Understanding how multiple co-occurring environmental stressors combine to affect biodiversity and ecosystem services is an on-going grand challenge for ecology. Currently, progress has been made through accumulating large numbers of smaller-scale empirical studies that are then investigated by meta-analyses to detect general patterns. There is particular interest in detecting, understanding and predicting 'ecological surprises' where stressors interact in a non-additive (e.g. antagonistic or synergistic) manner, but so far few general results have emerged. However, the ability of the statistical tools to recover non-additive interactions in the face of data uncertainty is unstudied, so crucially, we do not know how well the empirical results reflect the true stressor interactions. Here, we investigate the performance of the commonly implemented additive null model. A meta-analysis of a large (545 interactions) empirical dataset for the effectsenvironmental drivers, food chain, freshwater, Lotka-Volterra, meta-analysis, multiple stressors, observation error, theoretical ecologyThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

1. Most ecosystems are subject to co-occurring, anthropogenically driven changes and understanding how these multiple stressors interact is a pressing concern. Stressor interactions are typically studied using null models, with the additive and multiplicative null expectation being those most widely applied. Such approaches classify interactions as being synergistic, antagonistic, reversal, or indistinguishable from the null expectation. Despite their wide-spread use, there has been no thorough analysis of these null models, nor a systematic test of the robustness of their results to sample size or sampling error in the estimates of the responses to stressors. 2. We use data simulated from food web models where the true stressor interactions are known, and analytical results based on the null model equations to uncover how (i) sample size, (ii) variation in biological responses to the stressors and (iii) statistical significance, affect the ability to detect non-null interactions. 3. Our analyses lead to three main results. Firstly, it is clear the additive and multiplicative null models are not directly comparable, and over one third of all simulated interactions had classifications that were model dependent. Secondly, both null models have weak power to correctly classify interactions at commonly implemented sample sizes (i.e., ≤6 replicates), unless data uncertainty is unrealistically low. This means all but the most extreme interactions are indistinguishable from the null model expectation. Thirdly, we show that increasing sample size increases the power to detect the true interactions but only very slowly. However, the biggest gains come from increasing replicates from 3 up to 25 and we provide an R function for users to determine sample sizes required to detect a critical effect size of biological interest for the additive model. 4. Our results will aid researchers in the design of their experiments and the subsequent interpretation of results. We find no clear statistical advantage of using one null model over the other and argue null model choice should be based on biological relevance rather than statistical properties. However, there is a pressing need to increase experiment sample sizes otherwise many biologically important synergistic and antagonistic stressor interactions will continue to be missed.

While patients with resectable pancreatic ductal adenocarcinoma (PDAC) show improved survival compared to their non-resectable counterparts, survival remains low owing to occult metastatic disease and treatment resistance. Liquid biopsy based on circulating tumor cells (CTCs) and cell-free DNA (cfDNA) has been shown to predict recurrence and treatment resistance in various types of cancers, but their utility has not been fully demonstrated in resectable PDAC. We have simultaneously tracked three circulating biomarkers, including CTCs, cfDNA, and circulating tumor DNA (ctDNA), over a period of cancer treatment using a microfluidic device and droplet digital PCR (ddPCR). The microfluidic device is based on the combination of filtration and immunoaffinity mechanisms. We have measured CTCs, cfDNA, and ctDNA in a cohort of seven resectable PDAC patients undergoing neoadjuvant therapy followed by surgery, and each patient was followed up to 10 time points over a period of 4 months. CTCs were detectable in all patients (100%) at some point during treatment but were detectable in only three out of six patients (50%) prior to the start of treatment. Median cfDNA concentrations remained comparable to negative controls throughout treatment. ddPCR was able to find KRAS mutations in six of seven patients (86%); however, these mutations were present in only two of seven patients (29%) prior to treatment. Overall, the majority of circulating biomarkers (81% for CTCs and 91% for cfDNA/ctDNA) were detected after the start of neoadjuvant therapy but before surgery. This study suggests that a longitudinal study of circulating biomarkers throughout treatment provides more useful information than those single time-point tests for resectable PDAC patients.

Globally, ecosystems are being affected by multiple simultaneous stressors (also termed drivers, factors, or perturbations). While the effects of single stressors are becoming increasingly well understood, there remains substantial uncertainty regarding how multiple stressors may interact to affect ecosystems. Accordingly, there is substantial interest in documenting how stressors combine to impact individuals through to entire communities. Indeed, understanding how stressors interact represents one of the grand challenges currently facing ecologists and conservationists. Popular methods used to classify stressor interactions comprise multiple steps, including complex mathematical equations. Accordingly, there is the potential for errors to occur at multiple points, any of which can result in erroneous conclusions being drawn. Furthermore, there are frequently minor methodological differences between studies which may limit, or even prevent, direct comparisons of their results from being made. Here, we introduce the multiplestressR R package, a statistical tool which addresses the above issues. The package allows researchers to easily conduct a rigorous analysis of their multiple stressor data and provides results which are simple to interpret. The multiplestressR package can implement either the additive or multiplicative null model using iterations of these tools which are commonplace within multiple stressor ecology. The multiplestressR package can classify interactions as being synergistic, antagonistic, reversal, or null and requires minimal experience in either R or statistics to implement. Additionally, we provide example R code which can be easily modified to analysis any given factorial multiple stressor dataset. Indeed, widespread use of this software will allow for an easier and more robust comparison of results. Ultimately, we hope that the multiplestressR package will provide a stronger understanding of how stressors combine to affect individuals, populations, communities, and ecosystems.

Tulips (Tulipa spp.) are one of the most widely appreciated plants worldwide, nevertheless species taxonomy and biogeography are often poorly understood. Most wild tulips inhabit the mountains of Central Asia, a recognised biodiversity hotspot, and a centre of tulip diversity. Despite the presence of several country-level endemic Tulipa species, most taxa span the borders of several nations. With no globally Red Listed tulip taxa from this region national level conservation assessments are an important resource. Nonetheless, threats posed to tulips are still inadequately understood, especially climate change, and given the trans-national nature of most species, distributional information is restricted and often misleading. Here we collate 330 species records from the Global Biodiversity Information Facility with 85 newly collected records, to undertake species distribution modelling (MaxEnt) for ten native Central Asian species. This work showed that regional level models provide a much more comprehensive understanding of species’ extinction risks, proportions of habitat in different countries, and limitations in protected area coverage. Furthermore, our climate modelling, the first of its kind for tulips, suggests that climate change will have a significant negative impact on the range size of all species; including those that are currently widespread. We therefore add climate change to the list of threats affecting tulip populations in Central Asia, which already includes livestock overgrazing, urbanisation, wild collection, and mining. Overall, our work shows that although national information is important, a regional approach is crucial not just for tulip conservation efforts, but likely for Central Asian plant conservation in general.