A hypothesis is "[a]n assumption that

• is based on a formalized or nonformalized theoretical model of the real world and
• can deliver one or more testable predictions" (Heger et al. 2020, after Giere et al. 2006).

Hypotheses can arise at any step in a research cycle or even beyond, e.g. while observing a phenomenon or responding to a question, while exploring theoretical approaches to a problem, while reading or writing a manuscript, patent or proposal, while designing a data acquisition workflow, while curating, interpreting or integrating data or samples, or while incorporating new bits of information into an existing body of knowledge. Traditionally, few of these steps would be published on their own, and the publications resulting from a given research process may or may not contain all the hypotheses generated, explored or otherwise entertained on the way. Besides formal publications, there are various other channels through which hypotheses might enter scholarly discourse, including lectures or personal communications. Those hypotheses that were never communicated will essentially be forgotten, though any one of them might well be conceived independently by others, some of whom might eventually communicate them.

Many ways have been used to include a hypothesis - new or otherwise - in a publication. For instance, it could be in the title, which could be explicit or less so. Apart from the title, the hypothesis might be in any part of the publication and spelled out in detail. Across multiple publications, the same hypothesis (by any measure of sameness) might be referred to by one or more names (or even none), and the structures of different hypotheses might exhibit varying degrees of similarity. While hypotheses typically originate from a limited context, much of their appeal is in the extrapolation to new contexts, and much of their usage involves the delineation of their scope as well as aggregation of insights gathered from the study of multiple hypotheses. All of this could in principle be standardized.

On that basis, some research fields have developed practices that formalize the ways in which hypotheses (or certain aspects or variants thereof) are being stated, structured, delineated in scope, tested, or referred to. For instance, in formal logic and other branches of mathematics, conjectures are mathematical statements without a known proof, while theorems are mathematical statements that have been proven, and tools like lemmas and proof assistants can help in formalizing such statements while advancing from conjectures and proven lemmas to proofs of theorems (cf. Geuvers (2009)). This has matured to the point that conjectures, lemmas and theorems can be stated in a fully machine-actionable fashion (Buzzard 2020), that certain types of proofs can be generated (e.g. Nipkow (2001)) and verified (e.g. Avigad et al. (2007), Gonthier et al. (2013)) automatically, and that such automated systems routinely assist in both research (e.g. Cristiá and Rossi (2020)) and teaching (e.g. Villadsen et al. (2022)) within known theoretical limits (cf. Gödel (1930), From (2022)).

In other fields, formalization of hypotheses takes other forms. For instance, works in biological taxonomy typically contain taxon treatments (e.g. Douglas et al. 2023). These are sections that express - using highly standardized language in a highly standardized format (Agosti and Egloff 2009) - a hypothesis about how to delineate one taxon (e.g. a species, genus or subtribe) from others based on a set of materials and characteristics (cf. Härlin (2005), Kõljalg et al. (2020)). As these sets of materials (typically specimens or molecular sequences) and characteristics evolve, the need for taxon revisions may arise, i.e. modifications of the original taxon hypotheses, including potentially the creation of new ones (e.g. Srisonchai et al. 2018).

There are also fields in which there is less of a formal framework - if any - for expressing and handling hypotheses, which renders it more difficult to find pertinent hypotheses and work with them, including in automated fashions. This is the case, for instance, in some branches of ecology like invasion biology, where efforts are ongoing to map the landscape of existing hypotheses (Jeschke and Heger 2018, Enders et al. 2020, Jeschke et al. 2021). Such efforts would benefit from a more standardized approach to sharing hypotheses.

What could this look like? In short, the verbal definition of a hypothesis is translated into formulaic language, and that formalization of the hypothesis is then linked to existing knowledge by way of nanopublications annotated with standard identifiers (Bucur et al. 2023). Nanopublications are machine-readable assertions published in a standardized fashion and together with contextual and qualifying information, provenance and publication metadata (Groth et al. 2010). They are typically expressed via so-called semantic triples that combine three pieces of information and follow the basic form ‘subject-relationship-object’, with each element of the triple defined in a way that minimizes ambiguity. The current implementation of nanopublications in RIO is aligned with that for biodiversity publishing (cf. Penev et al. (2023)).

For instance, one of the assertions contained in Rodda and Savidge (2007) is that the brown tree snake (Boiga irregularis) is invasive to the Pacific island of Guam. In machine-friendly terms, this could be expressed with the following triple: "Boiga irregularis" as the subject, "Guam" as the object and "invasive to" as the relationship between subject and object. To further assist disambiguation, each of these three components would be expressed using suitable identifiers (e.g. the Wikidata identifiers Q900781 for "Boiga irregularis", Q16635 for "Guam" and P5588 for "invasive to") that point to additional pieces of information in the broader web of knowledge. The nanopublication approach can be applied to many different kinds of information, and the workflows we are establishing here for hypotheses, albeit demonstrated with an example from invasion biology, are applicable across many domains.

RIO is about communicating the research process all along the research cycle (cf. Mietchen et al. (2015)) and facilitating engagement with it (cf. Mietchen et al. (2021)). By providing a lightweight framework for expressing hypotheses in a standardized way useful to both humans and machines, we hope to support and encourage engagement with hypotheses in the context of a diverse set of research cycles.

Hypothesis Description manuscripts in RIO might well become a dedicated manuscript type eventually, but as long as the hypothesis-related workflows are still being ironed out, we suggest to use the existing manuscript type for Research Idea instead, as we have done in the example described below.

Any Hypothesis Description article should only have one target hypothesis, so as to avoid ambiguity and to facilitate the study of that particular hypothesis.

In the following, we will briefly outline the structure that we propose for Hypothesis Descriptions, provide preliminary instructions and an example as well as some further contextualization.

In this section, we introduce the initial structure of a Hypothesis description. This structure is also represented in the Hypothesis Description template (Heger et al. 2024a) as well as in the example outlined in the next section. Community feedback is invited on all of these aspects.

In terms of front matter (title, authors, abstract, keywords, ethics, funding etc.), Hypothesis Description manuscripts will be handled mostly like any other manuscript, the exception being that the title should be prefixed with "Hypothesis Description" (not italicized) and otherwise just contain the name of the hypothesis in question.

We propose the following sections for the body of a Hypothesis Description manuscript (mandatory ones are bolded):

• an introduction section that provides context for the hypothesis, e.g. historic background for the hypothesis itself or for the concepts or relationships it contains;
• a section with general information about the hypothesis in question, about relevant research fields, literature and related hypotheses or relevant identifiers;
• a section with one or more verbal definition(s) of the target hypothesis;
• a section with a formalized representation of the target hypothesis and potentially its variants;
• an outlook section that could outline, for instance, foreseeable developments that build on the formal description of the target hypothesis, or suggest some ways of testing it;
• an acknowledgement section;
• a nanopublications section;
• a reference section.

The template provides instructions for each of the sections. The outlook section is optional, and for now, the machine-friendly version is too, since the workflows for that are still being developed.

To illustrate how such Hypothesis Description papers can look like in practice, we accompany this editorial with an example (Heger et al. 2024b) from invasion biology that covers the Enemy Release Hypothesis (ERH). The ERH posits that when a given focal species is introduced into an area outside of its native range, there is a certain likelihood that its enemy species (or at least some of its enemies) will not be present in its non-native range, which would in turn increase the likelihood that the focal species becomes invasive in the new range.

Various textual definitions of the ERH have been stated in different scientific papers over time. They all relate to this overall idea, but differ slightly in their phrasing. Listing these differing definitions in a Hypothesis Description paper (see Table 1 in Heger et al. 2024b) can be useful for highlighting the differences, thus allowing researchers to make informed choices concerning which of them to use or to refer to. For example, taking a closer look at the exact formulation of the definitions reveals slight differences in specificity. Some definitions refer to 'invasion success' as the consequence of enemy release (e.g. Jeschke et al. (2012), Enders et al. (2018)), whereas others refer to 'increase in abundance and distribution' of the invader (Keane 2002, Daly et al. 2023).

The overall idea behind the ERH in fact is a rather complex mechanism, consisting of several elements: First, the process of transportation to a new area outside of the native range could lead to the situation that some enemies are 'left behind'. This is especially likely for those enemies that are specialized on the focal species. Second, the hypothetically reduced pressure by enemies in the new range could lead to a better performance of the invader. This complexity of the idea has led to the suggestion of naming a set of sub-hypotheses for the ERH (cf. Jeschke and Heger (2018) and Heger et al. (2020)). With the option to include formalized representations of hypothesis variants, a Hypothesis Description paper offers the opportunity to spell out these different elements even more explicitly. For instance, the variants could differ subtly or substantially in the way they specify the ecological context (e.g. terrestrial, freshwater or marine, pelagic or coastal), the focal group (e.g. grasses, rodents or one particular species of fish), the nature of the focal group's interactions with its enemies (e.g. host-parasite or predator-prey, specialist or generalist predator), or the mechanisms by which the release from enemies can lead to invasion success (e.g. whether it would primarily affect the establishment or spread stages of an invasion, and how).

Such a detailed definition of a hypothesis can be especially powerful when combined with the use of a controlled vocabulary, because this allows linking the used terms to definitions, while at the same time enhancing machine-actionability.

Both the listing of existing definitions and the formalized representation of hypothesis variants can enhance accuracy of scientific discussions around the respective hypothesis, and can allow a more reliable mapping of empirical evidence or experimental designs to hypothesized relationships. Likewise, meta-analyses that aggregate evidence from multipe tests would profit from such more explicit and formalized definitions, because this would decrease the likelihood of misinterpretations and wrong assignments.

Hypotheses can have a number of roles in scientific workflows. For instance, they can explain existing data or make predictions where data are missing. In principle, they can also be used to browse the scholarly literature by hypothesis (e.g. to see for which species, habitats or locations the Enemy Release Hypothesis has been tested), and a basic implementation of that is available via Scholia (Nielsen et al. 2017), e.g. for the Enemy Release Hypothesis*1.

If hypotheses were properly integrated with metadata about the research questions, methods and datasets relevant to them, it would be easier to keep track of which hypotheses have been put to a test, for which ones (or which aspects or variants of them) confirmatory evidence is accumulating or lacking, and how the evidence regarding one hypothesis might affect others.

For these various roles of hypotheses, it is important that their respective scope is clearly delineated and communicated. We think that turning hypotheses into research objects in and of themselves that can be published, cited and versioned is a good step in this direction.

As is current practice for Research Ideas and other article types, Hypothesis Description manuscripts will be subject to peer review, which shall include associated nanopublications. Just like any other RIO publication, Hypothesis Description manuscripts can be updated, resulting in a new version that has its own unique identifier.

We believe that Hypothesis Description papers can have several merits. First, disclosing the different meanings of hypotheses and formalizing them as suggested above can enhance theory development. For example, Heger (2022) suggested representing the Enemy Release Hypothesis as a causal network graph. Future work can build on this and integrate the different causal variants of the ERH in a larger causal network describing hypothesized mechanisms of biological invasions. Second, linking explicit definitions and formalizations to entries in machine-readable resources like Wikidata will allow for assistance from automated tools when working with hypotheses. We therefore encourage others to publish similar papers on other hypotheses, in invasion biology and other domains.

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.