Background and aims Since its emergence in the mid‐20th century, invasion biology has matured into a productive research field addressing questions of fundamental and applied importance. Not only has the number of empirical studies increased through time, but also has the number of competing, overlapping and, in some cases, contradictory hypotheses about biological invasions. To make these contradictions and redundancies explicit, and to gain insight into the field’s current theoretical structure, we developed and applied a Delphi approach to create a consensus network of 39 existing invasion hypotheses. Results The resulting network was analysed with a link‐clustering algorithm that revealed five concept clusters (resource availability, biotic interaction, propagule, trait and Darwin’s clusters) representing complementary areas in the theory of invasion biology. The network also displays hypotheses that link two or more clusters, called connecting hypotheses , which are important in determining network structure. The network indicates hypotheses that are logically linked either positively (77 connections of support) or negatively (that is, they contradict each other; 6 connections). Significance The network visually synthesizes how invasion biology’s predominant hypotheses are conceptually related to each other, and thus, reveals an emergent structure – a conceptual map – that can serve as a navigation tool for scholars, practitioners and students, both inside and outside of the field of invasion biology, and guide the development of a more coherent foundation of theory. Additionally, the outlined approach can be more widely applied to create a conceptual map for the larger fields of ecology and biogeography.

Invasion biology is a thriving ecological research field, and confusingly many hypotheses, concepts, and ideas about biological invasions populate today's literature. Moreover, some of these hypotheses are very similar, whereas others contradict each other. It is not clear whether in such a situation a plausible global relational structure—or map—of these hypotheses emerges in the minds of the involved researchers and, if so, how this map can be reliably reconstructed from the expertise of individuals. Here, we report results of an online survey with 357 experts on invasion biology and several reconstructions of such a map. Using the distance information between hypotheses provided in the survey, the resulting network is essentially random. This finding implies that invasion biologists currently do not have a joint vision how invasion hypotheses are related to each other. However, the pattern of pairwise familiarities between the hypotheses in the survey yields joint‐mentions networks with highly non‐random features. These networks allow us to assign conceptual roles to many of the hypotheses in the field on purely topological grounds. Such hypothesis networks can help everyone interested in research fields to understand their conceptual structure. They can serve as maps of research fields.

In the current era of Big Data, existing synthesis tools such as formal meta-analyses are critical means to handle the deluge of information. However, there is a need for complementary tools that help to (a) organize evidence, (b) organize theory, and (c) closely connect evidence to theory. We present the hierarchy-of-hypotheses (HoH) approach to address these issues. In an HoH, hypotheses are conceptually and visually structured in a hierarchically nested way where the lower branches can be directly connected to empirical results. Used for organizing evidence, this tool allows researchers to conceptually connect empirical results derived through diverse approaches and to reveal under which circumstances hypotheses are applicable. Used for organizing theory, it allows researchers to uncover mechanistic components of hypotheses and previously neglected conceptual connections. In the present article, we offer guidance on how to build an HoH, provide examples from population and evolutionary biology and propose terminological clarifications.

Invasion biology has been quickly expanding in the last decades so that it is now metaphorically flooded with publications, concepts, and hypotheses. Among experts, there is no clear consensus about the relationships between invasion concepts, and almost no one seems to have a good overview of the literature anymore. Similar observations can be made for other research fields. Science needs new navigation tools so that researchers within and outside of a research field as well as science journalists, students, teachers, practitioners, policy-makers, and others interested in the field can more easily understand its key ideas. Such navigation tools could, for example, be maps of the major concepts and hypotheses of a research field. Applying a bibliometric method, we created such maps for invasion biology. We analysed research papers of the last two decades citing at least two of 35 common invasion hypotheses. Co-citation analysis yields four distinct clusters of hypotheses. These clusters can describe the main directions in invasion biology and explain basic driving forces behind biological invasions. The method we outline here for invasion biology can be easily applied for other research fields.

Hypotheses of research disciplines are typically not isolated from each other but share similarities. In a broad sense as defined here, they form an important part of the theoretical-conceptual understanding of a given topic, e.g. invasion hypotheses sensu lato represent an important part of our understanding of biological invasions. Dynamic research disciplines such as invasion biology have so many hypotheses that it is even hard for experts to keep track, and researchers from other disciplines as well as policy-makers, managers and other interested people find it extremely complicated to get to grips with invasion hypotheses. To tackle this situation, we argue that it is useful to define key hypotheses and visualize their relationships. We define 35 of the arguably most common invasion hypotheses and outline three approaches to create hypothesis networks that visualize the similarities and dissimilarities between hypotheses: (i) the bibliometric approach; (ii) the survey approach; and (iii) the matrix approach. The latter approach is in the focus of this chapter. It is centred around a matrix that represents the characteristics or traits of each hypothesis. Here we assigned such traits to 35 invasion hypotheses based on 13 trait categories. We then calculated the similarities between them and created a hypothesis network visualizing these similarities. With the same trait matrix, we created a smaller network focused on the 12 hypotheses featured in this book. This network thus illustrates the relationships between these 12 hypotheses and can be used as a map for the following chapters.

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