Revisiting Offspring Maxima in Branching Processes

2000 Mathematics Subject Classification: 60J80; 60G70.

Extremes of Bivariate Geometric Variables with Application to Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80, 60G70.

Downhole variations in grain sizes at DSDP/ODP Hole 504B

The maximum grain sizes of plagioclase and magnetite in the groundmass of the sheeted dike complex drilled at Hole 504B have been measured. Downhole variations through a 440-m-long section show a crude zig-zag pattern consisting of a gradual decrease or increase followed by an abrupt jump. The gradual decrease or increase in grain size extends over many lithologic units, and hence, does not reflect variations in grain size within a single dike. Such a zig-zag pattern is well explained by grain-size variations through multiple dikes. By using the observed inclination of sheeted dikes of 81° ± 2.5°, thickness of the multiple dikes varies from 0.7 to 8.5 m and averages to 4 ± 1 m. The average thickness of individual dikes forming multiple dikes is 0.8 m. We expect such multiple dikes to be formed during rifting events beneath mid-oceanic spreading ridges. If the average expansion at rifting episodes is twice as wide as the average width of the multiple dike units, the full spreading rate of 7.2 cm/yr of Cocos Ridge gives 112 ± 33 yr for a time interval of the rifting. A simple one-dimensional conductive cooling model is applied to solidification of multiple dikes. Numerical simulations show that the grain-size variations observed through the drill hole are more consistent with a model where a new injection of a dike occurs periodically with a constant time interval rather than one where the next dike intrudes just after the solidification of the previous one. Grain-size variations within simple dikes from Iritono, Japan, and those for Makaopuhi lava lake, Hawaii, show that square root of crystallization time is linearly correlated with the logarithm of plagioclase size. By using an empirically derived relationship between these two variables, the variations of plagioclase size through Hole 504B are directly compared with the calculated times for crystallization. Each rifting episode at the Costa Rica Rift lasts for several years, and periodic injection of a new dike occurs into the center of a previously solidified multiple dike at time intervals varying from 1 to 12 months.

Use of the EM algorithm to detect QTL affecting multiple-traits in an across half-sib family analysis

QTL detection experiments in livestock species commonly use the half-sib design. Each male is mated to a number of females, each female producing a limited number of progeny. Analysis consists of attempting to detect associations between phenotype and genotype measured on the progeny. When family sizes are limiting experimenters may wish to incorporate as much information as possible into a single analysis. However, combining information across sires is problematic because of incomplete linkage disequilibrium between the markers and the QTL in the population. This study describes formulae for obtaining MLEs via the expectation maximization (EM) algorithm for use in a multiple-trait, multiple-family analysis. A model specifying a QTL with only two alleles, and a common within sire error variance is assumed. Compared to single-family analyses, power can be improved up to fourfold with multi-family analyses. The accuracy and precision of QTL location estimates are also substantially improved. With small family sizes, the multi-family, multi-trait analyses reduce substantially, but not totally remove, biases in QTL effect estimates. In situations where multiple QTL alleles are segregating the multi-family analysis will average out the effects of the different QTL alleles.

Impact of different pack sizes of paracetamol in the United Kingdom and Ireland on intentional overdoses: a comparative study

BACKGROUND: In order to reduce fatal self-poisoning legislation was introduced in the UK in 1998 to restrict pack sizes of paracetamol sold in pharmacies (maximum 32 tablets) and non-pharmacy outlets (maximum 16 tablets), and in Ireland in 2001, but with smaller maximum pack sizes (24 and 12 tablets). Our aim was to determine whether this resulted in smaller overdoses of paracetamol in Ireland compared with the UK. METHODS: We used data on general hospital presentations for non-fatal self-harm for 2002-2007 from the Multicentre Study of Self-harm in England (six hospitals), and from the National Registry of Deliberate Self-harm in Ireland. We compared sizes of overdoses of paracetamol in the two settings. RESULTS: There were clear peaks in numbers of non-fatal overdoses, associated with maximum pack sizes of paracetamol in pharmacy and non-pharmacy outlets in both England and Ireland. Significantly more pack equivalents (based on maximum non-pharmacy pack sizes) were used in overdoses in Ireland (mean 2.63, 95% CI 2.57-2.69) compared with England (2.07, 95% CI 2.03-2.10). The overall size of overdoses did not differ significantly between England (median 22, interquartile range (IQR) 15-32) and Ireland (median 24, IQR 12-36). CONCLUSIONS: The difference in paracetamol pack size legislation between England and Ireland does not appear to have resulted in a major difference in sizes of overdoses. This is because more pack equivalents are taken in overdoses in Ireland, possibly reflecting differing enforcement of sales advice. Differences in access to clinical services may also be relevant.

Effects of allometry, productivity and lifestyle on rates and limits of body size evolution

Body size affects nearly all aspects of organismal biology, so it is important to understand the constraints and dynamics of body size evolution. Despite empirical work on the macroevolution and macroecology of minimum and maximum size, there is little general quantitative theory on rates and limits of body size evolution. We present a general theory that integrates individual productivity, the lifestyle component of the slow–fast life-history continuum, and the allometric scaling of generation time to predict a clade's evolutionary rate and asymptotic maximum body size, and the shape of macroevolutionary trajectories during diversifying phases of size evolution. We evaluate this theory using data on the evolution of clade maximum body sizes in mammals during the Cenozoic. As predicted, clade evolutionary rates and asymptotic maximum sizes are larger in more productive clades (e.g. baleen whales), which represent the fast end of the slow–fast lifestyle continuum, and smaller in less productive clades (e.g. primates). The allometric scaling exponent for generation time fundamentally alters the shape of evolutionary trajectories, so allometric effects should be accounted for in models of phenotypic evolution and interpretations of macroevolutionary body size patterns. This work highlights the intimate interplay between the macroecological and macroevolutionary dynamics underlying the generation and maintenance of morphological diversity.

Life-history and spatial determinants of somatic growth dynamics in Komodo dragon populations

Somatic growth patterns represent a major component of organismal fitness and may vary among sexes and populations due to genetic and environmental processes leading to profound differences in life-history and demography. This study considered the ontogenic, sex-specific and spatial dynamics of somatic growth patterns in ten populations of the world's largest lizard the Komodo dragon (Varanus komodoensis). The growth of 400 individual Komodo dragons was measured in a capture-mark-recapture study at ten sites on four islands in eastern Indonesia, from 2002 to 2010. Generalized Additive Mixed Models (GAMMs) and information-theoretic methods were used to examine how growth rates varied with size, age and sex, and across and within islands in relation to site-specific prey availability, lizard population density and inbreeding coefficients. Growth trajectories differed significantly with size and between sexes, indicating different energy allocation tactics and overall costs associated with reproduction. This leads to disparities in maximum body sizes and longevity. Spatial variation in growth was strongly supported by a curvilinear density-dependent growth model with highest growth rates occurring at intermediate population densities. Sex-specific trade-offs in growth underpin key differences in Komodo dragon life-history including evidence for high costs of reproduction in females. Further, inverse density-dependent growth may have profound effects on individual and population level processes that influence the demography of this species.

Chemical analysis of ash layers in ODP Leg 104 holes

Numerous fresh ash layers comprise about 0.3% by volume of Neogene to Holocene sediments drilled at Leg 104 Sites 642 and 643 (Vøring Plateau, North Atlantic). Median grain sizes of the ashes are about 100 /µm and maximum grain sizes range up to 1200 µm. Rhyolitic pumice shards dominate, with minor bubble wall shards. Basaltic shards are poorly vesicular and blocky or round. Phenocrystic plagioclase, zircon, and clinopyroxene occur in the rhyolitic, plagioclase, and clinopyroxene phenocrysts and basaltic lithics in the basaltic tephra. Quartz, amphibole, clinozoisite, and rutile are interpreted as xenocrysts. All ash layers are well-sorted and represent distal fallout from major explosive eruptions. Most ashes are rhyolitic (high-K and low-K) in composition, some are bimodal (tholeiitic and rhyolitic). Early Miocene tephra is dominantly basaltic. Iceland is inferred to be the likely source region for most ashes. Late Miocene high-K rhyolites may have originated from the K-rich Jan Mayen magmatic province. One Quaternary layer with biotite and alkali feldspar phenocrysts may have been derived from Jan Mayen Island. Four individual Pliocene to Holocene ash layers from Sites 642 and 643 can be correlated fairly well. Upper Miocene layers are tentatively correlated as a sequence between Sites 642 and 643. Average calculated layer frequencies are about three layers/m.y. through the Pliocene and Pleistocene and five to eight layers per m.y. through the middle and late Miocene, suggesting rather continuous volcanic activity in the North Atlantic. Episodic magmatic activity during Neogene epochs in this part of the North Atlantic, as postulated in the literature, cannot be confirmed.

Rutting-induced permeability loss of open graded friction course mixtures

Functionality of an open graded friction course (OGFC) depends on the high interconnected air voids or pores of the OGFC mixture. The authors' previous study indicated that the pores in the OGFC mixture were easily clogged by rutting deformation. Such a deformation-related clogging can cause a significant rutting-induced permeability loss in the OGFC mixture. The objective of this study was to control and reduce the rutting-induced permeability loss of the OGFC based on mixture design and layer thickness. Eight types of the OGFC mixtures with different air void contents, gradations, and nominal maximum aggregate sizes were fabricated in the laboratory. Wheel-tracking rutting tests were conducted on the OGFC slabs to simulate the deformation-related clogging. Permeability tests after different wheel load applications were performed on the rutted OGFC slabs using a falling head permeameter developed in the authors' previous study. The relationships between permeability loss and rutting depth as well as dynamic stability were developed based on the eight OGFC mixtures' test results. The thickness effects of the single-layer and the two-layer OGFC slabs were also discussed in terms of deformation-related clogging and the rutting-induced permeability loss. Results showed that the permeability coefficient decreases linearly with an increasing rutting depth of the OGFC mixtures. Rutting depth was recommended as a design index to control permeability loss of the OGFC mixture rather than the dynamic stability. Permeability loss due to deformation-related clogging can be effectively reduced by using a thicker single-layer OGFC or two-layer OGFC.

Length at first maturity of two species of lantern sharks (Etmopterus spinax and Etmopterus pusillus) off southern Portugal

Etmoplerus spinax and Etmopterus pusillus are captured in large quantities in some deep-water fisheries along the Portuguesc coast and are always discarded. Specimens were collected from February 2003 to May 2004 from deep-water fisheries and classified as mature or immature. Maturity ogives were fitted and size at first maturity estimated for each sex of each of each species. Both species are late maturing, with the maturity size varying between 75% and 87% of the maximum observed sizes, depending on species and sex. For both species, females tended to mature at and grow to larger sizes than males. The late maturation of these deep-water shark species make these populations extremely vulnerable to increasing fishing mortality.

Population parameters of the smooth lantern shark, Etmopterus pusillus, in southern Portugal (NE Atlantic)

Etmopterus pusillus is a deep water lantern shark with a widespread global distribution that is caught in large quantities in some areas, but is usually discarded due to the low commercial value. In this work, the population biology was studied and life history parameters determined for the first time in this species. Age was estimated from sections of the second dorsal spine and validated by marginal increment analysis. Males attained a maximum age of 13 years, while 17-year-old females were found. Several growth models were fitted and compared for both size and weight at age data, showing that even though this is a small sized species, it has a relatively slow growth rate. This species matures late and at a relatively large size: at 86.81% and 79.40% of the maximum observed sizes and at 58.02% and 54.40% of the maximum observed ages for males and females, respectively. It has a low fecundity, with a mean ovarian fecundity of 10.44 oocytes per reproductive cycle. The estimated parameters indicate that this species has a vulnerable life cycle, typical of deep water squalid sharks. Given the high fishing pressures that it is suffering in the NE Atlantic, the smooth lantern shark may be in danger of severe declines in the near future. (c) 2007 Elsevier B.V. All rights reserved.

Thermal properties, sizes, and size distribution of Jupiter-family cometary nuclei

We present results from SEPPCoN, an on-going Survey of the Ensemble Physical Properties of Cometary Nuclei. In this report we discuss mid-infrared measurements of the thermal emission from 89 nuclei of Jupiter-family comets (JFCs). All data were obtained in 2006 and 2007 using imaging capabilities of the Spitzer Space Telescope. The comets were typically 4-5 AU from the Sun when observed and most showed only a point-source with little or no extended emission from dust. For those comets showing dust, we used image processing to photometrically extract the nuclei. For all 89 comets, we present new effective radii, and for 57 comets we present beaming parameters. Thus our survey provides the largest compilation of radiometrically-derived physical properties of nuclei to date. We have six main conclusions: (a) The average beaming parameter of the JFC population is 1.03 ± 0.11, consistent with unity; coupled with the large distance of the nuclei from the Sun, this indicates that most nuclei have Tempel 1-like thermal inertia. Only two of the 57 nuclei had outlying values (in a statistical sense) of infrared beaming. (b) The known JFC population is not complete even at 3 km radius, and even for comets that approach to ˜2 AU from the Sun and so ought to be more discoverable. Several recently-discovered comets in our survey have small perihelia and large (above ˜2 km) radii. (c) With our radii, we derive an independent estimate of the JFC nuclear cumulative size distribution (CSD), and we find that it has a power-law slope of around -1.9, with the exact value depending on the bounds in radius. (d) This power-law is close to that derived by others from visible-wavelength observations that assume a fixed geometric albedo, suggesting that there is no strong dependence of geometric albedo with radius. (e) The observed CSD shows a hint of structure with an excess of comets with radii 3-6 km. (f) Our CSD is consistent with the idea that the intrinsic size distribution of the JFC population is not a simple power-law and lacks many sub-kilometer objects.

Measurements of gastropods shell sizes from 23 fossil and extant long-lived lakes

Aim: To investigate shell size variation among gastropod faunas of fossil and recent long-lived European lakes and discuss potential underlying processes. Location: 23 long-lived lakes of the Miocene to Recent of Europe. Methods: Based on a dataset of 1412 species of both fossil and extant lacustrine gastropods, we assessed differences in shell size in terms of characteristics of the faunas (species richness, degree of endemism, differences in family composition) and the lakes (surface area, latitude and longitude of lake centroid, distance to closest neighbouring lake) using multiple and linear regression models. Because of a strong species-area relationship, we used resampling to determine whether any observed correlation is driven by that relationship. Results: The regression models indicated size range expansion rather than unidirectional increase or decrease as the dominant pattern of size evolution. The multiple regression models for size range and maximum and minimum size were statistically significant, while the model with mean size was not. Individual contributions and linear regressions indicated species richness and lake surface area as best predictors for size changes. Resampling analysis revealed no significant effects of species richness on the observed patterns. The correlations are comparable across families of different size classes, suggesting a general pattern. Main conclusions: Among the chosen variables, species richness and lake surface area are the most robust predictors of shell size in long-lived lake gastropods. Although the most outstanding and attractive examples for size evolution in lacustrine gastropods derive from lakes with extensive durations, shell size appears to be independent of the duration of the lake as well as longevity of a species. The analogue of long-lived lakes as 'evolutionary islands' does not hold for developments of shell size because different sets of parameters predict size changes.