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Identifying and characterizing stressor interactions is central to multiple stressor research. Such interactions refer to stronger (synergism) or weaker (antagonism) joint effects of co‐occurring stressors on biological entities, when compared to the predictions of a theoretical null model. Various null models have been developed, and the selection of the most appropriate null model for a specific research question is ideally based on assumptions on co‐tolerance patterns in communities and mechanisms of stressor effects. Statistical models are commonly used to evaluate the statistical significance of interaction terms. However, they introduce constraints by imposing a specific null hypothesis on stressor combinations that cannot be flexibly changed. This can introduce a mismatch between the null model that the analyst wants to test and the one imposed by the statistical model. Here, we show under which conditions the statistical null hypothesis for interaction terms misaligns with a multiple‐stressor null model and propose to resolve such misalignments using post‐estimation inference. Null‐model specific interaction estimates can be calculated from adjusted predictions of a fitted regression model, and associated standard errors are derived using the delta method, posterior simulations, or bootstrapping. We illustrate the suggested approach with three case studies and validate statistical conclusions through data simulations. Post‐estimation inference has the potential to advance hypothesis‐driven research on stressor interactions by flexibly testing any a priori defined null model independent from regression model structure. Multiple‐stressor research is relevant across ecological sub‐disciplines (terrestrial, marine, and freshwater), aiming to predict how anthropogenic stressors combine. Different null models have been developed for this purpose. Here, we introduce an analytical framework to statistically evaluate any a priori chosen null model to facilitate hypothesis‐driven research on multiple stressors.

As most ecosystems are being challenged by multiple, co‐occurring stressors, an important challenge is to understand and predict how stressors interact to affect biological responses. A popular approach is to design factorial experiments that measure biological responses to pairs of stressors and compare the observed response to a null model expectation. Unfortunately, we believe experiment sample sizes are inadequate to detect most non‐null stressor interaction responses, greatly hindering progress. Using both real and simulated data, we show sample sizes typical of many experiments (<6) can (i) only detect very large deviations from the additive null model, implying many important non‐null stressor‐pair interactions are being missed, and (ii) potentially lead to mostly statistical outliers being reported. Computer code that simulates data under either additive or multiplicative null models is provided to estimate statistical power for user‐defined responses and sample sizes, and we recommend this is used to aid experimental design and interpretation of results. We suspect that most experiments may require 20 or more replicates per treatment to have adequate power to detect nonadditive. However, estimates of power need to be made while considering the smallest interaction of interest, i.e., the lower limit for a biologically important interaction, which is likely to be system‐specific, meaning a general guide is unavailable. We discuss ways in which the smallest interaction of interest can be chosen, and how sample sizes can be increased. Our main analyses relate to the additive null model, but we show similar problems occur for the multiplicative null model, and we encourage similar investigations into the statistical power of other null models and inference methods. Without knowledge of the detection abilities of the statistical tools at hand or the definition of the smallest meaningful interaction, we will undoubtedly continue to miss important ecosystem stressor interactions. Determining adequate sample size for experiments investigating how multiple ecosystem stressors interact need to consider (i) costs; (ii) statistical ability to detect a deviation from the null expectation; and (iii) prior determination of what constitutes a biologically important deviation. Currently, only costs have been considered and this leads to experimental designs that are likely to miss important stressor interactions.

•Competitive null models may yield false positives from co-expression.•Self-contained null models may yield false positives from bimodal correlations.•Test statistics interact differently with two types of null models.•Supplementary analyses with various configurations support the findings. Correlating transcriptional profiles with imaging-derived phenotypes has the potential to reveal possible molecular architectures associated with cognitive functions, brain development and disorders. Competitive null models built by resampling genes and self-contained null models built by spinning brain regions, along with varying test statistics, have been used to determine the significance of transcriptional associations. However, there has been no systematic evaluation of their performance in imaging transcriptomics analyses. Here, we evaluated the performance of eight different test statistics (mean, mean absolute value, mean squared value, max mean, median, Kolmogorov-Smirnov (KS), Weighted KS and the number of significant correlations) in both competitive null models and self-contained null models. Simulated brain maps (n = 1,000) and gene sets (n = 500) were used to calculate the probability of significance (Psig) for each statistical test. Our results suggested that competitive null models may result in false positive results driven by co-expression within gene sets. Furthermore, we demonstrated that the self-contained null models may fail to account for distribution characteristics (e.g., bimodality) of correlations between all available genes and brain phenotypes, leading to false positives. These two confounding factors interacted differently with test statistics, resulting in varying outcomes. Specifically, the sign-sensitive test statistics (i.e., mean, median, KS, Weighted KS) were influenced by co-expression bias in the competitive null models, while median and sign-insensitive test statistics were sensitive to the bimodality bias in the self-contained null models. Additionally, KS-based statistics produced conservative results in the self-contained null models, which increased the risk of false negatives. Comprehensive supplementary analyses with various configurations, including realistic scenarios, supported the results. These findings suggest utilizing sign-insensitive test statistics such as mean absolute value, max mean in the competitive null models and the mean as the test statistic for the self-contained null models. Additionally, adopting the confounder-matched (e.g., coexpression-matched) null models as an alternative to standard null models can be a viable strategy. Overall, the present study offers insights into the selection of statistical tests for imaging transcriptomics studies, highlighting areas for further investigation and refinement in the evaluation of novel and commonly used tests.

Simulating biological realistic data is an important step to understand and investigate biodiversity. Simulated data can be used to generate null, base line or neutral models. These can be used either in comparison to observed data to estimate the mechanisms that generated the data. Or they can be used to explore, understand and develop theoretical advances by proposing toy models. In evolutionary biology, simulations often involve the need of an evolutionary process where descent with modification is at the core of how the simulated data are generated. These evolutionary processes can then be nearly infinitely modified to include complex processes that affect the simulations such as traits co‐evolution, competition mechanisms or mass extinction events. Here I present the treats package, a modular R package for trees and traits simulations. This package is based on a simple birth death algorithm from which all steps can easily be modified by users. treats also provides a tidy interface through the treats object, allowing users to easily run reproducible simulations. It also comes with an extend manual regularly updated following users' questions or suggestions.

1. Animals may anticipate and try to avoid, at some costs, physical encounters with other competitors. This may ultimately impact their foraging distribution and intake rates. Such cryptic interference competition is difficult to measure in the field, and extremely little is known at the interspecific level. 2. We tested the hypothesis that smaller species avoid larger ones because of potential costs of interference competition and hence expected them to segregate from larger competitors at the scale of a resource patch. We assessed fine-scale spatial segregation patterns between three African herbivore species (zebra Equus quagga, kudu Tragelaphus strepsiceros and giraffe Giraffa camelopardalis) and a megaherbivore, the African elephant Loxodonta africana, at the scale of water resource patches in the semi-arid ecosystem of Hwange National Park, Zimbabwe. 3. Nine waterholes were monitored every two weeks during the dry season of a drought year, and observational scans of the spatial distribution of all herbivores were performed every 15 min. We developed a methodological approach to analyse such fine-scale spatial data. 4. Elephants increasingly used waterholes as the dry season progressed, as did the probability of co-occurrence and agonistic interaction with elephants for the three study species. All three species segregated from elephants at the beginning of the dry season, suggesting a spatial avoidance of elephants and the existence of costs of being close to them. However, contrarily to our expectations, herbivores did not segregate from elephants the rest of the dry season but tended to increasingly aggregate with elephants as the dry season progressed. 5. We discuss these surprising results and the existence of a trade-off between avoidance of interspecific interference competition and other potential factors such as access to quality water, which may have relative associated costs that change with the time of the year.

Ecological networks depict the interactions between species, mainly based on observations in the field. The information contained in such interaction matrices depends on the sampling design, and typically, compounds preferences (specialization) and abundances (activity). Null models are the primary vehicles to disentangle the effects of specialization from those of sampling and abundance, but they ignore the feedback of network structure on abundances. Hence, network structure, as exemplified here by modularity, is difficult to link to specific causes. Indeed, various processes lead to modularity and to specific interaction patterns more generally. Inferring (co)evolutionary dynamics is even more challenging, as competition and trait matching yield identical patterns of interactions. A satisfactory resolution of the underlying factors determining network structure will require substantial additional information, not only on independently assessed abundances, but also on traits, and ideally on fitness consequences as measured in experimental setups.

Technological and data sharing advances have led to a proliferation of high-resolution structural and functional maps of the brain. Modern neuroimaging research increasingly depends on identifying correspondences between the topographies of these maps; however, most standard methods for statistical inference fail to account for their spatial properties. Recently, multiple methods have been developed to generate null distributions that preserve the spatial autocorrelation of brain maps and yield more accurate statistical estimates. Here, we comprehensively assess the performance of ten published null frameworks in statistical analyses of neuroimaging data. To test the efficacy of these frameworks in situations with a known ground truth, we first apply them to a series of controlled simulations and examine the impact of data resolution and spatial autocorrelation on their family-wise error rates. Next, we use each framework with two empirical neuroimaging datasets, investigating their performance when testing (1) the correspondence between brain maps (e.g., correlating two activation maps) and (2) the spatial distribution of a feature within a partition (e.g., quantifying the specificity of an activation map within an intrinsic functional network). Finally, we investigate how differences in the implementation of these null models may impact their performance. In agreement with previous reports, we find that naive null models that do not preserve spatial autocorrelation consistently yield elevated false positive rates and unrealistically liberal statistical estimates. While spatially-constrained null models yielded more realistic, conservative estimates, even these frameworks suffer from inflated false positive rates and variable performance across analyses. Throughout our results, we observe minimal impact of parcellation and resolution on null model performance. Altogether, our findings highlight the need for continued development of statistically-rigorous methods for comparing brain maps. The present report provides a harmonised framework for benchmarking and comparing future advancements.

In the analysis of spatial point patterns, an important role is played by statistical tests based on simulation envelopes, such as the envelope of simulations of Ripley's K function. Recent ecological literature has correctly pointed out a common error in the interpretation of simulation envelopes. However, this has led to a widespread belief that the tests themselves are invalid. On the contrary, envelope-based statistical tests are correct statistical procedures, under appropriate conditions. In this paper, we explain the principles of Monte Carlo tests and their correct interpretation, canvas the benefits of graphical procedures, measure the statistical performance of several popular tests, and make practical recommendations. There are several caveats including the under-recognized problem that Monte Carlo tests of goodness of fit are probably conservative if the model parameters have to be estimated from data. Finally, we discuss whether graphs of simulation envelopes can be used to infer the scale of spatial interaction.

1. Compartmentation has been less explored than other forms of community structure. We assessed compartmentation of associations between insects and plants on a regional scale, and analysed some of its causes and consequences. The data set used was the host records of fruit flies (Diptera; Tephritidae) that breed in flowerheads of plants ofo the tribe Vernonieae (Asteraceae) in the Espinhaço Mountain range, Minas Gerais, Brazil. This data set was obtained with a consistent sampling protocol and is taxonomically fully resolved. 2. The binary association matrix had a total of 35 insect and 81 plant species. Most of the insects were specialized on plants of a single subtribe, genus or species group. Correspondence analysis showed that the association matrix is divided in six well-delimited compartments of insects specialized on subcribes or genera of plants. 3. Host dissimilarity among insects and insect dissimilarity among plants were expressed as Jaccard distances. Tests with a multi-response permutation procedure (MRPP) showed that both kinds of dissimilarities were higher among compartments than within them. 4. Monte Carlo randomizations were used to compare matrix parameters with values expected in the absence of compartments. In 4000 runs, the number of insect species that shared at least one host plant (ecological neighbours) was smaller than expected. Nevertheless, mean host similarity among insects, and the proportion of exclusive host plants used by each insect species did not differ from null model predictions. Host similarity of insects with their nearest neighbours in niche space was higher than expected by the null model. On the other hand, host similarity with farthest neighbours was lower than expected. 6. The observed compartmentation of insect/plant associations can be ascribed to the marked specialization of flowerhead tephritids, and allows the reduction of diffuse competition among insects. However, compartmentation did not decrease overall niche overlap among insects because reduction in number of neighbours is offset by increased overlap with species in the same compartment. Therefore, the pattern in this system cannot be derived from resource partitioning alone.