Hammersley\u27s Law for the Van Der Corput Sequence: An Instance of Probability Theory for Pseudorandom Numbers

The analogue of Hammersley\u27s theorem on the length of the longest monotonic subsequence of independent, identically, and continuously distributed random variables is obtained for the pseudorandom van der Corput sequence. In this case there is no limit but the precise limits superior and inferior are determined. The constants obtained are closely related to those established in the independent case by Logan and Shepp, and Vershik and Kerov

Environmental Factors Influencing Reproduction in a Temperate Marine Reef Goby, Rhinogobiops nicholsii, and Associated Behaviors

The blackeye goby is a protogynous reef fish common to the northeastern Pacific Ocean. While this ubiquitous species has been the focus of numerous studies, there are several aspects of its reproductive ecology that are unknown. By directly quantifying reproduction from digital photographs of blackeye goby nests in the field, this study aimed to determine whether reproductive patterns were linked to 1) lunar phase or 2) ambient water temperature; and 3) whether the behavior of gobies changed when a nearby conspecific had eggs in his nest. At Santa Catalina Island, California, twenty 2.25-m2 artificial reefs were established and stocked with similar numbers and size-distributions of blackeye gobies during the summers of 2012 and 2013. Photographs of nests were taken weekly for ~3 months each summer. Through analysis of photographs, incubation time was found to be more than 7 days but less than 14 days. Nests, each guarded by one male, contained an average of 8664 eggs, in an area of 43.8 cm2, with 215 eggs cm-2. Blackeye gobies laid eggs during all lunar phases and the number of eggs produced was not related to lunar phase. Reproductive output, however, was negatively correlated with water temperature, with populations on reefs that experienced cooler temperatures producing more eggs. The presence of eggs in a nest had little effect on behavior of blackeye gobies on that reef. Additional observations made outside of summer months indicated that blackeye gobies can reproduce year-round in southern California. These results suggest a reproductive strategy aimed at maximizing total reproductive output by spreading the risk of reproductive failure throughout the year rather than optimizing the timing of reproduction

Exact Expectations of Minimal Spanning Trees for Graphs With Random Edge Weights

Two methods are used to compute the expected value of the length of the minimal spanning tree (MST) of a graph whose edges are assigned lengths which are independent and uniformly distributed. The first method yields an exact formula in terms of the Tutte polynomial. As an illustration, the expected length of the MST of the Petersen graph is found to be 34877/12012 = 2.9035 .... A second, more elementary, method for computing the expected length of the MST is then derived by conditioning on the length of the shortest edge. Both methods in principle apply to any finite graph. To illustrate the method we compute the expected lengths of the MSTs for complete graphs

The large‐scale freshwater cycle of the Arctic

This paper synthesizes our understanding of the Arctic\u27s large‐scale freshwater cycle. It combines terrestrial and oceanic observations with insights gained from the ERA‐40 reanalysis and land surface and ice‐ocean models. Annual mean freshwater input to the Arctic Ocean is dominated by river discharge (38%), inflow through Bering Strait (30%), and net precipitation (24%). Total freshwater export from the Arctic Ocean to the North Atlantic is dominated by transports through the Canadian Arctic Archipelago (35%) and via Fram Strait as liquid (26%) and sea ice (25%). All terms are computed relative to a reference salinity of 34.8. Compared to earlier estimates, our budget features larger import of freshwater through Bering Strait and larger liquid phase export through Fram Strait. While there is no reason to expect a steady state, error analysis indicates that the difference between annual mean oceanic inflows and outflows (∼8% of the total inflow) is indistinguishable from zero. Freshwater in the Arctic Ocean has a mean residence time of about a decade. This is understood in that annual freshwater input, while large (∼8500 km3), is an order of magnitude smaller than oceanic freshwater storage of ∼84,000 km3. Freshwater in the atmosphere, as water vapor, has a residence time of about a week. Seasonality in Arctic Ocean freshwater storage is nevertheless highly uncertain, reflecting both sparse hydrographic data and insufficient information on sea ice volume. Uncertainties mask seasonal storage changes forced by freshwater fluxes. Of flux terms with sufficient data for analysis, Fram Strait ice outflow shows the largest interannual variability

Cholinergic Modulation of Locomotion and Striatal Dopamine Release Is Mediated by α6α4* Nicotinic Acetylcholine Receptors

Dopamine (DA) release in striatum is governed by firing rates of midbrain DA neurons, striatal cholinergic tone, and nicotinic ACh receptors (nAChRs) on DA presynaptic terminals. DA neurons selectively express α6* nAChRs, which show high ACh and nicotine sensitivity. To help identify nAChR subtypes that control DA transmission, we studied transgenic mice expressing hypersensitive α6^(L9’S*) receptors. α6^(L9’S) mice are hyperactive, travel greater distance, exhibit increased ambulatory behaviors such as walking, turning, and rearing, and show decreased pausing, hanging, drinking, and grooming. These effects were mediated by α6 α4* pentamers, as α6^(L9’S) mice lacking α4 subunits displayed essentially normal behavior. In α6^(L9’S) mice, receptor numbers are normal, but loss of α4 subunits leads to fewer and less sensitive α6* receptors. Gain-of-function nicotine-stimulated DA release from striatal synaptosomes requires α4 subunits, implicating α6α4β2* nAChRs in α6^(L9’S) mouse behaviors. In brain slices, we applied electrochemical measurements to study control of DA release by α6^(L9’S) nAChRs. Burst stimulation of DA fibers elicited increased DA release relative to single action potentials selectively in α6^(L9’S), but not WT or α4KO/ α6^(L9’S), mice. Thus, increased nAChR activity, like decreased activity, leads to enhanced extracellular DA release during phasic firing. Bursts may directly enhance DA release from α6^(L9’S) presynaptic terminals, as there was no difference in striatal DA receptor numbers or DA transporter levels or function in vitro. These results implicate α6α4β2* nAChRs in cholinergic control of DA transmission, and strongly suggest that these receptors are candidate drug targets for disorders involving the DA system

A Macrophysiological Analysis of Energetic Constraints on Geographic Range Size in Mammals

Physiological processes are essential for understanding the distribution and abundance of organisms, and recently, with widespread attention to climate change, physiology has been ushered back to the forefront of ecological thinking. We present a macrophysiological analysis of the energetics of geographic range size using combined data on body size, basal metabolic rate (BMR), phylogeny and range properties for 574 species of mammals. We propose three mechanisms by which interspecific variation in BMR should relate positively to geographic range size: (i) Thermal Plasticity Hypothesis, (ii) Activity Levels/Dispersal Hypothesis, and (iii) Energy Constraint Hypothesis. Although each mechanism predicts a positive correlation between BMR and range size, they can be further distinguished based on the shape of the relationship they predict. We found evidence for the predicted positive relationship in two dimensions of energetics: (i) the absolute, mass-dependent dimension (BMR) and (ii) the relative, mass-independent dimension (MIBMR). The shapes of both relationships were similar and most consistent with that expected from the Energy Constraint Hypothesis, which was proposed previously to explain the classic macroecological relationship between range size and body size in mammals and birds. The fact that this pattern holds in the MIBMR dimension indicates that species with supra-allometric metabolic rates require among the largest ranges, above and beyond the increasing energy demands that accrue as an allometric consequence of large body size. The relationship is most evident at high latitudes north of the Tropics, where large ranges and elevated MIBMR are most common. Our results suggest that species that are most vulnerable to extinction from range size reductions are both large-bodied and have elevated MIBMR, but also, that smaller species with elevated MIBMR are at heightened risk. We also provide insights into the global latitudinal trends in range size and MIBMR and more general issues of phylogenetic and geographic scale

Estimating hardwood sawmill conversion efficiency based on sawing machine and log characteristics

Increased problems of hardwood timber availability have caused many sawmiller, industry analysts, and planners to recognize the importance of sawmill conversion efficiency. Conversion efficiency not only affects sawmill profits, but is also important on a much broader level. Timber supply issues have caused resource planners and policy makers to consider the effects of conversion efficiency on the utilization and depletion of the timber resource. Improvements in sawmill conversion efficiency would favorably impact sawmill profits, and would be equivalent in effect to extending existing supplies of standing timber. An equation was developed to estimate lumber recovery factor for hardwood sawmills based on the characteristics of sawing machines and log resources. Variables included in the model were headrig type, headrig kerf, average log diameter and length, and the influence of total sawing variation. The estimated coefficients significantly influenced lumber recovery factor. The model should be helpful in assessing conversion efficiency trends and potential benefits from gains in sawmill efficiency

Online Selection of Alternating Subsequences from a Random Sample

We consider sequential selection of an alternating subsequence from a sequence of independent, identically distributed, continuous random variables, and we determine the exact asymptotic behavior of an optimal sequentially selected subsequence. Moreover, we find (in a sense we make precise) that a person who is constrained to make sequential selections does only about 12 percent worse than a person who can make selections with full knowledge of the random sequence

Why compare marine ecosystems?

This paper is not subject to U.S. copyright. The definitive version was published in ICES Journal of Marine Science: Journal du Conseil 67 (2010): 1-9, doi:10.1093/icesjms/fsp221.Effective marine ecosystem-based management (EBM) requires understanding the key processes and relationships controlling the aspects of biodiversity, productivity, and resilience to perturbations. Unfortunately, the scales, complexity, and non-linear dynamics that characterize marine ecosystems often confound managing for these properties. Nevertheless, scientifically derived decision-support tools (DSTs) are needed to account for impacts resulting from a variety of simultaneous human activities. Three possible methodologies for revealing mechanisms necessary to develop DSTs for EBM are: (i) controlled experimentation, (ii) iterative programmes of observation and modelling ("learning by doing"), and (iii) comparative ecosystem analysis. We have seen that controlled experiments are limited in capturing the complexity necessary to develop models of marine ecosystem dynamics with sufficient realism at appropriate scales. Iterative programmes of observation, model building, and assessment are useful for specific ecosystem issues but rarely lead to generally transferable products. Comparative ecosystem analyses may be the most effective, building on the first two by inferring ecosystem processes based on comparisons and contrasts of ecosystem response to human-induced factors. We propose a hierarchical system of ecosystem comparisons to include within-ecosystem comparisons (utilizing temporal and spatial changes in relation to human activities), within-ecosystem-type comparisons (e.g. coral reefs, temperate continental shelves, upwelling areas), and cross-ecosystem-type comparisons (e.g. coral reefs vs. boreal, terrestrial vs. marine ecosystems). Such a hierarchical comparative approach should lead to better understanding of the processes controlling biodiversity, productivity, and the resilience of marine ecosystems. In turn, better understanding of these processes will lead to the development of increasingly general laws, hypotheses, functional forms, governing equations, and broad interpretations of ecosystem responses to human activities, ultimately improving DSTs in support of EBM

Segregating the effects of seed traits and common ancestry of hardwood trees on eastern gray squirrel foraging decisions

The evolution of specific seed traits in scatter-hoarded tree species often has been attributed to granivore foraging behavior. However, the degree to which foraging investments and seed traits correlate with phylogenetic relationships among trees remains unexplored. We presented seeds of 23 different hardwood tree species (families Betulaceae, Fagaceae, Juglandaceae) to eastern gray squirrels (Sciurus carolinensis), and measured the time and distance travelled by squirrels that consumed or cached each seed. We estimated 11 physical and chemical seed traits for each species, and the phylogenetic relationships between the 23 hardwood trees. Variance partitioning revealed that considerable variation in foraging investment was attributable to seed traits alone (27-73%), and combined effects of seed traits and phylogeny of hardwood trees (5-55%). A phylogenetic PCA (pPCA) on seed traits and tree phylogeny resulted in 2 global axes of traits that were phylogenetically autocorrelated at the family and genus level and a third local axis in which traits were not phylogenetically autocorrelated. Collectively, these axes explained 30-76% of the variation in squirrel foraging investments. The first global pPCA axis, which produced large scores for seed species with thin shells, low lipid and high carbohydrate content, was negatively related to time to consume and cache seeds and travel distance to cache. The second global pPCA axis, which produced large scores for seeds with high protein, low tannin and low dormancy levels, was an important predictor of consumption time only. The local pPCA axis primarily reflected kernel mass. Although it explained only 12% of the variation in trait space and was not autocorrelated among phylogenetic clades, the local axis was related to all four squirrel foraging investments. Squirrel foraging behaviors are influenced by a combination of phylogenetically conserved and more evolutionarily labile seed traits that is consistent with a weak or more diffuse coevolutionary relationship between rodents and hardwood trees rather than a direct coevolutionary relationship. © 2015 Sundaram et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited