Optimal Pebbling in Products of Graphs

We prove a generalization of Graham's Conjecture for optimal pebbling with arbitrary sets of target distributions. We provide bounds on optimal pebbling numbers of products of complete graphs and explicitly find optimal $t$-pebbling numbers for specific such products. We obtain bounds on optimal pebbling numbers of powers of the cycle $C_5$. Finally, we present explicit distributions which provide asymptotic bounds on optimal pebbling numbers of hypercubes.Comment: 28 pages, 1 figur

Heterospecific interactions and the proliferation of sexually dimorphic traits

Sexual selection is expected to promote speciation by fostering the evolution of sexual traits that minimize reproductive interactions among existing or incipient species. In species that compete for access to, or attention of, females, sexual selection fosters more elaborate traits in males compared to females. If these traits also minimize reproductive interactions with heterospecifics, then species with enhanced risk of interactions between species might display greater numbers of these sexual dimorphic characters. We tested this prediction in eight families of North American birds. In particular, we evaluated whether the number of sexually dimorphic traits was positively associated with species richness at a given site or with degree of sympatry with congeners. We found no strong evidence of enhanced sexual dimorphism with increasing confamilial species richness at a given site. We also found no overall relationship between the number of sexually dimorphic traits and overlap with congeners across these eight families. However, we found patterns consistent with our prediction within Anatidae (ducks, geese and swans) and, to a lesser degree, Parulidae (New World warblers). Our results suggest that sexually selected plumage traits in these groups potentially play a role in reproductive isolation

Statistical Methods for Detecting Ichthyoplankton Density Patterns that Influence Entrainment Mortality

Samples of drifting American shad eggs were collected at two transects in the Savannah River near industrial water intakes. At each transect the river was divided into four sectors that were sampled at two hour intervals over a 24 hour period. The actual risk of entrainment was approximately 35-50% lower that if the shad eggs were uniformly distributed, and the risk of entrainment was lower at one intake than the other

A mesocosm experiment investigating the effects of substratum quality and wave exposure on the survival of fish eggs

In a mesocosm experiment, the attachment of bream (Abramis brama) eggs to spawning substrata with and without periphytic biofilm coverage and their subsequent survival with and without low-intensity wave exposure were investigated. Egg attachment was reduced by 73% on spawning substrata with a natural periphytic biofilm, compared to clean substrata. Overall, this initial difference in egg numbers persisted until hatching. The difference in egg numbers was even increased in the wave treatment, while it was reduced in the no-wave control treatment. Exposure to a low-intensity wave regime affected egg development between the two biofilm treatments differently. Waves enhanced egg survival on substrata without a biofilm but reduced the survival of eggs on substrata with biofilm coverage. In the treatment combining biofilm-covered substrata and waves, no attached eggs survived until hatching. In all treatments, more than 75% of the eggs became detached from the spawning substrata during the egg incubation period, an

Assessing the Health of Richibucto Estuary with the Latent Health Factor Index

The ability to quantitatively assess the health of an ecosystem is often of great interest to those tasked with monitoring and conserving ecosystems. For decades, research in this area has relied upon multimetric indices of various forms. Although indices may be numbers, many are constructed based on procedures that are highly qualitative in nature, thus limiting the quantitative rigour of the practical interpretations made from these indices. The statistical modelling approach to construct the latent health factor index (LHFI) was recently developed to express ecological data, collected to construct conventional multimetric health indices, in a rigorous quantitative model that integrates qualitative features of ecosystem health and preconceived ecological relationships among such features. This hierarchical modelling approach allows (a) statistical inference of health for observed sites and (b) prediction of health for unobserved sites, all accompanied by formal uncertainty statements. Thus far, the LHFI approach has been demonstrated and validated on freshwater ecosystems. The goal of this paper is to adapt this approach to modelling estuarine ecosystem health, particularly that of the previously unassessed system in Richibucto in New Brunswick, Canada. Field data correspond to biotic health metrics that constitute the AZTI marine biotic index (AMBI) and abiotic predictors preconceived to influence biota. We also briefly discuss related LHFI research involving additional metrics that form the infaunal trophic index (ITI). Our paper is the first to construct a scientifically sensible model to rigorously identify the collective explanatory capacity of salinity, distance downstream, channel depth, and silt-clay content --- all regarded a priori as qualitatively important abiotic drivers --- towards site health in the Richibucto ecosystem.Comment: On 2013-05-01, a revised version of this article was accepted for publication in PLoS One. See Journal reference and DOI belo

Habitat filtering determines spatial variation of macroinvertebrate community traits in northern headwater streams

Although our knowledge of the spatial distribution of stream organisms has been increasing rapidly in the last decades, there is still little consensus about trait-based variability of macroinvertebrate communities within and between catchments in near-pristine systems. Our aim was to examine the taxonomic and trait based stability vs. variability of stream macroinvertebrates in three high-latitude catchments in Finland. The collected taxa were assigned to unique trait combinations (UTCs) using biological traits. We found that only a single or a highly limited number of taxa formed a single UTC, suggesting a low degree of redundancy. Our analyses revealed significant differences in the environmental conditions of the streams among the three catchments. Linear models, rarefaction curves and beta-diversity measures showed that the catchments differed in both alpha and beta diversity. Taxon- and trait-based multivariate analyses also indicated that the three catchments were significantly different in terms of macroinvertebrate communities. All these findings suggest that habitat filtering, i.e., environmental differences among catchments, determines the variability of macroinvertebrate communities, thereby contributing to the significant biological differences among the catchments. The main implications of our study is that the sensitivity of trait-based analyses to natural environmental variation should be carefully incorporated in the assessment of environmental degradation, and that further studies are needed for a deeper understanding of trait-based community patterns across near-pristine streams

BioTIME: A database of biodiversity time series for the Anthropocene.

MotivationThe BioTIME database contains raw data on species identities and abundances in ecological assemblages through time. These data enable users to calculate temporal trends in biodiversity within and amongst assemblages using a broad range of metrics. BioTIME is being developed as a community-led open-source database of biodiversity time series. Our goal is to accelerate and facilitate quantitative analysis of temporal patterns of biodiversity in the Anthropocene.Main types of variables includedThe database contains 8,777,413 species abundance records, from assemblages consistently sampled for a minimum of 2 years, which need not necessarily be consecutive. In addition, the database contains metadata relating to sampling methodology and contextual information about each record.Spatial location and grainBioTIME is a global database of 547,161 unique sampling locations spanning the marine, freshwater and terrestrial realms. Grain size varies across datasets from 0.0000000158 km2 (158 cm2) to 100 km2 (1,000,000,000,000 cm2).Time period and grainBioTIME records span from 1874 to 2016. The minimal temporal grain across all datasets in BioTIME is a year.Major taxa and level of measurementBioTIME includes data from 44,440 species across the plant and animal kingdoms, ranging from plants, plankton and terrestrial invertebrates to small and large vertebrates.Software format.csv and .SQL

Environmental Effects on Vertebrate Species Richness: Testing the Energy, Environmental Stability and Habitat Heterogeneity Hypotheses

Background: Explaining species richness patterns is a central issue in biogeography and macroecology. Several hypotheses have been proposed to explain the mechanisms driving biodiversity patterns, but the causes of species richness gradients remain unclear. In this study, we aimed to explain the impacts of energy, environmental stability, and habitat heterogeneity factors on variation of vertebrate species richness (VSR), based on the VSR pattern in China, so as to test the energy hypothesis, the environmental stability hypothesis, and the habitat heterogeneity hypothesis. Methodology/Principal Findings: A dataset was compiled containing the distributions of 2,665 vertebrate species and eleven ecogeographic predictive variables in China. We grouped these variables into categories of energy, environmental stability, and habitat heterogeneity and transformed the data into 1006100 km quadrat systems. To test the three hypotheses, AIC-based model selection was carried out between VSR and the variables in each group and correlation analyses were conducted. There was a decreasing VSR gradient from the southeast to the northwest of China. Our results showed that energy explained 67.6 % of the VSR variation, with the annual mean temperature as the main factor, which was followed by annual precipitation and NDVI. Environmental stability factors explained 69.1 % of the VSR variation and both temperature annual range and precipitation seasonality had important contributions. By contrast, habitat heterogeneity variables explained only 26.3 % of the VSR variation. Significantly positive correlations were detected among VSR, annua