Determination of sample size (the number of replications) is a key step in the design of an observational study or randomized experiment. Statistical procedures for this purpose are readily available. Their treatment in textbooks is often somewhat marginal, however, and frequently the focus is on just one particular method of inference (significance test, confidence interval). Here, we provide a unified review of approaches and explain their close interrelationships, emphasizing that all approaches rely on the standard error of the quantity of interest, most often a pairwise difference of two means. The focus is on methods that are easy to compute, even without a computer. Our main recommendation based on standard errors is summarized as what we call the 1-2-3 rule for a difference of two treatment means.

Electromagnetic inverse-scattering problems (ISPs) are concerned with determining the properties of an unknown object using measured scattered fields. ISPs are often highly nonlinear, causing the problem to be very difficult to address. In addition, the reconstruction images of different optimization methods are distorted which leads to inaccurate reconstruction results. To alleviate these issues, we propose a new linear model solution of generative adversarial network-based (LM-GAN) inspired by generative adversarial networks (GAN). Two sub-networks are trained alternately in the adversarial framework. A linear deep iterative network as a generative network captures the spatial distribution of the data, and a discriminative network estimates the probability of a sample from the training data. Numerical results validate that LM-GAN has admirable fidelity and accuracy when reconstructing complex scatterers.

Habrobracon hebetor (Say) is a parasitoid of various Lepidoptera including Helicoverpa armigera (Hübner), a key pest of different crops and vegetables. The development of both H. armigera and H. hebetor were simultaneously evaluated against a wide range of constant temperatures (10, 15, 17.5, 20, 25, 27.5, 30, 35, 37.5 and 40 °C). Helicoverpa armigera completed its development from egg to adult within a temperature range of 17.5–37.5 °C and H. hebetor completed its life cycle from egg to adult within a temperature range of 15–40 °C. Based on the Ikemoto and Takai model the developmental threshold (To) and thermal constant (K) to complete the immature stages, of H. armigera were calculated as 11.6 °C and 513.6 DD, respectively, and 13 °C and 148 DD, respectively, for H. hebetor. Analytis/Briere-2 and Analytis/Briere-1 were adjudged the best non-linear models for prediction of phenology of H. armigera and H. hebetor, respectively and enabled estimation of the optimum (Topt) and maximum temperature (Tmax) for development with values of 34.8, 38.7, 36.3, and 43 °C for host and the parasitoid, respectively. Parasitisation by H. hebetor was maximal at 25 °C but occurred even at 40 °C. This study suggests although high temperature is limiting to insects, our estimates of the upper thermal limits for both species are higher than previously estimated. Some biological control of H. armigera by H. hebetor may persist in tropical areas, even with increasing temperatures due to climate change.

Density and spatial arrangement (rectangularity) effects on the competitive relationships, yield performance, and dynamics in canopy dominance of winter wheat and Italian ryegrass were evaluated using two addition series experiments. In experiment 1, combinations of six densities of each species formed the treatment matrix of addition series. In experiment 2, each species was tested at four densities and three rectangularities (RE) of winter wheat. In monocultures, crop density (plants per square meter) explained 82 to 85% of the total variation in the per-plant biomass of winter wheat in experiment 1. In mixtures of crop and weed, initial wheat density (N1) and initial ryegrass density (N2) and interaction of N1 and N2 explained 74 to 80% of the total variation in the per-plant biomass of winter wheat and 68 to 79% of Italian ryegrass in experiment 1. Intraspecific competition was apparent between 15 and 90 days after emergence (DAE) in winter wheat and between 90 and 170 DAE in Italian ryegrass. In mixtures, RE influenced plant size of Italian ryegrass up to 50 DAE only. Maximum winter wheat intraspecific competition occurred at 170 DAE, but maximum interspecific competition occurred during reproductive stages in mixtures. High RE increased seed yield, seed size, and harvest index of winter wheat and reduced biomass of Italian ryegrass. Grain yield of winter wheat was reduced up to 92% by competition from ryegrass. Even nine ryegrass plants in 100 winter wheat plants m−2 reduced winter wheat grain yield by 33%. However, the extent of loss in winter wheat grain yield was less in RE 16 (wider spacing) than in RE 1 (square planting) or 4 (close row spacing). Winter wheat was the stronger competitor during vegetative stages, but Italian ryegrass became the stronger competitor during the reproductive stages of development. Winter wheat leaves dominated at the top canopy during the vegetative stage, but ryegrass dominated at the top canopy during the reproductive stages. In the top canopy of mixtures at 200 DAE, the leaf area indices (LAI) of ryegrass was 6.6 times greater than winter wheat at RE 1 compared to only 1.6 times at RE 16. Greater LAI of Italian ryegrass in the top canopy reduced photosynthetically active radiation available to winter wheat by 68% at booting stage.

The objective of this study was to compare linear models and survival analysis for genetic evaluation of ovulatory disorders, which included veterinary treatments of silent heat/anestrus and cystic ovaries. Data of 23 450 daughters of 274 Austrian Fleckvieh sires were analyzed. For linear model analyses, ovulatory disorders were defined as a binary response (presence or absence) in the time periods from calving to 150 days after calving and from calving to 300 days after calving. For survival analysis, ovulatory disorders were defined either as the number of days from calving to the day of the first treatment for an ovulatory disorder (uncensored record) or from calving to the day of culling, or the last day of the period under investigation (until 150 or 300 days after calving; censored record). Estimates of heritability were very similar (0.016 to 0.020) across methods and periods. Correlations between sire estimated breeding value from linear model and survival analysis were 0.98, whereas correlations between different time periods were somewhat lower (0.95 and 0.96). The results showed that the length of time period had a larger effect on genetic evaluation than methodology.

We present two approaches for linear prediction of long-memory time series. The first approach consists in truncating the Wiener-Kolmogorov predictor by restricting the observations to the last k terms, which are the only available data in practice. We derive the asymptotic behaviour of the mean-squared error as k tends to +∞. The second predictor is the finite linear least-squares predictor i.e.  the projection of the forecast value on the last k observations. It is shown that these two predictors converge to the Wiener Kolmogorov predictor at the same rate k -1.

The present paper suggests a method for estimating the fishing power of vessels and for analysing fleet dynamics. The approach is based on quantification of stocks catchability (q), derived from fishing mortality coefficients (F) as calculated by virtual population analysis. Catchabilities for each harvested stock are thus estimated relatively to the fishing effort (fn) of each vessel, according to the equation: q = (F/fn). A linear model is then fitted to these catchabilities. The model allows the identification and quantification of trends in average mortality rates per fishing hour for each stock. Under some assumptions, trends are interpreted as variations in the overall fishing power of each fleet. The approach is applied to three industrial and semi-industrial fleets of Brittany (Lorient, Concarneau and Douarnenez) and to the main gadoid stocks they exploit off the west coast of Scotland (ICES area VIa), and in the Celtic Sea (ICES area VIIf,g,h) for Concarneau. Results show large variations in fishing power. Particularly, a marked increase trend in the fishing power exerted on saithe (Pollachius virens) is highlighted for the three fleets, over the period 1983-1989. These variations can be explained by the redirection of fishing strategies, which may occur on a large scale. Thus, we show how the collapse of saithe stock at first led the three fleets to intensify the harvesting of saithe, and from 1989 on, to adopt different strategies. The possible causes of the observed dynamics are discussed, as well as their consequences for fisheries management. In particular, the relevance of direct control of fishing effort as a regulatory tool is questioned.

The rapid development of the albacore tuna (Thunnus alalunga) driftnet fishery in the Bay of Biscay (Atlantic ocean, France) has incited European management authorities to ask for a study of its ecological impact on populations of common dolphins and striped dolphins. A programme with onboard observers has been led during 1992 and 1993, and a sighting survey has allowed the evaluation of the abundances of fractions of populations in the studied area. For the population of common dolphins, the biological parameter estimation has allowed the building of a discrete age-structured model based on a Leslie matrix. Sensitivity studies have been conducted using four model parameters (age of first reproduction, interval between births, juvenile and adult survival rates. Results show that the increase rate of the population presents the highest sensitivity versus adult survival rate and, in second place versus the interval between births.