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About 1100 studies focusing on 12 major invasion hypotheses have been analysed in Chapters 8-16 of this book. A network of these 12 hypotheses, in which topically similar hypotheses are connected, was presented in Chapter 7. We here combine and synthesize these previous chapters, colour coding the hypothesis network depending on the level of empirical support of each hypothesis. Overall, six of the 12 hypotheses were supported by the majority of available empirical studies, three hypotheses were questioned by the majority of studies, and empirical studies were undecided for the three remaining hypotheses. The three questioned hypotheses were: evolution of increased competitive ability (EICA), biotic resistance and the tens rule. On the basis of these findings, we propose an alternative hypothesis network in which the biotic resistance hypothesis and the tens rule are replaced by revised hypotheses that are better empirically supported, and the EICA hypothesis is abandoned because the better empirically supported shifting defence hypothesis already is a refinement of this hypothesis. The revised hypothesis network therefore consists of 11 major hypotheses. Most studies analysed in this book focused on terrestrial plants in affluent countries, whereas other taxonomic groups, habitats and other countries are underrepresented in the invasion literature. Observational studies currently dominate the field. We further found that the level of empirical support has declined over time for some but not all focal hypotheses. The hypothesis network featured here is provided online, where it is also connected to the empirical data analysed in this book. This website is envisioned as the initiation of an advanced online tool that grows beyond invasion biology and should cover different scientific disciplines such as community ecology, biodiversity science and evolutionary biology. It is meant to visualize the major concepts, ideas and hypotheses in these disciplines including their links and connections, thus featuring a large structured network that is connected to the data generated in these disciplines.

Reviewing empirical evidence for major hypotheses in ecology is connected to two methodological challenges. First, all available empirical tests for a given hypothesis should be identified, collected and organized. This can be difficult due to divergent formulations of the hypothesis in the literature and divergent empirical approaches to address it. Second, the entire body of available data should be used to systematically assess the overall level of support of the hypothesis. Many approaches (e.g. formal meta-analyses) typically use only a fraction of the available data, often because of inconsistencies in the data. In this chapter, we show how the new hierarchy-of-hypotheses (HoH) approach can be used to overcome these challenges.

In Chapters 3, 4 and 5, three groups of authors have commented on the hierarchy-of-hypotheses (HoH) approach as introduced in Chapter 2. Here, we make suggestions on how to account for the issues raised in Chapters 3-5, whilst also considering several comments by other colleagues that we received during discussions or in response to our presentations on this topic. We focus on five issues and address each in a separate section of this chapter. In the concluding section, we suggest treating the HoH approach as a toolbox; we describe its core as well as an array of modules that can be chosen.

Positive interactions among species can be central for community structure and ecosystem functioning. Given the current scenario of species invasions worldwide, the question arises how non-native species will interact in the new environment. Such reasoning has led to the invasional meltdown hypothesis (IM) which states that non-native species facilitate one another's invasion, increasing their likelihood of survival, ecological impact and possibly the magnitude of their impact. However, given the importance of antagonistic interactions in natural communities, it is not yet known to what extent these facilitative effects of non-native species occur. We used the hierarchy-of-hypotheses (HoH) approach to differentiate key aspects of IM and link empirical studies to specific sub-hypotheses of the overall hypothesis. Evidence related to IM was gathered by assessing citations of Simberloff and Von Holle (1999) who first defined it. Our HoH was categorized by the type of interaction among non-native species (e.g. facilitation, mutualism and multi-species interactions), ecological level of evidence and the outcome of the interaction for each non-native species (i.e. response variable measured in the study). We additionally looked for taxonomic and geographic variability. On the basis of the 208 relevant studies we found, the broad hypothesis and the majority of sub-hypotheses indicate that positive interactions among non-natives are happening more frequently than negative ones. Thus, IM is broadly supported by currently available studies. Evidence against IM relates to sub-hypotheses involving reciprocal interactions (e.g. competition between non-native species). We suggest that future research focuses on controlled experimental setups aiming at elucidating the community- or ecosystem-level effects of non-native species interactions, especially for reciprocal interactions.

In Chapters 8-16, the hierarchy-of-hypotheses (HoH) toolbox has been applied in various ways. The results displayed as HoHs and additional bar graphs in most chapters, and as networks in Chapter 17, can now be used to identify knowledge gaps and promising paths for future research. We suggest some further steps that could be taken, making use of the data gathered for this book (which are freely available at www. hi-knowledge.org) and possible avenues for more general methodological advancements. To strengthen research in invasion biology, we specifically suggest four steps: (i) a more efficient provision and use of existing data and knowledge; (ii) a stronger focus on experiments or ideally research projects combining field studies with experiments; (iii) the development of sets of conceptually based 'case-sensitive' generalizations; and (iv) continuous integration of newly gained data and knowledge into a growing and developing atlas of invasion biology, which could potentially be expanded into an atlas of science. In this final chapter, we will first discuss how the chapters in Part II of the book made use of the HoH approach, what we think was achieved and which further methodological steps can be taken. The second section of this chapter, and final section of the book, will be an overall brief conclusion about the current state of invasion biology and possible ways forward.