On the exponential transform of lemniscates

It is known that the exponential transform of a quadrature domain is a rational function for which the denominator has a certain separable form. In the present paper we show that the exponential transform of lemniscate domains in general are not rational functions, of any form. Several examples are given to illustrate the general picture. The main tool used is that of polynomial and meromorphic resultants.Comment: 19 pages, to appear in the Julius Borcea Memorial Volume, (eds. Petter Branden, Mikael Passare and Mihai Putinar), Trends in Mathematics, Birkhauser Verla

A Preference for a Sexual Signal Keeps Females Safe

Predation is generally thought to constrain sexual selection by female choice and limit the evolution of conspicuous sexual signals. Under high predation risk, females usually become less choosy, because they reduce their exposure to their predators by reducing the extent of their mate searching. However, predation need not weaken sexual selection if, under high predation risk, females exhibit stronger preferences for males that use conspicuous signals that help females avoid their predators. We tested this prediction in the fiddler crab Uca terpsichores by increasing females' perceived predation risk from crab-eating birds and measuring the attractiveness of a courtship signal that females use to find mates. The sexual signal is an arching mound of sand that males build at the openings of their burrows to which they attract females for mating. We found that the greater the risk, the more attractive were males with those structures. The benefits of mate preferences for sexual signals are usually thought to be linked to males' reproductive contributions to females or their young. Our study provides the first evidence that a female preference for a sexual signal can yield direct survival benefits by keeping females safe as they search for mates

Community Compensatory Trend Prevails from Tropical to Temperate Forest

Community compensatory trend (CCT) is thought to facilitate persistence of rare species and thus stabilize species composition in tropical forests. However, whether CCT acts over broad geographical ranges is still in question. In this study, we tested for the presence of negative density dependence (NDD) and CCT in three forests along a tropical-temperate gradient. Inventory data were collected from forest communities located in three different latitudinal zones in China. Two widely used methods were used to test for NDD at the community level. The first method considered relationships between the relative abundance ratio and adult abundance. The second method emphasized the effect of adult abundance on abundance of established younger trees. Evidence for NDD acting on different growth forms was tested by using the first method, and the presence of CCT was tested by checking whether adult abundance of rare species affected that of established younger trees less than did abundance of common species. Both analyses indicated that NDD existed in seedling, sapling and pole stages in all three plant communities and that this effect increased with latitude. However, the extent of NDD varied among understory, midstory and canopy trees in the three communities along the gradient. Additionally, despite evidence of NDD for almost all common species, only a portion of rare species showed NDD, supporting the action of CCT in all three communities. So, we conclude that NDD and CCT prevail in the three recruitment stages of the tree communities studied; rare species achieve relative advantage through CCT and thus persist in these communities; CCT clearly facilitates newly established species and maintains tree diversity within communities across our latitudinal gradient

You Name It – How Memory and Delay Govern First Name Dynamics

The adoption and abandonment of first names through time is a fascinating phenomenon that may shed light on social dynamics and the forces that determine cultural taste in general. Here we show that baby name dynamics is governed almost solely by deterministic forces, even though the emerging abundance statistics resembles the one obtained from a pure drift model. Exogenous events are shown to affect the name dynamics very rarely, and most of the year-to-year fluctuations around the deterministic trend may be attributed solely to demographic noise. We suggest that the rise and fall of a name reflect an “infection” process with delay and memory. The symmetry between adoption and abandonment speed emerges from our model without further assumptions

Temperature effects on an InGaP (GaInP) (55)Fe X-ray photovoltaic cell.

This paper investigates the effects of temperature on an InGaP (GaInP) (55)Fe X-ray photovoltaic cell prototype for a radioisotope microbattery (also called a nuclear microbattery). An In0.5Ga0.5P p-i-n (5 μm i-layer) mesa photodiode was illuminated by a standard 206 MBq (55)Fe radioisotope X-ray source and characterised over the temperature range -20 °C to 100 °C. The electrical power output of the device reached its maximum value of 1.5 pW at a temperature of -20 °C. An open circuit voltage and a short circuit current of 0.82 V and 2.5 pA, respectively, were obtained at -20 °C. While the electrical power output and the open circuit voltage decreased with increasing temperature, an almost flat trend was found for the short circuit current. The cell conversion efficiency decreased from 2.1% at -20 °C to 0.7% at 100 °C

Low-dimensional network formation in molten sodium carbonate

Molten carbonates are highly inviscid liquids characterized by low melting points and high solubility of rare earth elements and volatile molecules. An understanding of the structure and related properties of these intriguing liquids has been limited to date. We report the results of a study of molten sodium carbonate (Na2CO3) which combines high energy X-ray diffraction, containerless techniques and computer simulation to provide insight into the liquid structure. Total structure factors (Fx(Q)) are collected on the laser-heated carbonate spheres suspended in flowing gases of varying composition in an aerodynamic levitation furnace. The respective partial structure factor contributions to Fx(Q) are obtained by performing molecular dynamics simulations treating the carbonate anions as flexible entities. The carbonate liquid structure is found to be heavily temperature-dependent. At low temperatures a low-dimensional carbonate chain network forms, at T = 1100 K for example ~55% of the C atoms form part of a chain. The mean chain lengths decrease as temperature is increased and as the chains become shorter the rotation of the carbonate anions becomes more rapid enhancing the diffusion of Na+ ions

Why Do Species Co-Occur? A Test of Alternative Hypotheses Describing Abiotic Differences in Sympatry versus Allopatry Using Spadefoot Toads

Areas of co-occurrence between two species (sympatry) are often thought to arise in regions where abiotic conditions are conducive to both species and are therefore intermediate between regions where either species occurs alone (allopatry). Depending on historical factors or interactions between species, however, sympatry might not differ from allopatry, or, alternatively, sympatry might actually be more extreme in abiotic conditions relative to allopatry. Here, we evaluate these three hypothesized patterns for how sympatry compares to allopatry in abiotic conditions. We use two species of congeneric spadefoot toads, Spea multiplicata and S. bombifrons, as our study system. To test these hypotheses, we created ecological niche models (specifically using Maxent) for both species to create a map of the joint probability of occurrence of both species. Using the results of these models, we identified three types of locations: two where either species was predicted to occur alone (i.e., allopatry for S. multiplicata and allopatry for S. bombifrons) and one where both species were predicted to co-occur (i.e., sympatry). We then compared the abiotic environment between these three location types and found that sympatry was significantly hotter and drier than the allopatric regions. Thus, sympatry was not intermediate between the alternative allopatric sites. Instead, sympatry occurred at one extreme of the conditions occupied by both species. We hypothesize that biotic interactions in these extreme environments facilitate co-occurrence. Specifically, hybridization between S. bombifrons females and S. multiplicata males may facilitate co-occurrence by decreasing development time of tadpoles. Additionally, the presence of alternative food resources in more extreme conditions may preclude competitive exclusion of one species by the other. This work has implications for predicting how interacting species will respond to climate change, because species interactions may facilitate survival in extreme habitats

Reproductive Isolation and Ecological Niche Partition among Larvae of the Morphologically Cryptic Sister Species Chironomus riparius and C. piger

Background One of the central issues in ecology is the question what allows sympatric occurrence of closely related species in the same general area? The non-biting midges Chironomus riparius and C. piger, interbreeding in the laboratory, have been shown to coexist frequently despite of their close relatedness, similar ecology and high morphological similarity. Methodology/Principal Findings In order to investigate factors shaping niche partitioning of these cryptic sister species, we explored the actual degree of reproductive isolation in the field. Congruent results from nuclear microsatellite and mitochondrial haplotype analyses indicated complete absence of interspecific gene-flow. Autocorrelation analysis showed a non-random spatial distribution of the two species. Though not dispersal limited at the scale of the study area, the sister species occurred less often than expected at the same site, indicating past or present competition. Correlation and multiple regression analyses suggested the repartition of the available habitat along water chemistry gradients (nitrite, conductivity, CaCO3), ultimately governed by differences in summer precipitation regime. Conclusions We show that these morphologically cryptic sister species partition their niches due to a certain degree of ecological distinctness and total reproductive isolation in the field. The coexistence of these species provides a suitable model system for the investigation of factors shaping the distribution of closely related, cryptic species

Inferring Ecological Processes from Taxonomic, Phylogenetic and Functional Trait β-Diversity

Understanding the influences of dispersal limitation and environmental filtering on the structure of ecological communities is a major challenge in ecology. Insight may be gained by combining phylogenetic, functional and taxonomic data to characterize spatial turnover in community structure (β-diversity). We develop a framework that allows rigorous inference of the strengths of dispersal limitation and environmental filtering by combining these three types of β-diversity. Our framework provides model-generated expectations for patterns of taxonomic, phylogenetic and functional β-diversity across biologically relevant combinations of dispersal limitation and environmental filtering. After developing the framework we compared the model-generated expectations to the commonly used “intuitive” expectation that the variance explained by the environment or by space will, respectively, increase monotonically with the strength of environmental filtering or dispersal limitation. The model-generated expectations strongly departed from these intuitive expectations: the variance explained by the environment or by space was often a unimodal function of the strength of environmental filtering or dispersal limitation, respectively. Therefore, although it is commonly done in the literature, one cannot assume that the strength of an underlying process is a monotonic function of explained variance. To infer the strength of underlying processes, one must instead compare explained variances to model-generated expectations. Our framework provides these expectations. We show that by combining the three types of β-diversity with model-generated expectations our framework is able to provide rigorous inferences of the relative and absolute strengths of dispersal limitation and environmental filtering. Phylogenetic, functional and taxonomic β-diversity can therefore be used simultaneously to infer processes by comparing their empirical patterns to the expectations generated by frameworks similar to the one developed here