A major goal of invasion biology is to understand global species flows between donor and recipient regions. Our current view of such flows assumes that species are moved directly from their native to their introduced range. However, if introduced populations serve as bridgehead population that generate additional introductions, tracing intercontinental flows between donor and recipient regions misrepresents the introduction history. Our aim was to assess to what extent bridgehead effects distort our view of global species flows. We separately mapped "flows" of 252 alien ant species established on one to six continents, representing a gradient of relatively certain to completely unreliable flows. In 83% of countries, more than 50% of alien ants were established on six continents, indicating that flows to these countries are unreliable. Flows of species established on a single continent were linked to global trade flows, while flows including cosmopolitan species were not linked to global trade. It is crucial to account for bridgehead effects when assessing the biogeography and intercontinental flows of alien species. This is urgent for improving our understanding of how species are moved around the planet.

Species distributions and flows
To determine the number of alien ant species that are established in each country, we used the geo-referenced database Antmaps (an authoritative database maintained and updated regularly by experts based on new records from the peer-reviewed scientific literature). The Antmaps database includes information on the native and alien ranges of 252 ant species (https://antmaps.org/?). We did not consider occurrence records that may be dubious (needing taxonomic verification). We kept both indoor and outdoor locations because all parts of the species’ distribution are the consequence of human-mediated dispersal. Populations that occurred at indoor locations were also a possible source of new invasions, for example if material such as potted plants and soil are moved from an indoor location to a different location. The aim of our analyses was not to distinguish between factors (climate, habitat) filtering out species at the establishment stage of the invasion process, but to understand what drives global species movements. As all species records are a reflection of global species flows, we kept all records for the analyses presented in the main part of the manuscript.

We delimited the countries and continents based on the administrative database GADM version 3.6. For mapping, we used the Mollweide projection. We defined a species “flow” as the number of species introduced from one region to another region. To calculate the species flows from donor to recipient regions, we defined the species’ native range as all countries containing native populations according to Antmaps. For species whose native range covers more than one continent, we weighted the flow from each of the continents by the number of political regions where the species is native (i.e., non-overlapping country or sub-country polygons, representing states, counties or islands and which are more homogenous in size than entire countries.

Countries
In total, 173 countries worldwide host alien ant species. To compare species flows, we focused on the 41 countries which had both species exotic in only one continent and species exotic in several continents. In that way, we were able to compare the different species flows for all alien species (hereafter ALL species) or species exotic in one continent (Exo1) or two (Exo2), three (Exo3), four (Exo4), five (Exo5) or all continents except Antarctica (Exo6).

Interception data
We have sourced previously published interception records for the United States and New Zealand from 1914-2013 (described in detail in Bertelsmeier et al. 2018, PNAS). In total, this dataset contains 69 alien ant species intercepted on cargo, goods, mail and baggage and has information on the country of origin for each interception, and therefore allows calculating the proportion of secondary interceptions for each species (i.e., the proportion of all interceptions of a species which come from a country where the species is not native).

Trade data
Most biological invasions arise via human-mediated transport, allowing species to establish in new geographic regions. In particular, accidental transport with traded commodities is an important dispersal pathway for insects in general and especially ants. We used general import flows to represent global flows of potential transport vectors. To calculate import flows to all countries, we used cumulative import data from 1998 to 2017 extracted from the UN Comtrade Database (United Nations Commodity Trade Statistics Database, http://comtrade.un.org/db/ (accessed May 2019)). This dataset contains dyadic trade flows between pairs of countries, given in US dollars per year. Such comprehensive data is not available for earlier periods; as most imports over the last two centuries have occurred during this recent period of globalization, we expect these relatively recent imports to have left their footprint on the flows of ants. Because no import data was available for four previously defined administrative units (Puerto Rico, Christmas Island, Norfolk Island and Marshall Islands), they were excluded from this analysis. The flows to each of the remaining 37 countries were standardized by dividing the flows by the total imports to each country in order to study variations in the proportions of geographic origins of the flows (and not the absolute quantities).