Statistical power calculation and sample size determination for environmental studies with data below detection limits

Power calculation and sample size determination are critical in designing environmental monitoring programs. The traditional approach based on comparing the mean values may become statistically inappropriate and even invalid when substantial proportions of the response values are below the detection limits or censored because strong distributional assumptions have to be made on the censored observations when implementing the traditional procedures. In this paper, we propose a quantile methodology that is robust to outliers and can also handle data with a substantial proportion of below-detection-limit observations without the need of imputing the censored values. As a demonstration, we applied the methods to a nutrient monitoring project, which is a part of the Perth Long-Term Ocean Outlet Monitoring Program. In this example, the sample size required by our quantile methodology is, in fact, smaller than that by the traditional t-test, illustrating the merit of our method.

An extravariation model for improving confidence intervals of population size estimates from removal data

We propose a new model for estimating the size of a population from successive catches taken during a removal experiment. The data from these experiments often have excessive variation, known as overdispersion, as compared with that predicted by the multinomial model. The new model allows catchability to vary randomly among samplings, which accounts for overdispersion. When the catchability is assumed to have a beta distribution, the likelihood function, which is refered to as beta-multinomial, is derived, and hence the maximum likelihood estimates can be evaluated. Simulations show that in the presence of extravariation in the data, the confidence intervals have been substantially underestimated in previous models (Leslie-DeLury, Moran) and that the new model provides more reliable confidence intervals. The performance of these methods was also demonstrated using two real data sets: one with overdispersion, from smallmouth bass (Micropterus dolomieu), and the other without overdispersion, from rat (Rattus rattus).

Size-dependent natural mortality of juvenile banana prawns Penaeus merguiensis in the Gulf of Carpentaria, Australia

Natural mortality of marine invertebrates is often very high in the early life history stages and decreases in later stages. The possible size-dependent mortality of juvenile banana prawns, P. merguiensis (2-15 mm carapace length) in the Gulf of Carpentaria was investigated. The analysis was based on the data collected at 2-weekly intervals by beam trawls at four sites over a period of six years (between September 1986 and March 1992). It was assumed that mortality was a parametric function of size, rather than a constant. Another complication in estimating mortality for juvenile banana prawns is that a significant proportion of the population emigrates from the study area each year. This effect was accounted for by incorporating the size-frequency pattern of the emigrants in the analysis. Both the extra parameter in the model required to describe the size dependence of mortality, and that used to account for emigration were found to be significantly different from zero, and the instantaneous mortality rate declined from 0.89 week(-1) for 2 mm prawns to 0.02 week(-1) for 15 mm prawns.

Does the size of subsamples taken from multispecies trawl catches affect estimates of catch composition and abundance?

Although subsampling is a common method for describing the composition of large and diverse trawl catches, the accuracy of these techniques is often unknown. We determined the sampling errors generated from estimating the percentage of the total number of species recorded in catches, as well as the abundance of each species, at each increase in the proportion of the sorted catch. We completely partitioned twenty prawn trawl catches from tropical northern Australia into subsamples of about 10 kg each. All subsamples were then sorted, and species numbers recorded. Catch weights ranged from 71 to 445 kg, and the number of fish species in trawls ranged from 60 to 138, and invertebrate species from 18 to 63. Almost 70% of the species recorded in catches were "rare" in subsamples (less than one individual per 10 kg subsample or less than one in every 389 individuals). A matrix was used to show the increase in the total number of species that were recorded in each catch as the percentage of the sorted catch increased. Simulation modelling showed that sorting small subsamples (about 10% of catch weights) identified about 50% of the total number of species caught in a trawl. Larger subsamples (50% of catch weight on average) identified about 80% of the total species caught in a trawl. The accuracy of estimating the abundance of each species also increased with increasing subsample size. For the "rare" species, sampling error was around 80% after sorting 10% of catch weight and was just less than 50% after 40% of catch weight had been sorted. For the "abundant" species (five or more individuals per 10 kg subsample or five or more in every 389 individuals), sampling error was around 25% after sorting 10% of catch weight, but was reduced to around 10% after 40% of catch weight had been sorted.

A Bayesian decision approach for sample size determination in phase II trials

Stallard (1998, Biometrics 54, 279-294) recently used Bayesian decision theory for sample-size determination in phase II trials. His design maximizes the expected financial gains in the development of a new treatment. However, it results in a very high probability (0.65) of recommending an ineffective treatment for phase III testing. On the other hand, the expected gain using his design is more than 10 times that of a design that tightly controls the false positive error (Thall and Simon, 1994, Biometrics 50, 337-349). Stallard's design maximizes the expected gain per phase II trial, but it does not maximize the rate of gain or total gain for a fixed length of time because the rate of gain depends on the proportion: of treatments forwarding to the phase III study. We suggest maximizing the rate of gain, and the resulting optimal one-stage design becomes twice as efficient as Stallard's one-stage design. Furthermore, the new design has a probability of only 0.12 of passing an ineffective treatment to phase III study.

Dynamics of plant populations in Heteropogon contortus(black speargrass) pastures on a granite landscape in southern Queensland. 1. Dynamics of H. contortus populations

The dynamics of Heteropogon contortus (black speargrass) populations were measured in a subset of treatments contained within an extensive grazing study conducted between 1990 and 1996 in H. contortus pasture in southern Queensland. This subset included 2 landscape positions and 3 stocking rates in both native pasture and legume-oversown native pasture. Severe drought conditions throughout much of the study necessitated ongoing adjustments to the original stocking rates and, as a result, drought was the major influence on the dynamics of H. contortus populations. Plant density and basal area in the silver-leaved ironbark landscape were consistently higher than those in the narrow-leaved ironbark landscape. There was limited evidence of any impact by either light or moderate stocking rate but there was evidence of an impact at the heaviest stocking rate. There was minimal impact of legume oversowing. Relatively large fluctuations in plant density occurred during this study resulting from the death of existing plants, due mainly to drought, and seedling recruitment. Similarly, there were relatively large fluctuations in basal area caused mainly by changes in plant size. Rates for turnover of plant numbers were relatively high whereas plant turnover rates of basal areas were relatively low. Regular seedling recruitment appeared necessary to ensure the persistence of this species. Despite the high turnover, populations were maintained at reasonable levels indicating the overall resilience of H. contortus.

Variable Size Population NSGA-II: VPNSGA-II

Multi-objective optimization is an active field of research with broad applicability in aeronautics. This report details a variant of the original NSGA-II software aimed to improve the performances of such a widely used Genetic Algorithm in finding the optimal Pareto-front of a Multi-Objective optimization problem for the use of UAV and aircraft design and optimsaiton. Original NSGA-II works on a population of predetermined constant size and its computational cost to evaluate one generation is O(mn^2 ), being m the number of objective functions and n the population size. The basic idea encouraging this work is that of reduce the computational cost of the NSGA-II algorithm by making it work on a population of variable size, in order to obtain better convergence towards the Pareto-front in less time. In this work some test functions will be tested with both original NSGA-II and VPNSGA-II algorithms; each test will be timed in order to get a measure of the computational cost of each trial and the results will be compared.

Size-dependent melting of nanoparticles: Hundred years of thermodynamic model

Thermodynamic model first published in 1909, is being used extensively to understand the size-dependent melting of nanoparticles. Pawlow deduced an expression for the size-dependent melting temperature of small particles based on the thermodynamic model which was then modified and applied to different nanostructures such as nanowires, prism-shaped nanoparticles, etc. The model has also been modified to understand the melting of supported nanoparticles and superheating of embedded nanoparticles. In this article, we have reviewed the melting behaviour of nanostructures reported in the literature since 1909.

Unusual stress and grain size dependence for creep in nanocrystalline materials

Analyses of diffusion and dislocation creep in nanocrystals needs to take into account the generally utilized low temperatures, high stresses and very fine grain sizes. In nanocrystals, diffusion creep may be associated with a nonlinear stress dependence and dislocation creep may involve a grain size dependence.

Effects of severity of threshing damage on seed quality of Gatton panic Panicum maximum)

Different degrees of severity of threshing were imposed during combine-harvesting of seed of Gatton panic, a cultivar of Panicum maximum , to determine effects of degree of threshing damage on subsequent properties of seed. Threshing cylinder peripheral speeds and concave clearances covering the normal range employed commercially were varied experimentally in the harvest of 2 crops grown in north Queensland. Harvested seed was dried and cleaned, then stored under ambient conditions. The extent of physical damage was measured, and samples were tested at intervals for viability, germination, dormancy and seedling emergence from soil in a glasshouse and in the field over the 2 seasons following harvest. Physical damage increased as peripheral rotor speed rose and (though less markedly) as concave clearance was reduced. As the level of damage increased, viability was progressively reduced, life expectancy was shortened, and dormancy was broken. When the consequences were measured as seedling emergence from soil, the adverse effects on viability tended to cancel out the benefits of dormancy-breaking, leaving few net differences attributable to the degree of threshing severity. We concluded that there would be no value in trying to manipulate the quality of seed produced for normal commercial use through choice of cylinder settings, but that deliberate light or heavy threshing could benefit special-purpose seed, destined, respectively, for long-term storage or immediate use.

Selective herbicide strategies for use in Australian desmanthus seed crops

Grass and broad-leaved weeds can reduce both yields and product marketability of desmanthus (Desmanthus virgatus) seed crops, even when cultural control strategies are used. Selective herbicides might economically control these weeds, but, prior to this study, the few herbicides tolerated by desmanthus did not control key weed contaminants of desmanthus seed crops. In this study, the tolerance of desmanthus cv. Marc to 55 herbicides used for selective weed control in other leguminous crops was assessed in 1 pot trial and 3 Queensland field trials. One field trial assessed the tolerance of desmanthus seedlings to combinations of the most promising pre-emergent and post emergent herbicides. The pre-emergent herbicides, imazaquin, imazethapyr, pendimethalin, oryzalin and trifluralin, gave useful weed control with very little crop damage. The post-emergent herbicides, haloxyfop, clethodim, propyzamide, carbetamide and dalapon, were safe for controlling grass weeds in desmanthus. Selective post-emergence control of broad-leaved weeds was achieved using bentazone, bromoxynil and imazethapyr. One trial investigated salvaging second-year desmanthus crops from mature perennial weeds, and atrazine, terbacil and hexazinone showed some potential in this role. Overall, our results show that desmanthus tolerates herbicides which collectively control a wide range of weeds encountered in Queensland. These, in combination with cultural weed control strategies, should control most weeds in desmanthus seed crops.

Field evaluation of micropropagated and conventionally propagated ginger in subtropical Queensland

The growth and performance of micropropagated ginger (Zingiber officinale Roscoe) was compared with 'seed'-derived plants in field trials conducted in south-eastern Queensland. In the first generation ex vitro, micropropagated plants had significantly (P<0.01) reduced rhizome yield with smaller knobs and more roots. Micropropagated plants had a greater (P<0.01) shoot: root (rhizome) ratio compared with seed-derived plants. Shoots from micropropagated plants were also significantly (P<0.01) smaller with a greater number of shoots per plant. The unusual shoot morphology of the micropropagated plants did not appear to be related to the presence of benzylaminopurine, a plant growth hormone added to the multiplication medium, as plants subcultured for 3 cycles on a hormone-free medium also exhibited similar characteristics. Seed collected from the micropropagated plants and seed-derived plants was harvested and, despite the micropropagated seed being significantly (P<0.01) smaller, by the second generation ex vitro there were no significant differences between the treatments. Factors that can improve rhizome size, while reducing production costs, need to be identified before micropropagated plants can be recommended for routine use in the ginger industry as a source of disease and pest-free planting material.

Impact of cold storage on glucosinolate levels in seed-sprouts of broccoli, rocket, white radish and kohl-rabi

The effect of cold storage on glucosinolate concentration was examined in 7-day-old seed-sprouts of broccoli, kohl rabi, white radish and rocket. Principal glucosinolates identified were glucoraphanin and glucoerucin (in broccoli, kohl rabi and rocket), glucoiberin (in broccoli and kohl rabi), and glucoraphenin and glucodehydroerucin (in white radish). Generally, sprouts showed no significant changes in individual glucosinolate concentrations during storage at 4°C for 3 weeks. The exception to this was rocket, which showed a significant decline in glucoerucin and glucoraphanin after 1 and 2 weeks, respectively. These preliminary results indicate that as there is no significant loss of glucosinolates in broccoli, radish and kohl rabi sprouts, these sprouts may be stored under domestic refrigeration conditions without significant loss of potential anti-cancer compounds. Rocket sprouts, on the other hand, should be consumed soon after purchase if glucosinolate levels are to be maintained.

Effect of microwave radiation on seed mortality of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.)

A trial was undertaken to evaluate the effect of microwaves on seed mortality of three weed species. Seeds of rubber vine (Cryptostegia grandiflora R.Br.), parthenium (Parthenium hysterophorous L.) and bellyache bush (Jatropha gossypiifolia L.) were buried at six depths (0, 2.5, 5, 10, 20 and 40 cm) in coarse sand maintained at one of two moisture levels, oven dry or wet (field capacity), and then subjected to one of five microwave radiation durations of (0, 2, 4, 8 and 16 min). Significant interactions between soil moisture level, microwave radiation duration, seed burial depth and species were detected for mortality of seeds of all three species. Maximum seed mortality of rubber vine (88%), parthenium (67%) and bellyache bush (94%) occurred in wet soil irradiated for 16 min. Maximum seed mortality of rubber vine and bellyache bush seeds occurred in seeds buried at 2.5 cm depth whereas that of parthenium occurred in seeds buried at 10 cm depth. Maximum soil temperatures of 114.1 and 87.5°C in dry and wet soil respectively occurred at 2.5 cm depth following 16 min irradiation. Irrespective of the greater soil temperatures recorded in dry soil, irradiating seeds in wet soil generally increased seed mortality 2.9-fold compared with dry soil. Moisture content of wet soil averaged 5.7% compared with 0.1% for dry soil. Results suggest that microwave radiation has the potential to kill seeds located in the soil seed bank. However, many factors, including weed species susceptibility, determine the effectiveness of microwave radiation on buried seeds. Microwave radiation may be an alternative to conventional methods at rapidly depleting soil seed banks in the field, particularly in relatively wet soils that contain long lived weed seeds.