Ecological time has a structure that ordinary randomisation can obscure. Habitat, food and time are major dimensions of a species’ niche, and access to resources during particular parts of the daily cycle may influence survival. Species can partition resources spatially or trophically, as well as through differences in the timing of resource use. Daily activity, tidal patterns and annual phenology are cyclical because observations repeat around a closed sequence: the end connects back to the beginning. Adjacent time intervals in these observations are temporally dependent, so treating them as unrelated categories can erase the autocorrelation that gives cyclical patterns their shape.

Rosario was designed specifically for data with this circular structure. Its null model generates alternative arrangements by shifting entire empirical time-use patterns around the cycle and adding mirror images of those shifts. Each alternative retains the original frequency distribution and temporal autocorrelation but changes the location of the pattern within the full time extent. This approach differs from the scrambled-zeros and conserved-zeros randomisation models, which were developed for non-sequential resource matrices in which resource categories are unordered. Those models treat zero values differently and disrupt the circular structure of cyclical observations.

The rosario() function performs the initial randomisation step. It advances an observed pattern sequentially until its modal value has occupied each interval in the complete time extent, producing a set of cyclic shifts. It also constructs mirror images by reversing the order of each pattern. For an analysis involving several biological identities, the package randomly selects one shifted or mirrored scenario for each identity and combines those choices into a pseudo-observation matrix. It then calculates the mean of all pairwise overlaps in that matrix and repeats the operation to generate a null frequency distribution, commonly through about 1,000 simulations.

Two indices are available for quantifying similarity in resource use, here interpreted as time use: Pianka’s overlap index and the Czekanowski index. The observed value can be compared with the simulated distribution to evaluate concurrent overlap among all included identities. This is the principal analytical distinction between Rosario and tools centred on pairwise comparison. Pairwise estimates can characterise similarity between two organisms, but aggregating those estimates does not directly test the overlap exhibited simultaneously by an entire assemblage. Rosario’s null model evaluates that shared pattern within one analysis involving three or more biological identities.

The R package provides functions for the main stages of this workflow. The temp_overlap() function calculates observed mean pairwise overlap using the selected index, and get_null_model() performs the randomisation test. Plotting tools show the first ten hypothetical time-use distributions for a selected identity and display the simulated overlap frequencies alongside the observed value. Input takes the form of a matrix, with rows representing individuals, species or populations and columns representing time intervals. Researchers can also use rescale_matrix() to convert rows to proportions, which can be useful when comparisons involve entities with very different sample sizes. The stable release is available through CRAN, with a development repository and a real-world vignette hosted on GitHub.

The demonstration drew on summer observations from the SIM Deer project in British Columbia, obtained through the publicly accessible Wildlife Insights platform. The analysis covered June, July and August in 2020, 2021 and 2022 and included 85,929 capture events: 51,691 involving mule deer, 19,395 involving elk and 14,843 involving white-tailed deer. Capture records were assigned to 30-minute intervals, with the interval width chosen before analysis according to the study objectives and the need for biologically meaningful comparisons. The input matrix contained one row for each of the three cervid species and one column for each interval in the 24-hour cycle.

The resulting activity curves suggested that the species shared some timing while varying in their daily distributions. Mule deer showed peaks around dawn, at approximately 06:00, and dusk, at approximately 18:00, with additional activity during nighttime hours. Elk displayed a strong peak around dusk, a substantial daytime peak around 10:00 to 11:00 and some nocturnal activity. White-tailed deer also showed dawn and dusk peaks, although its dusk peak was less pronounced than that of mule deer, and it exhibited noticeable activity around midday. Taken together, the curves were consistent with a degree of crepuscular behaviour across the three species. Their visible similarities and variations, however, cannot by themselves establish whether concurrent overlap is unusual; that question is addressed by comparing the observed value with the cyclic null distribution.

Calculations from Rosario, the activity package and the overlap package produced broadly similar overlap values, indicating that Rosario’s Pianka and Czekanowski indices yielded results comparable to those obtained with the other R approaches. The analytical scope nevertheless differed. The activity and overlap tools chiefly supplied statistical comparisons between species pairs, whereas Rosario additionally returned pairwise indices and a null-model assessment of overlap among all three cervids. The example therefore combines two kinds of output: a numerical description of activity and overlap and an evaluation of the combined pattern against an alternative distribution generated while preserving the circular structure of the observations.

Several limitations constrain how the method should be applied. Rosario is designed for cyclical rather than sequential data. Sequential observations have a genuine beginning and end and do not possess the same circular structure, although long-term camera-trap records can be mapped onto a cyclical domain such as time of day, season or year before analysis. Comparisons among organisms that are not sympatric require additional care because differences in yearly variation can affect activity or phenology. For diel data, time transformation may be required depending on a study’s location, duration and latitudinal separation among sampling sites. These constraints make temporal alignment and explicit ecological assumptions essential, while the move to R broadens access to the algorithm and supports more standardised comparison with existing packages for activity, overlap and cyclical ecological data.

Subject of Research: Null-model analysis of concurrent temporal niche overlap in cyclical ecological data

Article Title: Rosario: An algorithm to analyse cyclical data in Ecology

Article References: Velásquez-Roa, T., Hurtado-Materon, M., Robles-Fernández, A., & Castro-Arellano, I. (2026). Rosario: An algorithm to analyse cyclical data in Ecology. Biodiversity Data Journal, 14, Article e176358. https://doi.org/10.3897/bdj.14.e176358

Image Credits: AI Generated

DOI: 10.3897/BDJ.14.e176358

Keywords: Rosario algorithm, R package, temporal niche overlap, null models, cyclic randomisation, camera traps, cervid activity, Pianka overlap, Czekanowski overlap, ecological time series, Rosario, algorithm

The researchers focus on what they call component systems: ensembles of realizations built from a shared repertoire of modular parts. A genome is assembled from genes, a book from words, a city from neighborhoods and functions, a codebase from software modules. When scientists count how often each part appears, how many distinct parts show up, and how these quantities scale with system size, the resulting curves often satisfy what physicists would recognize as bona fide laws: they are simple, general, and remarkably robust across domains. Heaps’ law, Zipf’s law, and related scaling relationships have been documented for decades in linguistics, genomics, ecology, and urban science, and their persistence has encouraged many researchers to interpret them as fingerprints of specific generative mechanisms.

The core argument of the new work is more sobering, and more interesting. The very generality and simplicity of these laws may be a consequence of basic combinatorial or sampling constraints rather than evidence of system-specific dynamics. When you draw parts from a finite repertoire and aggregate them into larger and larger ensembles, certain statistical trends are almost inevitable. The authors suggest that many of the celebrated regularities observed across component systems fall into this category: they are null trends, patterns that would emerge even in the absence of any particular biological, cultural, or technological mechanism. This reframing echoes a long-standing methodological debate in ecology, where null models have been used for decades to test whether observed community patterns exceed what random assembly would produce.

To make this argument precise, the team developed a unifying mathematical framework that allows modular systems from different fields to be compared on common ground. The framework treats each system as a collection of components drawn from a shared vocabulary and characterizes the ensemble through its counting statistics: how the number of distinct parts grows with the number of sampled elements, how part frequencies are distributed, and how fluctuations behave across realizations. By expressing these quantities in a shared formal language, the researchers can separate the contributions that any component system would display from those that are genuinely distinctive to genomes, texts, cities, or software.

The practical payoff of this framework is twofold. First, it explains why the general regularities emerge in the first place, identifying the constraints that link them together and the general principles from which they originate. Rather than treating each scaling law as an independent empirical discovery, the framework shows how they are mathematically intertwined: knowing one trend often fixes the others, given only weak assumptions about sampling. This kind of constraint analysis is familiar from statistical mechanics, where macroscopic regularities such as universal equations of state follow from counting microscopic configurations rather than from any detailed knowledge of the interactions involved.

Second, and perhaps more consequentially, the framework offers a way to subtract the null trends from real data. Once the generic combinatorial background is removed, what remains are the deviations: the informative features that cannot be explained by sampling alone. These residuals, the authors argue, are the true signatures of the underlying generative dynamics, carrying information about hidden mechanistic and causal processes. In a genome, such deviations might reflect the action of natural selection, duplication events, or functional organization. In a text, they might reveal stylistic choices, topic structure, or the idiosyncrasies of an author. In a city, they could point to planning decisions, economic forces, or historical contingencies that no neutral aggregation process would produce.

This subtraction strategy connects the work to two of the most powerful toolkits in modern quantitative science: statistical mechanics and machine learning. Statistical mechanics provides the conceptual apparatus for defining ensembles, computing expectations under null hypotheses, and quantifying how unlikely an observed configuration is under those hypotheses. Machine learning, meanwhile, supplies flexible generative models that can be trained on real data and then interrogated for the structure they capture beyond the null. The authors envision using these tools in combination: first establishing what a generic component system must look like, then deploying learned models to isolate and interpret the departures from that baseline.

The implications reach across disciplines. In genomics, where the statistics of gene families and functional categories have been studied for decades, the framework offers a principled way to decide which patterns demand biological explanation and which are artifacts of counting. In linguistics and the digital humanities, it provides a rigorous baseline for claims about authorship, complexity, and cultural evolution. In urban science and technology studies, it can help distinguish the generic scaling of cities and software systems from the specific interventions of planners and engineers. In every case, the message is the same: a pattern must first be compared against what combinatorics alone would produce before it can be credited to a mechanism.

The study also carries a cautionary lesson for the popular narrative that big data reveals universal laws of complexity. Universality can be seductive, but it can also be cheap: patterns that appear in everything may explain nothing in particular. By making the null expectations explicit and quantitative, the new framework turns that criticism into a research program. The goal is not to dismiss the regularities but to use them as a filter, sharpening the search for the features that genuinely distinguish one system from another and that therefore encode the physics, biology, or culture of that system.

What emerges is a methodological vision for the study of complex systems in the era of abundant data. Component systems everywhere share a common statistical skeleton imposed by the mathematics of parts and ensembles; the science of interest lies in the flesh that grows around that skeleton. By combining a unifying null framework with statistical mechanics and modern machine learning, Mazzolini and colleagues propose a disciplined path from pattern to process: explain the general, subtract it, and then read what remains as evidence of the hidden generative dynamics that make a genome a genome, a text a text, and a city a city.

Subject of Research: Null models and statistical regularities in component systems across biological, ecological, technological, and socio-cultural domains

Article Title: Component systems: Do null models explain everything?

Article References: Mazzolini, A., Corigliano, M., Droghetti, R., Osella, M., & Cosentino Lagomarsino, M. (2026). Component systems: Do null models explain everything?. PLOS Complex Systems, 3(6), e0000114. https://doi.org/10.1371/journal.pcsy.0000114

Image Credits: AI Generated

DOI: 10.1371/journal.pcsy.0000114

Keywords: component systems, null models, complex systems, statistical mechanics, scaling laws, genomics, linguistics, urban science, machine learning, combinatorics, heavy-tailed distributions, generative processes

A team at the Montréal Neurological Institute of McGill University has now published a detailed account of how they have managed this complexity, both inside their own laboratory and for the wider community. Writing in Nature Protocols, Zhen-Qi Liu, Vincent Bazinet and colleagues, led by Bratislav Misic, describe netneurotools, an open-source Python toolkit that has been continuously developed and maintained by the laboratory’s trainees since its inception. The paper is both a practical protocol for carrying out network neuroscience analyses and a manifesto for a different way of building scientific software, one in which the informal, ad hoc scripts that every laboratory accumulates are treated as a legitimate, shareable scientific resource.

The philosophy behind the toolkit is disarmingly simple. The authors describe netneurotools as the Swiss army knife of the laboratory: a collection of functions and routines that the group uses constantly but that belong to no established pipeline or package. Where large neuroimaging platforms excel at well-defined tasks such as preprocessing functional magnetic resonance imaging or reconstructing diffusion data, they are not designed to interoperate with one another. The gaps between them, the authors argue, are precisely where trainees are forced to improvise isolated heuristics and workarounds. netneurotools formalizes those improvisations, turning scattered personal scripts into documented, tested, reusable code that anyone can pick up.

Technically, the toolkit is built on the familiar foundations of the scientific Python ecosystem, drawing on array programming libraries such as NumPy, the algorithms of SciPy, machine learning utilities from scikit-learn, graph structures from NetworkX, and file-reading capabilities from nibabel and nilearn. It extends these foundations with capabilities that are specific to network neuroscience. These include utilities for handling cortical surface meshes and transforming data between the many parcellation schemes that fragment the field, from volumetric atlases to multi-resolution cortical subdivisions. Because a brain map computed on one parcellation cannot be directly compared with a map on another, robust surface-based resampling and interpolation are among the most valuable functions the package provides, sparing researchers from the error-prone manual conversions that have long been a rite of passage in the field.

Network analysis itself forms a second major pillar. The toolkit implements routines for generating group-representative structural brain networks using distance-dependent consensus thresholding, an approach designed to respect the fact that anatomical connection probability falls with physical distance in the brain. It provides algorithms for randomizing weighted networks while preserving key topological properties, a crucial step in any null-model-based analysis, including a simulated annealing method developed by the same group for rigorously controlling network structure. It also implements a library of network communication models, which ask how signals could theoretically travel along the wiring of the brain, from classical shortest-path routing inspired by the Floyd, Roy and Warshall algorithms to navigation strategies and diffusion-style models that better capture the biology of neural signaling.

Statistical machinery rounds out the package. Network neuroscience increasingly relies on spatial statistics, because brain measures are arranged in space and neighboring regions are not independent. netneurotools includes implementations of spatial autocorrelation measures such as Moran’s I and Geary’s C, along with bivariate extensions that quantify spatial associations between two brain maps. It offers null models that preserve the spatial autocorrelation of data before statistical testing, a safeguard against the inflated significance that naive permutation schemes can produce. Dominance analysis, a technique from psychology for assessing the relative importance of correlated predictors in regression, is also available, addressing a common challenge when multiple brain properties compete to explain a neural phenomenon.

The protocol paper walks readers through complete workflows that chain these functions together to answer neurobiologically meaningful questions. Example analyses include relating brain network organization to microarchitectural features such as receptor distributions and cell-type composition, examining how strongly the brain’s structural wiring constrains its functional dynamics across different imaging modalities, and generating spatially informed null models for testing whether an observed pattern of structure-function coupling is unusual. Workflow diagrams in the paper show how data flow from raw parcellated imaging outputs, through the toolkit’s conversion, modeling and statistical layers, to interpretable figures, giving trainees a template they can adapt to their own projects rather than a black box they must trust blindly.

Beyond its technical content, the article makes a cultural argument that is likely to resonate far beyond one laboratory. The authors position netneurotools as a necessary counterweight to out-of-the-box software packages, arguing that smaller, ad hoc functions deserve recognition as real scientific contributions. By opening a window into the inner workings of a laboratory, the toolkit invites a new kind of discourse among research groups, one in which the unglamorous glue code that actually holds a project together is shared, critiqued and improved collectively. The package has been open to contributions from neuroscientists across the globe since its inception, and its development by trainees reflects a deliberate pedagogical choice: writing and maintaining shared infrastructure is itself a form of scientific training.

The timing of this publication is significant. A recent assessment of open-source neuroscience software described the field’s dependence on volunteer-maintained tools as precarious, and the proliferation of analysis pipelines has made reproducibility a persistent concern. By documenting their toolkit in a peer-reviewed protocols journal, the Misic laboratory is making a case that sustainability in computational neuroscience depends not only on large, polished platforms but also on transparent, community-maintained collections of mid-sized tools that bridge the gaps between them. The approach aligns with the FAIR principles for research software, which call for software to be findable, accessible, interoperable and reusable.

For a field whose data keep multiplying in modality and scale, the message is practical and quietly radical at once. The connectome may be the most complicated object ever mapped, but the daily work of studying it is made of thousands of small, concrete operations: converting a file, resampling a surface, rewiring a network, testing a spatial statistic. netneurotools gathers those operations into one open, living toolbox, and in doing so suggests that the health of network neuroscience may depend as much on how generously its practitioners share their everyday tools as on any single breakthrough analysis.

Subject of Research: An open-source, trainee-developed Python toolkit for network neuroscience analysis and brain imaging data integration

Article Title: netneurotools: a trainee-oriented approach to network neuroscience

Article References: Liu, Z.-Q., Bazinet, V., Hansen, J. Y., Milisav, F., Luppi, A. I., Ceballos, E. G., Farahani, A., Suarez, L. E., Shafiei, G., Markello, R. D., & Misic, B. (2026). netneurotools: a trainee-oriented approach to network neuroscience. Nature Protocols. https://doi.org/10.1038/s41596-026-01446-7

Image Credits: AI Generated

DOI: 10.1038/s41596-026-01446-7

Keywords: netneurotools, network neuroscience, Python toolkit, brain imaging, connectomics, open-source software, brain networks, spatial statistics, null models, FAIR principles, McGill University, Nature Protocols