libitum. Although not essential, sugar water and pollen pellets were used as boosters.

#### 2.1.2. Laboratory experiments

Life history traits of *T. absoluta* and *N. tenuis* (i.e., stage duration and mortality of juveniles, longevity of adults, and fertility of females) and the daily *per capita* kill rate (defined as the number of prey killed per predator per unit of time) of adults of *N. tenuis* were measured in climatic chambers (I-30 VL, Percival Scientific, Inc., USA) under six temperature regimes at 12L:12D photoperiod and 70 ± 10 % RH. The six temperature
regimes comprised five with constant temperatures (25, 30, 35, 40, and 45 °C) and one with two temperatures (40:35 °C) alternating following the light and dark cycle. These temperatures cover the current and future range of hot temperatures in West Africa (Diallo et al., 2012).

The duration of stage and mortality rate of *T. absoluta* juveniles were evaluated by placing 30 eggs per temperature regime on two 20-day-old tomato plants (15 eggs per plant and one egg per leaflet) in the climatic chamber. After egg hatching, the first instar larvae were individually transferred to a trifoliate with the stem inserted in a flower foam in a Petri dish (90×15 mm). The trifoliate was watered daily and changed when necessary. The death of each individual, the hatching of eggs, and the pupation and emergence of adults were recorded daily. Another batch of individuals was reared to obtain up to 15 couples of synchronized males and females per temperature regime (as far as it allows juvenile development) for adult monitoring. Adult survival and fecundity were evaluated by placing a couple in an arena made of two superposed plastic cups, the one below serving as a water tank and the one above (8 × 11 cm) containing the insect and the plant, following the Biondi et al. (2012) protocol. Individuals had access to water due to the cotton sealing the leaf through the cup. No additional food source was provided. Individual survivorship was monitored daily. Couples were transferred each second day to a new arena, and the number of eggs laid by females during the two days was directly recorded under a binocular microscope. Monitoring continued until the death of the female while dead males were replaced.

The duration of the stage and the mortality rate of *N. tenuis* juveniles were also assessed in climatic chambers. Young females were allowed to oviposit on plants for 24 hours under conditions similar to colony rearing, after which the plants were transferred to the climatic chambers. The inability to observe and count eggs on plants did not allow us to record their emergence rate. After egg hatching, 30 nymphs per temperature regime were individually transferred to a Petri dish using similar disposal as for *T. absoluta*. Nymphs and adults were fed *E. kuehniella* eggs ad libitum throughout the experiment. Each individual's death or adult emergence was recorded daily. Another batch of individuals was reared for adult monitoring to allow pairing. Adult survival and fecundity were assessed similarly as for *T. absoluta* by placing 15 couples individually in arenas, monitoring individual survival daily, and transferring couples to a new arena each second day. After transfer, each arena was incubated to check for nymph emergence for fecundity assessment.

The daily per capita kill rate of *N. tenuis* was assessed using one-week-old individuals (± 24 hours) (approximately 10 males and 10 females per temperature regime) from the rearing colony. Individuals were starved for 24 hours (no food but plant access) and then transferred to arenas. Each arena contained an adult *N. tenuis* and 100 eggs of *T. absoluta*. Eggs were previously deposited on the trifoliate (on both sides) using a paintbrush. Twenty-four hours later, the number of eggs consumed was recorded.

### 2.1.3. Statistical analysis

The effect of the temperature regime on the life history traits of *T. absoluta* and *N. tenuis* and the daily per capita kill rate of *N. tenuis* were analyzed using generalized linear models (GLM) with appropriate distributions, followed by deviance tests. The duration of juvenile stages and the longevity of adults were examined using Gamma GLMs. In contrast, fecundity and the daily per capita kill rate were analyzed using negative binomial GLMs and mortality with a binomial GLM. For adult longevity and daily per capita kill rate, the effect of temperature was analyzed separately for females and males. When a significant effect was observed, multiple post hoc comparisons of means were performed using the Tukey test.

## 2.2. Modeling framework

### 2.2.1. Model description

The dynamics of stage-structured *T. absoluta* and *N. tenuis* populations were formulated using a discrete-time stochastic individual-based model. Those dynamics were described under conditions of non-limiting resources, assuming that plants were a nonlimiting resource for *T. absoluta* and that *N. tenuis* could feed on alternative food in the absence of *T. absoluta*. The model explicitly describes the development, mortality, and reproduction of all individuals progressing through successive life stages. Life stages were eggs (E), larvae (L), pupae (P), and adults for *T. absoluta*, and juveniles (J, consisting of eggs and nymphs) and adults for *N. tenuis*. The adults were subdivided into males (M) and females (F). Demographic stochasticity was considered by modeling the development, natural mortality (i.e., excluding mortality from predation), and reproduction of individuals as random processes according to process-specific probability distributions. The additional mortality of *T. absoluta* individuals due to predation was considered using a functional response model. All these biological processes depended on the temperature regime. The dynamics of the two populations were obtained by the time evolution of the number of individuals within each life stage, summarized at a daily time step.

**Development.** The duration of life stage *s* of an individual *j*, denoted $d_{j,s}^*$ (days), is randomly assigned to the individual according to a Gamma distribution with a lower bound set at 0.1 day:

$$d_{j,s}^* \sim \min\{0.1, \Gamma(\alpha_{p,s,T}^d, \beta_{p,s,T}^d)\} \quad (1)$$

where $\alpha_{p,s,T}^d$ and $\beta_{p,s,T}^d$ are the population (p)-, life stage (s)- and temperature (T)-dependent shape and rate parameters of the Gamma distribution. On day *i*, individual *j* develops from life stage *s* to the next stage $s^+$ if $d_{j,s}^{i-1} + 1 > d_{j,s}^*$, and the time it spends within the stage $s^+$ is $d_{j,s}^i = d_{j,s}^{i-1} + 1 - d_{j,s}^*$, where $d_{j,s}^{i-1}$ (days) is the time it has spent within stage *s* up to and including day *i*-1. When no development occurs, $d_{j,s}^i = d_{j,s}^{i-1} + 1$. For the egg or juvenile life stages, $d_{j,s}^{i-1}$ was set to $i - t_{k,j}$ if individual *j* was laid at day *i*, where $t_{k,j}$ (days) is the time when individual *j* was laid by a female *k*. Individuals entering the adult stage are randomly assigned to the male or female stage according to a Bernoulli distribution with probability *p* = 0.5 (based on a 1:1 sex ratio).

**Natural mortality.** For the adult life stages $s \in \{M,F\}$, an individual *j* dies at day *i* if $d_{j,s}^{i-1} + 1 > d_{j,s}^*$ (here, $d_{j,s}^*$ stands for the individual longevity). In rare cases where $d_{j,s}^* < 1$, the individual may die on the same day that it has developed from the previous life stage. For the juvenile life stages $s \in \{E,L,P,J\}$, daily mortality is applied at *prorata* of the time an individual *j* has spent within the life stage *s* during day *i* ($\Delta d_{j,s}^i$, days) according to a Bernoulli distribution with probability *p* = 1 - $(1 - m_{p,s,T})^{\Delta d_{j,s}^i/d_{j,s}^*}$, where $m_{p,s,T}$ is the population-, life stage- and temperature-dependent mortality rate of individuals. Daily mortality is applied to all the life stages the individual experienced during the day.

**Reproduction.** The fecundity of a female *j* (i.e., the number of eggs the female lays), denoted $f_j$, is assumed to follow a negative binomial (also known as a Gamma-Poisson mixture) distribution:

$$f_j \sim \mathcal{P}(\lambda), \quad \lambda \sim \Gamma(\alpha_{p,T}^f, \alpha_{p,T}^f / \mu_{p,T}^f) \quad (2)$$

where $\alpha_{p,T}^f$ and $\alpha_{p,T}^f/\mu_{p,T}^f$ are the population- and temperature-dependant shape and rate parameters of the Gamma distribution ($\mu_{p,T}^f$ is the Gamma-Poisson mixture distribution mean). Eggs are laid at different times during the life of the female. The age at which the female *j* lays an egg $k \in \{1: f_j\}$, denoted $l_{j,k}$ (days), is assumed to follow a Gamma distribution with a lower bound set at 0.1 day and an upper bound set at the female longevity:
$$l_{j,k} = \min\{0.1, \max\{L, d_{j,F}^i\}\}, L \sim \Gamma(a_{p,T}^l, b_{p,T}^l) \quad (3)$$

where $a_{p,T}^l$ and $b_{p,T}^l$ are the population- and temperature-dependent shape and rate parameters of the Gamma distribution. If female j has emerged on day i, the time at which it will lay egg k is $t_{j,k} = (i + 1 - \Delta d_{j,F}^i) + l_{j,k}$, where $(i + 1 - \Delta d_{j,F}^i)$ is the exact time of female emergence.

**Predation.** Adults of *N. tenuis* were assumed to prey on *T. absoluta* eggs. Even though *N. tenuis* nymphs can prey, and young *T. absoluta* larvae can be preyed; this was considered marginal in the field because the wingless *N. tenuis* nymphs have a reduced foraging capacity, and *T. absoluta* larvae can escape, unlike eggs. It was also assumed that eggs dead for two days (stage $E_d$) could be preyed on before decay. On day i, the daily per capita kill rate of a *N. tenuis* adult j ($KR_j^i$, day$^{-1}$) is assumed to follow a type-II functional response (Sharifian et al., 2015):

$$KR_j^i = \frac{a(1 - \delta)(I_E^i + I_{E_d}^i)}{1 + a(1 - \delta)Th_{s,T}(I_E^i + I_{E_d}^i)} \quad (4)$$

where $I_E^i$ and $I_{E_d}^i$ are the densities of *T. absoluta* eggs alive and $\le 2$-days old dead eggs at day i, a (day$^{-1}$) is the attack rate, $Th_{s,T}$ (day) is the sex- and temperature-dependent handling times, and $0 \le \delta \le 1$ is a reduction rate (named ‘attack reduction rate’). $\delta$ accounts for habitat complexity in the field that can affect predator foraging efficiency. As the time an individual spends daily within the life stages can be $< 1$ day, daily densities of prey and predators were considered using a ‘day-individuals’ density $I_s^i = \sum_{j \in \Omega_s} \Delta d_{j,s}^i$ (days), where $\Omega_p$ is the set of individuals in population p. On day i, the number of *T. absoluta* eggs consumed by *N. tenuis* adults ($C_{egg}^i$), within the set of individuals that have been at the egg or $\le 2$-days old dead egg stages during the day ($\Omega_{egg}^i$), is:

Figure A3). Although the two parameters of the functional response may be sex- and temperature-dependent, the data available for calibration were not sufficient to solve the optimization problem without setting one parameter constant. Parameter a was set constant because it provided the most accurate fit. The values of all model parameters are given in Appendix A, Table A1.

### 2.2.3. Simulations

The dynamics of the *T. absoluta* and *N. tenuis* populations were simulated over 80 days, representing the time frame of a tomato cropping cycle for both isolated and interacting populations. Simulations were carried out in each temperature regime according to the simulation design described in Table 1.

Regarding *T. absoluta* adults infesting the field on day 7, the arrival of *N. tenuis* was set on day 1 (pre-infestation establishment of the predator) to mimic conservation biological control, where measures are taken to preventatively maintain predators in the field environment, and on day 28 (post-invasion establishment of the predator) to mimic natural regulation in the absence of conservative measures, as observed in the field where predators respond to increased pest resources. When fixed, the attack reduction rate was set at a high value of 0.8 to transfer our laboratory data, where no searching was required for the predator to feed on the prey to represent a more realistic field situation. The effect of $\delta$ on the daily per capita kill rate is described in Appendix B. All the simulations were repeated 20 times. Simulation outputs were the daily and total number of individuals per life stage and the occurrence of population collapse. The daily number of individuals at stage s is set at the end of the day after all biological processes are applied. The total number of individuals at stage s is the number of individuals who reached stage s during the simulation time frame. A population collapses when the daily number of individuals is 0 for all life stages.

## 2.3. Supporting methods and software

$$C_{egg}^i = \min\left\{\left|\Omega_{egg}^i\right|, \frac{a(1 - \delta)(I_E^i + I_{E_d}^i)}{1 + a(1 - \delta)Th_{M,T}(I_E^i + I_{E_d}^i)I_M^i + \frac{a(1 - \delta)(I_E^i + I_{E_d}^i)}{1 + a(1 - \delta)Th_{F,T}(I_E^i + I_{E_d}^i)I_F^i}\right\} \quad (5)$$

where $I_M^i$, and $I_F^i$, are the ‘day-individuals’ densities for *N. tenuis* males and females, respectively. The eggs consumed were randomly sampled within the set $\Omega_{egg}^i$.

### 2.2.2. Model calibration

The population (p), life stage (s), and temperature (T)-dependent parameters of the model were calibrated using the laboratory data. The parameters $m_{p,s,T}$ were set as the measured mortality rates. Parameters $a_{p,s,T}^d$, $\beta_{p,s,T}^d$, $\alpha_{p,T}^d$, $\beta_{p,T}^d$, $\alpha_{p,T}^f$ and $\mu_{p,T}^f$ (Eq. 1-3) were calibrated for the measured life history traits by fitting their respective distributions to the data. (Appendix A: Figures A1-2). As the number of eggs laid by a female for *N. tenuis* could not be recorded, female fecundity represents the number of eggs that develop to nymphs, and the mortality rate of juveniles represents only the mortality rate of nymphs. For stage duration and female age at egg laying, individuals were monitored in a k-day interval ($k = 1$ or 2). Thus, an observed value $n \in \mathbb{N}^*$ means that the real value is in the $[n-k, n]$ interval. For female fecundity, observed values were the exact numbers of eggs laid by females. Accordingly, the first two distributions were fitted to interval-censored data, and the third one to uncensored data, all three by maximum likelihood. Parameters a and $Th_{s,T}$ (Eq. 4) were calibrated on the measured daily per capita kill rates, using a non-linear constrained optimization method (Appendix A:

Statistical analyses, model calibration, simulations, and figures were performed using R software, version 4.0.5 (R Core Team, 2021). Multiple comparisons were performed with the glht() function in the mult-comp package (Hothorn et al., 2008). Fitting distributions to uncensored and censored data were performed respectively with the fitdist() and fitdistcens() functions in the fitdistrplus package (Delignette-Muller and Dutang, 2015). Non-linear constrained optimization via differential evolution was performed with the JDEoptim() function in the DEoptimR package (Conceicao, 2016).

## 3. Results

### 3.1. Laboratory measurement of life history traits

Laboratory experiments showed that both *T. absoluta* and *N. tenuis* could not complete their life cycle at 40 and 45 °C, as no eggs survived at these temperatures (Tables 2 and 3). For the four other temperature regimes, the mortality of juvenile stages was significantly affected by the temperature (all $P < 0.001$, except for the eggs of *T. absoluta* with $P = 0.06$). Mortality increased with temperature, from 26.7 % at 25 °C to 90 % at 35 and 40:35 °C for *T. absoluta* eggs, larvae plus pupae, and from approximately 13.5 % at 25 and 30 °C to 93.3 % at 40:35 °C for *N. tenuis* nymphs. The temperature regime significantly affected the duration of all the juvenile stages of *T. absoluta* and *N. tenuis* and adult longevity (all
<caption>**Table 1**</caption>

Sets of simulations performed per temperature regime for isolated and interacting populations. *n* is the number of simulations within a simulation set: it results from the combination of the values tested for the initial number of adult pairs, the day these adults arrive in the field, and the attack reduction rate (δ). One adult pair is composed of one female and one male.

<table><caption>**Table 2**</caption><thead><tr><th colspan="3">Simulation sets</th><th colspan="2">The initial number of adult pairs</th><th colspan="2">Day of adult arrival</th><th rowspan="2">Attack reduction rate (δ)</th></tr><tr><th>Set</th><th>Population</th><th>(n)</th><th>T. absoluta</th><th>N. tenuis</th><th>T. absoluta</th><th>N. tenuis</th></tr></thead><tbody><tr><td>1</td><td>Isolated</td><td>(1)</td><td>5</td><td>0</td><td>1</td><td>-</td><td>-</td></tr><tr><td>2</td><td>Isolated</td><td>(1)</td><td>0</td><td>5</td><td>-</td><td>1</td><td>-</td></tr><tr><td>3</td><td>Interacting</td><td>(242)</td><td>5</td><td>0 to 10</td><td>7</td><td>1, 28</td><td>0 to 1</td></tr><tr><td>4</td><td>Interacting</td><td>(220)</td><td>1 to 10</td><td>0 to 10</td><td>7</td><td>1, 28</td><td>0.8</td></tr><tr><td>5</td><td>Interacting</td><td>(495)</td><td>5</td><td>0 to 10</td><td>7</td><td>1 to 45</td><td>0.8</td></tr></tbody></table>

Life history traits of *Tuta absoluta* (means ± SE) at different temperature regimes and statistical significance of temperature. T is the temperature regime; *n* is the number of replicates; Stat., d.f., and P are the χ2- or F-statistics, the degrees of freedom, and the P-values of the analysis of deviance tables for GLM fit, respectively. Values followed by different letters within a column significantly differ at *P* < 0.05 (Tukey test, only when *n* > 1).

<table><caption>(a) Juveniles</caption><thead><tr><th rowspan="2">T (°C)</th><th rowspan="2">Egg<sup>1</sup></th><th colspan="3">Larva<sup>1</sup></th><th colspan="3">Pupa<sup>1</sup></th><th colspan="2">Egg to adult<sup>2</sup></th></tr><tr><th>n</th><th>Mortality (%)</th><th>Duration (days)</th><th>n</th><th>Mortality (%)</th><th>Duration (days)</th><th>n</th><th>Mortality (%)</th><th>Duration (days)</th></tr></thead><tbody><tr><td>25</td><td>30</td><td>10.0 a</td><td>4.8 ± 0.14 a</td><td>27</td><td>14.8 b</td><td>10.9 ± 0.23 a</td><td>23</td><td>4.3 b</td><td>9.2 ± 0.29 a</td><td>26.7 b</td></tr><tr><td>30</td><td>29</td><td>13.8 a</td><td>4.9 ± 0.12 a</td><td>25</td><td>36.0 ab</td><td>8.1 ± 0.06 b</td><td>16</td><td>12.5 b</td><td>6.4 ± 0.14 b</td><td>51.7 b</td></tr><tr><td>35</td><td>30</td><td>33.3 a</td><td>2.5 ± 0.18 b</td><td>20</td><td>45.0 ab</td><td>8.3 ± 0.14 b</td><td>11</td><td>72.7 a</td><td>5.7 ± 0.33 b</td><td>90.0 a</td></tr><tr><td>40:35</td><td>30</td><td>30.0 a</td><td>2.7 ± 0.11 b</td><td>21</td><td>71.4 a</td><td>10.2 ± 0.40 a</td><td>6</td><td>50.0 ab</td><td>6.3 ± 0.33 b</td><td>90.0 a</td></tr><tr><td>40</td><td>30</td><td>100</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>100</td></tr><tr><td>45</td><td>30</td><td>100</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>100</td></tr><tr><td>Stat.</td><td></td><td>7.3(χ<sup>2</sup>)</td><td>71.0(F)</td><td></td><td>17.0(χ<sup>2</sup>)</td><td>58.4(F)</td><td></td><td>21.5(χ<sup>2</sup>)</td><td>34.7(F)</td><td>40.5(χ<sup>2</sup>)</td></tr><tr><td>d.f.</td><td></td><td>3</td><td>3, 89</td><td></td><td>3</td><td>3, 52</td><td></td><td>3</td><td>3, 38</td><td>3</td></tr><tr><td>P</td><td></td><td>0.06</td><td>&lt;0.001</td><td></td><td>&lt;0.001</td><td>&lt;0.001</td><td></td><td>&lt;0.001</td><td>&lt;0.001</td><td>&lt;0.001</td></tr></tbody></table>

<table><caption>(b) Adults</caption><thead><tr><th rowspan="2">T (°C)</th><th colspan="3">Female</th><th colspan="2">Male</th></tr><tr><th>n</th><th>Longevity (days)</th><th>Fecundity</th><th>n</th><th>Longevity (days)</th></tr></thead><tbody><tr><td>25</td><td>15</td><td>10.9 ± 0.56 a</td><td>66.5 ± 8.5 a</td><td>19</td><td>9.5 ± 0.73 b</td></tr><tr><td>30</td><td>15</td><td>10.0 ± 1.17 a</td><td>42.5 ± 9.8 a</td><td>15</td><td>15.0 ± 1.48 a</td></tr><tr><td>35</td><td>15</td><td>5.7 ± 0.84 b</td><td>5.1 ± 1.6 b</td><td>17</td><td>6.3 ± 1.04 c</td></tr><tr><td>40:35</td><td>1</td><td>2.0±NA</td><td>4.0±NA -</td><td>1</td><td>3.0±NA -</td></tr><tr><td>40</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>45</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Stat.</td><td></td><td>8.7(F)</td><td>53.6(χ<sup>2</sup>)</td><td></td><td>9.7(F)</td></tr><tr><td>d.f.</td><td></td><td>3, 42</td><td>3</td><td></td><td>3, 48</td></tr><tr><td>P</td><td></td><td>&lt;0.001</td><td>&lt;0.001</td><td></td><td>&lt;0.001</td></tr></tbody></table>

*P* < 0.001). The developmental time from egg to adult decreased significantly from 25 to 35 °C for both species. At 40:35 °C, it remained the same as at 30 °C for *T. absoluta* and was between the 30 and 35 °C values for *N. tenuis*. Adults' longevity followed a similar trend for both species and sexes. For *T. absoluta*, it was significantly higher at 25 and 30 °C and lower at 35 and 40:35 °C for females, while it was considerably higher at 30 °C for males. For *N. tenuis*, it was significantly higher at 25 and 30 °C, lower at 35 °C, and intermediate at 40:35 °C. Fecundity decreased substantially with temperature (*P* < 0.001 for both species). It was significantly higher at 25 and 30 °C and lower at 35 and 40:35 °C. At 35 and 40:35 °C, the *T. absoluta* females were > 8 times less fecund, compared to 25 and 30 °C, and *N. tenuis* fecundity (representing in fact fecundity plus egg mortality; see §2.1.2) dropped to < 1 nymph per female.

Predation of *T. absoluta* eggs by adults of *N. tenuis* occurred at all temperatures and was significantly affected by the temperature regime for both sexes (Table 4). The highest daily per capita kill rate occurred at 40:35 °C, with 97.9 and 78.3 eggs predated per female and per male, respectively, of the 100 eggs available. It represents an increase of 51.5 % for females and 64.2 % for males compared to the number of eggs predated at 25 °C. At 45 °C, the daily per capita kill rate decreased to 31.1 and 16.2 eggs for females and males, respectively. All adults died within

24 hours of the experiment at this temperature, while no adult died in the five other temperature regimes. The daily per capita kill rate was, on average, 1.4 times higher for females than for males.

## 3.2. Simulation of isolated population dynamics

Simulations based on these life history traits showed that populations initiated with five adult pairs increased during the 80-day simulation period at 25 and 30 °C. In contrast, they collapsed at 35 °C and 40:35 °C for both species (Fig. 1). In addition to this general pattern, rare events of population collapse at low temperatures have been observed for both populations when the initial number of adults was one to two pairs, and rare events of population persistence at high temperatures have been observed for *T. absoluta* (Appendix C: Figure C1). The dynamics of the *T. absoluta* and *N. tenuis* populations were cycling, and one more cycle occurred at 30 °C than at 25 °C (Fig. 1). The population size resulting from these dynamics was higher at 30 °C than 25 °C for *N. tenuis*, while it was almost the same for *T. absoluta*.

## 3.3. Simulation of interacting population dynamics

As isolated populations collapsed naturally at 35 and 40:35 °C,

<footnote n="1">¹ *n* is the number of individuals entering the stage and only those who survived until the next stage are included in the duration calculation. ² Only individuals who survived until the adult stage are included in the calculation of duration.</footnote>
<caption>**Table 3**</caption>

Life history traits of *Nesidiocoris tenuis* (means ± SE) at different temperature regimes and statistical significance of temperature. T is the temperature regime; *n* is the number of replicates; Stat., d.f., and P are the χ2- or F-statistics, the degrees of freedom, and the P-values of the analysis of deviance tables for GLM fit, respectively. Values followed by different letters within a column significantly differ at *P* < 0.05 (Tukey test).

<table><caption>(a) Juveniles</caption><thead><tr><th rowspan="2">T (°C)</th><th colspan="3">Egg<sup>1</sup></th><th colspan="3">Nymph<sup>1</sup></th><th colspan="2">Egg to adult<sup>2</sup></th></tr><tr><th>n</th><th>Mortality (%)</th><th>Duration (days)</th><th>n</th><th>Mortality (%)</th><th>Duration (days)</th><th>Mortality (%)</th><th>Duration (days)</th></tr></thead><tbody><tr><td>25</td><td>-</td><td>unknown</td><td>9.0 ± 0.00 a</td><td>29</td><td>13.8 c</td><td>12.6 ± 0.14 a</td><td>unknown</td><td>21.6 ± 0.14 a</td></tr><tr><td>30</td><td>-</td><td>unknown</td><td>7.0 ± 0.00 b</td><td>30</td><td>13.3 c</td><td>10.3 ± 0.09 b</td><td>unknown</td><td>17.3 ± 0.09 b</td></tr><tr><td>35</td><td>-</td><td>unknown</td><td>6.0 ± 0.00 d</td><td>30</td><td>56.7 b</td><td>8.2 ± 0.10 d</td><td>unknown</td><td>14.2 ± 0.10 d</td></tr><tr><td>40:35</td><td>-</td><td>unknown</td><td>6.2 ± 0.08 c</td><td>30</td><td>93.3 a</td><td>9.0 ± 0.00 c</td><td>unknown</td><td>15.0 ± 0.00 c</td></tr><tr><td>40</td><td>-</td><td>100</td><td>-</td><td>-</td><td>-</td><td>-</td><td>100</td><td>-</td></tr><tr><td>45</td><td>-</td><td>100</td><td>-</td><td>-</td><td>-</td><td>-</td><td>100</td><td>-</td></tr><tr><td>Stat.</td><td></td><td></td><td>848.4(F)</td><td></td><td>61.0(χ<sup>2</sup>)</td><td>226.3(F)</td><td></td><td>654.9(F)</td></tr><tr><td>d.f.</td><td></td><td></td><td>3, 115</td><td></td><td>3</td><td>3, 62</td><td></td><td>3, 62</td></tr><tr><td>P</td><td></td><td></td><td>&lt;0.001</td><td></td><td>&lt;0.001</td><td>&lt;0.001</td><td></td><td>&lt;0.001</td></tr></tbody></table>

<table><caption>(b) Adults</caption><thead><tr><th rowspan="2">T (°C)</th><th colspan="3">Female</th><th colspan="2">Male</th></tr><tr><th>n</th><th>Longevity (days)</th><th>Fecundity<sup>3</sup></th><th>n</th><th>Longevity (days)</th></tr></thead><tbody><tr><td>25</td><td>12</td><td>21.2 ± 1.83 a</td><td>22.8 ± 6.5 a</td><td>12</td><td>24.3 ± 1.68 a</td></tr><tr><td>30</td><td>15</td><td>17.1 ± 2.14 a</td><td>31.8 ± 7.2 a</td><td>15</td><td>23.2 ± 3.78 a</td></tr><tr><td>35</td><td>15</td><td>6.3 ± 0.60 c</td><td>0.3 ± 0.2 b</td><td>15</td><td>5.3 ± 0.97 c</td></tr><tr><td>40:35</td><td>12</td><td>10.1 ± 1.08 b</td><td>0.2 ± 0.1 b</td><td>12</td><td>11.0 ± 0.83 b</td></tr><tr><td>40</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>45</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Stat.</td><td></td><td>24.9(F)</td><td>147.7(χ<sup>2</sup>)</td><td></td><td>23.1(F)</td></tr><tr><td>d.f.</td><td></td><td>3, 50</td><td>3</td><td></td><td>3, 50</td></tr><tr><td>P</td><td></td><td>&lt;0.001</td><td>&lt;0.001</td><td></td><td>&lt;0.001</td></tr></tbody></table>

<caption>**Table 4**</caption>

Number of *Tuta absoluta* eggs (means ± SE) predated by one *Nesidiocoris tenuis* adult male or female over 100 eggs available during 24 hours at different temperature regimes, and statistical significance of temperature. T is the temperature regime; *n* is the number of replicates; Stat., d.f., and P are the χ2-statistics, the degrees of freedom, and the P-values of the analysis of deviance tables for GLM fits, respectively. Values followed by different letters within a column significantly differ at *P* < 0.05 (Tukey test).

<table><thead><tr><th rowspan="2">T (°C)</th><th colspan="2">Male</th><th colspan="2">Female</th></tr><tr><th>n</th><th>Predated eggs</th><th>n</th><th>Predated eggs</th></tr></thead><tbody><tr><td>25</td><td>10</td><td>47.7 ± 4.9 b</td><td>10</td><td>64.6 ± 7.7 b</td></tr><tr><td>30</td><td>10</td><td>52.3 ± 7.0 ab</td><td>10</td><td>72.5 ± 5.2 ab</td></tr><tr><td>35</td><td>11</td><td>74.0 ± 7.0 a</td><td>9</td><td>85.6 ± 6.4 ab</td></tr><tr><td>40:35</td><td>10</td><td>78.3 ± 3.5 a</td><td>10</td><td>97.9 ± 1.6 a</td></tr><tr><td>40</td><td>10</td><td>72.9 ± 6.4 a</td><td>10</td><td>90.4 ± 2.2 ab</td></tr><tr><td>45</td><td>9</td><td>16.2 ± 2.6 c</td><td>11</td><td>31.1 ± 4.8 c</td></tr><tr><td>Stat. (χ<sup>2</sup>)</td><td></td><td>114.4</td><td></td><td>108.1</td></tr><tr><td>d.f.</td><td></td><td>5</td><td></td><td>5</td></tr><tr><td>P</td><td></td><td>&lt; 0.001</td><td></td><td>&lt; 0.001</td></tr></tbody></table>

simulations of interacting populations were performed only at 25 and 30 °C. When the populations of *T. absoluta* were initiated with five adult pairs, the biological control outcome was weakly affected by the attack reduction rate (δ), and effective pest control was achieved with only one to two adult pairs of *N. tenuis* at both temperatures (Fig. 2a). It corresponds to an initial predator-to-prey ratio (PPR) of 0.2 to 0.4. Here, we assumed pest control was adequate if the percentage of *T. absoluta* population collapse was ≥ 95 %. Under natural regulation, more predators were required to achieve such pest control, particularly at 25 °C, and the pest control was much more sensitive to δ. The number of adult pairs of *N. tenuis* required for effective pest control increased with increasing δ (i.e., with decreasing predator *per capita* kill rate), from 5 to >10 at 25 °C and 2 to 6 at 30 °C. Without predation (i.e., adult pairs of *N. tenuis* = 0 or δ = 1), the average number of *T. absoluta* larvae

produced during 80 days was 176,954 at 25 °C and 149,925 at 30 °C. The number of larvae was severely reduced when predation occurred and was globally lower and less variable under biological control than under natural regulation (Fig. 2b). It was < 350 under biological control for both temperatures but ranged from 275 to 95,640 at 25 °C and 137 to 4680 at 30 °C under natural regulation. The minimum initial number of adult pairs of *N. tenuis* necessary to maintain the number of larvae < 1000 under natural regulation increased with δ, from 3 to 6 at 25 °C and only 1 to 2 at 30 °C.

When the attack reduction rate δ was set at 0.8, biological control provides effective pest control with only two initial pairs of adult *N. tenuis* at both temperatures, whatever the initial number of adults of *T. absoluta*, ranging from 1 to 10 pairs (Fig. 3a). Under natural regulation, the number of adult pairs of *N. tenuis* required to provide effective pest control at 30 °C also showed little variation, but was slightly higher (from 3 to 4). In contrast, it highly increased with the number of adult pairs of *T. absoluta* at 25 °C (from 4 to > 10). The required PPR steadily decreased as the initial number of prey increased under all conditions. However, the decrease was less pronounced under natural regulation at 25 °C (from 4 to > 1) compared to the other conditions (from 2 to 0.2 at both temperatures under biological control, and from 3 to 0.4 under natural regulation at 30 °C; Fig. 3a). Similar trends to natural regulation were observed under biological control when the initial number of adults of *T. absoluta* was well over 10 pairs (Appendix C: Figure C2). Without predation (i.e., adult pairs of *N. tenuis* = 0), the number of larvae produced by *T. absoluta* during 80 days increased with the initial number of adult pairs of *T. absoluta*, from 32,291 to 364,062 at 25 °C and 8398 to 304,626 at 30 °C. When predation occurred, the number of larvae was < 660 under biological control but could increase to 243,352 at 25 °C and 14,122 at 30 °C under natural regulation. The minimum initial number of adult pairs of *N. tenuis* necessary to maintain the number of larvae < 1000 under natural regulation increased with the initial number of prey, from 2 to 9 at 25 °C and only 1 to 3 at 30 °C.

The day the predator arrived in the field strongly affected the

<footnote n="1">¹ *n* is the number of individuals entering the stage, and only individuals who survived until the next stage are included in the calculation of the duration.</footnote>

<footnote n="2">² Only individuals who survived until the adult stage are included in the calculation of duration. ³ As the number of eggs laid by a female could not be recorded for *N. tenuis*, female fecundity represents the number of eggs that develop to nymphs.</footnote>
<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Dynamics of *Tuta absoluta* and *Nesidiocoris tenuis* populations during an 80-day simulation period, when each population developed separately under four temperature regimes (25, 30, 35, and 40:35 °C). Lines and bands are, respectively, the mean and 90 % confidence intervals of the log(x + 1)-transformed daily number of individuals per life stage of 20 simulations. The initial number of *T. absoluta* and *N. tenuis* was set at five adult pairs.</figcaption></figure>

outcome of pest control (Fig. 4). When setting the initial number of *T. absoluta* at five adult pairs and δ at 0.8, there was a threshold at day 14 at both temperatures, before which effective pest control occurred with only one to three initial adult pairs of *N. tenuis* (i.e., PPR = 0.6). After this, it could not happen unless more predators were present, particularly at 25 °C (Fig. 4a). The initial required number of adult pairs of *N. tenuis* at 25 °C increased to > 10 on days 20–22, slightly decreased to 6, and then increased to > 10 on day 38. At 30 °C it increased to 5 on days 18–21, slightly decreased to 3 and then increased to > 10 on day 33. This pattern could be explained by the cycling dynamic of the *T. absoluta* population (Fig. 4c), with a higher predator efficiency when its arrival was synchronized with the early increase in abundance of the susceptible egg stage of its prey. When predation occurred (i.e., *N. tenuis* adult pairs > 0), the number of *T. absoluta* larvae produced during 80 days could increase to 142,863 at 25 °C and 104,608 at 30 °C. High values were observed for low initial numbers and late arrival of predators (Fig. 4b). The number of larvae was < 1000 when the predator arrived before day 13 at 25 °C and day 15 at 30 °C. Subsequently, the minimum number of adult pairs of *N. tenuis* required to maintain the number of larvae < 1000 first stabilized at around 4–5 at 25 °C and 2 at 30 °C, then increased sharply to > 10 from day 39 at 25 °C and day 35 at 30 °C.

## 4. Discussion

Using laboratory experiments and in silico simulations of predator-prey dynamics, we assessed the effect of warmer temperatures on the control of the invasive pest *T. absoluta* by the generalist predator *N. tenuis*. We identified key factors affecting this control for further anticipation in the context of global change. In the laboratory, neither *T. absoluta* nor *N. tenuis* from West African populations developed at 40 and 45 °C. Furthermore, although some complete developmental cycles

were recorded at 35 °C and 40:35 °C in the laboratory for both species. simulations showed that their populations could not persist at these temperatures. However, cooler night temperatures may help individuals withstand very high daytime temperatures that they would not otherwise survive without allowing population growth. The effect of temperature on life history traits of *T. absoluta* and *N. tenuis* has already been tested in previous studies, but never in the West African population and rarely at such high temperatures. In particular, the thermal tolerance of *T. absoluta* has never been tested above 30 °C. The West African population of *T. absoluta* investigated in this study has quite similar stage durations but a higher emergence rate at 25 °C than those of a population from Portugal (Cuthbertson et al., 2013). At 25 °C and 30 °C, its life history traits were also similar to those of a population from southern Brazil (Krechemer and Foerster, 2015). Krechemer and Foerster (2015) estimated an upper-temperature threshold of 37.3 °C for the egg-adult cycle, consistent with our findings. Regarding *N. tenuis*, a population from Morocco was shown to survive and develop up to 32 °C (Hughes et al., 2009), and a population from southern Sicily was shown to grow up to 35 °C but with lower survival than at 30 °C (Siscaro et al., 2019). The highest temperature tested for *N. tenuis* development was 40 °C, with a population from southern Spain that did not develop (Sanchez et al., 2009). Our results for a West African population of *N. tenuis*, when compared to those of these studies, support the observation of Pazyuk et al. (2014), who found that a subtropical population of *N. tenuis* did not perform better than a temperate population at high temperature.

Regarding the effect of temperature on predation, laboratory experiments showed that the *per capita* kill rate of *N. tenuis* adults increased with temperature, with even very high kill rates at temperatures where *N. tenuis* could not survive. This is probably due to the predator's unbalanced response to warming, with a gain from increased ingestion that is smaller than the increase in its metabolic requirement (Rall et al., 2010; Vucic-Pesticet al., 2011). Even if predator activity increases with
<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Percentage of *Tuta absoluta* population collapse (a) and total number of *T. absoluta* larvae produced (b) during an 80-day simulation period according to the initial number of *Nesidiocoris tenuis* adult pairs and attack reduction rate (δ), under biological control and natural regulation conditions and two temperature regimes (25 °C and 30 °C). Percentages and numbers are calculated on 20 simulations. Numbers are the mean of log(x + 1)-transformed data. The initial number of *T. absoluta* was set at five adult pairs. *T. absoluta* invasion was set on day 7. *N. tenuis* arrival was set on day 1 under biological control and day 28 under natural regulation.</figcaption></figure>

temperature, their *per capita* kill rate may not necessarily increase because prey mobility may also increase with temperature (Kruse et al., 2008). In our case study, the predator (i.e., *N. tenuis* adults) preys on immobile eggs, so it is expected that the increase in the *per capita* kill rate of *N. tenuis* adults observed in the confined laboratory conditions would also occur in more open field conditions. Therefore, predation is expected to increase until it reaches an unfavorable temperature for the survival of *N. tenuis* adults.

Factors influencing predator-prey dynamics and contexts driving pest control were further investigated using a stochastic and individual-based model based on laboratory data. Unlike most predator-prey models, the predator and prey dynamics were decoupled (in that the growth rate of the predator population does not depend on the prey consumed) to consider that generalist predators and even more zoo-phytophagous predators such as *N. tenuis* (Biondi et al., 2016; Sanchez, 2008), are not dependent on a single prey. Indeed, they can still build up population when pest prey is low by feeding on alternative food resources (plants and non-pest prey). Conversely, alternative food resources, depending on their availability and quality, may also partially

divert the predator from the targeted prey. More globally, we simulated predator-prey dynamics assuming no resource limitation for both *T. absoluta* and *N. tenuis* and without explicitly considering possible competition for resources for *N. tenuis*. At temperatures at which *T. absoluta* populations do not naturally collapse (25 and 30 °C), simulations show better pest control at 30 °C than at 25 °C. This logically results from an increase in the *per capita* kill rate and, at the same time, no greater adverse effects on *N. tenuis* than on *T. absoluta*. The population dynamics of *N. tenuis* was higher at 30 °C than at 25 °C, while it was pretty similar at 30 °C and 25 °C for *T. absoluta*. Both species had a shorter development time, leading to one more cycle at 30 °C, but this was counterbalanced by higher mortality from immature stages and lower female fecundity for *T. absoluta*. Consequently, a higher temperature, from 25 °C to 30 °C, benefited the control of *T. absoluta*. Despite concerns raised about the potential for parasitoids (Furlong and Zalucki, 2017) and predators to maintain their efficiency under climate warming (Aguilar-Fenollosa and Jacas, 2014), generalists are expected to be less affected due to their capacity to feed on several prey (Aguilar-Fenollosa and Jacas, 2014). Furthermore, recent studies have highlighted that in
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Percentage of *Tuta absoluta* population collapse (a) and total number of *T. absoluta* larvae produced (b) during an 80-day simulation period according to the initial number of *Nesidiocoris tenuis* and *T. absoluta* adult pairs under biological control and natural regulation conditions and two temperature regimes (25 and 30 °C). Percentages and numbers are calculated on 20 simulations. Numbers are the mean of log(x + 1)-transformed data. The attack reduction rate (δ) was set at 0.8. *T. absoluta* invasion was set on day 7. *N. tenuis* arrival was set on day 1 under biological control and day 28 under natural regulation.</figcaption></figure>

ectotherms, the efficiency of carnivorous diets is decreased at higher temperatures, while the efficiency of herbivorous diets is increased (Carriera et al., 2016; 2017; Lang et al., 2017). Thus, *N. tenuis* may have been favored by its zoophytophagy compared to strictly carnivorous predators. To our knowledge, attention had never been paid until now to the case of zoophytophagous predators. They belong to different trophic levels by feeding on plants, herbivorous prey, and intraguild prey. Zoophytophagous predators would probably be the most resilient natural enemies under climate change and should be the focus of biological control research.

A substantial reduction of the *per capita* kill rates observed in the laboratory was introduced in our simulations (through a reduction of the predator attack rate) to mimic more realistic field conditions, where habitat complexity can impair the searching efficiency of the predator or alternative resources can partially divert it from the target pest, and thereby avoid an overestimation of simulated predation. Variations in *per capita* kill rate had little effect on prey population dynamics, and it did not hamper pest control unless it was strongly reduced. Other studies

have suggested this small effect and have demonstrated that the prey population dynamic is better explained by the ratio of predator-to-prey densities (Hebblewhite, 2013; Vucetich et al., 2011). Our simulations also evidenced an effect of the initial predator-to-prey ratio, but only under a natural regulation context, that is, when the predator arrives in the field several days after the pest infestation. If the arrival of predators precedes pest infestation, which corresponds to the biological control context, the effect of the predator-to-prey ratio becomes low, and the *T. absoluta* population could be controlled with a few initial numbers of *N. tenuis*. Globally, biological control (i.e., pre-invasion establishment of the predator) provided a higher pest control than natural regulation (i. e., post-invasion establishment of the predator), and its outcome was less affected by temperature, initial predator-to-prey ratio, or attack reduction rate. Thus, our simulations demonstrated the paramount importance of predator arrival timing for population dynamics and pest control outcomes. They showed that if *N. tenuis* arrived in the field between seven days before or after *T. absoluta* infestation, strong pest control with a low number of predators was achieved. After this time
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Percentage of *Tuta absoluta* population collapse (a) and total number of *T. absoluta* larvae produced (b) during an 80-day simulation period according to the initial number of *Nesidiocoris tenuis* adult pairs and the day of arrival of *N. tenuis*, under two temperature regimes (25 °C and 30 °C). Percentages and numbers are calculated on 20 simulations. Numbers are the mean of log(x + 1)-transformed data. The attack reduction rate (δ) was set at 0.8. The initial number of *T. absoluta* was set at five adult pairs. *T. absoluta* invasion was set on day 7. The dynamics of *T. absoluta* population at 25 °C and 30 °C, when developing in isolation (c), is presented herein for the first 38 days following the invasion so that the population structure of *T. absoluta* at the time of *N. tenuis* arrival can easily be determined. Panel (c) has been adapted from Fig. 1.</figcaption></figure>

window, there is still room for successful pest control, but at the cost of
increasing the number of predators to reach the required
predator-to-prey ratio, which is even higher at 25 than at 30 °C. How-
ever, the number of predators can be reduced by optimizing their effi-
ciency. In populations with cycling dynamics, this can be achieved by
synchronizing the arrival of *N. tenuis* adults with the oviposition of
*T. absoluta* females and the early increase in egg abundance. From an
applied point of view, pre-invasion establishment of the predator can be
achieved through actions that preserve or protect naturally occurring
predators (conservation biological control) or preventive releases of
reared predators (inoculative biological control). The latter allows the
release of very few individuals, which is essential because natural en-
emies are complex and expensive to rear. Furthermore, our results
suggested that releasing *N. tenuis* at the time of transplantation or a few

days after transplantation is possible. This means farmers who did not
buy already colonized seedlings (Calvo et al., 2012) could still do it
themselves with the same expected pest control efficiency. However,
this needs to be tested empirically under real-field conditions.

**5. Conclusions**

Ecological modeling has served biological control by integrating
biological data to address issues regarding the biological control of the
invasive pest T. *absoluta* by the zoophytophagous and generalist pred-
ator *N. tenuis* under climate warming. In our study, there was no evi-
dence of outbreaks of the *T. absoluta* population at high temperatures,
either due to its successful control by *N. tenuis* at 30 °C or due to its
natural collapse at 35 °C and above, as *T. absoluta* approaches its critical
thermal maximum. Contrary to our expectations, *N. tenuis* was not affected by high temperatures more than *T. absoluta*. Therefore, pest control was higher at 30 °C than at 25 °C due to a higher predation efficiency and asymmetries between insect fitness responses to temperature in favor of the predator. This sheds light on the potential of zoophytophagous generalist predators under global-change conditions, i.e., invasive species and climate warming. Their diet makes them more resilient than other predators, such as strict carnivores and specialists. Simulations also highlighted that the timing of predator and pest establishment is a primary factor conditioning the pest control outcome. They showed that the early arrival of the predator *N. tenuis* (i.e., before or close to the prey infestation) prevents the local population of the prey *T. absoluta* from persisting, or at least prevents its outbreak, with less effect of other factors (i.e., initial predator-to-prey ratio, predator kill rate efficiency, and temperature) under these conditions. These conclusions are probably valid for most zoophytophagous and generalist predators that could outperform *N. tenuis*, for which the *per capita* kill rate was low, the life cycle was as long as that of the pest, and the female fecundity was much lower than that of the pest. Based on a modeling approach, future research should test whether pre-infestation establishment of a generalist predator allows efficient pest control when the pest's life cycle is much shorter than that of the predator, such as aphids preyed by hoverflies. In our study, we assumed that the pest and the predator arrived in the field only on a single date (specific to each), resulting in highly cycling population dynamics, but other temporal patterns could be further investigated by simulation. In addition, the absence of spatialization (Fagan et al., 2002) and resource limitations in our model should be seen as limitations and could be considered for further research.

## CRediT authorship contribution statement

**Isabelle Grechi:** Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Formal analysis, Conceptualization. **Mame Diarra Bousso Ba:** Writing – review & editing, Investigation. **Philippe Correa:** Writing – review & editing, Investigation. **Massamba Diakhaté:** Writing – review & editing, Investigation. **Thierry Nordey:** Writing – review & editing, Software, Methodology. **Serigne Sylla:** Writing – review & editing, Investigation. **Thierry Brévault:** Writing – review & editing, Resources, Funding acquisition, Conceptualization. **Anaïs Chailleux:** Writing – review & editing, Writing – original draft, Supervision, Resources, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgments

We are grateful for the financial support of the French National Research Agency (ANR) provided through CIRAD under Award No ANR-16-CE32-0010-01 (Eco-plus research project) and IPM Innovation Lab funded by USAID Cooperative Agreement No AID-OAA-L-15-00001 (Spread research project).

## Supplementary materials

Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.ecolmodel.2025.111186.

## Data availability

Raw data on the fitness of *Tuta absoluta* and *Nesidiocoris tenuis* and predation at different temperatures and associated R code for model-based exploration of predator-prey dynamics are available at: https://doi.org/10.18167/DVN1/CFQNUG.

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