Applications of likelihood asymptotics for nonlinear regression in herbicide bioassays

Dose-response models are intensively used in herbicide bioassays. Despite recent advancements in the development of new herbicides, statistical analyses are commonly based on asymptotic approximations that are sometimes poor. This paper presents the use of recent results in higher order asymptotics for likelihood-based inference in nonlinear regression. The methods presented provide accurate approximation for the distribution of test statistics and for prediction limits. Analyses of the fit and measures of detection limits of the bioassays are considered, and the potential of the methods is illustrated by examples with real data.     

Risk assessment for quantitative responses using a mixture model

A problem that frequently occurs in biological experiments with laboratory animals is that some subjects are less susceptible to the treatment than others. A mixture model has traditionally been proposed to describe the distribution of responses in treatment groups for such experiments. Using a mixture dose-response model, we derive an upper confidence limit on additional risk, defined as the excess risk over the background risk due to an added dose. Our focus will be on experiments with continuous responses for which risk is the probability of an adverse effect defined as an event that is extremely rare in controls. The asymptotic distribution of the likelihood ratio statistic is used to obtain the upper confidence limit on additional risk. The method can also be used to derive a benchmark dose corresponding to a specified level of increased risk. The EM algorithm is utilized to find the maximum likelihood estimates of model parameters and an extension of the algorithm is proposed to derive the estimates when the model is subject to a specified level of added risk. An example is used to demonstrate the results, and it is shown that by using the mixture model a more accurate measure of added risk is obtained.     

Allometry of axis length, diameter, and taper in the devil's walking stick (Aralia spinosa; Araliaceae)

The allometry of axis length, diameter, and taper is described for the trunk, rachis, and rachilla of nonbranching ramets of Aralia spinosa. Significant log-linear relationships were found between length and diameter for all axis categories, and in all cases, scaling was negatively allometric. Linear models best described the relationship between length and diameter for the rachis and rachilla, while a quadratic model best described this relationship for the trunk. During the trunk-building stage, the safety factors for trunk height were size dependent, with larger trunks exceeding their predicted critical buckling height. Taper was described by a linear relationship between diameter and position along the axis for all axis categories. All rachises and rachillas sampled exhibited taper along the length of the axis, however, only 51% of the trunks showed continuous taper. The trunk was less tapered than the rachis, but no differences in taper were found between the trunk and the rachilla, or the rachis and the rachilla. In unbranched ramets the large bipinnately compound leaves occupy the space normally occupied by lateral branches. We suggest that the rachis and rachilla are functionally equivalent to branches, that is, acting as axes of exploration and exploitation of the environment.     

A hot summer,cold winters,and the geographical limit of Trochocochlea lineat in Somerset

The common or toothed topshell, Trochocochlea lineata (da Costa, 1778), is at its northeastern geographical limit in the south and west of the British Isles. It is likely that these limits are related to some feature of air or water temperature. Along the Somerset coast, as elsewhere in southern Britain, the summer of 1995 was warmer for longer than most of its predecessors and the 1995–1996 winter was colder for longer than any since 1978. This combination of circumstances prompted an investigation into the relative effects of these two seasons. Recruitment of the 1995 cohort was unusually successful at some sites but the subsequent cold winters have removed much of that advantage on Gore Point, probably the easternmost permanent population in the Bristol Channel. The two most easterly populations, either side of Helwell Bay (Watchet), did not survive the winter of 1996–1997. The conclusion from these observations is that a hot summer can encourage recruitment but that the geographical limit in Somerset may be maintained by cold weather in winter.     

一类一级饱和反应系统的极限环

本文研究生化反应中一类饱和反应的数学模型：应用微分方程定性理论,完整地解决了该系统极限环的存在性、唯一性和不存在性等问题．     

关于极限定理的一个新结果

设{X_n,n≥0}是可列非齐次马氏链,S_n(i_1,…,i_m,w)表示m元状态序组(i_1,…,i_m)在序列(X_1,…,X_m),(X_2,…,X_m 1)…,(X_n,…,X_n m-1)中出现的次数．本文通过利用{X_n,n≥O}在Wiener概率空间的一种实现,给出了关于S_n(i_1,…,i_m,w)的一个对任意可列非齐次马氏链普遍成立的强级限定理．     

Temperature tolerances in the Namib Desert dune ant, Camponotus detritus

The mean preferred temperature of workers and brood of Camponotus detritus was 35°C at 100% r.h. and 31–33°C at 30% r.h. The critical maximal temperature of workers was 53°C at both 100% r.h. and 30% r.h. while the critical minimal temperature was 4.57°C at 100% r.h. Workers tolerated ?1°C and 95% r.h.; 45°C and 95% r.h. and 45°C and 45% r.h. for 24 h.     

Oxygen supply limits the heat tolerance of lizard embryos

The mechanisms that set the thermal limits to life remain uncertain. Classically, researchers thought that heating kills by disrupting the structures of proteins or membranes, but an alternative hypothesis focuses on the demand for oxygen relative to its supply. We evaluated this alternative hypothesis by comparing the lethal temperature for lizard embryos developing at oxygen concentrations of 10–30%. Embryos exposed to normoxia and hyperoxia survived to higher temperatures than those exposed to hypoxia, suggesting that oxygen limitation sets the thermal maximum. As all animals pass through an embryonic stage where respiratory and cardiovascular systems must develop, oxygen limitation may limit the thermal niches of terrestrial animals as well as aquatic ones.     

Effects of grass species and grass growth on atmospheric nitrogen deposition to a bog ecosystem surrounded by intensive agricultural land use

We applied a ¹⁵N dilution technique called “Integrated Total Nitrogen Input” (ITNI) to quantify annual atmospheric N input into a peatland surrounded by intensive agricultural practices over a 2-year period. Grass species and grass growth effects on atmospheric N deposition were investigated using Lolium multiflorum and Eriophorum vaginatum and different levels of added N resulting in increased biomass production. Plant biomass production was positively correlated with atmospheric N uptake (up to 102.7 mg N pot⁻¹) when using Lolium multiflorum. In contrast, atmospheric N deposition to Eriophorum vaginatum did not show a clear dependency to produced biomass and ranged from 81.9 to 138.2 mg N pot⁻¹. Both species revealed a relationship between atmospheric N input and total biomass N contents. Airborne N deposition varied from about 24 to 55 kg N ha⁻¹ yr⁻¹. Partitioning of airborne N within the monitor system differed such that most of the deposited N was found in roots of Eriophorum vaginatum while the highest share was allocated in aboveground biomass of Lolium multiflorum. Compared to other approaches determining atmospheric N deposition, ITNI showed highest airborne N input and an up to fivefold exceedance of the ecosystem-specific critical load of 5–10 kg N ha⁻¹ yr⁻¹.