Bevan established that the growth rate of a monotone grid class of permutations is equal to the square of the spectral radius of a related bipartite graph. We give an elementary and self-contained proof of a generalization of this result using only Stirling's formula, the method of Lagrange multipliers, and the singular value decomposition of matrices. Our proof relies on showing that the maximum over the space of n × n matrices with non-negative entries summing to one of a certain function of those entries, parametrized by the entries of another matrix Γ of non-negative real numbers, is equal to the square of the largest singular value of Γ and that the maximizing point can be expressed as a Hadamard product of Γ with the tensor product of singular vectors for its greatest singular value.

Greenhouse studies were conducted to determine the relative salinity tolerance of foxtail barley and seven desirable pasture grasses. Grass species were reed canarygrass, timothy, altai wildrye, tall fescue, tall wheatgrass, orchardgrass, creeping meadow foxtail, and foxtail barley. Grasses were exposed to increasing electrical conductivity levels of NaCl and CaCl2 salt solution over time. Grass species were compared using a cumulative value of salt exposure (ECdays), which was calculated to account for the electrical conductivity (EC) and the time a plant was exposed at that level of conductivity. Salinity tolerance varied among grass species. Increasing EC significantly reduced plant biomass of all species. All grass species experienced a 50% biomass reduction (GR50) between 271 and 512 ECdays in 2008 and between 297 and 575 ECdays in 2009. Foxtail barley was among the most salt tolerant (GR50 = 512 and 525 ECdays), requiring the highest salt exposure in 2008 and the second-highest exposure in 2009 to reduce biomass 50%. Grass mortality increased with increasing EC levels. Reed canarygrass and timothy were most susceptible to increasing salinity, with 50% mortality (LD50) of both grass species occurring between 983 and 1,186 ECdays. Moderate salinity tolerance was exhibited by orchardgrass, which required 1,977 and 1,844 ECdays; creeping foxtail, which required 1,998 and 2,431 ECdays; and tall fescue, which required 2,501 and > 2,840 ECdays to LD50 in 2008 and 2009, respectively. Foxtail barley, altai wildrye, and tall wheatgrass were most tolerant of salinity and persisted with little mortality occurring at 3,033 and 2,840 ECdays in 2008 and 2009, respectively. All grass species with higher growth rates than foxtail barley and altai wildrye were more susceptible to salinity, with the exception of tall wheatgrass. Growth rates of foxtail barley and altai wildrye were less than they were for other grasses, suggesting that slower growth rates may aid in salinity tolerance.

Some species-rich secondary forests in New Caledonia have a monodominant canopy. Here we investigate growth and biomass allocation traits that might explain single-species’ dominance of these post-disturbance stands, and their later decline in the absence of large-scale disturbance. Seedlings of 20 rain-forest trees were grown in two light treatments in a nursery house. In the sun treatment, monodominants grew faster (56.7 ± 1.4 mg g−1 wk−1) than subordinates (40.2 ± 2.6 mg g−1 wk−1). However, some episodically regenerating (ER) subordinates had high growth rates similar to those of monodominants. In the shade treatment, monodominants and subordinates had similar growth rates (33.7 ± 2.6 and 34.0 ± 1.9 mg g−1 wk−1 respectively). Notably, monodominants in both sun and shade treatments had lower root mass fraction (0.29 ± 0.02 and 0.27 ± 0.02 g g−1 respectively) than subordinates (0.39 ± 0.02 and 0.37 ± 0.02 g g−1). Fast growth in sunny conditions is probably imperative for these relatively shade-intolerant ER monodominants. In field conditions, high shoot mass fraction combined with efficient root performance may facilitate faster growth in monodominants competing with other ER species in sunlit sites. Slower growth in shade may contribute to loss of dominance over time in undisturbed forests.

Long-term tagging studies, particularly those that target life stages away from nesting beaches can provide important insights in key life history traits, which are essential for the effective management of endangered species. The coast of Bahia hosts important green turtle foraging areas, but information on demography, spatial use and foraging ecology in this region is lacking. Here, we (1) examined the size-class structure of green turtles in Bahia, (2) compared the size distribution from Bahia to other foraging aggregations in Brazil, and (3) studied the somatic growth dynamics. Additionally, we investigated the (4) diet, (5) habitat use and (6) activity patterns of green turtles along shallow reefs in Bahia. From 2009 to 2013, 322 green turtles were captured and 44 were recaptured between 7 and 1218 days after initial tagging. Curved carapace length varied from 32.9 to 122.5 cm. Mean annual growth rate was 3.03 ± 1.18 cm year−1. The diet of the turtles was mainly composed of red algae of the family Gelidiaceae, Gelidiellaceae and Cystocloniaceae. There was a positive relationship between the abundance of red algae and the number of turtle sightings, with a significant increase in foraging activity during late afternoon. This study highlights the importance of this area as a mixed foraging aggregation of juvenile and adult green turtles, and reveals that foraging grounds for this species in Brazil exhibit southern immature-dominated assemblages and northern mixed aggregations. Areas with high aggregation of green turtles comprising individuals from different life stages must be targeted for conservation management.

This study examines the cause of higher (5% or more) economic growth rates in countries around the world over the past 35 years. It explores the long- and short-term relationships between GDP and government expenditures in these countries. A panel data set of 60 countries over the period from 1976 to 2010 is deployed to implement pooled mean group estimation. Countries are divided into three economic growth rate groups: high, middle, and low. Panel-based/error correction models are used to estimate long-term equilibrium relationships and short-term dynamics between government expenditures and GDP growth rates. Results indicate that the hypothesis of a common long-term elasticity and a short-term dynamic relationship between GDP growth rates and government expenditures cannot be rejected for high group countries, whereas for middle group countries this is true only for the long term, not for the short term. No long-term or short-term relationship between these two variables exists for low-growth-rate countries.

Scotland's economic performance and fiscal make-up are key elements in the debate leading up to the forthcoming referendum on independence. However, in terms of understanding Scotland's economic performance, the situation is complicated by the high degree of overseas ownership, especially with regards to North Sea activity, and the importance of a natural commodity, oil. This makes the use of traditional measures of economic performance, like GDP or GDP per capita, less relevant than for most countries and suggests a greater need to use both constant price and cash GNI, neither of which are currently available. In terms of its fiscal balance, Scotland's independence would require taxes derived from its offshore (North Sea) activity to be sufficient to offset the extra monies (in per head terms) currently transferred from the rest of the UK (via the Barnett formula system) in order to pay for the current level of public services. Based on current projections, such North Sea related tax revenues would amount to less than the likely Barnett transfer, leading to a net loss in funding at the time of independence. Under such circumstances the question of whether or not Scotland could afford to initiate the building up of an ‘Oil Fund’, is largely a redundant one. However, uncertainties over both future oil and gas revenues and over the continuation of the existing Barnett system make it difficult to predict with any great certainty whether Scotland would see a longer-term net fiscal gain or loss post-independence. Apparent inconsistencies between official GNI and Scottish revenue figures also means that the existing fiscal balance position remains open to question.

The age of most temperate tree species can be estimated accurately by counting the annual rings revealed by concentric changes in their wood anatomy. In the tropics and sub-tropics, this growth periodicity is seldom clearly and unambiguously defined. This research investigates whether a wood anatomical feature is present that delimits annual periods in one of the most widely distributed genera in the semi-arid and arid areas of Africa, Acacia.

Most research on this topic has been based on sample trees from natural stands, often the largest and putatively oldest trees. In contrast, the trees sampled for this study were actively sought from material of known age, particularly those for which the history of management was known. Several African Acacia species were examined for growth rings. These were apparent in most species as narrow bands of marginal parenchyma filled with long crystal chains. The crystals were sub-sequendy identified as calcium oxalate through the use of a scanning proton microprobe. The number of bands formed annually corresponded to the number of peaks in the annual rainfall distribution. Ring widths were highly correlated with total annual rainfall.

The growth rate of two species of whip black corals belonging to the genera Cirrhipathes and Stichopathes has been evaluated in different experiments conducted in the Marine Park of Bunaken (Indonesia) for over one year. Unbranched, unpinnulated black corals result among the fastest growing colonial organisms, with maximal growth rates of 13.25 cm month−1 for Cirrhipathes cfr anguina and 1.3 cm month−1 for Stichopathes cfr maldivensis. Several observations made both on transplants and on natural colonies add new information on the growth strategy of black corals. The easy handling, the high rate of survivorship and the fast growth of transplants indicate that black corals can be successfully employed in the recovery projects of harvested reefs.

This paper gives explicit, applicable bounds for solutions of a wide class of third-order difference equations with nonconstant coefficients. The techniques used are readily adaptable for higher-order equations. The results extend recent work of the authors for second-order equations.

The historical regulation of African elephant Loxodonta africana populations could provide guidelines for management efforts and decisions in areas where elephant numbers are now increasing. However, there are few detailed records of the natural mortality processes of the past. Therefore, we modelled elephant population growth to evaluate possible effects of age-specific mortality. Model projections indicated that an annual mortality of 17.1% of juveniles or 10.5% of adults would be sufficient to prevent population growth. For age classes below or just at sexual maturity (i.e. 0-3, 4-7, 8-11) 37.5% annual mortality of one of these classes was required to achieve 0% population growth. These mortality levels are much higher than those reported in southern Africa today. Simulations of episodic mortality events (e.g. droughts) indicated that such events would need to occur every 16 years at a severity that would cause the mortality of all infants and weaned calves (0-7 years old), as well as 10% of adults and subadults (8-60 years old) to prevent long-term population growth. An 8-year frequency required the mortality of 84.7% of infants and weaned calves. Historically, it is possible that high drought mortality and frequency, and high predation levels, may have reduced population growth significantly but current mortality rates and frequencies are insufficient to constrain long-term average population growth at 0%. The natural limitation of existent elephant populations through mortality is therefore unlikely, indicating a need for active management of the increasing elephant populations in southern Africa.

Fascioliasis pathogenesis depends on fluke burden. In human hyperendemic zones, individual infection intensities reach very high levels and the majority of infected subjects should be in the advanced chronic phase. The rat model offers a useful approach for pathological research in the advanced chronic period. The influence of infection intensity per rat on fluke development, pre-patent period and egg shedding (eggs/g faeces/worm) was analysed in 3 groups (I: 1–3 worms/rat; II: 4–6; III: 7–9). Ontogenetic trajectories of fluke body measures followed a logistic model. Results showed that when the burden increases, the maximum values of fluke measures decrease. The crowding effect is manifest when fluke measures approximate their maximums in the advanced chronic stage. The pre-patent period and egg production decrease when the burden increases. This means that measurements of eggs per gramme of faeces tend to underestimate the fluke burden. The present study demonstrates how to quantify the fascioliasis experimental rat model crowding effect on adult growth, pre-patent period and egg production. This quantification may be of great interest in epidemiological studies and in experimental research on the in vivo actions of different anthelminthic drugs and vaccines, pathology, immunology and resistance studies.

To investigate the effect of red clover formononetin concentration on lamb growth rate and carcass characteristics, 20 lambs (10 ewe lambs and 10 wethers) were grazed on each of three forages : red clover with a high formononetin concentration (HF), red clover with a low formononetin concentration (LF) and a control perennial ryegrass. Animals were finished at condition score 3L, at which point half of all animals were slaughtered immediately, while the other half of the animals were moved to a common ryegrass plot for 3 weeks as a 'withdrawal' period. Mean formononetin concentrations were 0-0, 4-7 and 3-3 g/kg dry matter (DM) for grass, HF and LF swards respectively. The clover swards had higher crude protein concentrations and lower fibre and water-soluble carbohydrate concentrations than the control ryegrass sward. Lambs grazing the HF clover gained 40 g/day live weight more (P < 0-1) than lambs on the other two forages without an increase in forage DM intake as estimated using the nalkane technique. There was no difference in the empty body weight, killing-out proportion, carcass fat class or condition score between animals finished on any of the three forages. Following the 3-week withdrawal period on ryegrass, there were significant residual effects of previous grazed forage on carcass weight, with HF lambs producing heavier carcasses than other lambs. Plasma concentrations of growth hormone and insulin-like growth factor-1 were highest in lambs grazing the HF clover, and suggest a physiological mechanism for the increased growth rates of these animals. There were no differences in the equol contents of the meat of lambs finished on the clover, compared with animals finished on grass, suggesting that there would be no implications for human health following consumption of meat produced from lambs grazing red clover, even with a relatively high concentration of formo'nonetin.

A detailed profile of the ice fabric, the deuterium content and the sodium concentration of a 1.64 m long, first-year sea-ice core from Breid Bay, near Syowa station (Antarctica), is described. The core consists mainly of frazil ice (77%), a common feature observed in recent extended studies of the first-year sea-ice cover in the Weddell Sea area. Neither snow ice, nor platelet ice is present. The remainder of the core consists of congelation ice. The typical substructure of ice plates/brine lamellae occurs only at the bottom of the core. Otherwise fine-grained congelation ice is ‘sandwiched’ between layers of frazil. It lacks the intracrystalline substructure but shows a strong textural elongation and c-axis clustering in the horizontal plane. The evolution processes of the first-year sea-ice cover in Breid Bay are analysed. The dynamical component, demonstrated to play a major role in the eastern Weddell Sea, seems to be of minor importance in this area, where thermodynamics satisfactorily explains the isotopic, chemical and textural characteristics of the core. It is proposed that the topmost part of the core consists of frazil ice produced by wind- and wave-induced turbulence. Once a consolidated ice cover is provided, the growth proceeds at a slower rate, through congelation ice formation and frazil ice production, initiated by thermohaline convection processes in the water column. The lower alternate layers of fine grained congelation ice and frazil ice could result from cyclic thermal and salinity regimes at the ice-water interface, connected with the major meteorological events of the year.

Population growth rates of Antarctic and temperate isolates of the microflagellate Heteromita globosa Stein and of the ciliate Colpoda cucullus Müller were determined during incubation both under constant 3.5° and 8.0°C, and under temperature regimes fluctuating on 24-hour cycles, between 0° and 15°C, to simulate Antarctic microclimates. Fluctuating temperatures did not inhibit growth. No growth of Colpoda occurred at 3.5°C. It is suggested that successful growth in nature depends upon the microclimate providing sufficient degree-hours per day above encystment/excystment threshold temperature (+1.5°C for Heteromita about +4°C for Colpoda). The minimum number of degree-hours above threshold needed for growth of Colpoda is estimated to lie between 48 and 96. Monitored microclimates in the maritime Antarctic do not provide enough degree-hours per day, though subantarctic microclimates are more favourable, as may be exceptionally warm localities in the continental Antarctic where daily insolation is high in summer. These data are consistent with the recorded presence of Colpoda spp. in the subantarctic and rarely in the continental Antarctic, and their absence from the maritime Antarctic.

The statolith microstructure was studied in 142 females (mantle length, ML, ranging from 77–402 mm) and 119 males (72–328 mm ML) of Martialia hyadesi caught on the Patagonian and Falkland shelves and at the Antarctic Polar Frontal Zone between 1989–94. The statolith microstructure dark zone in this species, contains narrower and more numerous growth increments than the dark zones of other ommastrephid squids. Assuming daily production of putative growth increments within statoliths males live up to 12 months, and females live up to 13 months. It is likely that the life cycle lasts c. 1 yr, but immature squids with ages >330–340 d suggest that a part of M. hyadesi populations could have life span >1 yr. Growth in length was best described by the Gompertz function, whereas growth in weight was best described by the logistic function. M. hyadesi is characterized by slow juvenile growth (<100 mm ML), fast growth of immature squids and a sharp decrease in growth rates during maturation. M. hyadesi mature later (at ages >270 d) than other temperate ommastrephids, but maturation is rather rapid (2–3 months). In the south-west Atlantic, M. hyadesi hatch throughout the year.

Post-metamorphic growth patterns were analysed in the tropical caecilian amphibian Ichthyophis cf. kohtaoensis (Amphibia: Gymnophiona) experimentally in captivity over 6 years. Two questions were addressed. (1) Does this Ichthyophis display sexual dimorphism for size? (2) Do ichthyophiid caecilians express an indeterminate growth pattern? Total length did not differ between sexes in the first, second or third year after metamorphosis. In the fourth, fifth and sixth years, females were significantly larger than males. The index of sexual size dimorphism increased from zero in the first year after metamorphosis to 0.104 in the sixth year. Relative growth rates of total length were different for each sex. In the first two growth seasons males grew at higher rates, while from the third growth season females grew faster than males. In general, growth rates increased from the first to the second year after metamorphosis and decreased dramatically after both sexes became mature. As all Ichthyophis in this study grew constantly throughout the first 6 years after metamorphosis, indeterminate growth probably occurs in caecilians as reported for frogs and salamanders. Additionally, growth curves for both sexes of Ichthyophis cf. kohtaoensis were estimated based on the von Bertalanffy model.