Managing biological invasions: the cost of inaction

<jats:title>Abstract</jats:title>         <jats:p>Ecological and socio-economic impacts from biological invasions are rapidly escalating worldwide. While effective management underpins impact mitigation, such actions are often delayed, insufficient or entirely absent. Presently, management delays emanate from a lack of monetary rationale to invest at early invasion stages, which precludes effective prevention and eradication. Here, we provide such rationale by developing a conceptual model to quantify the cost of inaction, i.e., the additional expenditure due to delayed management, under varying time delays and management efficiencies. Further, we apply the model to management and damage cost data from a relatively data-rich genus (  Aedes   mosquitoes). Our model demonstrates that rapid management interventions following invasion drastically minimise costs. We also identify key points in time that differentiate among scenarios of timely, delayed and severely delayed management intervention. Any management action during the severely delayed phase results in substantial losses   of the potential maximum loss). For   Aedes   spp., we estimate that the existing management delay of 55 years led to an additional total cost of approximately $ 4.57 billion, compared to a scenario with management action only 7 years prior. Moreover, we estimate that in the absence of management action, long-term losses would have accumulated to US$ 32.31 billion. These results highlight the need for more timely management of invasive alien species — either pre-invasion, or as soon as possible after detection — by demonstrating how early investments rapidly reduce long-term economic impacts.</jats:p>

section_content: Invasive alien species (IAS) can have deleterious impacts on ecosystem structure and 67 function (e. g., Bellard et al., 2017; Ricciardi & MacIsaac, 2011; Shabani et al., 2020), and on 68 multiple sectors of the economy such as agriculture, fisheries and forestry (Paini et al., 2016; 69 Holmes et al., 2009; Haubrock et al., 2021), human health (Shepard et al., 2011; Schaffner et 70 al., 2020) and human and social well-being (Pejchar & Mooney, 2009; Jones, 2017). Even 71 though many of these impacts are not yet fully understood or quantified (Vilà et al., 2010; 72 Kumschick et al., 2015; Crystal-Ornelas & Lockwood, 2020), the scientific consensus is that 73 IAS impactsalthough variable in their natureare massive, growing, and constitute a 74 major driver of biodiversity loss and global change (Simberloff et al., 2013; IPBES 2019; 75 Pyšek et al., 2020; Seebens et al., 2017). As a result, resource management agencies and 76 conservation practitioners worldwide are continuously working to develop management tools 77 legal, institutional and methodologicalto respond to new invasions through the 78 prevention of introduction, limitation of spread, and mitigation of impacts (e. g., Hoffmann & 79 Broadhurst, 2016; Jones et al., 2016). 80

There are, however, several aspects hindering the effective management of invasive 81 populations (Courchamp et al., 2017). In particular, the justification of management 82 expenditures is a challenge, as management is costly, IAS are numerous and budgets are 83 limited. Even though it is generally assumed that early responses are cost-effective in the 84 long-term (Leung et al., 2002; Timmins & Braithwaite, 2002; Russell et al., 2015), in 85 practice, applied management is often delayed, if implemented at all. This situation is 86 exacerbated by the fact that the proliferation of IAS and their impacts are often delayed due 87 to time lags (Crooks, 2005; Francis et al., 2021). However, while delays to perceived impact 88 or population detectability could provide rationale for delaying management actions, a failure 89 to consider time lags and act early can render IAS management unnecessarily expensive 90 (Francis et al., 2021). 91

For decision makers, preventative management can be seen as a riskier strategy than 92 waiting to control IAS after establishment, because neither its effectiveness, nor the eventual 93 invasion of a given IAS can be predicted with high certainty (Finnoff et al., 2007). In a 94 system where impacts are not necessarily borne by the same societal entities as those who 95 fund management actions, immediate spending always needs to be strongly justified. In 96 addition, with the existence of budget limitations and competing conservation needs, it is 97 tempting to wait for impacts to be demonstrated, to be realised, or even to be severe before 98 investing in management. In the absence of an explicit counterfactual analysis, the cost of 99 inaction i. e., the additional expenditure due to delayed management, may be implicitly 100 assumed to be negligible. Nevertheless, bioeconomic risk analysis, exemplified with zebra 101 mussel invasions in US lakes, has suggested preventative measures benefit society 102 substantially, but have been underfunded (Leung et al., 2002). Past studies have examined 103 total invasion costs as a proxy for the benefit of prevention (Epanchin-Niell & Liebhold 104 2015). However, no studies have focused on a direct quantification of the monetary costs of 105 delayed action under different invasion and management timing scenarios. Further, previous 106 analyses have been limited to the local scale, and have relied on abundance data, which are 107 frequently unavailable for IAS, and have used external estimates of management efficiency 108 rather than a direct quantification (Leung et al. 2002; Hastings et al. 2007 (Diagne et al., 2020a (Diagne et al.,, 2020b)). 121

Our central hypothesis and model assumption is that the cumulative costs of both 122 damage and management of IAS follow a logistic curve with time (sigmoidal type curve). 123

This assumption follows the well-accepted "invasion curve" (Leung et al., 2002; Lodge et al., 124 2016), which predicts that the area invaded or impacted by an IAS initially increases slowly, 125 but then accelerates, and eventually reaches a plateau (Fig. 1 ), and is also a common pattern 126 of growth in invasion models (Shigesada et al. 1995 ). If we assume that impact is 127 proportional to the area invaded (Parker et al., 1999), the costs associated with a single IAS 128 should follow a similar logistic curve. While the precise shape of the curve may depend on 129 case-specific details (e. g., on the environmental properties or stage of invasion), the 130 assumption of logistic IAS impacts has lacked large-scale empirical testing until recently 131 (Ahmed et al. 2021). 132

Given the assumption of a logistic description of cumulative costs, it follows that 133 marginal damage and management costs are distributed logistically (i. e., according to a bell-134 shaped curve). Building upon this, we formulate a theoretical cost model for marginal, 135 realized damage costs and for the total expenditure (inclusive of damage and management 136 costs), whilst allowing for variable management delay times and time-dependent 137 management efficiencies. The model incorporates key parameters such as initial costs, cost 138 growth rates and cost carrying capacities, that are useful to help better understand the 139 resulting cost dynamics. Furthermore, we compute the cost of inaction to estimate the 140 additional expenditure due to further management delays. We demonstrate the utility of our 141 cost model with application to the relatively data rich Aedes genus in the InvaCost database. 142

In this way, we provide a coherent framework for the valuation of the foregone costs due to 143 damages, which can be used as an imperative to manage biological invasions as proactively 144 as possible. 145 for ease of interpretation. 161
section_name: Introduction 66

section_content: In developing a theoretical cost model, we focused on reactive management, i. e., the scenario 164 where management is introduced after the arrival and establishment of an IAS. As a first step, 165 following the classical invasion curve (see Fig. 1 ), we assumed that the cumulative damage 166 cost as a function of time () in the absence of management onset is modelled by a 167 sigmoidal-type curve given by the (modified) logistic function: 168

where is the intrinsic growth rate of damage costs, is the cumulative damage cost in the 170 long term (henceforth referred to as the damage cost carrying capacity), and is a parameter 171 which modulates the shape of the logistic curve. 172

It follows that the marginal (or instantaneous) damage cost () can be computed as 173 the derivative of Eq. ( 1 ), resulting in the logistic distribution (bell-shaped curve), given as: 174 Eq. (2) (i. e., bell-shaped curve) and can be described as: 184 Ahmed et al. 2021). 197 We assume that the management expenditure directly reduces the cost due to 198 damages, and therefore once management is introduced at time =, the realized marginal 199 damage cost * is: 200

which is a positive quantity, or otherwise equal to zero. Within this equation, we propose a 203 management efficiency term as a function of time: 204

(5) 205 which quantifies the amount of reduction in the damage cost for every $ 1 spent on 206 management. 207

At the time of management introduction =, efficiency can be either effective if 208 0 > 1 or ineffective if 0 = 1. In the case that 0 > 1, the efficiency can either increase, 209

decrease or remain constant depending on the growth rate. If > 0 the efficiency grows, 210 approaching a constant maximum value 1 in the long term. If < 0, then the efficiency 211 decays to 1. In the case that = 0, the efficiency remains constant at 0. Since > 1 for all 212 time, it is assumed that management action is effective, as $ 1 spent on management always 213 reduces the damage cost by an amount greater than $ 1, see Fig. 2. If, however, 0 = 1, then 214 the efficiency remains constant at this value for all time, i. e., = 1, and therefore 215 management is considered as ineffective as $ 1 spent on management reduces the damage 216 cost by the exact same amount, see Eq. ( 5 ). 217 increases if > 0 or decreases if < 0. In either case management is assumed to be 220 effective since the efficiency is always greater than 1 once management is introduced. 221

However, if 0 = 1, then the efficiency remains constant at this value, and management is 222 deemed to be ineffective. Although not shown here, we note that if lies between 0 and 1, 223 then management is counterproductive, as $ 1 spent on management reduces the damage cost 224 by less than $ 1. 225

With management action and the subsequent reduction in damage costs, the total cost 226 incurred by the invasion is the sum of realized damage and management costs: 227 (, ) = * (, ) + ( -). 

(6) 228

In the case that management is effective ( 0 > 1), the total cost is always less than the cost 229 due to damages i. e., <, whereas if management is ineffective ( 0 = 1) then the total 230 expenditure is equal to the damage cost, i. e., =. Note that if lies between 0 and 1, then 231 > and therefore in this case, management is deemed counterproductive. The cost dynamics differ depending on whether management efficiency increases or 242 decreases over time. In the case of increasing efficiency ( > 0) the maximum costs for 243 * and are lower than in the case of decreasing efficiency ( < 0), and these maxima 244 occur earlier if management is delayed (Table 1 ). Also, irrespective of, * and approach 245 zero faster in the presence of a management delay compared to immediate management, c. f. 246 Fig. 3 plots (c) and (d). However, note that both * and exhibit larger maximum cost values 247 with delayed management (Table 1 ). 248 249
section_name: Damage and management costs 162 163

section_content: We define the marginal cost of inaction as the cost difference at time between two 263 distinct scenarios where management is introduced at a fixed time * and at a further delayed 264 time, given as: 265 (, ) = (, ) -(, * ), > * (7) 266 which is a positive quantity, or otherwise equal to zero. The cumulative cost of inaction is 267 then given by: 268

which is the total additional expenditure at time due to delayed management intervention. 270

The integral in Eq. ( 8 ) is not analytically tractable, however an approximation can be 271 determined using techniques of numerical integration (i. e., trapezoidal rule). 272 8 ). The coloured markers represent points 309 that differentiate among scenarios of the severity of delayed management. In the long term, 310 the additional expenditure in the absence of management is estimated at = 33. 34. All 311 parameter values are the same as that in the caption of Fig. 3, except that we only consider 312 the case where management efficiency is increasing with time, = 0. 01 > 0, see also Fig. 3 standardised against a single currency (2017 US$). This currency was selected as it is a 335 common metric in environmental economics, standardised to 2017 to account for inflation in 336 the year of the main cost search. These descriptors include, among other things, the cost type 337

("Type of cost merged"), which groups costs into three distinct categories: (a) "Damage" 338 referring to damages or losses incurred by the invasion (e. g., costs for damage repair, 339 resource losses, medical care), (b) "Management" comprising any expenditures dedicated to 340 prevent, limit and/or mitigate invasion impacts (e. g., monitoring, prevention, control, 341 education, eradication) and (c) "Mixed" including indistinguishable damage and management 342 costs (cases where reported costs were not clearly separable from the aforementioned cost 343 types categories). We considered all types of damage costs, but only post-invasion 344 management costs, in order to eliminate preventative management (i. e., for species that have 345 not yet arrived). This was done using the "Management_type" column of the database by 346 selecting the "Post-invasion management" category therein. We further filtered our dataset to 347 examine only costs incurred at larger scales (up to national), using only "Country" and "Site" 348 spatial scales from the "Spatial_scale" column. We also removed any extrapolated 349 ("Potential") costs (i. e., those extrapolated from different spatial scales) by limiting our 350 search to "Observed" costs in the "Implementation" column. Furthermore, we considered 351 only costs in peer-reviewed literature and official documents, or grey literature with fully 352 reproducible methods, defined as having "High" reliability under the "Method_reliability" 353 column (Diagne et al., 2020b). 354

For consistency and to aid comparisons across data, all costs in the original database 355

were 'expanded' so that cost entries could be considered on an annual basis. Fig. 5 illustrates that the theoretical cost model was highly predictive of the Aedes spp. 396 marginal management and damage cost data, as evidenced by their respective 2 values. We 397 estimated that with a management delay of 55 years, the maximum management expenditure 398 amounted to $ 0. 17 billion, resulting in a significant reduction of the maximum damage cost 399 from $ 8. 34 billion to $ 4. 39 billion (∼ 47% decrease), and a total maximum cost of $ 4. 56 400 billion. 401 402 Fig. 6 shows the cumulative cost of inaction which determines the additional 419 expenditure due to delayed management relative to the scenario where management is 420 introduced in the year 1969 ( * = 48). We found that remained very low for a short time 421 period, with a subsequent rapid increase, and eventually approached saturation i. e., the 422 estimated no action cost = $ 32. 31 billion. The base year of 1969 was chosen since it is 423 the first instance where the reported damage cost (of value $ 0. 12 million) exceeds the 424 estimated initial management cost 0 = $ 0. 11 million. Moreover, the sum of all reported 425 costs over the time period < 48 is $ 0. 42 million, amounting to < 0. 01% of, and thus 426 provides a negligible contribution. To put the magnitude of these estimated costs into 427 perspective, note that the long-term cumulative cost of damages in the absence of 428 management amounts to approx. = $ 100 billion. 429

We identified four markers of relevance in Fig. 6. First, the blue marker represents a 430 cumulative cost value $ 0. 32 billion when management is introduced at = 52. 63 years after 431 the first recorded damage cost, which is 1% of the expenditure in the scenario where no 432 action is ever taken, i. e.,. Second, the red marker (runaway point) occurs at delay time 433 = 59. 67 years, where amounts to $ 16. 16 billion, which is approx. 50% of. long-term → ∞) for different management delay times, relative to * = 48, using Eq. ( 8 ). 446

Coloured markers represent points that differentiate among scenarios of the severity of 447 delayed management. In the long-term, the additional expenditure in the absence of 448 management is estimated at = $ 32. 31 billion. All estimated parameter values are 449 mentioned in the caption of Fig. 5, see also Appendix A2. 450

In general, any management intervention during the period between the blue and red 451 markers can be considered 'delayed', with cost impacts of delay exacerbated closer to the 452 latter marker. Our work highlights that failing to begin managing an invasion can quickly lead to immense 461 economic costs. The cost of inaction increases rapidly prior to a certain threshold time, after 462 which the rate of accumulation slows down, and eventually saturates at a high level (see Fig. 463 6). This means not only that IAS costs can quickly increase to unbearable amounts, but also 464 that they may initially be deceitfully slow to accrue, therefore not signalling to policy makers 465 the urgency to invest in management. Indeed, during this initial time period, the willingness 466 to allocate funds to IAS management may be low due to the lack of perceived risk or impact 467 detection (Finnoff et al., 2007). A lack of willingness to invest may also represent a potential 468 moral problem, whereby invader impacts are seemingly incurred by other regions, sectors, or 469 generations than those that take management action-paralleling challenges in moral 470 responsibilities for climate change (Gardiner, 2006). However, as we have shown here, these 471 costs can inflate suddenly and potentially overwhelm major sectors of the economy. 472

Our findings are generally in line with the resource economics literature and 473 associated bioeconomic analyses that suggest a higher value for today's benefits compared to 474 future benefits. This is because today's benefits can be invested and yield more value through 475 time, which confers a higher advantage compared to delaying those benefits. This in turn 476 implies that the effect of control actions applied earlier are worth more, which also explains 477 why prevention and early action are also prominent in bioeconomic analyses for invasions 478 (Hui and Richardson, 2017 ; see also McDermott et al., 2013; Polasky 2020 for more 479 examples of how early identification and removal bears the strongest benefits). These 480 findings tie into efforts to combat policy makers' hesitancy to commit to more proactive 481 management spending, given limited conservation budgets that could alternatively be used 482 only for reactive management actions. Bioeconomic frameworks using real options theory 483 have shown that, particularly in cases of fast-spreading species where diffusion is too fast and 484 unpredictable, immediate action is the only option (Sims et al., 2016). Controlling such 485 species immediately has large potential returns and therefore incentivizes larger investments, 486 even if the spread's volatility increases the risk in these investments (Sims et al., 2016). 487

Since our theoretical cost model predicts the damage cost and total expenditure from 488 model fitting against realized damage and management cost data (see Fig. 5 ), it provides a 489 simpler yet conceptual description of the resulting cost dynamics, in contrast to more 490 complex models that are reliant on time series of IAS abundances (Leung et al., 2002). Also, 491 our approach goes beyond prescriptive frameworks for optimal control, as it allows for a 492 direct estimation of management efficiency from empirical cost data. Further, our approach is 493 focused at the global rather than regional or site-specific scales. As such, we show that when 494 management is effective ( > 1) and less costly than damage: (i) initiating management at 495 any time can reduce the total cost of a given IAS over a short time period; (ii) greater 496 reductions in the total expenditure are achieved with increasing management efficiency (see 497

Table 1, Fig. 3 ); and (iii) there are critical time windows that distinguish among timely, 498 delayed and severely delayed management, corresponding to different phases of the invasion 499 curve, where IAS eradication transitions from feasible to difficult and to unlikely, 500 respectively (see Fig. 1 ). Importantly, (iv) we compute the time taken to reach the runaway 501 point, where initiation of management action prior can lead to a considerable amount of cost 502 savings (< 50% of the potential cost in the absence of management), with more cost savings 503

given earlier management (see Fig. 6 ). Also, note that the model also allows not only for an 504 estimation of the cost of inaction but also of the reverse scenario, i. e., estimating the cost 505 savings of timely management based on counterfactual analyses of hypothetical delays. 506

In the Aedes case study, the cost of inaction grew relatively slowly over an initial 53 507 year period, but then accumulated rapidly within a critical ~ 7 year period by at least two 508 orders of magnitude. This resulted from a sudden rapid increase in the cost due to damages, 509 combined with a delayed suboptimal management strategy (see Fig. 6 ). In practice, this 510 window of opportunity may be difficult to identify due to context-dependencies that influence 511 invasion debt as well as the magnitude of impact and differences in detection timing among 512 regions. These challenges indicate that acting sooner, even when costs accrue slowly, is the 513 optimal risk averse strategy (see also Leung et al. 2002). Given these uncertainties, we 514 suggest that policy makers should prioritise investments at the earliest possible invasion stage 515 to improve efficiency and reduce future invasion costs, while also maintaining effort to 516 curtail the invasion and increasing awareness of IAS impacts throughout the duration of the 517 invasion. Additionally, the fact that the cost of inaction saturates in the long-term should not 518 deter management effort at late invasion stages, whereby control can still be effective and 519 help mitigate ongoing and emerging ecological and socio-economic impacts through, for 520 example, novel arbovirus emergence in our Aedes model taxon (Barrera et al., 2019). Indeed, 521 despite management being delayed by 55 years and incurring an inaction cost of $ 4. 57 522 billion, our model estimates that an additional cost of $ 27. 74 billion could have been 523

incurred in the absence of any Aedes management whatsoever. As a cautionary note, given 524 that we only presented a single case study for Aedes spp., the model should be treated as a 525 conceptual one, and our aim is not to be prescriptive about the costs of inaction. Rather, this 526 should be seen as an illustrative example, where cost estimates are subject to improvements 527 upon availability of more refined data, and further development of the underlying model with 528 added complexity to better reflect reality. 529

In the cost model, damage and management costs are parametrized by their initial 530 costs ( 0, 0 ), intrinsic cost growth rates (, ) and cost carrying capacities (, ), as per 531

Appendix A2. Although we demonstrated an example with Aedes, the model can be applied 532 to other genera, and parameters can thus be estimated given the availability of sufficient 533 empirical cost data for these taxa. We expect these parameters to be inherently affected by, 534 for example, the taxonomic group, size of the invasible area, introduction pathways and traits 535 of IAS. In light of this, we predict that large-bodied IAS such as raccoons and squirrels 536 (Procyon, Callosciurus), as well as other rapidly spreading invaders, such as ballast 537 water/hull contaminants (e. g., mollusks and copepods; Lin et al., 2020) The implications of data limitations are as follows: firstly, given the general tendency 559 to research and record species with higher costs for both management and damage, the cost 560 data available to us through InvaCost are likely skewed to highly damaging species and 561 species requiring costly management. Further, due to lags in IAS detection along with their 562 impacts (Essl et al., 2011), the actual occurrence of impacts is likely earlier on in the 563 timelines, compared to the ones we report in this study, and varies across species and invaded 564 countries (Seebens et al., 2020). Furthermore, our cost saturation estimations could reflect 565 delays in more contemporary cost reporting, and do not preclude the possibility of future 566 spikes in cost due to range expansions of these IAS (Louppe et al., 2019), new types of 567 impacts (e. g., virus emergence) or advances in cost quantification methods, and should 568 therefore be interpreted with caution. Secondly, as our data pooled multiple Aedes spp. 569 also help minimize IAS risk at that pathway level (Leung et al., 2014; Turbellin et al., this 613 issue). In these cases, modest initial biosecurity investments can yield substantial returns in 614 reduced invasion risk across multiple taxonomic groups. 615
section_name: Cost of inaction 262

section_content: There are many well-documented cases where even simple, conceptual models made 617 a direct and significant effect on ecosystem management, in particular assisting in an efficient 618 and cost-saving strategy (e. g., DeAngelis et al., 2021). In studies on biological invasion, 619 mathematical models have been used efficiently for a few decades aiming to identify 620 different invasion scenarios, to reveal the effect of various factors on invasion success and 621 thus to facilitate understanding of the phenomenon (Hengeveld, 1989; Shigesada and 622 Kawasaki, 1997; Roemer et al., 2002; Courchamp et al., 2004; Lewis et al., 2016). Economic 623 issues such as losses and associated costs have been a focus of modelling studies too (e. g., 624

see Marten and Moore, 2011), although this line of research, in our opinion, remains under-625 developed. 626

The present study, for the first time, presents a conceptual model which monetizes the 627 cost of inaction surrounding IAS management. While the cost of inaction is often implicitly 628 assumed to be negligible, we show that it can take on a very high value and can grow quickly 629 from small values at difficult-to-predict threshold times. We hope that this conceptual 630 demonstration can help motivate the collection of necessary cost data that allows for more 631 comprehensive empirical estimates of the cost of inaction. Further, we have confirmed, using 632 our relatively data-rich Aedes spp. case study, that more rapid management interventions can 633 greatly reduce inaction costsat the multi-billion $ scale over a few decades for this genus 634 alone. Moreover, our cautionary identification of a runaway point should motivate timely 635 management prior to the closing of IAS windows of opportunity for efficient and effective 636

control; yet it should also spur immediate management as soon as possible after IAS 637 detection, or ideally, pre-invasion. We expect our results to help resource managers justify 638 early action, even if costly, and accordingly decision makers to fund it, in order to 639 simultaneously increase efficiency and efficacy while decreasing overall costs. 640
section_name: Conclusion 616

section_content: Vocabulary relating to invasion costs used throughout the manuscript. 642
section_name: Appendix A1: Cost terminology 641

section_content: The sum of management and damage (cumulative or instantaneous) costs
section_name: Cost type Definition Total Cost

section_content: The sum of (management, damage, or total) costs incurred by an IAS since its first reported cost of that type. 

The data used in this work come from publicly available databases (InvaCost: https://doi. org/10. 6084/m9. figshare. 12668570). Transformed data used for curve parameterization are provided at https://github. com/emmajhudgins/CostOfInaction.
section_name: Cumulative cost

section_name: Code availability

section_content: Code and derived data are provided at https://github. com/emmajhudgins/CostOfInaction.
section_name: Code availability

section_name: Marginal cost

section_content: (although primarily Aedes aegypti and Aedes albopictus), we did not account for differential 570 environmental tolerances and life histories among congenerics that could influence 571 invasiveness in different regions (Juliano and Lounibos, 2005; Medlock et al., 2012, 572 Appendix A3). For example, A. albopictus is better-adapted to temperate regions due to the 573 production of cold-resistant eggs, with temperate climates reported to preclude A. aegypti 574 invasion success (Medlock et al., 2012). Finally, the costs incurred are subject to country-575 level differences considering, for example, the importance of certain industries (e. g., see 576 estimated impacts to agriculture across different countries in Paini et al., 2016, see map in 577 Appendix A3), the different research capacity, effort and funding landscapes, the suitability 578 of habitat for each IAS (Parker 1999), and other socioeconomic or environmental factors that 579 differ across countries. 580

We note that given the potential for Aedes to vector arboviruses at relatively low 581 population densities (Barrera et al., 2019), management of this genus may have been 582

perceived to be necessary by decision makers even at very early invasion stages, which is 583 currently unlikely to be the case for most other IAS. (Allen et al., 2021). However, management of other genera or future Aedes spp. management 595 may experience the opposite trend due to reduced public participation, biotic facilitation, 596 alternative stable states or phenomena such as emerging resistance to control approaches 597 (e. g., insecticide resistance) (Fung et al., 2011; Moyes et al., 2017; Agha et al., 2021). Future 598 research should address knowledge gaps and focus on further empirical validation, where the 599 suitability of this model is tested across multiple taxa, habitats, and costs from different 600 sectors of the economy-including situations where management was immediate but could 601 have been costlier if delayed. This calls for more effort into estimating and reporting costs in 602 a standardized way (Diagne et al., 2021). 603

It is also worth noting that while our analysis was done only on Aedes spp, it is likely 604 that in many cases, biosecurity measures and other proactive approaches can be rendered 605 even more cost effective when several species are managed simultaneously. For instance, 606 airport quarantine and interception services deal with very large lists of potential invaders 607 such as insect species, with only marginal costs for each additional species (Lougheed et al., 608 2007). Aquatic biosecurity measures such as Check Clean Dry campaigns and ballast water 609 treatment systems similarly target a range of taxa indiscriminately (e. g., plants, invertebrates, 610 and vertebrates; Anderson et al., 2015; Shannon et al., 2018; Coughlan et al., 2020; Lin et al., 611 2020). Transport legislation such as wood-packing material treatment protocol ISPM15 can 612

section_content: The change in the cumulative (management, damage, or total) cost of a given IAS between two timesteps (which we model as being equivalent to the instantaneous cost).
section_name: Marginal cost

section_content: The amount of dollars in reduced damages caused by one dollar spent on management
section_name: Management efficiency

section_content: The difference in total cost of an invasion at a given point in time compared to the total cost in a scenario where management began immediately 643 Appendix A2: Definitions of parameters and their precise values as used in section 3. 3 644

The parameter values reported in the manuscript for Aedes spp. are rounded for brevity (see 645 section 3. 3 and the caption of Fig. 5 ), whereas the cost of inaction calculation (see Fig. 6 ) 646 used estimated best-fit parameters to a higher degree of accuracy. We have also included the 647 definitions of each parameter here for reference. 648
section_name: Cost of inaction

section_content: Intrinsic growth rate for cumulative management costs (year
section_name: Management cost parameters

section_content: The authors have declared that no competing interests exist.
section_name: Conflict of interest

section_name: Availability of data and material