1 INTRODUCTION

Plants and insects together make up the majority of multicellular species diversity (Schoonhoven et al., 2005). Moreover, they are linked through a wide array of interactions, and such plant–insect interactions play key roles in numerous ecological processes and functions (Herrera & Pellmyr, 2009; Schoonhoven et al., 2005; Weisser & Siemann, 2008). For instance, insect herbivory regulates nutrient cycling, plant production and diversity in ecological communities; meanwhile, insect pollination is critical for the reproduction of a significant part of angiosperms. The understanding of plant–insect interactions has therefore long been a central ecological research pursuit, and is crucial for resolving and maintaining the integrity of biodiversity (Fisher, 1998; Samways, 1993).

Recent evidence suggests that global change is resetting the spatial and ecological equilibrium of interacting plants and insects (DeLucia et al., 2012; Pincebourde et al., 2017). Generally, global change drives two major aspects of species distribution: species change their distributional range and colonise new places, and species go locally extinct (Brook et al., 2008; Freeman et al., 2018; Thomas et al., 2006). The former is associated to species’ spatial movement to track their suitable or tolerable niches, while the latter by species’ inability to adapt to environmental changes. These influences thus present spatial processes that alter the distribution of species, as well as the composition of local communities. In the context of plant–insect interaction, effects on one (or multiple) species at one trophic level will cascade to the interacting others, creating trophic cascades between plants and their insect consumers (Dyer & Letoumeau, 1999; Jamieson et al., 2012). Such cascading effects should be particularly pronounced when the dependence on the respective other trophic level is strong, as is often the case in specific plant–insect interaction networks.

Lepidoptera (butterflies and moths) are one of the most widespread and species-rich insect orders that exhibits such tight relationships (Scoble, 1995). Most Lepidoptera are exclusive plant feeders and rely two-fold on plants across their life stages: their larvae are key herbivorous consumers to their host plants, whereas feeding adults pollinate their nectar plants (Boggs, 1987). Therefore, their trophic reliance on plants as a biotic filter shaping their spatial distribution is especially effective, on top of their climate niche as an abiotic filter (Nakadai et al., 2018). Consequently, Lepidoptera–plant interaction networks should be particularly sensitive to the alterations of species co-occurrence, and present a suitable object for projecting possible cascading influences triggered by common global change-induced spatial processes (Tscharntke & Brandl, 2004).

Two scenarios are of particular research interest: (i) resource plants go (locally) extinct, and (ii) Lepidoptera expand their range. While other scenarios (e.g., plant range expansion) are also valid, these two are well-grounded on evidence and expected to happen relatively quickly (Hällfors et al., 2021; Suckling et al., 2017). Loss of local plant occurrences is an important part of the ongoing biodiversity crisis, as about 40% of the world's plants are at risk of either local or global extinction (Nic Lughadha et al., 2020). The robustness of Lepidoptera–plant communities—as interaction networks—responding to this change (or not) through trophic cascade is thus a critical feature to be understood (Banza et al., 2015; Pearse & Altermatt, 2013a). Being able to predict the response of such Lepidoptera–plant networks helps to identify the Lepidoptera that are prone to secondary extinction due to losing food. Meanwhile, adult Lepidoptera are generally highly mobile and able to change their range rapidly (Neve et al., 1996). Tracking climate niche under climate change is considered a main trigger of the reported Lepidoptera expansion (Hill et al., 2021). Notably, theory has specifically suggested that the “warm” boundary of spatial distribution is often driven more by a species’ intrinsic climate niche (e.g., temperature tolerance), while the “cold” boundary by its biotic interactions (Paquette & Hargreaves, 2021). In a warming world, Lepidoptera are expected to expand their cold boundaries and reach places where they have not been, forming interactions with the locals, thereby creating a need to account for the bio-interaction context to better predict the consequences of such expansion. For instance, in the absence of diet shifts, successful Lepidoptera range expansion depends on the availability of respective food plants in the new range, and may alter the trophic structure and functions of the communities therein.

To resolve, and further to predict possible influences of global change on Lepidoptera–plant communities, here we exploit extensive empirical data of a real-world landscape to explore in silico the consequences of the two focal spatial processes, namely the secondary extinction of Lepidoptera caused by plant extinction, and the change in functional relationships among plants caused by Lepidoptera expansion. Importantly, while relevant previous studies are mostly spatially implicit (e.g., Pearse & Altermatt, 2013a), our simulations are spatially explicit and based on simple but realistic information of the topography, species occurrences, and interactions within the landscape (echoing Tscharntke & Brandl, 2004), thereby integrating empirical biogeographical and bio-interaction knowledge. As for plant extinction, we specifically compare between regional (spatially implicit null) and distributional isolation-driven (spatially explicit) schemes. In analogy, for Lepidoptera expansion, we compare among random shifting (spatially implicit null) and directional (northward and upward, spatially explicit) schemes, respectively. Their community-wise consequences, including secondary extinction and functional changes, are evaluated with realistic community composition and trophic structure resolved to the local scale. We expect that spatially explicit simulations will bring about more constrained yet arguably more realistic consequences than the nulls, and those consequences tend to be negative to local communities. Also, we expect that spatially explicit schemes will reveal certain localised patterns of response shaped by the realistic correspondence of communities.

2 MATERIALS AND METHODS

2.3 Global change-induced spatial processes simulation

Starting with all the local Lepidoptera–plant networks as above addressed, we simulated the focal spatial processes—plant extinction and Lepidoptera expansion—in the study region. All simulations therefore shared the same initial state, and had consequences emerged from the same regional trophic structure, both given by empirical data.

For plant extinction, we first looked at two main schemes, namely “regional” and “isolation-driven”. With the former, at each simulation step, a plant species (from the 848 focal food plants) was randomly selected and set extinct across the whole region, i.e., being removed from all the local communities where it originally occurred. This was therefore a spatially implicit, and arguably unrealistic, simulation of plant extinction. With the latter, again a plant species was randomly selected at each step, yet its extinction only happened locally at the most-isolated or most-periphery cell(s) according to the selected plant's current regional cell occupation (Figure 1; for detailed algorithm see Supplementary Information Section S1). A plant species thus must be selected several times to become fully extinct in the region. The isolation-driven scheme thus incorporates and stresses, from a biogeographic perspective and in a spatially explicit manner, that isolated or periphery populations are often at higher extinction risk (Channell & Lomolino, 2000). Besides the above, to consider that certain species-level features (in addition to spatial isolation) may differentiate the extinction likelihoods among plants and lead to different extinction dynamics, we also simulated another two schemes mirroring the previous two, but with the plants' status of being threatened integrated as a weighting factor to plant–extinction simulations (“status-weighted”, in combination with “regional” or “isolation-driven”). That is, the sequence of plants' going extinct became no longer purely random; highly-threatened plants tended to go extinct early (details see Section S2). For all four schemes, after each step, we locally removed Lepidoptera species that lost completely either its larval or adult food plants due to the simulated plant extinction according to our metaweb, and such procedure presented the trophic cascade-driven Lepidoptera's secondary extinction due to the lack of food. The simulations ended when all 848 focal plants (and thus all 423 interacting focal Lepidoptera) are fully extinct in the region, and we carried out 20 independent simulations for each scheme. Although different schemes required computationally different numbers of steps to reach the final state, the simulation steps per se were not temporally meaningful but only reflecting extinction events, thus the consequences (e.g., trajectories of secondary extinctions) of the schemes can be compared altogether given their shared initial and final states being aligned (Figure 2).

For Lepidoptera expansion, in analogy, we first looked at two main schemes that phenomenologically mimic the shifting of Lepidoptera cold boundaries: orientational “northward” and elevational “upward”. With the former, at each simulation step, we randomly picked 50 percent (a fixed parameter) of the Lepidoptera at each cell, and their occurrences were added to the cell at the adjacent north. With the latter, it was the same process yet the occurrences of the picked Lepidoptera were added to whichever of the eight adjacent cells having higher mean elevation than the original. Here we again additionally accounted for species-level features that may influence the likelihood of Lepidoptera's expansion, thereby having another two schemes where Lepidoptera species-specific flying ability (proxied by inversed wing-load (Ebert, 1991–2005)) as a weighting factor (“wingload-weighted”, in combination with “northward” or “upward”). That is, the expanding 50% local Lepidoptera were no longer randomly picked at each step; instead, better flyers were more likely to expand (Section S3). Notably, northward expansion was cell-wise one-to-one per step, while upward expansion could be one-to-several. The per-step spatial extents of Lepidoptera expansion were thus inequal between northward and upward (and corresponding wingload-weighted) schemes. To set a baseline allowing across-scheme comparisons, we also performed two spatially-irrelevant null schemes. With these two nulls, the expanding Lepidoptera did not go to adjacent cells but randomly selected one(s), thus the spatial contexts of expansion were discarded. Meanwhile, the nulls respectively accounted for the number of Lepidoptera-receiving cells at each step of the norward and upward simulations, thus kept the same spatial extents of expansion corresponding to respective northward or upward schemes. For all six schemes, an expanding Lepidopteran could only successfully establish in the new cell(s) if food plants were therein available supporting its both life stages, otherwise was removed instantly; in other words, lacking local food at the destination would impede its colonisation and range expansion. Throughout the simulations, some expanded Lepidoptera may already exist in the new cell(s) before expansion so would not lead to any compositional changes, while others changed the Lepidoptera composition in local networks. The (non-null) schemes thus explicitly covered compositional (thus interactional), orientational, and topographical spatial contexts of Lepidoptera expansion. We simulated all schemes for three consecutive steps, for 20 independent replicates, and presented the consequences after the final step (other steps see Section S4).

In the above-mentioned simulations, all extinction and expansion events that may change local Lepidoptera–plant communities’ composition operated at the spatial scale of our cells, which could be seen as a discrete approximation of the realistic gradual distribution changes of species over time. Consequently, the consequences of each simulation step should be relatively substantial, as they already reflected an integration of continuous processes over an implicit period of time.

3 RESULTS

The predicted consequences of accumulating regional plant extinction on regional and averaged local Lepidoptera richness were similar, leading to gradual and smooth decreases in remaining richness, where the status-weighted schemes kept higher Lepidoptera richness than the non-weighted schemes (Figure 2). The proportion of local Lepidoptera extinction indicated that the rates of secondary extinction were rather even across grid cells (Figure 2). Contrarily, with isolation-driven plant extinction (status-weighted or not), regional Lepidoptera richness barely decreased in the first half of the simulations then exhibited an accelerating drop in the second, while averaged local Lepidoptera richness still exhibited gradual and smooth decreases (Figure 2). Throughout the simulations, the isolation-driven schemes kept having more regional remaining Lepidoptera than the regional schemes; however, this pattern reversed when looking at averaged local remaining Lepidoptera. Between the isolation-driven schemes, random extinction kept slightly more regional remaining Lepidoptera than status-weighted extinction, yet the reverse when regarding local remaining Lepidoptera (Figure 2). With isolated-driven plant extinction, the middle part of the landscape turned out to be particularly vulnerable to secondary extinction, i.e., with higher proportion of local Lepidoptera extinction than other areas, particularly later in the simulations (Figure 2), and such vulnerability was associated with lower elevation (Figure 3; Figure S2).

Lepidoptera's secondary extinction at individual cells further changed their landscape-wise distributions. With regional plant extinction, the distribution of Lepidoptera that were originally broadly distributed (and relatively non-fragmented) within our study landscape became gradually fragmented, while that of those originally intermediately or narrowly distributed (and already relatively fragmented) remain unchanged until very late phase of simulations (Figure 4). Meanwhile, with isolation-driven plant extinction, broadly distributed Lepidoptera first had minimal response, then became more fragmented, further then more intact; instead, intermediately and narrowly distributed Lepidoptera gradually became more intact (Figure 4).

As for Lepidoptera expansion's influences on the functional features of communities, in general, the nectar plants in local imago–plant networks were functionally more distant than the host plants in larva-plant networks, which was consistent before (given by empirical data) and after simulated expansion (Figure 5; Figures S3–S5). The plants' functional distance dropped as a result of Lepidoptera expansion no matter it was northward or upward, but particularly in the upward schemes the dropping was weaker than the corresponding null (Figure 5). The functional distance of host plants in larval networks dropped slightly more than the nectar plants in adult networks (Figure 5). Spatially speaking, we observed no obvious patterns of any sub-region having particularly intensive functional changes (Figures S4 & S5). The outcomes of wingload-weighted and corresponding non-weighted schemes were very similar, thus expansion at random or depending on (inferred) flying ability made little difference to the consequences of Lepidoptera expansion (Figure 5). The analogous results regarding Lepidoptera niche overlap were qualitatively mirroring those regarding functional distance (Figures 6, S6–S8).

Overall, our expectations were partially realised. Spatially explicit isolated-driven plant extinction indeed led to more constrained regional Lepidoptera secondary extinction, and northward and upward Lepidoptera expansion brought about more constrained plants' functional distance changes, compared to respective, spatially implicit null models. A localised (sub-regional) pattern of vulnerability to Lepidoptera secondary extinction was also revealed by isolated-driven plant extinction. Yet, some metrics reflected stronger consequences in spatially explicit schemes than in implicit ones, for example, the averaged local Lepidoptera secondary extinction across the whole landscape.

4 DISCUSSION

We predicted possible consequences of key global change-induced processes—plant extinction and Lepidoptera expansion—on the richness, composition, and trophic structures of lepidoptera–plant communities using spatially explicit simulations considering a real-world topography.

When plants’ extinction scenarios were (distributional) isolation-driven, Lepidoptera were more robust to secondary extinction if evaluated by regional Lepidoptera richness, but less robust if evaluated by averaged local Lepidoptera richness, in comparison to the case of regional plant extinction. This is reasonable, as with isolation-driven extinction, a plant gradually disappears from individual cells where it occurs. Correspondingly, should this plant's extinction trigger any secondary extinction of its Lepidopteran consumers, it would be also gradual and local, and thus can only be detected via local but not regional richness of Lepidoptera. If isolation-driven plant extinctions were status-weighted, compared to non-weighted ones, they led to less robust regional richness but more robust local richness of Lepidoptera. This is likely because the status of being threatened evaluates multifaced properties of plants, not only abundance but also distributional ones, such as the level of fragmentation (Section S2). Thus, compare to the random case, status-weighted extinction tends to make threatened plants that are already fragmented/isolated experience local extinction earlier in the simulations, quickly resulting in these plants’ regional extinction; correspondingly, we saw a faster accumulation of Lepidoptera regional extinctions. Meanwhile, threatened plants are already scarce, and the Lepidoptera-plant communities constructed with empirical observations should have (quasi-)equilibrated at conditions where these threatened plants do not (or no longer) play critical trophic roles. Thus, the Lepidoptera impacted by their local extinctions should be comparatively fewer, and correspondingly we saw a slower accumulation of Lepidoptera local extinctions. Importantly, different spatial perspectives may provide different, sometimes even opposite, predictions of the communities’ biogeographic change. Even when addressing processes at the landscape scale, localised contexts (e.g., trophic structure) and responses (e.g., local species loss) should not be neglected, as biodiversity management may require fine-tuned, multi-scalar practises (Ballare et al., 2019).

Adding to our previous understanding of Lepidoptera in this area (Habel et al., 2019; Karbiener & Trusch, 2022; Ho et al., 2024), isolation-driven plant extinction revealed that the central part of Baden-Württemberg, at lower elevation, was more prone to Lepidoptera secondary extinction. We see two possible mechanisms: (i) the localised, original trophic structure of the communities in this sub-region were more prone to secondary extinction, e.g., many Lepidoptera fed on a few plants; (ii) the isolation-driven plant extinction targeted more frequently at the cells in this sub-region. With the former, regional plant extinction schemes would have also generated the same spatial pattern of secondary extinction, yet this was not the case, making the latter more likely. This sub-region of Baden-Württemberg has low forest coverage and relative intensive agriculture (Petig et al., 2019; Schindler et al., 2009). As intensive agriculture has been recognised to cause habitat fragmentation of species by breaking the continuity of natural distribution (Walker et al., 2009), it is unsurprising that our focal food plants distributed as relatively isolated cells within this sub-region (Figure S10). Notably, plants' distributional isolation was evaluated at the resolution of our grid cell (10 × 10 km²) constrained by our biological data.

Local secondary extinction of a Lepidopteran may make its regional distribution less fragmented by removing some already isolated cells, or more fragmented by disconnecting some larger patches of cells. Particularly for broadly distributed Lepidoptera under isolation-driven plant extinction, we saw both happened, as their level of fragmentation first changed minimally, then increased relatively rapidly, and then dropped in the late phase of the simulation. Intermediately and narrowly distributed Lepidoptera may not have large enough original distribution to allow the formation of disconnected patches, thus could not respond as variably. Distribution fragmentation (and the likely resultant small populations) is known to associate with impeded genetic flows (Kwak et al., 1998; Williams et al., 2003) and vulnerability to extinctions driven by ecological drift (Gilbert & Levine, 2017). Therefore, beyond our estimated secondary extinctions caused by trophic cascade, plant extinction may impose additional harm to the Lepidoptera (especially broadly distributed ones) via disrupting their population interaction. We note that, however, some patterns we report here occurred only in the later phase of simulations, after half of the focal food plant has gone extinct. Such a devastating level of plant loss would come along with whole ecosystem's malfunction, and be unrealistic to be focused through our lens of effects on insect-plant networks only.

In general, plants’ functional distance decreased as Lepidoptera expand. This implied that apparent competition among plants via sharing herbivores became stronger in larva-plant networks, and so did direct competition over pollinators in imago-plant networks. Thus, via altering the local trophic structure at the arrived communities, Lepidoptera expansion may modify the plants' local competitive structure (sensu Orrock et al., 2010; Rand, 2003). Though the observed extent of functional distance drop was larger in the upward than the northward expansion schemes, this was due to the larger per-step extent of expansion of the former; comparing with respective nulls actually showed the opposite. After the joining of expanded Lepidoptera, the level of dietary niche overlap among local Lepidoptera also dropped, indicating a decreased level of direct competition over food plants in both life stages. Thus, although the successfully expanded Lepidoptera surely brough about some previously inexistent resource competition to the communities, overall, they tended not to share as many food plants with the original residents as among the residents themselves. The negative impacts of Lepidoptera expansion appeared to be more pronounced on the plant assemblages than the Lepidoptera ones. Notably, these functional consequences were evaluated purely based on lepidoptera–plant interactions, but we cannot judge their relative importance when looking at a bigger picture where Lepidoptera’ and plants' interactions with many other taxa are also included; for instance, plants' competition for pollinating Lepidopterans may not be of high ecological importance if many other insects can help pollinate the same plants. Also, our simulative predictions emerged via assuming Lepidoptera have fixed diets throughout the space, yet we acknowledge that Lepidoptera's diet is partially plastic and can include novel plants (e.g., Graves & Shapiro, 2003). As such, our simulations may underestimate the impacts of Lepidoptera expansion. If the extent of utilising new food is somewhat predictable (e.g., Pearse & Altermatt, 2013b), it could be an extension of the current work to further incorporate the predicted food utilisation into the criteria for successful Lepidoptera expansion.

We used detailed lepidoptera–plant trophic reliance across both Lepidopteran life stages as a biotic filter predicting the viability of Lepidoptera to remain after local plant extinction or to establish in new sites after their expansion. This approach highlighted the fact that for holometabolous species, their different life stages may rely on non-identical food resources, and corresponding food for each stage must be available to allow their completion of life cycle within a given space. We argue that such a consideration of the bio-interaction context is needed whenever predicting species spatial distributional change (Robinson et al., 2011; Werner & Gilliam, 1984). We did not apply the same filter from the plants’ perspective, since to our knowledge, most of the flowering plants in our study area do not obligatorily rely on Lepidoptera's pollination to achieve their reproduction. Nonetheless, when addressing other animal–plant interaction systems where the reliance is more mutually important, e.g., between certain mistletoe and hummingbird species (Rodriguez-Cabal et al., 2013), such a biotic filter may also matter to the plants’ viability at places.

Since our biological understanding lies in the study area, we could only detect the discontinuity of species distributions (at the resolution of our cell size) within this area, but whether such discontinuity would capture the Lepidopterans’ realistic “continental” thermal range boundaries was unknown. This may be particularly relevant as for the simulated northward expansion of Lepidoptera, as it is supposed to mimic the spatial shift of species’ cold boundaries in response to northern hemisphere's climate warming. We note that, however, if a Lepidopteran has its cold boundary further north from our study area, meanwhile its population widely distributed within, then its simulated northward expansion would basically trigger no compositional change to the cells. In other words, all consequences generated by our northward expansion simulations were driven by those Lepidopterans having northward discontinuity in their original “regional” distributions (i.e., having northward adjacent cell(s) without their occurrences). Such regional distributional discontinuity could be shaped by many factors, but most likely climatic and topographical ones, as a previous study in the same region (Ho et al., 2024) showed that local Lepidoptera richness is highly associated with temperature and elevation. Even for continentally widely distributed Lepidoptera species, it is possible that they form discontinuous (sub)populations, and each exhibit respective thermal range adapted to local climate (Bestion et al., 2015; Herrando-Pérez et al., 2019). Thus, the northward expansion simulations may not be strictly realistic, yet is still relevant. On the other hand, the upward expansion simulations are more intuitively sensible, as literature have shown that the distributions of Lepidopterans are constrained by the elevational thermal gradient and responsive to climate change (Chen et al., 2009). Future studies could be expanded to include species’ continental ranges, possibly by utilising the occurrence data available from the Global Biodiversity Information Facility (GBIF; https://www.gbif.org). By doing so, the same questions as asked in the current study could be tackled but at a continental spatial scale, at which the species’ thermal ranges could be fully captured. Such data would be even less systematic, though, so one may need to compile the data to an even coarser level (e.g., spatially speaking, adopting a larger cell size) to control the uncertainties among different places. Alternatively, future studies could ask taxa-oriented questions and thereby focusing on a subset of species for which more-systematic and spatially better-covered data are available (e.g., Neu et al., 2021).

In this study, we used Lepidoptera and flowering plants—predominant and well-studied taxa in the terrestrial ecosystem—as the model system to predict potential biogeographic influences of global change. With the accumulation of bio-interaction understanding, we have seen more and more metawebs becoming available recently (e.g., Gravel et al., 2019; O'Connor et al., 2020), covering other taxa and various ecosystems. A transition to study interaction networks in a spatially explicit (versus spatially implicit) approach is needed, as all interactions occur in a spatially structured world, exposed to global change-associated shift in species' co-occurrence. Our simulations integrate biogeographical and bio-interaction knowledge, and provide prospects with mechanistic inferences of extinction- and expansion-driven community change. This makes a step of advancement from previously spatially implicit explorations, and presents a paradigm shift of predictive biogeography that highlight the importance of integrating both the spatial and biological contexts of the focal processes (echoing Gravel et al., 2019; Thuiller et al., 2024; Tscharntke & Brandl, 2004). Given such an advancement, though, the current study had to adopt the spatial and temporal resolutions of the empirical data collected, and thus was operated at relatively coarse scales. Should finer-scaled data become available, a more realistic approach mirroring the current study would be to fit species distribution models for all the focal species, then simulate their realistic distributional changes under detailed climate change scenarios (e.g., Adde et al., 2023); this approach would better benefit the scientific and applicative fields, arguably particularly the latter, as it could precisely inform the conservation of certain taxa at certain places. In this respect, the predictions of our simulative study help identify some penetrating points for empirical work. For instance, our simulations indicate that the Lepidoptera assemblages at the central sub-region of Baden-Württemberg are particularly prone to secondary extinctions. Empirical studies can thus prioritise the collection of high-quality data in this sub-region. In general, we call for future work to keep accumulating finely resolved spatio-temporal data of species, or to revisit and recompile the currently available datasets to achieve better resolutions. We also encourage future work to keep generating the same predictive understanding of other biological systems by exploiting the distribution and interaction data available. We believe that the accumulation of such understanding will together lay an important foundation for the management of biodiversity under global change.

AUTHOR CONTRIBUTIONS

Hsi-Cheng Ho: Conceptualization (equal); data curation (equal); formal analysis (lead); funding acquisition (supporting); methodology (equal); visualization (lead); writing – original draft (lead); writing – review and editing (lead). Florian Altermatt: Conceptualization (equal); data curation (equal); funding acquisition (lead); methodology (equal); project administration (lead); supervision (lead); validation (lead); writing – original draft (supporting); writing – review and editing (supporting).

FUNDING INFORMATION

Funding is through the University of Zurich Research Priority Program in Global Change and Biodiversity (URPP GCB) as well as the Swiss National Science Foundation (Grant Nr. 310030_197410) to FA. HH is supported by the Ministry of Education of Taiwan through the Yushan Young Fellow Program (Grant No. MOE-112-YSFAG-0003-005-P1) and by the National Science and Technology Council of Taiwan (Grant No. NSTC 112-2621-B-002-006-MY3).

CONFLICT OF INTEREST STATEMENT

The authors claim that there are no conflicts of interest.