G-IRAE: a Generalised approach for linking the total Impact of invasion to species' Range, Abundance and per-unit Effects

The total impact of an alien species was conceptualised as the product of its range size, local abundance and per-unit effect in a seminal paper by Parker and colleagues in 1999, but a practical approach for estimating the three components has been lacking. Here, we generalise the impact formula and, through use of regression models, estimate the relationship between the three components of impact, an approach we term G-IRAE (Generalised Impact - Range size - Abundance - per-unit Effect). Moreover, we show that G-IRAE can also be applied to damage and management costs. We propose two methods for applying G-IRAE. The species-specific method computes the relationship for a given species across multiple invaded sites or regions, assuming a constant per-unit effect across the invaded area. The multi-species method combines data from multiple species across multiple sites or regions to calculate a per-unit effect for each species. While the species-specific method is more accurate, it requires a large amount of data for each species. The multi-species method is more easily applicable and data-parsimonious. We illustrate the multi-species method using data about money spent managing plant invasions in different biomes of South Africa. We found clear differences between species in terms of money spent per unit area invaded, with per-unit expenditures varying substantially between biomes for some species. G-IRAE offers a versatile and practical method which can be applied to many different types of data, to better understand and manage invasions.