A Note on Testing Equality of Means when Sample Sizes are Random with Application

The problem of testing the equality of means of two normal populations is considered when independent random samples of random sizes are given with the total number of observations from both populations being a fixed number. An application in forestry is discussed.     

Root responses to legume plants integrate information on nitrogen availability and neighbour identity

Rhizobial symbiosis is known to increase the nitrogen availability in the rhizosphere of legumes. Therefore, it has been hypothesized that other plants’ roots should forage towards legume neighbours, but avoid non-legume neighbours. Yet, root distribution responding to legume plants as opposed to non-legumes has not yet been rigorously tested and might well be subject to integration of multiple environmental cues.In this study, wedevised an outdoor mesocosm experiment to examine root distributions of the two plant species Pilosella officinarum and Arenaria serpyllifolia in a two-factorial design. While one factor was ‘neighbour identity’, where plants were exposed to different legume or non-legume neighbours, the other factor was ‘nitrogen supply’. In the latter the nutrient-poor soil was supplemented with either nitrogen-free or with nitrogen-containing fertilizer.Unexpectedly, of all treatments that included a legume neighbour (eight different species or factor combinations), we found merely one case of root aggregation towards a legume neighbour (P. officinarum towards Medicago minima under nitrogen-fertilized conditions). In this very treatment, also P. officinarum root–shoot allocation was strongly increased, indicating that neighbour recognition is coupled with a contesting strategy.Considering the various response modes of the tested species towards the different legume and non-legume neighbours, we can conclude that roots integrate information on neighbour identity and resource availability in a complex manner. Especially the integration of neighbour identity in root decisions must be a vital aptitude for plants to cope with their complex biotic and abiotic environment in the field.     

Root growth dynamics linked to above-ground growth in walnut (Juglans regia)

Background and Aims Examination of plant growth below ground is relatively scant compared with that above ground, and is needed to understand whole-plant responses to the environment. This study examines whether the seasonal timing of fine root growth and the spatial distribution of this growth through the soil profile varies in response to canopy manipulation and soil temperature.Methods Plasticity in the seasonal timing and vertical distribution of root production in response to canopy and soil water manipulation was analysed in field-grown walnut (Juglans regia ‘Chandler’) using minirhizotron techniques.Key Results Root production in walnuts followed a unimodal curve, with one marked flush of root growth starting in mid-May, with a peak in mid-June. Root production declined later in the season, corresponding to increased soil temperature, as well as to the period of major carbohydrate allocation to reproduction. Canopy and soil moisture manipulation did not influence the timing of root production, but did influence the vertical distribution of roots through the soil profile. Water deficit appeared to promote root production in deeper soil layers for mining soil water. Canopy removal appeared to promote shallow root production.Conclusions The findings of this study add to growing evidence that root growth in many ecosystems follows a unimodal curve with one marked flush of root growth in coordination with the initial leaf flush of the season. Root vertical distribution appeared to have greater plasticity than timing of root production in this system, with temperature and/or carbohydrate competition constraining the timing of root growth. Effects on root distribution can have serious impacts on trees, with shallow rooting having negative impacts in years with limited soil water or positive impacts in years with wet springs, and deep rooting having positive impacts on soil water mining from deeper soil layers but negative impacts in years with wet springs.     

A Bayesian scoring rule on clustered event data for familial risk assessment – An example from colorectal cancer screening

Colorectal cancer screening is well established. The identification of high risk populations is the key to implement effective risk‐adjusted screening. Good statistical approaches for risk prediction do not exist. The family's colorectal cancer history is used for identification of high risk families and usually assessed by a questionnaire. This paper introduces a prediction algorithm to designate a family for colorectal cancer risk and discusses its statistical properties. The new algorithm uses Bayesian reasoning and a detailed family history illustrated by a pedigree and a Lexis diagram. The algorithm is able to integrate different hereditary mechanisms that define complex latent class or random factor structures. They are generic and do not reflect specific genetic models. This is comparable to strategies in complex segregation analysis. Furthermore, the algorithm can integrate different statistical penetrance models for right censored event data. Computational challenges related to the handling of the likelihood are discussed. Simulation studies assess the predictive quality of the new algorithm in terms of ROC curves and corresponding AUCs. The algorithm is applied to data of a recent study on familial colorectal cancer risk. Its predictive performance is compared to that of a questionnaire currently used in screening for familial colorectal cancer. The results of the proposed algorithm are robust against different inheritance models. Using the simplest hereditary mechanism, the simulation study provides evidence that the algorithm improves detection of families with high cancer risk in comparison to the currently used questionnaire. The applicability of the algorithm goes beyond the field of colorectal cancer.     

Settlement and habitat use by juvenile pike in early winter

The spatial distribution and social behaviour of young-of-the-year pike Esox lucius was investigated in early winter. Reed beds were selected in the early exploration phase but thereafter, pike congregated in the pool habitat. A significant increase in pool occupancy combined with a decrease in reed bed occupancy and movement indicated settlement within 3 days. There was no evidence of territoriality, which has been reported previously in adult pike: indeed, inter-individual spacing was consistent with social grouping rather than territory defence. The strong preference for reed cover among juveniles reported in other studies that were undertaken during summer was not observed here. Among-individual variation in exploratory behaviour was observed but this was not related to activity levels or habitat use.     

Geochemical baseline determination and pollution assessment of heavy metals in urban soils of Karachi,Pakistan

Karachi is one of the most populated urban agglomerations in the world. No categorical study has yet discussed the geochemical baseline concentrations of metals in the urban soil of Karachi. The main objectives of this study were to establish geochemical baseline values and to assess the pollution status of different heavy metals. Geochemical baseline concentrations of heavy metals were estimated using the cumulative frequency distribution (CDF) curves. The estimated baseline concentrations of Pb, Cr, Cu, Zn and Fe were 56.23, 12.9, 36.31, 123.03 and 11,776 mg kg⁻¹, respectively. The pollution status of heavy metals in urban soils was evaluated using different quantitative indices (enrichment factor–EF, Geo-accumulation Index–I_geo, and pollution index–PI). Enrichments factors of the selected heavy metals determined by using Fe as a normalizer showed that metal contamination was the product of anthropogenic activities. The urban soils of Karachi were found to have a moderate to moderately severe enrichment with Pb, whereas Cr and Cu has moderate and Zn has minor enrichment. I_geo results indicated moderate soil contamination by Pb at some of the sampling locations. PI for Pb, Cr, Cu and Zn was found in the range of 0.04–3.42, 0.19–1.55, 0.27–2.45 and 0.32–1.57, respectively. Large variations in PI values of Pb revealed that soil in those areas of the city which are influenced by intensive anthropogenic activities have exceptionally high concentrations of Pb. The findings of this study would contribute to the environmental database of the soil of the region and would also facilitate both at the local and the international scales, in a more accurate global environmental monitoring, which will eventually facilitate the development of management and remediation strategies for heavy metal contaminated urban soil.