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ABSTRACT AimThe global, human‐mediated dispersal of invasive insects is a major driver of ecosystem change, biodiversity loss, crop damage and other effects. Trade flows and invasive species propagule pressure are correlated, and their relationship is essential for predicting and managing future invasions. Invaders do not disperse exclusively from the species' native range. Instead, the bridgehead effect, where established, non‐native populations act as secondary sources of propagule, is recognised as a major driver of global invasion. The resulting pattern of global spread arises from a mixture of global interactions between invasive species, their vectors and, their invaded ranges, which has yet to be fully characterised. LocationGlobal. Time Period1997–2020. Major Taxa StudiedInsects. MethodsWe analysed 319,283 border interception records of 514 insect species from a broad range of taxa from four national‐level phytosanitary organisations. We classified interceptions as coming from species native range or from bridgehead countries and examined taxonomic autocorrelation of global movement patterns between species. ResultsWhile 65% of interceptions originated from bridgehead countries, highlighting the importance of the bridgehead effect across taxa, patterns among individual species were highly variable and taxonomically correlated. Forty per cent of species originated almost exclusively from their native range, 28% almost exclusively from their non‐native range and 32% from a mix of source locations. These patterns of global dispersal were geographically widespread, temporally consistent, and taxonomically correlated. ConclusionsDispersal exclusively from bridgeheads represents an unrecognised pattern of global insect movement; these patterns emphasise the importance of the bridgehead effect and suggest that bridgeheads provide unique local conditions that allow invaders to proliferate differently than in their native range. We connect these patterns of global dispersal to the conditions during the human driven global dispersal of insects and provide recommendations for modellers and policymakers wishing to control the spread of future invasions. 

Given a graph and an integer k, Densest k-Subgraph is the algorithmic task of finding the subgraph on k vertices with the maximum number of edges. This is a fundamental problem that has been subject to intense study for decades, with applications spanning a wide variety of fields. The state-of-the-art algorithm is an O(n^{1/4+ϵ})-factor approximation (for any ϵ>0) due to Bhaskara et al. [STOC '10]. Moreover, the so-called log-density framework predicts that this is optimal, i.e. it is impossible for an efficient algorithm to achieve an O(n^{1/4−ϵ})-factor approximation. In the average case, Densest k-Subgraph is a prototypical noisy inference task which is conjectured to exhibit a statistical-computational gap. In this work, we provide the strongest evidence yet of hardness for Densest k-Subgraph by showing matching lower bounds against the powerful Sum-of-Squares (SoS) algorithm, a meta-algorithm based on convex programming that achieves state-of-art algorithmic guarantees for many optimization and inference problems. For k ≤ n^1/2, we obtain a degree n^δ SoS lower bound for the hard regime as predicted by the log-density framework. To show this, we utilize the modern framework for proving SoS lower bounds on average-case problems pioneered by Barak et al. [FOCS '16]. A key issue is that small denser-than-average subgraphs in the input will greatly affect the value of the candidate pseudo-expectation operator around the subgraph. To handle this challenge, we devise a novel matrix factorization scheme based on the positive minimum vertex separator. We then prove an intersection tradeoff lemma to show that the error terms when using this separator are indeed small. 

Abstract Non‐native plant pests and pathogens threaten biodiversity, ecosystem function, food security, and economic livelihoods. As new invasive populations establish, often as an unintended consequence of international trade, they can become additional sources of introductions, accelerating global spread through bridgehead effects. While the study of non‐native pest spread has used computational models to provide insights into drivers and dynamics of biological invasions and inform management, efforts have focused on local or regional scales and are challenged by complex transmission networks arising from bridgehead population establishment. This paper presents a flexible spatiotemporal stochastic network model called PoPS (Pest or Pathogen Spread) Global that couples international trade networks with core drivers of biological invasions—climate suitability, host availability, and propagule pressure—quantified through open, globally available databases to forecast the spread of non‐native plant pests. The modular design of the framework makes it adaptable for various pests capable of dispersing via human‐mediated pathways, supports proactive responses to emerging pests when limited data are available, and enables forecasts at different spatial and temporal resolutions. We demonstrate the framework using a case study of the invasive planthopper spotted lanternfly (Lycorma delicatula). The model was calibrated with historical, known spotted lanternfly introductions to identify potential bridgehead populations that may contribute to global spread. This global view of phytosanitary pandemics provides crucial information for anticipating biological invasions, quantifying transport pathways risk levels, and allocating resources to safeguard plant health, agriculture, and natural resources. 

Abstract Models that are both spatially and temporally dynamic are needed to forecast where and when non-native pests and pathogens are likely to spread, to provide advance information for natural resource managers. The potential US range of the invasive spotted lanternfly (SLF, Lycorma delicatula ) has been modeled, but until now, when it could reach the West Coast’s multi-billion-dollar fruit industry has been unknown. We used process-based modeling to forecast the spread of SLF assuming no treatments to control populations occur. We found that SLF has a low probability of first reaching the grape-producing counties of California by 2027 and a high probability by 2033. Our study demonstrates the importance of spatio-temporal modeling for predicting the spread of invasive species to serve as an early alert for growers and other decision makers to prepare for impending risks of SLF invasion. It also provides a baseline for comparing future control options.