Positive definite metric spaces

Magnitude is a numerical invariant of finite metric spaces, recently introduced by T. Leinster, which is analogous in precise senses to the cardinality of finite sets or the Euler characteristic of topological spaces. It has been extended to infinite metric spaces in several a priori distinct ways. This paper develops the theory of a class of metric spaces, positive definite metric spaces, for which magnitude is more tractable than in general. Positive definiteness is a generalization of the classical property of negative type for a metric space, which is known to hold for many interesting classes of spaces. It is proved that all the proposed definitions of magnitude coincide for compact positive definite metric spaces and further results are proved about the behavior of magnitude as a function of such spaces. Finally, some facts about the magnitude of compact subsets of l_p^n for p \le 2 are proved, generalizing results of Leinster for p=1,2, using properties of these spaces which are somewhat stronger than positive definiteness.Comment: v5: Corrected some misstatements in the last few paragraphs. Updated reference

Characterization of Geographically Distinct Bacterial Communities Associated with Coral Mucus Produced by Acropora spp. and Porites spp

ABSTRACT Acropora and Porites corals are important reef builders in the Indo-Pacific and Caribbean. Bacteria associated with mucus produced by Porites spp. and Acropora spp. from Caribbean (Punta Maroma, Mexico) and Indo-Pacific (Hoga and Sampela, Indonesia) reefs were determined. Analysis of pyrosequencing libraries showed that bacterial communities from Caribbean corals were significantly more diverse (H′, 3.18 to 4.25) than their Indonesian counterparts (H′, 2.54 to 3.25). Dominant taxa were Gammaproteobacteria , Alphaproteobacteria , Firmicutes , and Cyanobacteria , which varied in relative abundance between coral genera and region. Distinct coral host-specific communities were also found; for example, Clostridiales were dominant on Acropora spp. (at Hoga and the Mexican Caribbean) compared to Porites spp. and seawater. Within the Gammproteobacteria , Halomonas spp. dominated sequence libraries from Porites spp. (49%) and Acropora spp. (5.6%) from the Mexican Caribbean, compared to the corresponding Indonesian coral libraries (&lt;2%). Interestingly, with the exception of Porites spp. from the Mexican Caribbean, there was also a ubiquity of Psychrobacter spp., which dominated Acropora and Porites libraries from Indonesia and Acropora libraries from the Caribbean. In conclusion, there was a dominance of Halomonas spp. (associated with Acropora and Porites [Mexican Caribbean]), Firmicutes (associated with Acropora [Mexican Caribbean] and with Acropora and Porites [Hoga]), and Cyanobacteria (associated with Acropora and Porites [Hoga] and Porites [Sampela]). This is also the first report describing geographically distinct Psychrobacter spp. associated with coral mucus. In addition, the predominance of Clostridiales associated with Acropora spp. provided additional evidence for coral host-specific microorganisms. </jats:p

An Experimental Field Study of Delayed Density Dependence in Natural Populations of Aedes albopictus

Aedes albopictus, a species known to transmit dengue and chikungunya viruses, is primarily a container-inhabiting mosquito. The potential for pathogen transmission by Ae. albopictus has increased our need to understand its ecology and population dynamics. Two parameters that we know little about are the impact of direct density-dependence and delayed density-dependence in the larval stage. The present study uses a manipulative experimental design, under field conditions, to understand the impact of delayed density dependence in a natural population of Ae. albopictus in Raleigh, North Carolina. Twenty liter buckets, divided in half prior to experimentation, placed in the field accumulated rainwater and detritus, providing oviposition and larval production sites for natural populations of Ae. albopictus. Two treatments, a larvae present and larvae absent treatment, were produced in each bucket. After five weeks all larvae were removed from both treatments and the buckets were covered with fine mesh cloth. Equal numbers of first instars were added to both treatments in every bucket. Pupae were collected daily and adults were frozen as they emerged. We found a significant impact of delayed density-dependence on larval survival, development time and adult body size in containers with high larval densities. Our results indicate that delayed density-dependence will have negative impacts on the mosquito population when larval densities are high enough to deplete accessible nutrients faster than the rate of natural food accumulation

The Leverage of Demographic Dynamics on Carbon Dioxide Emissions: Does Age Structure Matter?

This article provides a methodological contribution to the study of the effect of changes in population age structure on carbon dioxide (CO2) emissions. First, I propose a generalization of the IPAT equation to a multisector economy with an age-structured population and discuss the insights that can be obtained in the context of stable population theory. Second, I suggest a statistical model of household consumption as a function of household size and age structure to quantitatively evaluate the extent of economies of scale in consumption of energy-intensive goods, and to estimate age-specific profiles of consumption of energy-intensive goods and of CO2 emissions. Third, I offer an illustration of the methodologies using data for the United States. The analysis shows that per-capita CO2 emissions increase with age until the individual is in his or her 60s, and then emissions tend to decrease. Holding everything else constant, the expected change in U.S. population age distribution during the next four decades is likely to have a small, but noticeable, positive impact on CO2 emissions

Comparison of geometric morphometric outline methods in the discrimination of age-related differences in feather shape

BACKGROUND: Geometric morphometric methods of capturing information about curves or outlines of organismal structures may be used in conjunction with canonical variates analysis (CVA) to assign specimens to groups or populations based on their shapes. This methodological paper examines approaches to optimizing the classification of specimens based on their outlines. This study examines the performance of four approaches to the mathematical representation of outlines and two different approaches to curve measurement as applied to a collection of feather outlines. A new approach to the dimension reduction necessary to carry out a CVA on this type of outline data with modest sample sizes is also presented, and its performance is compared to two other approaches to dimension reduction. RESULTS: Two semi-landmark-based methods, bending energy alignment and perpendicular projection, are shown to produce roughly equal rates of classification, as do elliptical Fourier methods and the extended eigenshape method of outline measurement. Rates of classification were not highly dependent on the number of points used to represent a curve or the manner in which those points were acquired. The new approach to dimensionality reduction, which utilizes a variable number of principal component (PC) axes, produced higher cross-validation assignment rates than either the standard approach of using a fixed number of PC axes or a partial least squares method. CONCLUSION: Classification of specimens based on feather shape was not highly dependent of the details of the method used to capture shape information. The choice of dimensionality reduction approach was more of a factor, and the cross validation rate of assignment may be optimized using the variable number of PC axes method presented herein

Long-Term Climate Forcing in Loggerhead Sea Turtle Nesting

The long-term variability of marine turtle populations remains poorly understood, limiting science and management. Here we use basin-scale climate indices and regional surface temperatures to estimate loggerhead sea turtle (Caretta caretta) nesting at a variety of spatial and temporal scales. Borrowing from fisheries research, our models investigate how oceanographic processes influence juvenile recruitment and regulate population dynamics. This novel approach finds local populations in the North Pacific and Northwest Atlantic are regionally synchronized and strongly correlated to ocean conditions—such that climate models alone explain up to 88% of the observed changes over the past several decades. In addition to its performance, climate-based modeling also provides mechanistic forecasts of historical and future population changes. Hindcasts in both regions indicate climatic conditions may have been a factor in recent declines, but future forecasts are mixed. Available climatic data suggests the Pacific population will be significantly reduced by 2040, but indicates the Atlantic population may increase substantially. These results do not exonerate anthropogenic impacts, but highlight the significance of bottom-up oceanographic processes to marine organisms. Future studies should consider environmental baselines in assessments of marine turtle population variability and persistence

The potential to encode sex, age, and individual identity in the alarm calls of three species of Marmotinae

In addition to encoding referential information and information about the sender’s motivation, mammalian alarm calls may encode information about other attributes of the sender, providing the potential for recognition among kin, mates, and neighbors. Here, we examined 96 speckled ground squirrels (Spermophilus suslicus), 100 yellow ground squirrels (Spermophilus fulvus) and 85 yellow-bellied marmots (Marmota flaviventris) to determine whether their alarm calls differed between species in their ability to encode information about the caller’s sex, age, and identity. Alarm calls were elicited by approaching individually identified animals in live-traps. We assume this experimental design modeled a naturally occurring predatory event, when receivers should acquire information about attributes of a caller from a single bout of alarm calls. In each species, variation that allows identification of the caller’s identity was greater than variation allowing identification of age or sex. We discuss these results in relation to each species’ biology and sociality

Empirical Models of Transitions between Coral Reef States: Effects of Region, Protection, and Environmental Change

There has been substantial recent change in coral reef communities. To date, most analyses have focussed on static patterns or changes in single variables such as coral cover. However, little is known about how community-level changes occur at large spatial scales. Here, we develop Markov models of annual changes in coral and macroalgal cover in the Caribbean and Great Barrier Reef (GBR) regions

Isotope Analysis Reveals Foraging Area Dichotomy for Atlantic Leatherback Turtles

Background: The leatherback turtle (Dermochelys coriacea) has undergone a dramatic decline over the last 25 years, and this is believed to be primarily the result of mortality associated with fisheries bycatch followed by egg and nesting female harvest. Atlantic leatherback turtles undertake long migrations across ocean basins from subtropical and tropical nesting beaches to productive frontal areas. Migration between two nesting seasons can last 2 or 3 years, a time period termed the remigration interval (RI). Recent satellite transmitter data revealed that Atlantic leatherbacks follow two major dispersion patterns after nesting season, through the North Gulf Stream area or more eastward across the North Equatorial Current. However, information on the whole RI is lacking, precluding the accurate identification of feeding areas where conservation measures may need to be applied. Methodology/Principal Findings: Using stable isotopes as dietary tracers we determined the characteristics of feeding grounds of leatherback females nesting in French Guiana. During migration, 3-year RI females differed from 2-year RI females in their isotope values, implying differences in their choice of feeding habitats (offshore vs. more coastal) and foraging latitude (North Atlantic vs. West African coasts, respectively). Egg-yolk and blood isotope values are correlated in nesting females, indicating that egg analysis is a useful tool for assessing isotope values in these turtles, including adults when not available. Conclusions/Significance: Our results complement previous data on turtle movements during the first year following the nesting season, integrating the diet consumed during the year before nesting. We suggest that the French Guiana leatherback population segregates into two distinct isotopic groupings, and highlight the urgent need to determine the feeding habitats of the turtle in the Atlantic in order to protect this species from incidental take by commercial fisheries. Our results also emphasize the use of eggs, a less-invasive sampling material than blood, to assess isotopic data and feeding habits for adult female leatherbacks