## Introduction

For millennia, insects have been responsible for spreading devastating infectious diseases in both humans1 and livestock2, ravaging crops and food stocks3, damaging forests4, destroying infrastructure5, altering ecosystem functions6 and weakening the resilience of ecosystems to other disturbances7. This single invertebrate class (2.5 million species8) is therefore probably the costliest animal group to human society.

A global challenge this century will be meeting the world’s food requirements while maintaining economic productivity and conserving biodiversity. Globally, insect pests have been reported to reduce agricultural yields by 10–16% before harvest, and to consume a similar amount following harvest9. In fact, the largest food-producing countries, China and the United States, exhibit the highest potential losses from invasive insects10. Several other insect pests defoliate trees4 and degrade plant biodiversity, threaten commercial forestry and hamper climate change mitigation via increased tree mortality and associated increases in greenhouse-gas emissions11. Many other insects are nuisance species or disease vectors that directly erode public health—from the Seventeenth to Twentieth centuries, insect-borne diseases caused more human disease and death than all other causes combined12.

Insects are also among the most pervasive of invasive species. For example, 87% of the 2,500 non-native terrestrial invertebrates in Europe are insects13. Yet, reliable estimates of their impacts are difficult to obtain, in particular for economic assessments. Most cost estimates are disparate, regionally focused, cover variable periods and are not always grounded in verifiable data (see Methods). The types of costs also vary and include both direct and indirect components (Fig. 1). Consequently, extrapolating local costs to global scales is challenging and few have attempted to overcome the many inherent flaws in this approach.

### Validity of annual cost rate metric

It is possible that the impact rate of any invasive species will vary over time, with rates being initially low following original establishment, and then increasing as the species expands its range and possibly declining as hosts are eliminated or humans adapt to the invasion. Consequently, a simple sum of rates from many species that invaded at different points in time might not provide a practical measure of standardized costs. However, ascertaining the year of invasion of all species we examined was impossible or suspect, given a lack of monitoring data for many species. To examine the potential problem indirectly, we plotted the cost rates versus the applicable year (median or publishing year for most goods and services estimates; initial year of reporting interval for human health estimates) for the goods and services and human health estimates separately. The subsequent bivariate plots (Supplementary Fig. 1) do not reveal any relationship with time. We therefore consider the use of cost rates as an appropriate metric for standardizing costs across species, regions and time intervals.

### Determining cost estimate reproducibility

We determined the reliability of the cost estimates given in each study by identifying the source of all the figures used to extrapolate regional costs. When monetary values were based on available calculation methodologies, traceable original references and clearly identified uncertainties, we deemed the resulting final costs to be ‘reproducible’. This reproducibility is not an assessment of quality or realism of the estimation; rather, it is a qualitative assessment of whether the initial values, assumptions and methodology applied to obtain the monetary value can be fully understood (and ideally repeated). Conversely, we defined as ‘irreproducible’ any monetary values that could not be fully traced, clearly understood or justified. Thus, we deemed a monetary value to be irreproducible when it was not properly referenced, was not traceable, was derived from a potentially subjective source (for example, a personal communication or a web page with no supporting references), did not have the full details of the calculations or did not provide a clear list of the underlying assumptions. We assessed reproducibility for every monetary value we found in the literature; hence, some values might be reproducible and others irreproducible in the same study (for example, ref. 36).

We could not apply the criteria in the same way to all types of monetary values. For example, assumptions and calculations are necessary when monetary values result from extrapolations (for example, see the calculations in Table 3 of ref. 37 or the values in ref. 38), but not when they are reports of raw expenses and costs (for example, values reported in ref. 39). The attribution of reproducibility was therefore a qualitative procedure specific to each monetary value. As a consequence, we supported our choices with narrative details about each value in the database (see, for example, ‘detailed notes’ worksheet in Supplementary Data 1).

The attribution of reproducibility to monetary estimates was clear in most cases. For example, values provided in refs 28, 37, 38 were explained clearly with respect to details, methodologies, assumptions and limits; therefore, we classified them as ‘reproducible’. Conversely, values for Ae. albopictus were classified as irreproducible in ref. 6 because they were associated to a reference on Anoplophora glabripennis. Likewise, some values in ref. 7 were either non-sourced or were associated with personal communications, and were thus deemed irreproducible. However, in some cases, the attribution was less certain. For example, in several cases we were not able to obtain the sources of the estimates, especially for non-English sources; therefore, we conservatively decided to attribute irreproducibility to these (for example, the various values in ref. 8), although we acknowledge that they might in fact be reproducible. In the case of raw reports of expenses and costs, we generally classified values provided by official institutions as reproducible (for example, those in ref. 4), and from uncertain sources such as personal communications with no more details than the name (for example, those in ref. 8) or from conferences (for example, those in ref. 9) as irreproducible.

### Data availability

The authors declare that all data supporting the findings of this study are available within the article and its Supplementary Information files.