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ABSTRACT In this short note, we address the identifiability issues inherent in the degree‐corrected stochastic block model (DCSBM). We provide a rigorous proof demonstrating that the parameters of the DCSBM are identifiable up to a scaling factor and a permutation of the community labels, under a mild condition. 

Phenology refers to the seasonal timing patterns commonly exhibited by life on Earth, from blooming flowers to breeding birds to human agriculture. Climate change is altering abiotic seasonality (e.g., longer summers) and in turn, phenological patterns contained within. However, how phenology should evolve is still an unsolved problem. This problem lies at the crux of predicting future phenological changes that will likely have substantial ecosystem consequences, and more fundamentally, of understanding an undeniably global phenomenon. Most studies have associated proximate environmental variables with phenological responses in case-specific ways, making it difficult to contextualize observations within a general evolutionary framework. We outline the complex but universal ways in which seasonal timing maps onto evolutionary fitness. We borrow lessons from life history theory and evolutionary demography that have benefited from a first principles-based theoretical scaffold. Lastly, we identify key questions for theorists and empiricists to help advance our general understanding of phenology. 

Abstract Populations in nature are comprised of individual life histories, whose variation underpins ecological and evolutionary processes. Yet the forces of environmental selection that shape intrapopulation life‐history variation are still not well‐understood, and efforts have largely focused on random (stochastic) fluctuations of the environment. However, a ubiquitous mode of environmental fluctuation in nature is cyclical, whose periodicities can change independently of stochasticity. Here, we test theoretically based hypotheses for whether shortened (‘Fast’) or lengthened (‘Slow’) environmental cycles should generate higher intrapopulation variation of life history phenotypes. We show, through a combination of agent‐based modelling and a multi‐generational laboratory selection experiment using the tidepool copepodTigriopus californicus, that slower environmental cycles maintain higher levels of intrapopulation variation. Surprisingly, the effect of environmental periodicity on variation was much stronger than that of stochasticity. Thus, our results show that periodicity is an important facet of fluctuating environments for life‐history variation. 

Herbarium sheets present a unique view of the world's botanical history, evolution, and biodiversity. This makes them an all–important data source for botanical research. With the increased digitization of herbaria worldwide and advances in the domain of fine–grained visual classification which can facilitate automatic identification of herbarium specimen images, there are many opportunities for supporting and expanding research in this field. However, existing datasets are either too small, or not diverse enough, in terms of represented taxa, geographic distribution, and imaging protocols. Furthermore, aggregating datasets is difficult as taxa are recognized under a multitude of names and must be aligned to a common reference. We introduce the Herbarium 2021 Half–Earth dataset: the largest and most diverse dataset of herbarium specimen images, to date, for automatic taxon recognition. We also present the results of the Herbarium 2021 Half–Earth challenge, a competition that was part of the Eighth Workshop on Fine-Grained Visual Categorization (FGVC8) and hosted by Kaggle to encourage the development of models to automatically identify taxa from herbarium sheet images. 

Abstract Diaryl difluoromethanes are valuable targets for medicinal chemistry because they are bioisosteres of diaryl ethers and can function as replacements for diaryl methane, ketone, and sulfone groups. However, methods to prepare diaryl difluoromethanes are scarce, especially methods starting from abundant aryl halides. We report the Pd‐catalyzed aryldifluoromethylation of aryl halides with aryldifluoromethyl trimethylsilanes (TMSCF₂Ar). The reaction occurs when the catalyst contains a simple, but unusual, dialkylaryl phosphine ligand that promotes transmetallation of the silane. Computational studies show that reductive elimination following transmetallation occurs with a low barrier, despite the fluorine atoms on the α‐carbon, due to coordination of the difluorobenzyl π‐system to palladium. The co‐development of a cobalt‐catalyzed synthesis of the silanes broadened the scope of the process including several applications to the synthesis biologically relevant diaryl difluoromethanes.