This publication is a Hypothesis Description paper according to Mietchen et al. (2024) and following the template provided by Heger et al. (2024). It focuses on the enemy release hypothesis (ERH), a major and well-known hypothesis in invasion biology (Enders et al. 2018). The ERH offers a potential explanation for why species are able to establish and spread outside of their native range. To our knowledge, its earliest albeit implicit mention was in a work by the Swiss botanist Albert Thellung (Thellung 1915; see also Kowarik and Pyšek 2012). The publication usually cited as an explicit description is Keane and Crawley (2002), where the hypothesis was formulated specifically for alien plants. Many studies have been designed to study its relevance, for plants as well as other taxonomic groups, and respective reviews as well as meta-analyses abound (Mitchell and Power 2003, Torchin et al. 2003, Colautti et al. 2004, Liu and Stiling 2006, Heger and Jeschke 2014; see also the section 'Reviews and meta-analyses' below).

Along with this widespread use of the ERH came a shift in its definition (see Heger 2022). Jeschke et al. (2012) suggested a very broad definition to capture these different meanings, while Heger and Jeschke 2014 and Heger and Jeschke 2018 suggested several refined versions, which they called ‘sub-hypotheses’.

The previously broad definition suggested by Jeschke et al. (2012), “the absence of enemies in the exotic range is a cause of invasion success”, has some shortcomings that we would like to address here by offering a revised definition. First, the term “absence” does not really capture the intended meaning of this hypothesis, because in the new range, enemies are rarely fully absent. The concept of “enemy release” rather refers to a decrease in enemy numbers and their effects on the non-native organisms. We therefore suggest the formulation “reduced pressure by enemies” instead of “absence of enemies”. “Enemy pressure” is here used to indicate a compound measure of the number of species and individuals of enemies and their individual impacts on invading organisms (see also Heger and Jeschke 2018, Nunes and Kotanen 2018, Najberek et al. 2019, Molleman et al. 2022, Brian and Catford 2023). Second, we suggest replacing “is a cause of invasion success” with “contributes to invasion success”, because this new formulation allows for better alignment with ontologies (e.g. Bucur et al. 2021). The revised definition thus reads as follows: "A reduced pressure by enemies in the non-native range contributes to invasion success."

In the following, we summarize general information about the ERH. We provide a list of definitions or textual descriptions of the ERH and closely related ideas, and a second list with formalized representations of some of the variants of the ERH. These variants include formalized versions of the 'sub-hypotheses' formerly suggested by Heger and Jeschke (2018)Heger and Jeschke 2018. Heger and Jeschke 2018. The aim of this contribution is thus to provide an overview of the various ways the ERH can be interpreted, and deliver citable definitions and formalized versions for them. We hope that this can help disambiguate research around this important hypothesis. The work described here is part of ongoing efforts to map the landscape of hypotheses in invasion biology (Jeschke et al. 2021) and related fields, such as urban ecology (Lokatis et al. 2023).

Table 1 provides a list of definitions of the ERH. This list is not a complete list of all definitions that have been used in the literature. It instead focuses on early definitions as well as those that were part of hypothesis compilations.

As outlined in the accompanying editorial (Mietchen et al. 2024), expressing hypotheses in a formalized way can have many advantages. In ecology, we are not aware of any existing suggestion for a formalized representation of hypotheses that can be turned into a machine-actionable form. We suggest that representing hypotheses in the form subject - relationship - object can contribute to a clarification of the meaning of textual statements, and offers the opportunity to highlight the various possible meanings of a hypothesis, thus aiding with disambiguating research on this hypothesis. Here, we made use of a controlled vocabulary for stating the hypothesized relationship, namely the list of relations in the Super Pattern Ontology (Bucur et al. 2021). The use of a controlled vocabulary for expressing hypothesized relationships can contribute to reducing ambiguity, and enhances machine interpretability. This, in turn, can allow the use of AI methodology for processing text and data related to scientific hypotheses.

Table 2 gives suggestions for formalized representations of variants of the enemy release hypothesis. Some of them are based on previous work (see column "Based on"), e.g. also including the sub-hypotheses suggested in Heger and Jeschke (2018), and one that has been developed by the authors for this publication. The first three columns in this table give the respective variant of the ERH in the form ‘subject - relationship - object’. Depending on the kind of relationship between subject and object, we suggest classifying the hypotheses as either causal or comparative, which is shown in the fourth column. The rightmost column provides a link to a Wikidata identifier (see Agosti et al. 2022), through which the hypothesis can be further annotated and integrated into the wider linked open data landscape. The entries are ordered according to the date of the associated publication.

With this hypothesis paper on the enemy release hypothesis, we would like to contribute to a clarification of the meaning of the ERH. For this purpose, we provided a list of existing definitions (Table 1), suggested a revised general definition, introduced formalized representations of different variants (Table 2) and expressed these formalizations as nanopublications (see respective section below).

The overview of the ERH we provide here is to be understood as a first version. Our list of definitions and related meanings of the ERH is most likely incomplete. As emphasized in Mietchen et al. (2024), this newly introduced publication format invites updates. We very much hope that experts working on the ERH or other hypotheses will add content by publishing their own versions and that the approach will be refined over time.

Disclosing the different meanings of hypotheses and formalizing them as suggested in Table 2 can enhance theory development. For example, Heger (2022) suggested representing the ERH as a causal network graph. We presume that future work can build on this and integrate the different causal variants of the ERH into a larger causal network describing hypothesized mechanisms of biological invasions.

Enhancing machine interpretability of statements of the ERH could in the future open up new opportunities for AI applications, including the use of text mining tools for facilitating conceptual synthesis, or data mining tools combined with inductive reasoning for data synthesis (see e.g. Silva et al. 2013). We believe that all of these will be exciting steps forward. We hope that this contribution will therefore be useful for future research on the ERH as an important mechanism of biological invasions, and that it will also trigger publication of analogous papers on other important hypotheses in ecology and beyond.

This research was supported by the VolkswagenStiftung (grant number 97 863; Jeschke et al. 2021) and the Deutsche Forschungsgemeinschaft DFG (HE 5893/8-1; Heger et al. 2022). We thank Ella Daly and Laura Meyerson for their helpful comments on an earlier version of this text.