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The legacy of deliberate and accidental introductions of invasive alien species to Australia has had a hefty economic toll, yet quantifying the magnitude of the costs associated with direct loss and damage, as well as for management interventions, remains elusive. This is because the reliability of cost estimates and undersampling have not been determined. We provide the first detailed analysis of the reported costs associated with invasive species to the Australian economy since the 1960s, based on the recently published InvaCost database and supplementary information, for a total of 2078 unique cost entries. Since the 1960s, Australia has spent or incurred losses totalling at least US$298.58 billion (2017 value) or AU$389.59 billion (2017 average exchange rate) from invasive species. However, this is an underestimate given that costs rise as the number of estimates increases following a power law. There was an average 1.8-6.3-fold increase in the total costs per decade since the 1970s to the present, producing estimated costs of US$6.09-57.91 billion year-1 (all costs combined) or US$225.31 million-6.84 billion year-1 (observed, highly reliable costs only). Costs arising from plant species were the highest among kingdoms (US$151.68 billion), although most of the costs were not attributable to single species. Of the identified weedy species, the costliest were annual ryegrass (Lolium rigidum), parthenium (Parthenium hysterophorus) and ragwort (Senecio jacobaea). The four costliest classes were mammals (US$48.63 billion), insects (US$11.95 billion), eudicots (US$4.10 billion) and monocots (US$1.92 billion). The three costliest species were all animals - cats (Felis catus), rabbits (Oryctolagus cuniculus) and red imported fire ants (Solenopsis invicta). Each State/Territory had a different suite of major costs by species, but with most (3-62%) costs derived from one to three species per political unit. Most (61%) of the reported costs applied to multiple environments and 73% of the total pertained to direct damage or loss compared to management costs only, with both of these findings reflecting the availability of data. Rising incursions of invasive species will continue to have substantial costs for the Australian economy, but with better investment, standardised assessments and reporting and coordinated interventions (including eradications), some of these costs could be substantially reduced. [ABSTRACT FROM AUTHOR]