# A qualitative model suggests that the soil ecosystem is resilient to the invasion by the land flatworm *Obama nungara*

Yoan Fourcade, Léa Poirier, Adrien Fauré, Cédric Gaucherel, Lise Dupont

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Yoan Fourcade, Léa Poirier, Adrien Fauré, Cédric Gaucherel, Lise Dupont. A qualitative model suggests that the soil ecosystem is resilient to the invasion by the land flatworm *Obama nungara*. Biological Invasions, 2025, 27, pp.96. 10.1007/s10530-025-03557-w. hal-05002965

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# A qualitative model suggests that the soil ecosystem is resilient to the invasion by the land flatworm *Obama nungara*

Yoan Fourcade ID • Léa Poirier • Adrien Fauré ID • Cédric Gaucherel ID • Lise Dupont ID

Received: 23 March 2024 / Accepted: 18 February 2025 / Published online: 5 March 2025
© The Author(s) 2025

**Abstract** Soil plays a critical role in ecosystem functioning and on the provision of ecosystem services. The soil fauna, especially earthworms, contributes to these processes through their action on the physical, chemical and biological properties of the soil. Recently, however, several regions of the world have been invaded by alien land flatworms, among which some species are predators of earthworms, but also of gastropods. In particular, *Obama nungara*, a flatworm originating from South America, has been abundantly introduced in Western Europe. In order to test whether and how the community of soil organisms can be maintained after *O. nungara* is introduced, we employed the Ecological Discrete-Event Network (EDEN) modelling framework to model all the possible trajectories that the community could take in an invaded garden. For this purpose, we focused on a reduced set of variables and formal rules describing the trophic chain exposed to *O. nungara*

under two contrasting precipitation regimes. We demonstrated that the soil community is resilient to the invasion by *O. nungara*, since all losses of prey populations were reversible, except if the ecosystem was durably trapped in a situation of drought. Even in this case, endogeic earthworms could be maintained thanks to their limited reliance on the soil surface. We showed in this study the potential of possibilistic and qualitative models to conduct prospective studies on the impacts of invasive species on soil ecosystems, which can be more generally applied to a whole range of alien species and ecosystem types.

**Keywords** Platyhelminthes · Discrete-event model · Global changes · Soil drought · Earthworms · Predation

## Introduction

Soil plays a critical role in ecosystem functioning and delivers functions and services vital for the environment and human societies (Adhikari and Hartemink 2016). It also provides a habitat for soil biota, which is essential for soil processes and functions (Brussaard 1997). For example, earthworms represent the largest biomass of the soil fauna and contribute to many ecosystem services such as pedogenesis, development of soil structure, water regulation, nutrient cycling, primary production, climate regulation, pollution remediation and cultural services (Blouin et al.

<footnote>**Supplementary Information** The online version contains supplementary material available at https://doi.org/10.1007/s10530-025-03557-w.</footnote>

<footnote>Y. Fourcade (✉) · L. Poirier · L. Dupont
Univ Paris Est Creteil, Sorbonne Université, Université Paris-Cité, CNRS, IRD, INRAE, Institut d'écologie et des sciences de l'environnement, IEES, 94010 Créteil, France
e-mail: yoan.fourcade@u-pec.fr</footnote>

<footnote>A. Fauré · C. Gaucherel
AMAP – INRAE, CIRAD, CNRS, IRD, Université de Montpellier, 34398 Montpellier, France</footnote>
2013). According to their main habitat and feeding strategy, earthworms are traditionally grouped into three main ecological categories (anecic, endogeic, epigeic) which are often used as proxies for functional groups, although this has recently been questioned (Bottinelli et al. 2020; Capowiez et al. 2024). Endogeic earthworms are known for their ability to dig horizontal galleries, which allows the soil to be aerated, and for their ability to consume organic matter (at an advanced stage of decomposition) and mineral matter (Bouché 1977). Epigeic earthworm species, which live on the surface, participate in the fragmentation of litter and have a lesser effect on the incorporation of organic matter into the deeper layers of the soil. Anecic earthworms complete the process by incorporating surface organic matter into the lower layers of the soil via their vertical galleries (Bouché 1977). Disturbance in earthworm community structure caused by biological invasions may thus disrupt soil properties and ecosystem processes, making it essential to predict the potential impact of invaders on the soil fauna.

Earthworms feature in the diet of several native species of terrestrial vertebrates (e.g., hedgehogs) and invertebrates (e.g., ground beetles). Recently, new earthworm predators were recorded in several parts of the world. Some of the several carnivorous terrestrial planarians, also known as land flatworms, which have been accidentally introduced in Europe, America, Asia and Polynesia, consume earthworms (Fourcade et al. 2022; Sluys 2016), with implications for soil functioning. In the British Isles, the predation by the exotic planarian *Arthurdendyus triangulatus* led to severe reductions in earthworm populations, to changes in their vertical distribution, and thus resulted in major changes in their community structure (Blackshaw 1997; Boag et al. 1995; Jones et al. 2001; Murchie and Gordon 2013). These changes were driven by varying levels of predation depending on the species' ecotypes, the anecic species *Lumbricus terrestris* and *Aporrectodea longa* being more susceptible to *A. triangulatus* predation because of their feeding activity on the fresh litter on surface and the construction of vertical burrows (Murchie and Gordon 2013).

Among the land flatworms that pose a threat to earthworms is *Obama nungara*, an invasive planarian native to South America that has invaded several European countries (Justine et al. 2020). It is a

nocturnal species that lives in cool and damp conditions during the day and is sensitive to drought (Cabayo et al. 2016). Its invasion has been well described in France, where it is present in > 75% of the Metropolitan territory (Justine et al. 2020), as well as in Réunion island (Justine et al. 2022). It has been mainly reported in private gardens and anthropogenic habitats but can reach natural environments (Lago-Barcia et al. 2020). With global warming, a further expansion of the species' range is expected, with a large invasion potential in Africa (Fourcade 2021). *O. nungara* feeds mainly on earthworms and gastropods (slugs and snails) (Boll and Leal-Zanchet 2016), and reproduces rapidly (1–20 juveniles per cocoon) (Negrete et al. 2020). All these elements combined make it the most threatening invasive flatworm species in Europe for soil fauna and functioning (Justine et al. 2020).

The threat to biodiversity represented by invasive flatworms has been investigated through experimental and observational studies of their predation on native species (Cannon et al. 1999; Gerlach et al. 2021; Sugiura 2010). However, such predatory activity takes place in a large interaction network that is difficult to assess empirically, which limits our ability to predict the impact of an alien predator such as *O. nungara*. Because soil is a complex ecosystem with many physical, chemical, and biological interactions, which are only partly known, a promising approach is to use ecosystem models to investigate in silico how the invasion by an alien predatory flatworm may disturb biological communities of the soil fauna. However, few models can tackle so many variables simultaneously (Vereecken et al. 2016). Differential equation models can model physical and chemical interactions such as water flows (Feddes et al. 1988), distribution of species (Coudun et al. 2006), heat fluxes, solute transport, nutrient cycles (Vereecken et al. 2016) and soil erosion (Weltz et al. 1998). Since these existing models are generally quantitative, they use quantitative data that are unfortunately difficult to collect and often unavailable. Using qualitative models helps overcome this issue, while still providing usable results when the scientific objectives do not require a quantitative response (Cosme et al. 2023). Qualitatively modelling the soil ecosystem subjected to invasion by *O. nungara* would provide predictions over more or less long periods of time, representing changes in ecosystem properties, e.g., changes in
community composition, using state and transitions
graphs representing the system dynamics. Several
categories of qualitative models have been developed
in environmental sciences such as state and transition
models (Bestelmeyer et al. 2003), loop analysis (Sar-
riot et al. 2015), qualitative reasoning (Guerrin 1991)
and discrete-event models, which have been recently
applied to understand ecosystem dynamics (Cosme
et al. 2024; Gaucherel et al. 2023).

Here, we aimed to employ the Ecological Dis-
crete-Event Network (EDEN) modelling framework
(Cosme et al. 2023; Gaucherel and Pommereau 2019)
to develop a model of the soil ecosystem exposed to
the introduction of *O. nungara* in a context of global
changes. Although EDEN has already proved its
worth in modelling other ecosystem types (Cosme
et al. 2024; Gaucherel et al. 2023), we applied it for
the first time to the soil ecosystem and to answer a
question of invasion biology. The EDEN model uses
qualitative data and is possibilistic, i.e., it computes
all possible ecosystem trajectories given the pre-
defined rules, and the predicted qualitative changes
can be visualised with a State-Transition-Graph
(STG, i.e., a succession of reachable states from the
initial one) (Cosme et al. 2022). Therefore, it can be
applied to model all the possible trophic cascades that
derive from a predefined trophic chain (Gaucherel
et al. 2023).

We used the model to answer specific questions regarding the impacts of *O. nungara* on the biological communities of an invaded ecosystem, typically a garden such as the ones where *O. nungara* have been reported in France (Justine et al. 2020). Specifically, we asked whether the community of soil organisms can be maintained after *O. nungara* is introduced and whether some processes can enable soil species to be maintained despite the introduction of *O. nungara*. Due to the already known or suspected impacts of earthworm-predating flatworms described above, we expect (i) communities of soil organisms to be negatively impacted by the introduction of *O. nungara*, and (ii) to observe a greater impact on the populations of epigeic and anecic earthworms and snails than on endogeic earthworms. The model we developed contains only a minimum number of relevant variables, including *O. nungara* and its main prey items, as well as the main drivers that may affect the dynamics of these species. As such, it must be understood as a first attempt at modelling the soil ecosystem using such

framework, but also as a demonstration that even sim-
ple qualitative models can provide major insights into
the potential impacts of invasive species on native
communities.

**Materials and methods**

The modelled ecosystem

We modelled the trajectories of an ecosystem where
*O. nungara* has already been introduced, typically a
private garden managed for recreational purposes.
We did not include any process specifically related to
invasion dynamics such as the introduction in the gar-
den and its spread. Instead, the aim was to produce an
exploratory model of the potential impact of *O. nun-
gara* on the biological communities of its prey, con-
sidering its predatory behaviour but without assum-
ing a priori its invasive nature in the model definition
(Tables 1 and 2).

The diet of *O. nungara* can be described by four
main categories of prey. First are earthworms (Boll
and Leal-Zanchet 2016; Roy et al. 2022), whose three
main categories (endogeic, anecic and epigeic) have
contrasting ecologies (Bouché 1977) and may thus
behave differently with regard to the predation by
*O. nungara*. Gastropods are alternative prey for *O.
nungara* (Boll and Leal-Zanchet 2016). We have no
information or hypothesis regarding differences in
predation towards snails and slugs. Several potential
competitors may use the same resources as *O. nun-
gara*; however, here, we considered only hedgehogs,
as they consume the same prey as *O. nungara*, but
have a much broader diet than the latter (Notting-
ham 2019; Rautio et al. 2015). We acknowledge that
a more realistic model may have included more spe-
cies, but we preferred hiding them behind the hedge-
hog component, as they would likely not exhibit a
differential behaviour. Hedgehogs are not known to
eat *O. nungara*, and there is currently no evidence
that *O. nungara* has any predator in its invaded range.
From our own field experience, though, we know that
gardens' owners may choose to actively remove *O.
nungara* from their garden once it has been detected.
However, this behaviour is not guaranteed as they
can also choose not to remove it because of a lack of
awareness or interest. Humans can have other interac-
tions in a garden that we have not accounted for here.
<table><caption>**Table 1** Variables included in the model and their initial value, acronym, and description</caption><thead><tr><th>Acronym</th><th>Variable</th><th>Description</th><th>Initial value</th></tr></thead><tbody><tr><td colspan="4"><em>Biotic variables</em></td></tr><tr><td>Obn</td><td><em>Obama nungara</em></td><td><em>Obama nungara</em> in the garden; alien predatory flatworm</td><td>+</td></tr><tr><td>Gtp</td><td>Gastropods</td><td>Gastropods (snails, slugs) in the garden; prey for <em>O. nungara</em></td><td>+</td></tr><tr><td>Ewa</td><td>Anecic earthworms</td><td>Anecic earthworms in the garden; prey for <em>O. nungara</em></td><td>+</td></tr><tr><td>Ewe</td><td>Epigeic earthworms</td><td>Epigeic earthworms in the garden; prey for <em>O. nungara</em></td><td>+</td></tr><tr><td>Ewg</td><td>Endogeic earthworms</td><td>Endogeic earthworms in the garden; prey for <em>O. nungara</em></td><td>+</td></tr><tr><td>Hed</td><td>Hedgehog</td><td>Hedgehog in the garden; predator of the same prey as <em>O. nungara</em></td><td>+</td></tr><tr><td>Lit</td><td>Soil litter</td><td>Litter above the soil, composed of dead leaves and decaying organic matter</td><td>+</td></tr><tr><td colspan="4"><em>Anthropogenic variable</em></td></tr><tr><td>Hum</td><td>Human</td><td>Human(s) that can chose to remove <em>O. nungara</em> from the garden</td><td>+</td></tr><tr><td colspan="4"><em>Abiotic variables</em></td></tr><tr><td>Moi</td><td>Moisture in soil</td><td>Moisture in soil, results from rainfall</td><td>+</td></tr><tr><td>Rai</td><td>Rainfall</td><td>Average rainfall in a year</td><td>+/-</td></tr></tbody></table>

We assumed that the populations of *O. nungara* and its prey, as well as its predation behaviour, could be influenced by abiotic variables. Here, we focused largely on rainfall/precipitation, because there is evidence that flatworms, earthworms and gastropods are all sensitive to humidity (Nicolai and Ansart 2017; Singh et al. 2019; Winsor et al. 1998). Rainfall is responsible for bringing moisture to the soil (Eltahir 1998) and enables primary production (Cornic and Massacci 1996; Gao et al. 2011), and therefore litter production (Cornic and Massacci 1996). The soil moisture provided by rain enables the various invertebrate populations to develop properly (makes the individuals active, plays a role in predation processes, facilitates their meeting and food intake, favours egg/cocoon laying) (Edwards and Arancon 2022; Sluys 1999). Moreover, soil litter keeps the soil moist (Ogée and Brunet 2002; Wang et al. 2008), serves as a hiding place for invertebrates (Nicolai and Ansart 2017) and as a food source for gastropods and all earthworms except endogeic ones (Cesarz et al. 2016; Edwards and Arancon 2022). In this regard, we modelled the influence of changing weather conditions by creating two models describing conditions of droughts on the one hand, as opposed to a typical (averaged) year on the other hand. The purpose of this approach was both to examine the differential impact that *O. nungara* may have on the modelled ecosystem depending on abiotic conditions and to predict how climate change, which is expected to increase

the frequency of droughts (Jenkins and Warren 2015), could moderate this impact.

The modelled ecosystem was described by variables and rules, which were constructed by consulting the scientific literature (see e.g. Boll and Leal-Zanchet 2016; Eltahir 1998; Moreno-Rueda 2013; Nicolai and Ansart 2017; Singh et al. 2019) so that our model, even if simplified, was based on established scientific facts and close to reality (Table 2). Some rules, though, could not be backed up by a bibliographic reference because they were either common sense or based on unverified hypotheses. We limited those latter cases as much as possible to reinforce the credibility of the model.

## The EDEN modelling framework

We used the EDEN (Ecological Discrete-Event Networks) modelling framework (Cosme et al. 2023; Gaucherel and Pommereau 2019; Pommereau et al. 2022) to model the ecosystem of a garden invaded by *O. nungara*. Any EDEN model allows the dynamics of a given system to be computed and then visualised as a function of predefined rules. This method uses qualitative data/knowledge and is probabilistic, i.e., complementary to probabilistic and deterministic methods, as it models all the reachable states of a studied system from a chosen initial state. Every state, even when highly unlikely, is computed as it represents a possible state that we should not neglect for anticipating desirable and/or dangerous situations
<table><caption>**Table 2** Rules (Rᵢ) and constraints (Cᵢ) of the ecosystem modelled and their description</caption><thead><tr><th>N°</th><th>Condition &gg; realization</th><th>Description</th></tr></thead><tbody><tr><td>C1</td><td>Ewe-, Ewa-, Gtp-, Ewg-&gg; Obn-</td><td>With no prey to feed on, O. nungara population decreases (Slobodkin 1968)</td></tr><tr><td>C2</td><td>Moi-, Lit-&gg; Obn-</td><td>In dry soil and without soil litter to shelter against desiccation, O. nungara population decreases (Sluys 1999)</td></tr><tr><td>R1</td><td>Ewa+, Moi+ &gg; Lit-</td><td>Anecic earthworms can eat soil litter if the soil is moist enough for them to be active (Curry and Schmidt 2007; Edwards and Arancon 2022)</td></tr><tr><td>R2</td><td>Ewe+, Moi+ &gg; Lit-</td><td>Epigeic earthworms can eat soil litter if the soil is moist enough for them to be active (Curry and Schmidt 2007; Edwards and Arancon 2022)</td></tr><tr><td>R3</td><td>Hed+, Moi+ &gg; Ewa-</td><td>Hedgehogs can eat anecic earthworms, if the soil is moist enough for earthworms to be active (Nottingham 2019; Rautio et al. 2015)</td></tr><tr><td>R4</td><td>Hed+, Moi+ &gg; Ewe-</td><td>Hedgehogs can eat epigeic earthworms, if the soil is moist enough for earthworms to be active (Nottingham 2019; Rautio et al. 2015)</td></tr><tr><td>R5</td><td>Hed+, Moi+ &gg; Gtp-</td><td>Hedgehogs can eat gastropods, if the soil is moist enough for gastropods to be active (Carne-Cavagnaro et al. 2006; Moreno-Rueda 2013; Nottingham 2019; Rautio et al. 2015)</td></tr><tr><td>R6</td><td>Obn+, Moi+ &gg; Ewa-</td><td>O. nungara can eat anecic earthworms if the soil is moist enough for both of them to be active (Boll and Leal-Zanchet 2016; Edwards and Arancon 2022; Murchie and Gordon 2013; Singh et al. 2019; Sluys 1999)</td></tr><tr><td>R7</td><td>Obn+, Moi+ &gg; Ewe-</td><td>O. nungara can eat epigeic earthworms if the soil is moist enough for both of them to be active (Boll and Leal-Zanchet 2016; Edwards and Arancon 2022; Murchie and Gordon 2013; Singh et al. 2019; Sluys 1999)</td></tr><tr><td>R8</td><td>Obn+, Moi+ &gg; Gtp-</td><td>O. nungara can eat gastropods if the soil is moist enough for both of them to be active (Boll and Leal-Zanchet 2016; Carne-Cavagnaro et al. 2006; Moreno-Rueda 2013; Murchie and Gordon 2013; Sluys 1999)</td></tr><tr><td>R9</td><td>Ewe-, Ewa-, Gtp-, Obn+, Moi+ &gg; Ewg-</td><td>Without its main prey, and in presence of a moist soil, O. nungara can eat endogeic earthworms thanks to the tunnels produced by anecic earthworms (Edwards and Arancon 2022; Murchie and Gordon 2013; Roy et al. 2022; Sluys 1999)</td></tr><tr><td>R10</td><td>Ewa+, Obn+, Moi+ &gg; Ewg-</td><td>Thanks to the tunnels produced by anecic earthworms, O. nungara can eat endogeic earthworms in a moist soil (Edwards and Arancon 2022; Murchie and Gordon 2013; Roy et al. 2022; Singh et al. 2019; Sluys 1999)</td></tr><tr><td>R11</td><td>Hed-, Moi+, Lit+ &gg; Gtp+</td><td>The gastropod population can increase in presence of soil moisture, soil litter and a limited predation pressure (absence of hedgehog) (Carne-Cavagnaro et al. 2006; Moreno-Rueda 2013; Nicolai and Ansart 2017)</td></tr><tr><td>R12</td><td>Hed-, Moi+, Lit+ &gg; Ewa+</td><td>The anecic earthworm population can increase in presence of soil moisture, soil litter and a limited predation pressure (absence of hedgehog) (Edwards and Arancon 2022; Judas 1989; Roots 1956; Singh et al. 2019)</td></tr><tr><td>R13</td><td>Hed-, Moi+, Lit+ &gg; Ewe+</td><td>The epigeic earthworm population can increase in presence of soil moisture, soil litter and a limited predation pressure (absence of hedgehog) (Edwards and Arancon 2022; Judas 1989; Singh et al. 2019)</td></tr><tr><td>R14</td><td>Obn-, Moi+, Lit+ &gg; Gtp+</td><td>The gastropod population can increase in presence of soil moisture, soil litter and a limited predation pressure (absence of O. nungara) (Carne-Cavagnaro et al. 2006; Moreno-Rueda 2013; Nicolai and Ansart 2017)</td></tr><tr><td>R15</td><td>Obn-, Moi+, Lit+ &gg; Ewa+</td><td>The anecic earthworm population can increase in presence of soil moisture, soil litter and a limited predation pressure (absence of O. nungara) (Edwards and Arancon 2022; Judas 1989; Roots 1956; Singh et al. 2019)</td></tr><tr><td>R16</td><td>Obn-, Moi+, Lit+ &gg; Ewe+</td><td>The epigeic earthworm population can increase in presence of soil moisture, soil litter and a limited predation pressure (absence of O. nungara) (Edwards and Arancon 2022; Judas 1989; Singh et al. 2019)</td></tr><tr><td>R17</td><td>Obn-, Ewa+ &gg; Ewg+</td><td>With the depletion of O. nungara population, the population of endogeic earthworms can increase, as long as there are anecic earthworms (Judas 1989)</td></tr></tbody></table>
<table><caption>**Table 2 (continued)**</caption><thead><tr><th>N°</th><th>Condition &gg; realization</th><th>Description</th></tr></thead><tbody><tr><td>R18</td><td>Obn-, Ewe + &gg; Ewg +</td><td>With the depletion of <i>O. nungara</i> population, the population of endogeic earthworms can increase, as long as there are epigeic earthworms (Judas 1989)</td></tr><tr><td>R19</td><td>Hed- &gg; Hed +</td><td>For any reason (which is not included in the model) the population of hedgehog can increase (Rautio et al. 2015)</td></tr><tr><td>R20</td><td>Hed + &gg; Hed-</td><td>For any reason (which is not included in the model) the population of hedgehogs can decrease (Rautio et al. 2015)</td></tr><tr><td>R21</td><td>Gtp+, Moi+, Lit+, Hum- &gg; Obn+</td><td>The population of <i>O. nungara</i> can increase in the presence of one of their prey (gastropods), in moist soil, with soil litter to shelter and if humans do not actively remove them (Boll and Leal-Zanchet 2016; Carne-Cavagnaro et al. 2006; Murchie and Gordon 2013; Nicolai and Ansart 2017)</td></tr><tr><td>R22</td><td>Ewa+, Moi+, Lit+, Hum- &gg; Obn+</td><td>The population of <i>O. nungara</i> can increase in the presence of one of their prey (anecic earthworms), in moist soil, with litter available and if humans do not actively remove them (Boll and Leal-Zanchet 2016; Murchie and Gordon 2013)</td></tr><tr><td>R23</td><td>Ewe+, Moi+, Lit+, Hum- &gg; Obn+</td><td>The population of <i>O. nungara</i> can increase in the presence of one of their prey (epigeic earthworms), in moist soil, with soil litter to shelter, and when humans do not actively remove them (Boll and Leal-Zanchet 2016; Murchie and Gordon 2013)</td></tr><tr><td>R24</td><td>Ewg+, Moi+, Lit+, Hum- &gg; Obn+</td><td>The population of <i>O. nungara</i> can increase in the presence of one of their prey (endogeic earthworms), in moist soil, with litter available to shelter, and if humans do not actively remove them (Boll and Leal-Zanchet 2016; Murchie and Gordon 2013)</td></tr><tr><td>R25</td><td>Moi- &gg; Gtp-</td><td>The population of gastropods can decrease if the soil is dry (Darby et al. 2008; Nicolai and Ansart 2017)</td></tr><tr><td>R26</td><td>Lit- &gg; Gtp-</td><td>Without litter to shelter, the population of gastropods can decrease (Darby et al. 2008; Nicolai and Ansart 2017)</td></tr><tr><td>R27</td><td>Moi- &gg; Ewe-, Ewa-</td><td>Epigeic and anecic earthworms populations can decrease in dry soils (Singh et al. 2019)</td></tr><tr><td>R28</td><td>Lit- &gg; Ewe-, Ewa-</td><td>Lack of soil litter can decrease the population of epigeic and anecic earthworms (Curry and Schmidt 2007; Edwards and Arancon 2022)</td></tr><tr><td>R29</td><td>Hum + &gg; Obn-</td><td>Human can reduce <i>O. nungara</i> population by removing it from the garden (J-L Justine, personal communication)</td></tr><tr><td>R30</td><td>Obn- &gg; Hum-</td><td>Without <i>O. nungara</i>, human stops removing it from the garden (J-L Justine, personal communication)</td></tr><tr><td>R31</td><td>Obn + &gg; Hum +</td><td>Human can choose to remove <i>O. nungara</i> from the garden when the population is large (J-L Justine, personal communication)</td></tr><tr><td>R32.1</td><td>Rai + &gg; Rai-</td><td>From an average year to a dry year (common sense); activated only in scenario 1 for simulating the switch from an average to a dry year with no return back to average precipitation (see Fig. 2)</td></tr><tr><td>R32.2</td><td>Rai- &gg; Rai +</td><td>From a dry year to an average year (common sense); activated only in scenario 2 for simulating the switch from a dry to an average year with no return back to drought (see Fig. 3)</td></tr><tr><td>R33</td><td>Rai + &gg; Lit +</td><td>Rainfall can increase the primary production and thus increase the soil litter biomass (Gao et al. 2011)</td></tr><tr><td>R34</td><td>Rai- &gg; Lit-</td><td>Absence of rainfall can decrease the primary production and thus decrease the soil litter biomass (Cornic and Massacci 1996; Gao et al. 2011)</td></tr><tr><td>R35</td><td>Rai + &gg; Moi +</td><td>Soil litter can contribute to moisture retention (Ogée and Brunet 2002; Wang et al. 2008)</td></tr><tr><td>R36</td><td>Rai-, Lit- &gg; Moi-</td><td>Absence of soil litter can contribute to moisture loss (Ogée and Brunet 2002; Wang et al. 2008)</td></tr></tbody></table>
(Cosme et al. 2023). A brief presentation of EDEN principles is given in the following paragraphs, and readers may also refer to toy-models presented in Gaucherel and Pommereau (2019) and Cosme et al. (2022).

The EDEN modelling framework involves variables, rules, and constraints. The chosen variables represent the biotic, anthropogenic and abiotic components present in the ecosystem and relevant for the addressed question. Variables can take two values only, represented by (+) or (−) (Boolean variables) which make the variables respectively functional or non-functional. Such values are defined by a threshold that is unique to each variable and remains unchanged during the modelling task. The states of the system are thus defined by the sets of all variable values at each computed step during the single run (Gaucherel et al. 2023; Pommereau et al. 2022).

Variables are modified, from (+) value to (−) value and vice versa, by "if-then" rules that represent the potential interactions identified between variables. A rule is composed of two parts made up of functional (+) and/or non-functional (−) variables: the conditions under which the rule may be fired (applied) and the effects the application of this rule has on the rest (variables) of the modelled system. All rules with fulfilled conditions are applied, one by one from any system state encountered, so that all the possible transitions and trajectories (sequences of transitions) from a given (initial) state can be computed and visualised. For a rule to be fired, the previous state of a system must satisfy all the conditions of a rule (if) to move onto the next state (then) of the same system. If several states satisfy the conditions of a rule, then the rule is applied asynchronously to all the concerned states, resulting likely in branching and alternative trajectories. Constraints have the same properties than rules, except that their execution takes priority over all rules (Gaucherel et al. 2023; Pommereau et al. 2022). No transition time or probability is considered, making the model chronological and causal but not temporized; no quantity related to rules (e.g., intensities, fluxes, speed of change) is considered either.

The variables and the rules build the so-called interaction network (Fig. 1) of the modelled ecosystem, represented by a graph composed of nodes and edges (i.e., the variables and rules, respectively). Results of EDEN modelling are shown as State-Transition Graphs (STGs), displaying the system states

reached from the initial one and connected by transitions resulting from rule applications. Each transition is represented by at least one (one-way or two-way) edge, representing an instance of the corresponding process and modifying some system components. Some states, called deadlocks, are frozen systems since no rule allows exiting them (in the previously assumed model). Other STG structures (topologies) are informative, as some states of the STG can be mutually reachable and thus build so-called structural stabilities in which the modelled system may be trapped. By examining which variables are (non-) functional or possibly oscillating between (+) and (−) states, we may interpret the concerned system regime. Hence, the STG and its merged stabilities (deadlocks and structural stabilities, if any) show all the states and regimes the modelled system can reach from the initial state and the qualitative (often long term) changes that occur in the system.

## Model implementation

We defined ten variables in the model, with seven biotic variables, two abiotic variables and one anthropogenic variable (Table 1). The biotic variables describe the trophic chain of the modelled ecosystem, including *O. nungara* (*Obn*) and hedgehogs (*Hed*), and their various prey species: earthworms represented as endogeic (*Ewg*), epigeic (*Ewe*) and anecic (*Ewa*) earthworms, as well as gastropods (*Gtp*) that refer to both slugs and snails. Since the model is exploratory, we did not define specific thresholds in terms of abundance below which populations become non-functional. Instead, non-functional biotic variables must be understood as populations that remain present in the invaded garden but in numbers small enough to make them unable to have a significant impact on the other variables. The seventh biotic variable, litter on the soil surface (*Lit*), does not represent a population of a species but a food source that can be abundant enough (+) or not (−) to sustain earthworm and/or gastropod populations, and it also serves as a shelter for *O. nungara*, earthworms and gastropods. The model also incorporated abiotic variables: precipitation/rainfall (*Rai*) and soil moisture (*Moi*). The rainfall variable in its non-functional state (−) represents a period of drought. We define this drought by a prolonged period of low precipitation that is responsible for a substantial loss of soil moisture, typically
<figure><img src="image_2.png" /></figure>

**Fig. 1** Interaction network synthesizing the rules that govern the interactions between the various variables of the soil model. The direction of the arrows indicates the direction in which the variables interact with each other. A double arrow between two nodes indicates that the variables interact reciprocally, and a single arrow that the interaction is only in one

leading to values < 10% (Moi + can then switch to Moi-; see rule R36 in Table 2). Drought can be identified based on a calculation of long-term (9 or 12 month) Standardized Precipitation Index (SPI, McKee et al. 1993); we assume that Rai- corresponds to a SPI that has reached a peak lower than -1.5, which corresponds to severe to extreme droughts (McKee et al. 1993). Precipitations that maintain

direction (i.e., from conditions to realizations of the concerned rules). *Hed* variable corresponds to Hedgehogs, *Obn* to *O. nungara*, *Ewg*, *Ewa* and *Ewe* respectively to endogeic, anecic and epigeic earthworms, *Gtp* to gastropods, *Rai* to rainfall, *Lit* to soil litter, *Moi* to soil moisture and *Hum* to humans (see Tables 1 and 2 for details)

a SPI > -1.5 were treated later on as “average rainfall conditions”. Finally, the anthropogenic variable describes the presence of humans (*Hum*) in the system that may decide to remove (+) or not (-) *O. nungara* from their garden.

Thirty-six rules and two constraints were defined from these model variables (Table 2). We defined a set of ecosystem rules describing the predation of

<figure><img src="image_3.png" /></figure>
earthworms and gastropods, allowed only in the presence of sufficient soil moisture. We considered that predation by *O. nungara* or hedgehogs can cause the depletion of earthworm or gastropod populations. Because they are found deep in the soil, we assumed that *O. nungara* feeds on endogeic earthworms only when no alternative prey is available or when anecic earthworms have formed vertical tunnels that make endogeic earthworms more easily reachable. We allowed prey populations to become functional again after they have been depleted, providing that predation pressure is released (*O. nungara* and/or hedgehog are non-functional) and that food resource (litter) is available. We imposed (i.e., with a constraint) a decline of *O. nungara* population in the absence of earthworms and gastropods, as they are its only known prey. It must be noted that *O. nungara*, like other flatworms (e.g., Blackshaw 1992; Boag et al. 2006), have a survival strategy consisting in resorption of its tissues, resulting in body shrinkage, in case of starvation (personal observations in the lab). The depletion of *O. nungara* population may thus take some time, with individuals potentially surviving several months in the absence of prey. Per our model rules, rainfall influences soil moisture and increases litter production. Finally, we enabled the lack of soil moisture (*Moi*-), itself caused by a lack of precipitation (Rai-) and no litter (Lit-) to retain moisture, to cause the depletion of *O. nungara*, earthworms and gastropods populations. The full set of rules is presented in Table 2 and the resulting interaction network summarizing the studied ecosystem is shown in Fig. 1.

From one model, we defined two different scenarios by changing the initial state of the rainfall conditions (variable Rai) and activating a different rule to define how this variable is allowed to change in the model (rules R32.1 and R32.2 in Table 2). Scenario 1 takes place during a drought after an initial start in average rainfall conditions (Rai+), and we activated the rule allowing switching from an average year to a dry year (rule R32.1). In scenario 2, average rainfall conditions are allowed to come back through rule R32.2 after an initial state of drought (Rai-). All the other variables are functional in the initial state, i.e., *O. nungara* is present, as well as its whole community of prey and competitor. The model intends to predict the sharp (qualitative) changes of this integrated ecosystem at an intra-annual time scale and

with implicit space. By examining the ecosystem trajectories produced by the model in each scenario, we could assess whether the introduction of *O. nungara* leads to irreversible changes (i.e., no reverse transitions between states) in the community structure of its prey depending on precipitation conditions, and explore what mechanisms could contribute to community resilience.

## Results

### Scenario 1: average rainfall to drought

In the first scenario, the successive applications of the rules generated 564 states that could be grouped into 96 structural stabilities, including two terminal stabilities from which the system cannot exit (Fig. 2), with the transitions from one stability to another leading inevitably and irreversibly towards one of these terminal stabilities. The first structural stability was composed of 248 states in which the rainfall and the soil moisture variables were systematically functional, whereas all other variables could switch from functional to non-functional and vice-versa.

We observed that the rainfall variable rapidly became non-functional after the first structural stability, which reflects the switch towards drought, after which soil litter, as a rainfall-dependent variable, also became non-functional. Two trajectories seemed to emerge afterwards, composed of 92 and 96 possible states, respectively. On the right-hand side of Fig. 2, endogeic earthworms were immediately lost (i.e., non-functional), whereas the other earthworm categories, as well as gastropods, *O. nungara* and humans progressively became non-functional in different possible orders (see Supporting information, Figs. S1 and S2). This trajectory led to a terminal stability composed of only two states where all variables (except hedgehogs that are always allowed to switch) were non-functional, including rainfall, soil litter, soil moisture, prey populations and *O. nungara*. The second trajectory (left hand side of Fig. 2) was similar, except that endogeic earthworms remained functional, even in the terminal stability. From many stability on the right trajectory (except the terminal stability), it was possible to switch to the left trajectory via rules R17 or R18 that control the return of the population of
<figure><img src="image_4.png" /></figure>

**Fig. 2** Simplified representation of the State-Transition Graph (STG) of scenario 1 that goes from a state of average rainfall conditions to a drought (Rai+ in the initial state, rule R31.1 is activated and rule R32.2 is deactivated). Here, structural stabilities (or sequence of stabilities) that share similar properties have been merged to show the most important transitions between the modelled states. The blue octagon at the top represents the first stability derived from the initial state; the two dotted-lined red circles represent the two terminal stabilities, i.e., stabilities from which the system cannot escape. Pic-

tograms show the variables that are systematically functional (black) or systematically non-functional (light grey) in the merged stabilities, and so, variables not shown are oscillating. The big arrow portrays a set of transitions that features the progressive loss of the biotic variables shown in dark grey within them, that can happen in different orders. The detailed STG can be found in Supplementary Information, Figs. S1 and S2. Readers can refer to Fig. 1 and Table 1 for the meaning of the pictograms

endogeic earthworms when conditions are suitable for them. On the other hand, all stabilities located on the left trajectory that contained Obn+ and

Ewa+ variables could switch to the right-hand side via rule R10 that controls the predation of endogeic

<figure><img src="image_5.png" /></figure>
earthworms by *O. nungara* using galleries created by anecic earthworms.

## Scenario 2: drought to average rainfall

The second scenario generated 160 structural stabilities (grouping a total of 688 states) inevitably leading to a single terminal stability (Fig. 3). Here, the rainfall variable was non-functional in the 124 states of the initial structural stability, whereas soil litter and soil moisture were systematically functional.

Two main trajectories emerged that resemble the dynamics observed in scenario 1. In both trajectories, soil litter became immediately functional after the initial stability, corresponding to the loss of litter because of consumption by earthworms (rules R1 or R2) or because of the absence of rain (rule R34). The right-hand side of Fig. 3 corresponds to 164 states in which endogeic earthworms were lost from the beginning, all other species (including *O. nungara* and its prey as well as humans) becoming progressively non-functional in different possible orders. At the same time, rainfall and soil litter variables, which started in non-functional states, switch to Rai+ followed by Lit+, while soil moisture became non-functional. The left-hand trajectory featured the same dynamics, except that endogeic earthworms remained functional (see Supporting information, Figs. S3 and S4). As for scenario 1, it was possible to switch between the left and right trajectories through rules R17, R18 or R10. These trajectories can lead to two different stabilities that are largely analogous to the terminal stabilities of scenario 1, except that rainfall and litter were here functional: all biotic variables but hedgehogs were non-functional in one of them, whereas in the other endogeic earthworms remained functional.

All trajectories of scenario 2 led to the same terminal stability (with possible hedgehog oscillations), which was reached after rule R35 was applied, i.e., the rule that allowed soil moisture to return. All populations of prey and predator became functional again in some of the corresponding states. No variable was consistently non-functional in the terminal stability, meaning they were all present in some of the 248 possible states, such that their disappearance was always reversible.

## Discussion

The EDEN modelling framework (Gaucherel and Pommereau 2019; Pommereau et al. 2022) allowed us to understand soil ecosystem dynamics following the introduction of *O. nungara*. Our scenarios of drought vs. average rainfall provided additional insights into the potential influence of climate change and of inter-annual weather variability, since we tested the effect of a change in rainfall conditions. In our two scenarios, credible State-Transition-Graphs representing all possible ecosystem trajectories could be generated from a set of rules backed-up by literature evidence and expert knowledge of the system (e.g., Carbayo et al. 2016; Justine et al. 2020; Roy et al. 2022; Sluys 2016). The results we obtained provide unprecedented insights into the long-term development of soil communities under invasion by an introduced predator, and they helped decipher the respective roles of biotic and abiotic processes of soil ecosystem in this regard.

Both scenarios revealed that the action of *O. nungara* on the soil ecosystem was largely dependent on abiotic conditions. Here, we focused on two scenarios of precipitation regime because climate change is often affecting the frequency, intensity, and especially duration of drought events (Jenkins and Warren 2015), which appeared a priori as a potentially key driver for the dynamics of drought-sensitive species such as land flatworms, earthworms and gastropods. Specifically, we revealed that lack of rainfall could trigger the collapse of the entire soil community through an impact on litter and soil moisture. This was because litter was defined as an essential food resource for earthworms (Cesarz et al. 2016; Curry and Schmidt 2007; Edwards and Arancon 2022) while also controlling—in addition to the direct effect of rainfall—soil moisture through water retention on the soil surface. We also assumed that most feeding activities, of both *O. nungara* and its prey, were dependent on a sufficient soil moisture. As a consequence, our model predicts that a trophic cascade can positively or negatively affect the whole soil community depending on whether rainfall conditions correspond to an average year or exhibit characteristics of a drought, respectively. How this will manifest empirically depends largely on the quantitative relationships between rain, soil moisture and biological activity. Here, we assumed a precipitation threshold
<figure><img src="image_6.png" /></figure>

**Fig. 3** Simplified representation of the State-Transition Graph (STG) of scenario 2 that goes from a state of drought to average rainfall conditions (Rai- in the initial state, rule R31.2 is activated and rule R32.1 is deactivated). Here, structural stabilities (or sequence of stabilities) that share similar properties have been merged to show the most important transitions between the modelled states. The blue octagon at the top represents the first stability derived from the initial state; the dotted-lined red circles represent the terminal stability from which the system cannot escape. Pictograms show the variables that are systematically functional (black) or systemati-

cally non-functional (light grey) in the merged stabilities, and so, variables not shown are oscillating. The grey arrows por-tray respectively, from left to right, a set of transitions that fea-tures the loss of soil moisture while rainfall and litter become functional, and a progressive loss of the biotic variables shown in dark grey, that can happen in different orders, resulting in two main trajectories in which endogeic earthworms (Ewg) are maintained (left) or not (right). The detailed STG can be found in Supplementary Information, Figs. S3 and S4. Readers can refer to Fig. 1 and Table 1 for the meaning of the pictograms

<figure><img src="image_7.png" /></figure>
that causes the soil to lose its moisture, but many additional drivers control this relationship, including the physical properties of the soil (Rawls and Braken-siek 1982).

In the scenario of a transition from a normal year to a dry year, our model provides evidence that the entire trophic chain (Fig. 1) could collapse. Generally, drought episodes tend to cause biodiversity decline (Clark et al. 2016; Feng et al. 2021), with the lack of rain causing irreversible damage to the components of the ecosystem that depend on it (soil litter and soil moisture). Because of its need for a moist soil and its reliance on a set of drought-sensitive prey, we observed that *O. nungara* was eventually extirpated (or declined enough to become non-functional) from the community in case of dry conditions. This is an important property for understanding the impact of its predation in invaded ecosystems, since it means that environmental stochasticity can modulate *O. nungara* populations. In this regard, precipitation regime appears to be a key driver for predicting the impact of *O. nungara* introduction. As drought events are likely to become more frequent (Jenkins and Warren 2015), it suggests that environmental suitability for *O. nungara* will decrease in the near future, as was also shown in a recent modelling study (Fourcade 2021). Our model also showed that drought led to a gradual decline in populations of earthworms and gastropods (in various orders; Figs. 2 and 3). Earthworm species have different and complementary effects on soil (Heemsbergen et al. 2004), with epigeic earthworms species participating in the fragmentation of litter whereas anecic earthworms complete the process by incorporating surface organic matter into the lower layers of the soil via their vertical galleries (Eisenhauer 2010). Therefore, the lack of two of the ecological categories would ultimately lead to a non-functional ecosystem.

Although our model shows that drought can cause the collapse of the community even in the absence of *O. nungara*, another possibility exists. In alternative ecosystem trajectories (Fig. 2, left trajectory), we predict that endogeic earthworms could be the only biotic component to be maintained. The rules set up for endogeic earthworms make them less dependent on soil litter since they live deep in the soil and do not consume litter (Cesarz et al. 2016; Edwards and Arancon 2022). They are also less dependent on soil moisture since they actively search for soil moisture

by moving around, more than any other category of earthworm could (Roots 1956). Moreover, although we know that *O. nungara* can feed on endogeic earthworms (Roy et al. 2022), the fact that the latter are less dependent on what happens on the soil surface makes them less sensitive to predators such as introduced land flatworms. It is unclear, though, how long endogeic earthworms can be maintained in a soil that lack biological activity at the surface.

In the other scenario (starting from a drought with a possible return of precipitations), we noticed that the community of *O. nungara* and its prey, that are all functional in the initial state, can be resilient (i.e., some stabilities here have all biotic components that can switch between functional and non-functional) as long as soil moisture is maintained (Fig. 3, initial and terminal stabilities). On the other hand, as soon as litter is lost from the system, the soil ecosystem switches to a regime that is similar to what we observed in the first scenario, i.e., all components are gradually lost, endogeic earthworms being either lost or maintained in two alternative trajectories. However, in a second phase characterised by the reappearance of soil moisture allowed by rainfall, all components are able to become functional again in a terminal stability containing many possible states that are all reachable from every other state (Fig. 3). Although a sudden change in precipitation regime after a phase of drought could also have deleterious consequences (Vilonen et al. 2022), we demonstrate here that none of these effects are irreversible. Instead, in a normal precipitation regime (its definition may vary depending on which amount of rainfall allows water retention in the soil), all prey populations can recover even in the presence of their predator, showing a great resilience of the community to the introduction of *O. nungara* (Fig. 3, terminal stability). Importantly, this terminal stability could be reached after both terminal stabilities of the first scenarios, providing that drought conditions stop and are replaced by a typical precipitation regime, allowing soil moisture to come back. Thus, in a case where rainfall would alternate between periods of average precipitations and periods of drought, our model predicts a fully resilient system in which all prey populations, as well as their introduced predator, can be maintained. However, we also show that human action and competitors for resources would be insufficient to cause eradication of *O. nungara* in the invaded gardens (Figs. S1 and S3: rule
R29 is never causing a permanent transition towards the disappearance of *O. nungara*).

We kept our model simple on purpose, to explore all possible soil system trajectories from a broad, rigorous and qualitative point of view (Cosme et al. 2023). However, several improvements may enhance its ability to provide accurate predictions. Firstly, other species that are influenced by the presence of gastropods or earthworms may be included, for example plants. Indeed, by modifying the chemical, physical and biological properties of the soil (Derouard et al. 1997), earthworms significantly increase plant biomass and modify the composition of plant communities. Gastropods could also be separated into slugs and snails since these taxa do not necessarily behave in the same way with regard to some of the variables implemented here, such as soil moisture. Indeed, under conditions of low soil moisture, snails adopt a behavioural defence by hiding in their shells, giving them an advantage in the presence of prolonged drought compared to slugs (Laviolette 1950). Furthermore, gastropods, earthworms and *O. nungara* could be subdivided into adults, juveniles, and cocoons/eggs, as these different life stages do not react in the same way to existing variables. For example, gastropods' eggs need a good level of humidity to hatch (Willis et al. 2008) and juvenile growth rate decreases due to lack of moisture (Txurruka et al. 2005). Similarly, cocoons of some earthworm species allows them to survive dry seasons and help restore populations once environmental conditions are more favourable (Edwards and Arancon 2022). It would also be interesting to divide earthworms into more categories along the continuum found in French gardens. In fact, the three main categories of earthworms (i.e., anecic, endogeic and epigeic), are not well-separated classes but we observe instead a continuum between them (Bottinelli et al. 2020; Bouché 1977; Capowiez et al. 2024). We also neglected interactions between earthworm species, although we know that they can exist (Heemsbergen et al. 2004; Uvarov 2009). A more complex model including all these components may be able to elucidate more precisely the impact of *O. nungara* on soil functioning and could be used to make predictions on the potential alteration of this functioning in invaded ecosystems.

In conclusion, we demonstrated in this study the potential of possibilistic and qualitative models—here using the EDEN framework—to conduct prospective

studies of the impact of invasive species on soil ecosystems. We first gained important insights into the specific case of *O. nungara*, an introduced platyhelminth predator. The results we obtained will be completed by field and experimental works to test the predictions of the model and to specify the quantitative thresholds that trigger the rules we assumed herein. In addition, we emphasize that the same framework can be applied to a whole range of alien species to explore the possible trajectories of invaded ecosystems. It can be extended to entire socio-ecosystems by incorporating relevant variables describing human actions towards invaders, thereby providing an efficient tool for a better management of invasive species.

**Acknowledgements** We thank all collaborators of the PLATWORM project for inspiring discussions. We also deeply thank the editor and reviewers for their insightful comments and suggestions.

**Author contributions** All authors contributed to the study conception and design. LP designed the model with inputs from all authors. The first draft of the manuscript was started by LP and completed by YF. All authors contributed to and approved the final manuscript.

**Funding** Open access funding provided by Université Paris-Est Créteil. This work was funded by the Agence Nationale de la Recherche (Project PLATWORM, ANR-21-CE02-0016).

**Declarations**

**Conflict of interest** The authors have no relevant financial or non-financial interests to disclose.

**Open Access** This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
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