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Abstract PremiseChanges to flowering time caused by climate change could affects plant fecundity, but studies that compare the individual‐level responses of phenologically distinct, co‐occurring species are lacking. We assessed how variation in floral phenology affects the fecundity of individuals from three montane species with different seasonal flowering times, including in snowmelt acceleration treatments to increase variability in phenology. MethodsWe collected floral phenology and seed set data for individuals of three montane plant species (Mertensia fusiformis, Delphinium nuttallianum, Potentilla pulcherrima). To examine the drivers of seed set, we measured conspecific floral density and conducted pollen limitation experiments to isolate pollination function. We advanced the phenology of plant communities in a controlled large‐scale snowmelt acceleration experiment. ResultsDifferences in individual phenology relative to the rest of the population affected fecundity in our focal species, but effects were species‐specific. For our early‐season species, individuals that bloomed later than the population peak bloom had increased fecundity, while for our midseason species, simply blooming before or after the population peak increased individual fecundity. For our late‐season species, blooming earlier than the population peak increased fecundity. The early and midseason species were pollen‐limited, and conspecific density affected seed set only for our early‐season species. ConclusionsOur study shows that variation in individual phenology affects fecundity in three phenologically distinct montane species, and that pollen limitation may be more influential than conspecific density. Our results suggest that individual‐level changes in phenology are important to consider for understanding plant reproductive success. 

Given widespread concerns over human-mediated bee declines in abundance and species richness, conservation efforts are increasingly focused on maintaining natural habitats to support bee diversity in otherwise resource-poor environments. However, natural habitat patches can vary in composition, impacting landscape-level heterogeneity and affecting plant-pollinator interactions. Plant-pollinator networks, especially those based on pollen loads, can provide valuable insight into mutualistic relationships, such as revealing the degree of pollination specialization in a community; yet, local and landscape drivers of these network indices remain understudied within urbanizing landscapes. Beyond networks, analyzing pollen collection can reveal key information about species-level pollen preferences, providing plant restoration information for urban ecosystems. Through bee collection, vegetation surveys, and pollen load identification across ~350 km of urban habitat, we studied the impact of local and landscape-level management on plant-pollinator networks. We also quantified pollinator preferences for plants within urban grasslands. Bees exhibited higher foraging specialization with increasing habitat heterogeneity and visited fewer flowering species (decreased generality) with increasing semi-natural habitat cover. We also found strong pollinator species-specific flower foraging preferences, particularly for Asteraceae plants. We posit that maintaining native forbs and supporting landscape-level natural habitat cover and heterogeneity can provide pollinators with critical food resources across urbanizing ecosystems. 

Given an input stream of size N , a -heavy hiter is an item that occurs at least N times in S. The problem of finding heavy-hitters is extensively studied in the database literature. We study a real-time heavy-hitters variant in which an element must be reported shortly after we see its T = N - th occurrence (and hence becomes a heavy hitter). We call this the Timely Event Detection (TED) Problem. The TED problem models the needs of many real-world monitoring systems, which demand accurate (i.e., no false negatives) and timely reporting of all events from large, high-speed streams, and with a low reporting threshold (high sensitivity). Like the classic heavy-hitters problem, solving the TED problem without false-positives requires large space ((N ) words). Thus in-RAM heavy-hitters algorithms typically sacrfice accuracy (i.e., allow false positives), sensitivity, or timeliness (i.e., use multiple passes). We show how to adapt heavy-hitters algorithms to exter- nal memory to solve the TED problem on large high-speed streams while guaranteeing accuracy, sensitivity, and timeli- ness. Our data structures are limited only by I/O-bandwidth (not latency) and support a tunable trade-off between report- ing delay and I/O overhead. With a small bounded reporting delay, our algorithms incur only a logarithmic I/O overhead. We implement and validate our data structures empirically using the Firehose streaming benchmark. Multi-threaded ver- sions of our structures can scale to process 11M observations per second before becoming CPU bound. In comparison, a naive adaptation of the standard heavy-hitters algorithm to external memory would be limited by the storage device’s random I/O throughput, i.e., approx 100K observations per second. 

Abstract A critical goal for ecologists is understanding how ongoing local and global species losses will affect ecosystem functions and services. Diversity–functioning relationships, which are well‐characterized in primary producer communities, are much less consistently predictable for ecosystem functions involving two or more trophic levels, particularly in situations where multiple species in one trophic level impact functional outcomes at another trophic level. This is particularly relevant to pollination functioning, given ongoing pollinator declines and the value of understanding pollination functioning for single plant species like crops or threatened plants. We used spatially replicated, controlled single‐pollinator‐species removal experiments to assess how changes in bumble bee species richness impacted the production of fertilized seeds in a perennial herb—Delphinium barbeyi—in the Rocky Mountains of Colorado, USA. To improve predictability, we also assessed how traits and abundances in the plant and bumble bee communities were related toD. barbeyireproductive success. We hypothesized that trait‐matching between pollinator proboscis length andD. barbeyi's nectar spurs would produce a greater number of fertilized seeds, while morphological similarity within the floral community would dilute pollination services. We found that the effects of pollinator removal differed depending on the behavioral patterns of pollinators and compositional features of the plant and pollinator communities. While pollinator floral fidelity generally increasedD. barbeyiseed production, that positive effect was primarily evident when more than half of theBombuscommunity was experimentally removed. Similarly, communities comprising primarily long‐tongued bees were most beneficial toD. barbeyiseed production in tandem with a strong removal. Finally, we observed contrasting effects of morphological similarity in the plant community, with evidence of both competition and facilitation among plants. These results offer an example of the complex dynamics underlying ecosystem function in multitrophic systems and demonstrate that community context can impact diversity–functioning relationships between trophic levels. 

We consider the isoperimetric problem for the sum of two Gaussian densities in the line and the plane. We prove that the double Gaussian isoperimetric regions in the line are rays and that if the double Gaussian isoperimetric regions in the plane are half-spaces, then they must be bounded by vertical lines.